Finite Group Databasebeta

← C67×#14034 #30693285

Subgroups — C67×#14034 #30693285

Order 17152.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#390×C67C211yesmaximal, characteristic
2C2×#388×C67C211yesmaximal, characteristic, complemented
3C2×#387×C67C211yesmaximal, characteristic, complemented
4C2×#386×C67C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
6C67×#1445C211yesmaximal, characteristic, complemented
7C67×#1440C211yesmaximal, characteristic, complemented
8C67×#1439C211yesmaximal, characteristic, complemented
9C67×#1438C211yesmaximal, characteristic
10C67×#1437C211yesmaximal, characteristic, complemented
11C67×#1437C211yesmaximal, characteristic, complemented
12C67×#1437C211yesmaximal, characteristic, complemented
13C67×#1434C211yesmaximal, characteristic, complemented
14C67×C22⋊#95C211yesmaximal, characteristic, complemented
15C4×#95×C67C211yesmaximal, characteristic, complemented
16C23×D4×C67C2211yescharacteristic
17C24×C4×C67C2211yescharacteristic
18C22×C4⋊C4×C67C2211yescharacteristic
19C22×C4⋊C4×C67C2211yescharacteristic
20C22×C22⋊C4×C67C2211yescharacteristic
21C22×C22⋊C4×C67C2211yescharacteristic
22C22×C22⋊C4×C67C2211yescharacteristic
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C22⋊C4×C67C2211yescharacteristic
26C22×C22⋊C4×C67C2211yescharacteristic
27C22×C22⋊C4×C67C2211yescharacteristic
28C22×C22⋊C4×C67C2211yescharacteristic
29C22×C22⋊C4×C67C2211yescharacteristic
30C22×C22⋊C4×C67C2211yescharacteristic
31C22×C42×C67C2211yescharacteristic
32C22×C42×C67C2211yescharacteristic
33C22×C42×C67C2211yescharacteristic
34C22×C42×C67C2211yescharacteristic
35#390×C67C418yescomplemented
36#388×C67—24no—
37#387×C67—24no—
38#386×C67—24no—
39C4×C22⋊C4×C67—24no—
40C2×#95×C67C2211yescharacteristic
41C2×#95×C67C2211yescharacteristic
42C2×#95×C67C2211yescharacteristic
43C2×#95×C67C2211yescharacteristic
44C2×#95×C67C2211yescharacteristic
45C2×#95×C67C2211yescharacteristic
46C2×#95×C67C2211yescharacteristic
47C2×#95×C67C2211yescharacteristic
48C2×#95×C67C2211yescharacteristic
49C2×#95×C67C2211yescharacteristic
50C2×#95×C67C2211yescharacteristic
51C2×#95×C67C2211yescharacteristic
52C2×#95×C67C2211yescharacteristic
53C2×#95×C67C2211yescharacteristic
54C2×#95×C67C2211yescharacteristic
55C2×#95×C67C2211yescharacteristic
56C25×C67C2311yescharacteristic
57C25×C67C2311yescharacteristic
58C22×D4×C67—22no—
59C22×D4×C67—22no—
60C22×D4×C67—22no—
61C22×D4×C67—22no—
62C22×D4×C67—41no—
63C22×D4×C67—41no—
64C22×D4×C67C2×C414yes—
65C23×C4×C67—22no—
66C23×C4×C67—22no—
67C23×C4×C67—22no—
68C23×C4×C67—22no—
69C23×C4×C67—22no—
70C23×C4×C67—41no—
71C23×C4×C67—41no—
72C23×C4×C67C2311yescharacteristic
73C23×C4×C67C2311yescharacteristic
74C23×C4×C67C2311yescharacteristic
75C23×C4×C67C2311yescharacteristic
76C23×C4×C67C2311yescharacteristic
77C23×C4×C67C2311yescharacteristic
78C23×C4×C67C2311yescharacteristic
79C23×C4×C67C2311yescharacteristic
