Finite Group Databasebeta

← C67×#14100 #30693351

Subgroups — C67×#14100 #30693351

Order 17152.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C67C211yesmaximal, characteristic
2C2×#390×C67C211yesmaximal, characteristic, complemented
3C2×#388×C67C211yesmaximal, characteristic, complemented
4C2×#386×C67C211yesmaximal, characteristic, complemented
5C2×#386×C67C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
8C67×#1441C211yesmaximal, characteristic, complemented
9C67×#1438C211yesmaximal, characteristic, complemented
10C67×#1438C211yesmaximal, characteristic, complemented
11C67×#1438C211yesmaximal, characteristic, complemented
12C67×#1437C211yesmaximal, characteristic, complemented
13C67×#1437C211yesmaximal, characteristic, complemented
14C67×#1436C211yesmaximal, characteristic, complemented
15C67×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C67C2211yescharacteristic
17C23×D4×C67C2211yescharacteristic
18C23×D4×C67C2211yescharacteristic
19C24×C4×C67C2211yescharacteristic
20C24×C4×C67C2211yescharacteristic
21C2×#121×C67—24no—
22C2×#121×C67—24no—
23C2×#121×C67C418yescomplemented
24C22×C4⋊C4×C67C2211yescharacteristic
25C22×C4⋊C4×C67C2211yescharacteristic
26C22×C22⋊C4×C67C2211yescharacteristic
27C22×C22⋊C4×C67C2211yescharacteristic
28C22×C22⋊C4×C67C2211yescharacteristic
29C22×C22⋊C4×C67C2211yescharacteristic
30C22×C22⋊C4×C67C2211yescharacteristic
31C22×C22⋊C4×C67C2211yescharacteristic
32C22×C22⋊C4×C67C2211yescharacteristic
33C22×C22⋊C4×C67C2211yescharacteristic
34C22×C22⋊C4×C67C2211yescharacteristic
35C22×C22⋊C4×C67C2211yescharacteristic
36C22×C22⋊C4×C67C2211yescharacteristic
37C22×C22⋊C4×C67C2211yescharacteristic
38C22×C22⋊C4×C67C2211yescharacteristic
39C22×C42×C67C2211yescharacteristic
40C22×C42×C67C2211yescharacteristic
41C22×C42×C67C2211yescharacteristic
42#390×C67—24no—
43#388×C67—24no—
44#386×C67—24no—
45#386×C67—24no—
46C4×C22⋊C4×C67—24no—
47C4×C22⋊C4×C67—24no—
48C2×#95×C67C2211yescharacteristic
49C2×#95×C67C2211yescharacteristic
50C2×#95×C67C2211yescharacteristic
51C2×#95×C67C2211yescharacteristic
52C2×#95×C67C2211yescharacteristic
53C2×#95×C67C2211yescharacteristic
54C2×#95×C67C2211yescharacteristic
55C2×#95×C67C2211yescharacteristic
56C2×#95×C67C2211yescharacteristic
57C2×#95×C67C2211yescharacteristic
58C2×#95×C67C2211yescharacteristic
59C2×#95×C67C2211yescharacteristic
60C25×C67C2311yescharacteristic
61C25×C67C2311yescharacteristic
62C25×C67C2311yescharacteristic
63C22×D4×C67—22no—
64C22×D4×C67—22no—
65C22×D4×C67—22no—
66C22×D4×C67—22no—
67C22×D4×C67—22no—
68C22×D4×C67—22no—
69C22×D4×C67—22no—
70C22×D4×C67—22no—
71C22×D4×C67—22no—
72C22×D4×C67—22no—
73C22×D4×C67—22no—
74C22×D4×C67—22no—
75C22×D4×C67—41no—
76C22×D4×C67—41no—
77C22×D4×C67—41no—
78C22×D4×C67—41no—
79C22×D4×C67—41no—
80C22×D4×C67—41no—
81C22×D4×C67C2×C414yes—
82C22×D4×C67C2×C414yes—
83C22×D4×C67C2×C414yescomplemented
84C23×C4×C67—22no—
85C23×C4×C67—22no—
86C23×C4×C67—22no—
87C23×C4×C67—22no—
88C23×C4×C67—22no—
89C23×C4×C67—22no—
90C23×C4×C67—22no—
91C23×C4×C67—22no—
92C23×C4×C67—22no—