80C23×C4×C67C2311yescharacteristic
81C23×C4×C67C2311yescharacteristic
82C23×C4×C67C2311yescharacteristic
83C23×C4×C67C2311yescharacteristic
84C23×C4×C67C2311yescharacteristic
85C2×C4⋊C4×C67—22no—
86C2×C4⋊C4×C67—22no—
87C2×C4⋊C4×C67—22no—
88C2×C4⋊C4×C67—22no—
89C2×C4⋊C4×C67—41no—
90C2×C4⋊C4×C67C2×C414yescomplemented
91C2×C22⋊C4×C67—22no—
92C2×C22⋊C4×C67—22no—
93C2×C22⋊C4×C67—22no—
94C2×C22⋊C4×C67—22no—
95C2×C22⋊C4×C67—22no—
96C2×C22⋊C4×C67—22no—
97C2×C22⋊C4×C67—22no—
98C2×C22⋊C4×C67—22no—
99C2×C22⋊C4×C67—22no—
100C2×C22⋊C4×C67—22no—
101C2×C22⋊C4×C67—22no—
102C2×C22⋊C4×C67—22no—
103C2×C22⋊C4×C67—22no—
104C2×C22⋊C4×C67—22no—
105C2×C22⋊C4×C67—22no—
106C2×C22⋊C4×C67—22no—
107C2×C22⋊C4×C67—22no—
108C2×C22⋊C4×C67—22no—
109C2×C22⋊C4×C67—22no—
110C2×C22⋊C4×C67—41no—
111C2×C22⋊C4×C67—41no—
112C2×C22⋊C4×C67—41no—
113C2×C22⋊C4×C67—41no—
114C2×C22⋊C4×C67—41no—
115C2×C22⋊C4×C67—41no—
116C2×C22⋊C4×C67—41no—
117C2×C22⋊C4×C67—41no—
118C2×C22⋊C4×C67—41no—
119C2×C22⋊C4×C67—41no—
120C2×C22⋊C4×C67C2×C414yes—
121C2×C22⋊C4×C67C2×C414yes—
122C2×C22⋊C4×C67C2×C414yescomplemented
123C2×C22⋊C4×C67C2×C414yescomplemented
124C2×C42×C67—22no—
125C2×C42×C67—22no—
126C2×C42×C67—22no—
127C2×C42×C67—22no—
128C2×C42×C67—22no—
129C2×C42×C67—22no—
130C2×C42×C67—41no—
131C2×C42×C67—41no—
132C2×C42×C67—41no—
133C2×C42×C67—41no—
134C2×C42×C67—41no—
135C2×C42×C67C2×C414yescomplemented
136#95×C67—22no—
137#95×C67—22no—
138#95×C67—22no—
139#95×C67—22no—
140#95×C67—22no—
141#95×C67—22no—
142#95×C67—22no—
143#95×C67—22no—
144#95×C67—22no—
145#95×C67—22no—
146#95×C67—41no—
147#95×C67—41no—
148#95×C67—41no—
149#95×C67—41no—
150#95×C67D414yes—
151#95×C67D414yescomplemented
152C24×C67—21no—
153C24×C67—21no—
154C24×C67—21no—
155C24×C67—21no—
156C24×C67—21no—
157C24×C67—21no—
158C24×C67—21no—
159C24×C67—21no—
160C24×C67—21no—
161C24×C67—21no—
162C24×C67—21no—
163C24×C67—21no—
164C24×C67—21no—
165C24×C67—21no—
166C24×C67—21no—
167C24×C67—21no—
168C24×C67—21no—
169C24×C67—21no—
170C24×C67—21no—
171C24×C67—21no—
172C24×C67—21no—
173C24×C67—21no—
174C24×C67—21no—
175C24×C67—21no—
176C24×C67—21no—
177C24×C67—21no—
178C24×C67C22×C412yes—
179C24×C67C22×C412yes—
180C24×C67#4112yes—
181C24×C67#4112yes—
182C24×C67C2411yescharacteristic
183C2×D4×C67—28no—
184C2×D4×C67—28no—
185C2×D4×C67—44no—
186C2×D4×C67—44no—
187C2×D4×C67—44no—
188C2×D4×C67—44no—
189C2×D4×C67—44no—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—21no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—28no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—21no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—21no—
220C22×C4×C67—21no—
221C22×C4×C67—21no—
222C22×C4×C67—21no—
223C22×C4×C67—21no—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
228C22×C4×C67—21no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
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—21no—
261C22×C4×C67—21no—
262C22×C4×C67—21no—
263C22×C4×C67—21no—
264C22×C4×C67—21no—
265C22×C4×C67—44no—
266C22×C4×C67—44no—
267C22×C4×C67—44no—
268C22×C4×C67—44no—
269C22×C4×C67—44no—
270C22×C4×C67—44no—
271C22×C4×C67C22×C412yes—
272C22×C4×C67C22×C412yes—
273C22×C4×C67C22×C412yes—
274C22×C4×C67C22×C412yes—
275C22×C4×C67C22×C412yes—
276C22×C4×C67C2×D412yes—
277C22×C4×C67C2×D412yes—
278C22×C4×C67C2×D412yes—
279C22×C4×C67C2×D412yes—
280C22×C4×C67C2×D412yes—
281C22×C4×C67C2×D412yes—
282C22×C4×C67#4112yes—
283C22×C4×C67#4112yes—
284C22×C4×C67#4112yes—
285C22×C4×C67#4112yes—
286C22×C4×C67#4112yes—
287C22×C4×C67#4112yes—
288C4⋊C4×C67—28no—
289C4⋊C4×C67—44no—
290C22⋊C4×C67—28no—
291C22⋊C4×C67—28no—
292C22⋊C4×C67—28no—
293C22⋊C4×C67—44no—
294C22⋊C4×C67—44no—
295C22⋊C4×C67—44no—
296C22⋊C4×C67—44no—
297C22⋊C4×C67—44no—
298C22⋊C4×C67—44no—
299C22⋊C4×C67—44no—
300C22⋊C4×C67—44no—
301C42×C67—44no—
302C42×C67—44no—
303C42×C67—44no—
304C42×C67—44no—
305C23×C67—22no—
306C23×C67—22no—
307C23×C67—22no—
308C23×C67—22no—
309C23×C67—22no—
310C23×C67—22no—
311C23×C67—22no—
312C23×C67—22no—
313C23×C67—22no—
314C23×C67—22no—
315C23×C67—22no—
316C23×C67—22no—
317C23×C67—22no—
318C23×C67—22no—
319C23×C67—22no—
320C23×C67—22no—
321C23×C67—22no—
322C23×C67—22no—
323C23×C67—22no—
324C23×C67—22no—
325C23×C67—22no—
326C23×C67—22no—
327C23×C67—22no—
328C23×C67—22no—
329C23×C67—22no—
330C23×C67—41no—
331C23×C67—41no—
332C23×C67—41no—
333C23×C67—41no—
334C23×C67—41no—
335C23×C67—41no—
336C23×C67—41no—
337C23×C67—41no—
338C23×C67—41no—
339C23×C67—41no—
340C23×C67—41no—
341C23×C67—41no—
342C23×C67—41no—
343C23×C67—41no—
344C23×C67—41no—
345C23×C67—41no—
346C23×C67—41no—
347C23×C67—41no—
348C23×C67—41no—
349C23×C67—41no—
350C23×C67—41no—
351C23×C67—41no—
352C23×C67—41no—
353C23×C67—41no—
354C23×C67—41no—
355C23×C67—41no—
356C23×C67—41no—
357C23×C67—41no—
358C23×C67—41no—
359C23×C67—41no—
360C23×C67—41no—
361C23×C67—41no—
362C23×C67—41no—
363C23×C67—41no—
364C23×C67—41no—
365C23×C67—41no—
366C23×C67—41no—
367C23×C67—41no—
368C23×C67—41no—
369C23×C67—41no—
370C23×C67—41no—
371C23×C67—41no—
372C23×C67—41no—
373C23×C67—41no—
374C23×C67#11714yes—
375C23×C67C23×C411yescharacteristic
376C23×C67C22×D411yescharacteristic
377C23×C67C22×D411yescharacteristic
378C23×C67C2×#4111yescharacteristic
379C23×C67C2×#4111yescharacteristic
380C23×C67C2×#4111yescharacteristic
381C23×C67C2×#4111yescharacteristic
382C23×C67C2×#4111yescharacteristic
383C23×C67C2×#4111yescharacteristic
384C23×C67C2×#4111yescharacteristic
385C23×C67C2×#4111yescharacteristic
386C23×C67H(5,𝔽2)11yescharacteristic
387C23×C67H(5,𝔽2)11yescharacteristic
388C23×C67H(5,𝔽2)11yescharacteristic
389C23×C67H(5,𝔽2)11yescharacteristic
390D4×C67—416no—
391C2×C4×C67—22no—
392C2×C4×C67—22no—
393C2×C4×C67—22no—
394C2×C4×C67—22no—
395C2×C4×C67—22no—
396C2×C4×C67—22no—
397C2×C4×C67—22no—
398C2×C4×C67—22no—
399C2×C4×C67—22no—
400C2×C4×C67—22no—
401C2×C4×C67—22no—
402C2×C4×C67—22no—
403C2×C4×C67—22no—
404C2×C4×C67—22no—