93C23×C4×C67—41no—
94C23×C4×C67—41no—
95C23×C4×C67—41no—
96C23×C4×C67—41no—
97C23×C4×C67C2×C414yescomplemented
98C23×C4×C67C2311yescharacteristic
99C23×C4×C67C2311yescharacteristic
100C23×C4×C67C2311yescharacteristic
101C23×C4×C67C2311yescharacteristic
102C23×C4×C67C2311yescharacteristic
103C23×C4×C67C2311yescharacteristic
104C23×C4×C67C2311yescharacteristic
105C23×C4×C67C2311yescharacteristic
106C23×C4×C67C2311yescharacteristic
107C23×C4×C67C2311yescharacteristic
108C23×C4×C67C2311yescharacteristic
109C23×C4×C67C2311yescharacteristic
110#121×C67—232no—
111C2×C4⋊C4×C67—22no—
112C2×C4⋊C4×C67—22no—
113C2×C4⋊C4×C67—22no—
114C2×C4⋊C4×C67—22no—
115C2×C4⋊C4×C67—41no—
116C2×C4⋊C4×C67C2×C414yescomplemented
117C2×C22⋊C4×C67—22no—
118C2×C22⋊C4×C67—22no—
119C2×C22⋊C4×C67—22no—
120C2×C22⋊C4×C67—22no—
121C2×C22⋊C4×C67—22no—
122C2×C22⋊C4×C67—22no—
123C2×C22⋊C4×C67—22no—
124C2×C22⋊C4×C67—22no—
125C2×C22⋊C4×C67—22no—
126C2×C22⋊C4×C67—22no—
127C2×C22⋊C4×C67—22no—
128C2×C22⋊C4×C67—22no—
129C2×C22⋊C4×C67—22no—
130C2×C22⋊C4×C67—22no—
131C2×C22⋊C4×C67—22no—
132C2×C22⋊C4×C67—22no—
133C2×C22⋊C4×C67—22no—
134C2×C22⋊C4×C67—22no—
135C2×C22⋊C4×C67—22no—
136C2×C22⋊C4×C67—22no—
137C2×C22⋊C4×C67—22no—
138C2×C22⋊C4×C67—22no—
139C2×C22⋊C4×C67—22no—
140C2×C22⋊C4×C67—22no—
141C2×C22⋊C4×C67—22no—
142C2×C22⋊C4×C67—22no—
143C2×C22⋊C4×C67—41no—
144C2×C22⋊C4×C67—41no—
145C2×C22⋊C4×C67—41no—
146C2×C22⋊C4×C67—41no—
147C2×C22⋊C4×C67—41no—
148C2×C22⋊C4×C67—41no—
149C2×C22⋊C4×C67—41no—
150C2×C22⋊C4×C67—41no—
151C2×C22⋊C4×C67C2×C414yes—
152C2×C22⋊C4×C67C2×C414yescomplemented
153C2×C22⋊C4×C67D414yes—
154C2×C22⋊C4×C67D414yes—
155C2×C22⋊C4×C67D414yescomplemented
156C2×C42×C67—22no—
157C2×C42×C67—22no—
158C2×C42×C67—22no—
159C2×C42×C67—22no—
160C2×C42×C67—22no—
161C2×C42×C67—22no—
162C2×C42×C67—41no—
163C2×C42×C67—41no—
164C2×C42×C67—41no—
165#95×C67—22no—
166#95×C67—22no—
167#95×C67—22no—
168#95×C67—22no—
169#95×C67—22no—
170#95×C67—22no—
171#95×C67—22no—
172#95×C67—22no—
173#95×C67—22no—
174#95×C67—41no—
175#95×C67—41no—
176#95×C67D414yescomplemented
177C24×C67—21no—
178C24×C67—21no—
179C24×C67—21no—
180C24×C67—21no—
181C24×C67—21no—
182C24×C67—21no—
183C24×C67—21no—
184C24×C67—21no—
185C24×C67—21no—
186C24×C67—21no—
187C24×C67—21no—
188C24×C67—21no—
189C24×C67—21no—
190C24×C67—21no—
191C24×C67—21no—
192C24×C67—21no—
193C24×C67—21no—
194C24×C67—21no—
195C24×C67—21no—
196C24×C67—21no—
197C24×C67—21no—
198C24×C67—21no—
199C24×C67—21no—
200C24×C67—21no—
201C24×C67—21no—
202C24×C67—21no—
203C24×C67—21no—
204C24×C67—21no—
205C24×C67—21no—
206C24×C67—21no—
207C24×C67—21no—
208C24×C67—21no—
209C24×C67—21no—
210C24×C67—21no—
211C24×C67—21no—
212C24×C67—21no—
213C24×C67—21no—
214C24×C67—21no—
215C24×C67C22×C412yes—
216C24×C67C22×C412yes—
217C24×C67C22×C412yes—
218C24×C67C2×D412yes—
219C24×C67C2×D412yes—
220C24×C67C2×D412yes—
221C24×C67#4112yes—
222C24×C67C2411yescharacteristic
223C2×D4×C67—28no—
224C2×D4×C67—28no—
225C2×D4×C67—28no—
226C2×D4×C67—28no—
227C2×D4×C67—28no—
228C2×D4×C67—28no—
229C2×D4×C67—44no—
230C2×D4×C67—44no—