405C2×C4×C67—22no—
406C2×C4×C67—22no—
407C2×C4×C67—22no—
408C2×C4×C67—22no—
409C2×C4×C67—22no—
410C2×C4×C67—22no—
411C2×C4×C67—22no—
412C2×C4×C67—22no—
413C2×C4×C67—22no—
414C2×C4×C67—22no—
415C2×C4×C67—22no—
416C2×C4×C67—22no—
417C2×C4×C67—22no—
418C2×C4×C67—22no—
419C2×C4×C67—22no—
420C2×C4×C67—22no—
421C2×C4×C67—22no—
422C2×C4×C67—22no—
423C2×C4×C67—22no—
424C2×C4×C67—22no—
425C2×C4×C67—22no—
426C2×C4×C67—22no—
427C2×C4×C67—22no—
428C2×C4×C67—22no—
429C2×C4×C67—22no—
430C2×C4×C67—22no—
431C2×C4×C67—22no—
432C2×C4×C67—22no—
433C2×C4×C67—416no—
434C2×C4×C67—41no—
435C2×C4×C67—41no—
436C2×C4×C67—41no—
437C2×C4×C67—41no—
438C2×C4×C67—41no—
439C2×C4×C67—41no—
440C2×C4×C67—41no—
441C2×C4×C67—41no—
442C2×C4×C67—41no—
443C2×C4×C67—41no—
444C2×C4×C67—41no—
445C2×C4×C67—41no—
446C2×C4×C67—41no—
447C2×C4×C67—41no—
448C2×C4×C67—41no—
449C2×C4×C67—41no—
450C2×C4×C67—41no—
451C2×C4×C67—41no—
452C2×C4×C67—41no—
453C2×C4×C67—41no—
454C2×C4×C67—41no—
455C2×C4×C67—41no—
456C2×C4×C67—41no—
457C2×C4×C67—41no—
458C2×C4×C67—41no—
459C2×C4×C67—41no—
460C2×C4×C67—41no—
461C2×C4×C67—41no—
462C2×C4×C67—41no—
463C2×C4×C67—41no—
464C2×C4×C67—41no—
465C2×C4×C67—41no—
466C2×C4×C67—41no—
467C2×C4×C67—41no—
468C2×C4×C67—41no—
469C2×C4×C67—41no—
470C2×C4×C67—41no—
471C2×C4×C67—41no—
472C2×C4×C67—41no—
473C2×C4×C67—41no—
474C2×C4×C67—41no—
475C2×C4×C67—41no—
476C2×C4×C67—41no—
477C2×C4×C67—41no—
478C2×C4×C67—41no—
479C2×C4×C67—41no—
480C2×C4×C67C4×D414yes—
481C2×C4×C67C4×D414yes—
482C2×C4×C67#12414yes—
483C22×C67—24no—
484C22×C67—24no—
485C22×C67—24no—
486C22×C67—42no—
487C22×C67—42no—
488C22×C67—42no—
489C22×C67—42no—
490C22×C67—42no—
491C22×C67—42no—
492C22×C67—42no—
493C22×C67—42no—
494C22×C67—42no—
495C22×C67—42no—
496C22×C67—42no—
497C22×C67—42no—
498C22×C67—42no—
499C22×C67—42no—
500C22×C67—42no—
501C22×C67—42no—
502C22×C67—42no—
503C22×C67—42no—
504C22×C67—42no—
505C22×C67—81no—
506C22×C67—81no—
507C22×C67—81no—
508C22×C67—81no—
509C22×C67—81no—
510C22×C67—81no—
511C22×C67—81no—
512C22×C67—81no—
513C22×C67C2×#11711yescharacteristic
514C22×C67C2×C4×D411yescharacteristic
515C22×C67C2×C4×D411yescharacteristic
516C22×C67C4×#4111yescharacteristic
517C22×C67C4×#4111yescharacteristic
518C22×C67#51811yescharacteristic
519C22×C67#51811yescharacteristic
520C22×C67#52511yescharacteristic
521C22×C67#52511yescharacteristic
522C22×C67C2×#12411yescharacteristic
523C22×C67#52911yescharacteristic
524C22×C67#52911yescharacteristic
525C22×C67#52911yescharacteristic
526C22×C67#52911yescharacteristic
527C22×C67#53211yescharacteristic
528C22×C67#53811yescharacteristic
529C22×C67#53811yescharacteristic
530C22×C67#54011yescharacteristic
531C22×C67#54011yescharacteristic
532C22×C67D4211yescharacteristic
533C22×C67#54611yescharacteristic
534C22×C67#54611yescharacteristic
535C22×C67#54611yescharacteristic
536C22×C67#54611yescharacteristic
537C22×C67#55011yescharacteristic