231C2×D4×C67—44no—
232C2×D4×C67—44no—
233C2×D4×C67—44no—
234C2×D4×C67—44no—
235C2×D4×C67—44no—
236C2×D4×C67—44no—
237C2×D4×C67—44no—
238C2×D4×C67—44no—
239C2×D4×C67—44no—
240C2×D4×C67—44no—
241C2×D4×C67—44no—
242C2×D4×C67—44no—
243C2×D4×C67—44no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67—21no—
256C22×C4×C67—21no—
257C22×C4×C67—21no—
258C22×C4×C67—21no—
259C22×C4×C67—21no—
260C22×C4×C67—28no—
261C22×C4×C67—21no—
262C22×C4×C67—21no—
263C22×C4×C67—21no—
264C22×C4×C67—21no—
265C22×C4×C67—21no—
266C22×C4×C67—21no—
267C22×C4×C67—21no—
268C22×C4×C67—21no—
269C22×C4×C67—21no—
270C22×C4×C67—21no—
271C22×C4×C67—21no—
272C22×C4×C67—21no—
273C22×C4×C67—21no—
274C22×C4×C67—21no—
275C22×C4×C67—21no—
276C22×C4×C67—21no—
277C22×C4×C67—21no—
278C22×C4×C67—21no—
279C22×C4×C67—21no—
280C22×C4×C67—21no—
281C22×C4×C67—21no—
282C22×C4×C67—21no—
283C22×C4×C67—21no—
284C22×C4×C67—21no—
285C22×C4×C67—21no—
286C22×C4×C67—21no—
287C22×C4×C67—21no—
288C22×C4×C67—21no—
289C22×C4×C67—21no—
290C22×C4×C67—21no—
291C22×C4×C67—21no—
292C22×C4×C67—21no—
293C22×C4×C67—21no—
294C22×C4×C67—21no—
295C22×C4×C67—21no—
296C22×C4×C67—21no—
297C22×C4×C67—28no—
298C22×C4×C67—28no—
299C22×C4×C67—21no—
300C22×C4×C67—21no—
301C22×C4×C67—21no—
302C22×C4×C67—21no—
303C22×C4×C67—21no—
304C22×C4×C67—21no—
305C22×C4×C67—21no—
306C22×C4×C67—21no—
307C22×C4×C67—21no—
308C22×C4×C67—21no—
309C22×C4×C67—21no—
310C22×C4×C67—21no—
311C22×C4×C67—21no—
312C22×C4×C67—21no—
313C22×C4×C67—44no—
314C22×C4×C67—44no—
315C22×C4×C67—44no—
316C22×C4×C67—44no—
317C22×C4×C67—44no—
318C22×C4×C67—44no—
319C22×C4×C67—44no—
320C22×C4×C67—44no—
321C22×C4×C67—44no—
322C22×C4×C67—44no—
323C22×C4×C67—44no—
324C22×C4×C67C22×C412yes—
325C22×C4×C67C22×C412yes—
326C22×C4×C67C22×C412yes—
327C22×C4×C67C22×C412yes—
328C22×C4×C67C2×D412yes—
329C22×C4×C67C2×D412yes—
330C22×C4×C67C2×D412yes—
331C22×C4×C67C2×D412yes—
332C22×C4×C67C2×D412yes—
333C22×C4×C67C2×D412yes—
334C22×C4×C67C2×D412yes—
335C22×C4×C67C2×D412yes—
336C22×C4×C67C2×D412yes—
337C22×C4×C67#4112yes—
338C22×C4×C67#4112yes—
339C22×C4×C67#4112yes—
340C22×C4×C67#4112yes—
341C22×C4×C67#4112yes—
342C4⋊C4×C67—28no—
343C4⋊C4×C67—44no—
344C22⋊C4×C67—28no—
345C22⋊C4×C67—28no—
346C22⋊C4×C67—28no—
347C22⋊C4×C67—28no—
348C22⋊C4×C67—44no—
349C22⋊C4×C67—44no—
350C22⋊C4×C67—44no—
351C22⋊C4×C67—44no—
352C22⋊C4×C67—44no—
353C22⋊C4×C67—44no—
354C22⋊C4×C67—44no—
355C22⋊C4×C67—44no—
356C22⋊C4×C67C22⋊C4116yescomplemented
357C42×C67—44no—
358C42×C67—44no—
359C42×C67—44no—
360C23×C67—22no—
361C23×C67—22no—
362C23×C67—22no—
363C23×C67—22no—
364C23×C67—22no—
365C23×C67—22no—
366C23×C67—22no—
367C23×C67—22no—
368C23×C67—22no—
369C23×C67—22no—
370C23×C67—22no—
371C23×C67—22no—
372C23×C67—22no—
373C23×C67—22no—
374C23×C67—22no—
375C23×C67—22no—
376C23×C67—22no—
377C23×C67—22no—
378C23×C67—22no—
379C23×C67—22no—
380C23×C67—22no—
381C23×C67—22no—
382C23×C67—22no—
383C23×C67—22no—
384C23×C67—22no—
385C23×C67—22no—
386C23×C67—22no—
387C23×C67—22no—
388C23×C67—22no—
389C23×C67—22no—
390C23×C67—22no—
391C23×C67—22no—
392C23×C67—22no—
393C23×C67—22no—
394C23×C67—22no—
395C23×C67—22no—
396C23×C67—22no—
397C23×C67—22no—
398C23×C67—22no—
399C23×C67—22no—
400C23×C67—22no—
401C23×C67—22no—
402C23×C67—22no—
403C23×C67—41no—
404C23×C67—41no—
405C23×C67—41no—
406C23×C67—41no—
407C23×C67—41no—
408C23×C67—41no—
409C23×C67—41no—
410C23×C67—41no—
411C23×C67—41no—
412C23×C67—41no—
413C23×C67—41no—
414C23×C67—41no—
415C23×C67—41no—
416C23×C67—41no—
417C23×C67—41no—
418C23×C67—41no—
419C23×C67—41no—
420C23×C67—41no—
421C23×C67—41no—
422C23×C67—41no—
423C23×C67—41no—
424C23×C67—41no—
425C23×C67—41no—
426C23×C67—41no—
427C23×C67—41no—
428C23×C67—41no—
429C23×C67—41no—
430C23×C67—41no—
431C23×C67—41no—
432C23×C67—41no—
433C23×C67—41no—
434C23×C67—41no—
435C23×C67—41no—
436C23×C67—41no—
437C23×C67—41no—
438C23×C67—41no—
439C23×C67—41no—
440C23×C67—41no—
441C23×C67—41no—
442C23×C67—41no—
443C23×C67—41no—
444C23×C67—41no—
445C23×C67—41no—
446C23×C67—41no—
447C23×C67—41no—
448C23×C67—41no—
449C23×C67—41no—
450C23×C67—41no—
451C23×C67—41no—
452C23×C67—41no—
453C23×C67—41no—
454C23×C67—41no—
455C23×C67—41no—
456C23×C67—41no—
457C23×C67—41no—
458C23×C67—41no—
459C23×C67—41no—
460C23×C67—41no—
461C23×C67—41no—
462C23×C67—41no—
463C23×C67C2×C22⋊C414yes—
464C23×C67C4×D414yes—
465C23×C67C23×C411yescharacteristic
466C23×C67C22×D411yescharacteristic
467C23×C67C22×D411yescharacteristic
468C23×C67C22×D411yescharacteristic
469C23×C67C22×D411yescharacteristic
470C23×C67C2×#4111yescharacteristic
471C23×C67C2×#4111yescharacteristic
472C23×C67C2×#4111yescharacteristic
473C23×C67C2×#4111yescharacteristic
474C23×C67C2×#4111yescharacteristic
475C23×C67C2×#4111yescharacteristic
476C23×C67H(5,𝔽2)11yescharacteristic
477C23×C67H(5,𝔽2)11yescharacteristic
478C23×C67H(5,𝔽2)11yescharacteristic
479C23×C67H(5,𝔽2)11yescharacteristic
480D4×C67—416no—
481D4×C67—416no—
482D4×C67—416no—
483C2×C4×C67—22no—
484C2×C4×C67—22no—
485C2×C4×C67—22no—
486C2×C4×C67—22no—
487C2×C4×C67—22no—
488C2×C4×C67—22no—
489C2×C4×C67—22no—
490C2×C4×C67—22no—
491C2×C4×C67—22no—
492C2×C4×C67—22no—
493C2×C4×C67—22no—
494C2×C4×C67—22no—
495C2×C4×C67—22no—
496C2×C4×C67—22no—
497C2×C4×C67—22no—
498C2×C4×C67—22no—
499C2×C4×C67—22no—
500C2×C4×C67—22no—
501C2×C4×C67—22no—
502C2×C4×C67—22no—
503C2×C4×C67—22no—
504C2×C4×C67—22no—
505C2×C4×C67—22no—
506C2×C4×C67—22no—
507C2×C4×C67—22no—
508C2×C4×C67—22no—
509C2×C4×C67—22no—
510C2×C4×C67—22no—
511C2×C4×C67—22no—
512C2×C4×C67—22no—
513C2×C4×C67—22no—
514C2×C4×C67—22no—
515C2×C4×C67—22no—
516C2×C4×C67—22no—
517C2×C4×C67—22no—
518C2×C4×C67—22no—
519C2×C4×C67—22no—
520C2×C4×C67—22no—
521C2×C4×C67—22no—
522C2×C4×C67—22no—
523C2×C4×C67—22no—
524C2×C4×C67—22no—
525C2×C4×C67—416no—
526C2×C4×C67—416no—
527C2×C4×C67—41no—
528C2×C4×C67—41no—
529C2×C4×C67—41no—
530C2×C4×C67—41no—
531C2×C4×C67—41no—
532C2×C4×C67—41no—
533C2×C4×C67—41no—
534C2×C4×C67—41no—
535C2×C4×C67—41no—
536C2×C4×C67—41no—
537C2×C4×C67—41no—
538C2×C4×C67—41no—
539C2×C4×C67—41no—
540C2×C4×C67—41no—
541C2×C4×C67—41no—
542C2×C4×C67—41no—
543C2×C4×C67—41no—
544C2×C4×C67—41no—