538C22×C67#55011yescharacteristic
539C22×C67#55111yescharacteristic
540C22×C67#55111yescharacteristic
541C22×C67#55111yescharacteristic
542C22×C67#55111yescharacteristic
543C22×C67#55311yescharacteristic
544C22×C67#55311yescharacteristic
545C22×C67#55311yescharacteristic
546C22×C67#55311yescharacteristic
547C22×C67#55911yescharacteristic
548C4×C67—24no—
549C4×C67—24no—
550C4×C67—24no—
551C4×C67—42no—
552C4×C67—42no—
553C4×C67—42no—
554C4×C67—42no—
555C4×C67—42no—
556C4×C67—42no—
557C4×C67—42no—
558C4×C67—42no—
559C4×C67—81no—
560C4×C67—81no—
561#14034C6711yesmaximal, characteristic, direct product factor, Sylow
562C2×C67—44no—
563C2×C67—82no—
564C2×C67#229011yescharacteristic
565C2×C67C4×#12411yescharacteristic
566C2×C67#233311yescharacteristic
567C2×C67#234211yescharacteristic
568C2×C67#235311yescharacteristic
569C2×C67#236411yescharacteristic
570C2×C67#236611yescharacteristic
571C2×C67#246411yescharacteristic
572C2×C67#246711yescharacteristic
573C2×C67#247111yescharacteristic
574C2×C67#247211yescharacteristic
575C2×C67#249011yescharacteristic
576C2×C67#251611yescharacteristic
577C2×C67#255411yescharacteristic
578C2×C67#259511yescharacteristic
579C2×#390C2×C6711yescharacteristic
580C2×#388C2×C6711yescharacteristic, complemented
581C2×#387C2×C6711yescharacteristic, complemented
582C2×#386C2×C6711yescharacteristic
583C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
584#1445C2×C6711yescharacteristic, complemented
585#1440C2×C6711yescharacteristic, complemented
586#1439C2×C6711yescharacteristic, complemented
587#1438C2×C6711yescharacteristic
588#1437C2×C6711yescharacteristic, complemented
589#1437C2×C6711yescharacteristic, complemented
590#1437C2×C6711yescharacteristic, complemented
591#1434C2×C6711yescharacteristic, complemented
592C22⋊#95C2×C6711yescharacteristic, complemented
593C4×#95C2×C6711yescharacteristic, complemented
594C67#1403411yescharacteristic, direct product factor, Sylow
595C23×D4C22×C6711yescharacteristic
596C24×C4C22×C6711yescharacteristic
597C22×C4⋊C4C22×C6711yescharacteristic
598C22×C4⋊C4C22×C6711yescharacteristic
599C22×C22⋊C4C22×C6711yescharacteristic
600C22×C22⋊C4C22×C6711yescharacteristic
601C22×C22⋊C4C22×C6711yescharacteristic
602C22×C22⋊C4C22×C6711yescharacteristic
603C22×C22⋊C4C22×C6711yescharacteristic
604C22×C22⋊C4C22×C6711yescharacteristic
605C22×C22⋊C4C22×C6711yescharacteristic
606C22×C22⋊C4C22×C6711yescharacteristic
607C22×C22⋊C4C22×C6711yescharacteristic
608C22×C22⋊C4C22×C6711yescharacteristic
609C22×C22⋊C4C22×C6711yescharacteristic
610C22×C42C22×C6711yescharacteristic
611C22×C42C22×C6711yescharacteristic
612C22×C42C22×C6711yescharacteristic
613C22×C42C22×C6711yescharacteristic
614#390C4×C6718yescomplemented
615#388—24no—
616#387—24no—
617#386—24no—
618C4×C22⋊C4—24no—
619C2×#95C22×C6711yescharacteristic
620C2×#95C22×C6711yescharacteristic
621C2×#95C22×C6711yescharacteristic
622C2×#95C22×C6711yescharacteristic