545C2×C4×C67—41no—
546C2×C4×C67—41no—
547C2×C4×C67—41no—
548C2×C4×C67—41no—
549C2×C4×C67—41no—
550C2×C4×C67—41no—
551C2×C4×C67—41no—
552C2×C4×C67—41no—
553C2×C4×C67—41no—
554C2×C4×C67—41no—
555C2×C4×C67—41no—
556C2×C4×C67—41no—
557C2×C4×C67—41no—
558C2×C4×C67—41no—
559C2×C4×C67—41no—
560C2×C4×C67—41no—
561C2×C4×C67—41no—
562C2×C4×C67—41no—
563C2×C4×C67—41no—
564C2×C4×C67—41no—
565C2×C4×C67C2×C22⋊C414yes—
566C2×C4×C67C2×C22⋊C414yes—
567C2×C4×C67C4×D414yes—
568C2×C4×C67#12114yescomplemented
569C22×C67—24no—
570C22×C67—24no—
571C22×C67—24no—
572C22×C67—24no—
573C22×C67—24no—
574C22×C67—24no—
575C22×C67—42no—
576C22×C67—42no—
577C22×C67—42no—
578C22×C67—42no—
579C22×C67—42no—
580C22×C67—42no—
581C22×C67—42no—
582C22×C67—42no—
583C22×C67—42no—
584C22×C67—42no—
585C22×C67—42no—
586C22×C67—42no—
587C22×C67—42no—
588C22×C67—42no—
589C22×C67—42no—
590C22×C67—42no—
591C22×C67—42no—
592C22×C67—42no—
593C22×C67—42no—
594C22×C67—42no—
595C22×C67—42no—
596C22×C67—42no—
597C22×C67—42no—
598C22×C67—42no—
599C22×C67—42no—
600C22×C67—42no—
601C22×C67—42no—
602C22×C67—42no—
603C22×C67—42no—
604C22×C67—42no—
605C22×C67—42no—
606C22×C67—81no—
607C22×C67—81no—
608C22×C67—81no—
609C22×C67—81no—
610C22×C67—81no—
611C22×C67—81no—
612C22×C67—81no—
613C22×C67—81no—
614C22×C67C22×C22⋊C411yescharacteristic
615C22×C67C2×C4×D411yescharacteristic
616C22×C67C2×C4×D411yescharacteristic
617C22×C67C4×#4111yescharacteristic
618C22×C67C4×#4111yescharacteristic
619C22×C67#51811yescharacteristic
620C22×C67#51811yescharacteristic
621C22×C67C2×#12111yescharacteristic
622C22×C67#52511yescharacteristic
623C22×C67#52511yescharacteristic
624C22×C67#52511yescharacteristic
625C22×C67#52911yescharacteristic
626C22×C67#53211yescharacteristic
627C22×C67#53211yescharacteristic
628C22×C67#53211yescharacteristic
629C22×C67#53811yescharacteristic
630C22×C67#53811yescharacteristic
631C22×C67#54011yescharacteristic
632C22×C67#54011yescharacteristic
633C22×C67D4211yescharacteristic
634C22×C67D4211yescharacteristic
635C22×C67D4211yescharacteristic
636C22×C67D4211yescharacteristic
637C22×C67#54611yescharacteristic
638C22×C67#54611yescharacteristic
639C22×C67#54611yescharacteristic
640C22×C67#54611yescharacteristic
641C22×C67#54611yescharacteristic
642C22×C67#54611yescharacteristic
643C22×C67#54611yescharacteristic
644C22×C67#55011yescharacteristic
645C22×C67#55311yescharacteristic
646C22×C67#55311yescharacteristic
647C22×C67#55311yescharacteristic
648C22×C67#55511yescharacteristic
649C4×C67—24no—
650C4×C67—24no—
651C4×C67—24no—
652C4×C67—24no—
653C4×C67—42no—
654C4×C67—42no—
655C4×C67—42no—
656C4×C67—42no—
657C4×C67—42no—
658C4×C67—42no—
659C4×C67—81no—
660C4×C67—81no—
661#14100C6711yesmaximal, characteristic, direct product factor, Sylow
662C2×C67—44no—
663C2×C67—44no—
664C2×C67—82no—
665C2×C67#229711yescharacteristic
666C2×C67C4×#12111yescharacteristic
667C2×C67#233311yescharacteristic
668C2×C67D4×C22⋊C411yescharacteristic
669C2×C67D4×C22⋊C411yescharacteristic
670C2×C67#236311yescharacteristic
671C2×C67#236411yescharacteristic
672C2×C67#242411yescharacteristic
673C2×C67#242811yescharacteristic
674C2×C67#245611yescharacteristic
675C2×C67#246411yescharacteristic
676C2×C67#246411yescharacteristic
677C2×C67#247611yescharacteristic
678C2×C67#255511yescharacteristic
679C2×C67#255911yescharacteristic
680C22×#121C2×C6711yescharacteristic
681C2×#390C2×C6711yescharacteristic, complemented
682C2×#388C2×C6711yescharacteristic, complemented
683C2×#386C2×C6711yescharacteristic, complemented
684C2×#386C2×C6711yescharacteristic, complemented
685C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
686C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
687#1441C2×C6711yescharacteristic, complemented
688#1438C2×C6711yescharacteristic, complemented
689#1438C2×C6711yescharacteristic, complemented
690#1438C2×C6711yescharacteristic, complemented
691#1437C2×C6711yescharacteristic, complemented
692#1437C2×C6711yescharacteristic, complemented
693#1436C2×C6711yescharacteristic, complemented
694C22⋊#95C2×C6711yescharacteristic, complemented
695C67#1410011yescharacteristic, direct product factor, Sylow
696C23×D4C22×C6711yescharacteristic
697C23×D4C22×C6711yescharacteristic
698C23×D4C22×C6711yescharacteristic
699C24×C4C22×C6711yescharacteristic
700C24×C4C22×C6711yescharacteristic
701C2×#121—24no—
702C2×#121—24no—
703C2×#121C4×C6718yescomplemented
704C22×C4⋊C4C22×C6711yescharacteristic
705C22×C4⋊C4C22×C6711yescharacteristic
706C22×C22⋊C4C22×C6711yescharacteristic
707C22×C22⋊C4C22×C6711yescharacteristic
708C22×C22⋊C4C22×C6711yescharacteristic
709C22×C22⋊C4C22×C6711yescharacteristic
710C22×C22⋊C4C22×C6711yescharacteristic
711C22×C22⋊C4C22×C6711yescharacteristic
712C22×C22⋊C4C22×C6711yescharacteristic
713C22×C22⋊C4C22×C6711yescharacteristic
714C22×C22⋊C4C22×C6711yescharacteristic
715C22×C22⋊C4C22×C6711yescharacteristic
716C22×C22⋊C4C22×C6711yescharacteristic
717C22×C22⋊C4C22×C6711yescharacteristic
718C22×C22⋊C4C22×C6711yescharacteristic
719C22×C42C22×C6711yescharacteristic
720C22×C42C22×C6711yescharacteristic
721C22×C42C22×C6711yescharacteristic
722#390—24no—
723#388—24no—
724#386—24no—
725#386—24no—
726C4×C22⋊C4—24no—
727C4×C22⋊C4—24no—
728C2×#95C22×C6711yescharacteristic
729C2×#95C22×C6711yescharacteristic
730C2×#95C22×C6711yescharacteristic
731C2×#95C22×C6711yescharacteristic
732C2×#95C22×C6711yescharacteristic
733C2×#95C22×C6711yescharacteristic
734C2×#95C22×C6711yescharacteristic
735C2×#95C22×C6711yescharacteristic
736C2×#95C22×C6711yescharacteristic
737C2×#95C22×C6711yescharacteristic
738C2×#95C22×C6711yescharacteristic
739C2×#95C22×C6711yescharacteristic
740C25C23×C6711yescharacteristic
741C25C23×C6711yescharacteristic
742C25C23×C6711yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×C4×C6714yes—
762C22×D4C2×C4×C6714yes—
763C22×D4C2×C4×C6714yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—41no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4C2×C4×C6714yescomplemented
778C23×C4C23×C6711yescharacteristic
779C23×C4C23×C6711yescharacteristic
780C23×C4C23×C6711yescharacteristic
781C23×C4C23×C6711yescharacteristic