623C2×#95C22×C6711yescharacteristic
624C2×#95C22×C6711yescharacteristic
625C2×#95C22×C6711yescharacteristic
626C2×#95C22×C6711yescharacteristic
627C2×#95C22×C6711yescharacteristic
628C2×#95C22×C6711yescharacteristic
629C2×#95C22×C6711yescharacteristic
630C2×#95C22×C6711yescharacteristic
631C2×#95C22×C6711yescharacteristic
632C2×#95C22×C6711yescharacteristic
633C2×#95C22×C6711yescharacteristic
634C2×#95C22×C6711yescharacteristic
635C25C23×C6711yescharacteristic
636C25C23×C6711yescharacteristic
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—41no—
642C22×D4—41no—
643C22×D4C2×C4×C6714yes—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4C23×C6711yescharacteristic
652C23×C4C23×C6711yescharacteristic
653C23×C4C23×C6711yescharacteristic
654C23×C4C23×C6711yescharacteristic
655C23×C4C23×C6711yescharacteristic
656C23×C4C23×C6711yescharacteristic
657C23×C4C23×C6711yescharacteristic
658C23×C4C23×C6711yescharacteristic
659C23×C4C23×C6711yescharacteristic
660C23×C4C23×C6711yescharacteristic
661C23×C4C23×C6711yescharacteristic
662C23×C4C23×C6711yescharacteristic
663C23×C4C23×C6711yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4C2×C4×C6714yescomplemented
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4C2×C4×C6714yes—
700C2×C22⋊C4C2×C4×C6714yes—
701C2×C22⋊C4C2×C4×C6714yescomplemented
702C2×C22⋊C4C2×C4×C6714yescomplemented
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42C2×C4×C6714yescomplemented
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95D4×C6714yes—
730#95D4×C6714yescomplemented
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24C22×C4×C6712yes—
758C24C22×C4×C6712yes—
759C24#41×C6712yes—
760C24#41×C6712yes—
761C24C24×C6711yescharacteristic
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—28no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4C22×C4×C6712yes—
851C22×C4C22×C4×C6712yes—
852C22×C4C22×C4×C6712yes—
853C22×C4C22×C4×C6712yes—
854C22×C4C22×C4×C6712yes—
855C22×C4C2×D4×C6712yes—
856C22×C4C2×D4×C6712yes—
857C22×C4C2×D4×C6712yes—
858C22×C4C2×D4×C6712yes—
859C22×C4C2×D4×C6712yes—
860C22×C4C2×D4×C6712yes—
861C22×C4#41×C6712yes—
862C22×C4#41×C6712yes—
863C22×C4#41×C6712yes—
864C22×C4#41×C6712yes—
865C22×C4#41×C6712yes—
866C22×C4#41×C6712yes—
867C4⋊C4—28no—
868C4⋊C4—44no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C42—44no—
881C42—44no—
882C42—44no—
883C42—44no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23#117×C6714yes—
954C23C23×C4×C6711yescharacteristic
955C23C22×D4×C6711yescharacteristic
956C23C22×D4×C6711yescharacteristic
957C23C2×#41×C6711yescharacteristic
958C23C2×#41×C6711yescharacteristic
959C23C2×#41×C6711yescharacteristic
960C23C2×#41×C6711yescharacteristic
961C23C2×#41×C6711yescharacteristic
962C23C2×#41×C6711yescharacteristic
963C23C2×#41×C6711yescharacteristic
964C23C2×#41×C6711yescharacteristic
965C23H(5,𝔽2)×C6711yescharacteristic
966C23H(5,𝔽2)×C6711yescharacteristic