782C23×C4C23×C6711yescharacteristic
783C23×C4C23×C6711yescharacteristic
784C23×C4C23×C6711yescharacteristic
785C23×C4C23×C6711yescharacteristic
786C23×C4C23×C6711yescharacteristic
787C23×C4C23×C6711yescharacteristic
788C23×C4C23×C6711yescharacteristic
789C23×C4C23×C6711yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4C2×C4×C6714yescomplemented
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4C2×C4×C6714yes—
832C2×C22⋊C4C2×C4×C6714yescomplemented
833C2×C22⋊C4D4×C6714yes—
834C2×C22⋊C4D4×C6714yes—
835C2×C22⋊C4D4×C6714yescomplemented
836C2×C42—22no—
837C2×C42—22no—
838C2×C42—22no—
839C2×C42—22no—
840C2×C42—22no—
841C2×C42—22no—
842C2×C42—41no—
843C2×C42—41no—
844C2×C42—41no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—41no—
855#95—41no—
856#95D4×C6714yescomplemented
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24C22×C4×C6712yes—
896C24C22×C4×C6712yes—
897C24C22×C4×C6712yes—
898C24C2×D4×C6712yes—
899C24C2×D4×C6712yes—
900C24C2×D4×C6712yes—
901C24#41×C6712yes—
902C24C24×C6711yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—28no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4C22×C4×C6712yes—
1005C22×C4C22×C4×C6712yes—
1006C22×C4C22×C4×C6712yes—
1007C22×C4C22×C4×C6712yes—
1008C22×C4C2×D4×C6712yes—
1009C22×C4C2×D4×C6712yes—
1010C22×C4C2×D4×C6712yes—
1011C22×C4C2×D4×C6712yes—
1012C22×C4C2×D4×C6712yes—
1013C22×C4C2×D4×C6712yes—
1014C22×C4C2×D4×C6712yes—
1015C22×C4C2×D4×C6712yes—
1016C22×C4C2×D4×C6712yes—
1017C22×C4#41×C6712yes—
1018C22×C4#41×C6712yes—
1019C22×C4#41×C6712yes—
1020C22×C4#41×C6712yes—
1021C22×C4#41×C6712yes—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4C22⋊C4×C67116yescomplemented
1037C42—44no—
1038C42—44no—
1039C42—44no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊C4×C6714yes—
1144C23C4×D4×C6714yes—
1145C23C23×C4×C6711yescharacteristic
1146C23C22×D4×C6711yescharacteristic
1147C23C22×D4×C6711yescharacteristic
1148C23C22×D4×C6711yescharacteristic
1149C23C22×D4×C6711yescharacteristic
1150C23C2×#41×C6711yescharacteristic
1151C23C2×#41×C6711yescharacteristic
1152C23C2×#41×C6711yescharacteristic
1153C23C2×#41×C6711yescharacteristic
1154C23C2×#41×C6711yescharacteristic
1155C23C2×#41×C6711yescharacteristic
1156C23H(5,𝔽2)×C6711yescharacteristic
1157C23H(5,𝔽2)×C6711yescharacteristic
1158C23H(5,𝔽2)×C6711yescharacteristic
1159C23H(5,𝔽2)×C6711yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—416no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4C2×C22⋊C4×C6714yes—
1246C2×C4C2×C22⋊C4×C6714yes—
1247C2×C4C4×D4×C6714yes—
1248C2×C4#121×C6714yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊C4×C6711yescharacteristic
1295C22C2×C4×D4×C6711yescharacteristic
1296C22C2×C4×D4×C6711yescharacteristic
1297C22C4×#41×C6711yescharacteristic
1298C22C4×#41×C6711yescharacteristic
1299C22#518×C6711yescharacteristic
1300C22#518×C6711yescharacteristic
1301C22C2×#121×C6711yescharacteristic
1302C22#525×C6711yescharacteristic
1303C22#525×C6711yescharacteristic
1304C22#525×C6711yescharacteristic
1305C22#529×C6711yescharacteristic
1306C22#532×C6711yescharacteristic
1307C22#532×C6711yescharacteristic
1308C22#532×C6711yescharacteristic
1309C22#538×C6711yescharacteristic
1310C22#538×C6711yescharacteristic
1311C22#540×C6711yescharacteristic
1312C22#540×C6711yescharacteristic
1313C22D42×C6711yescharacteristic
1314C22D42×C6711yescharacteristic
1315C22D42×C6711yescharacteristic
1316C22D42×C6711yescharacteristic
1317C22#546×C6711yescharacteristic
1318C22#546×C6711yescharacteristic
1319C22#546×C6711yescharacteristic
1320C22#546×C6711yescharacteristic
1321C22#546×C6711yescharacteristic
1322C22#546×C6711yescharacteristic
1323C22#546×C6711yescharacteristic
1324C22#550×C6711yescharacteristic
1325C22#553×C6711yescharacteristic
1326C22#553×C6711yescharacteristic
1327C22#553×C6711yescharacteristic
1328C22#555×C6711yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C67×#229711yescharacteristic
1345C2C4×#121×C6711yescharacteristic
1346C2C67×#233311yescharacteristic
1347C2D4×C22⋊C4×C6711yescharacteristic
1348C2D4×C22⋊C4×C6711yescharacteristic
1349C2C67×#236311yescharacteristic
1350C2C67×#236411yescharacteristic
1351C2C67×#242411yescharacteristic
1352C2C67×#242811yescharacteristic
1353C2C67×#245611yescharacteristic
1354C2C67×#246411yescharacteristic
1355C2C67×#246411yescharacteristic
1356C2C67×#247611yescharacteristic
1357C2C67×#255511yescharacteristic
1358C2C67×#255911yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC22×#121×C67C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#390×C67C2semidirect
3. C2×#388×C67C2semidirect
4. C2×#386×C67C2semidirect
5. C2×#386×C67C2semidirect
6. C2×C4×C22⋊C4×C67C2semidirect
7. C2×C4×C22⋊C4×C67C2semidirect
8. C67×#1441C2semidirect
9. C67×#1438C2semidirect
10. C67×#1438C2semidirect
11. C67×#1438C2semidirect
12. C67×#1437C2semidirect
13. C67×#1437C2semidirect
14. C67×#1436C2semidirect
15. C67×C22⋊#95C2semidirect
23. C2×#121×C67C4semidirect
83. C22×D4×C67C2×C4semidirect
97. C23×C4×C67C2×C4semidirect
116. C2×C4⋊C4×C67C2×C4semidirect
152. C2×C22⋊C4×C67C2×C4semidirect
155. C2×C22⋊C4×C67D4semidirect
176. #95×C67D4semidirect
356. C22⋊C4×C67C22⋊C4semidirect
568. C2×C4×C67#121semidirect
661. #14100C67direct (N × H)
681. C2×#390C2×C67semidirect
682. C2×#388C2×C67semidirect
683. C2×#386C2×C67semidirect
684. C2×#386C2×C67semidirect
685. C2×C4×C22⋊C4C2×C67semidirect
686. C2×C4×C22⋊C4C2×C67semidirect
687. #1441C2×C67semidirect
688. #1438C2×C67semidirect
689. #1438C2×C67semidirect
690. #1438C2×C67semidirect
691. #1437C2×C67semidirect
692. #1437C2×C67semidirect
693. #1436C2×C67semidirect
694. C22⋊#95C2×C67semidirect
695. C67#14100direct (N × H)
703. C2×#121C4×C67semidirect
763. C22×D4C2×C4×C67semidirect
777. C23×C4C2×C4×C67semidirect
796. C2×C4⋊C4C2×C4×C67semidirect
832. C2×C22⋊C4C2×C4×C67semidirect
835. C2×C22⋊C4D4×C67semidirect
856. #95D4×C67semidirect
1036. C22⋊C4C22⋊C4×C67semidirect
1248. C2×C4#121×C67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#121×C672
C2×#390×C672
C2×#388×C672
C2×#386×C672
C2×C4×C22⋊C4×C672
C67×#14412
C67×#14382
C67×#14372
C67×#14362
C67×C22⋊#952
#1410067