967C23H(5,𝔽2)×C6711yescharacteristic
968C23H(5,𝔽2)×C6711yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4C4×D4×C6714yes—
1060C2×C4C4×D4×C6714yes—
1061C2×C4#124×C6714yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×#117×C6711yescharacteristic
1093C22C2×C4×D4×C6711yescharacteristic
1094C22C2×C4×D4×C6711yescharacteristic
1095C22C4×#41×C6711yescharacteristic
1096C22C4×#41×C6711yescharacteristic
1097C22#518×C6711yescharacteristic
1098C22#518×C6711yescharacteristic
1099C22#525×C6711yescharacteristic
1100C22#525×C6711yescharacteristic
1101C22C2×#124×C6711yescharacteristic
1102C22#529×C6711yescharacteristic
1103C22#529×C6711yescharacteristic
1104C22#529×C6711yescharacteristic
1105C22#529×C6711yescharacteristic
1106C22#532×C6711yescharacteristic
1107C22#538×C6711yescharacteristic
1108C22#538×C6711yescharacteristic
1109C22#540×C6711yescharacteristic
1110C22#540×C6711yescharacteristic
1111C22D42×C6711yescharacteristic
1112C22#546×C6711yescharacteristic
1113C22#546×C6711yescharacteristic
1114C22#546×C6711yescharacteristic
1115C22#546×C6711yescharacteristic
1116C22#550×C6711yescharacteristic
1117C22#550×C6711yescharacteristic
1118C22#551×C6711yescharacteristic
1119C22#551×C6711yescharacteristic
1120C22#551×C6711yescharacteristic
1121C22#551×C6711yescharacteristic
1122C22#553×C6711yescharacteristic
1123C22#553×C6711yescharacteristic
1124C22#553×C6711yescharacteristic
1125C22#553×C6711yescharacteristic
1126C22#559×C6711yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C2—44no—
1141C2—82no—
1142C2C67×#229011yescharacteristic
1143C2C4×#124×C6711yescharacteristic
1144C2C67×#233311yescharacteristic
1145C2C67×#234211yescharacteristic
1146C2C67×#235311yescharacteristic
1147C2C67×#236411yescharacteristic
1148C2C67×#236611yescharacteristic
1149C2C67×#246411yescharacteristic
1150C2C67×#246711yescharacteristic
1151C2C67×#247111yescharacteristic
1152C2C67×#247211yescharacteristic
1153C2C67×#249011yescharacteristic
1154C2C67×#251611yescharacteristic
1155C2C67×#255411yescharacteristic
1156C2C67×#259511yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC23×D4×C67C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C67C2semidirect
3. C2×#387×C67C2semidirect
5. C2×C4×C22⋊C4×C67C2semidirect
6. C67×#1445C2semidirect
7. C67×#1440C2semidirect
8. C67×#1439C2semidirect
10. C67×#1437C2semidirect
11. C67×#1437C2semidirect
12. C67×#1437C2semidirect
13. C67×#1434C2semidirect
14. C67×C22⋊#95C2semidirect
15. C4×#95×C67C2semidirect
35. #390×C67C4semidirect
90. C2×C4⋊C4×C67C2×C4semidirect
122. C2×C22⋊C4×C67C2×C4semidirect
123. C2×C22⋊C4×C67C2×C4semidirect
135. C2×C42×C67C2×C4semidirect
151. #95×C67D4semidirect
561. #14034C67direct (N × H)
580. C2×#388C2×C67semidirect
581. C2×#387C2×C67semidirect
583. C2×C4×C22⋊C4C2×C67semidirect
584. #1445C2×C67semidirect
585. #1440C2×C67semidirect
586. #1439C2×C67semidirect
588. #1437C2×C67semidirect
589. #1437C2×C67semidirect
590. #1437C2×C67semidirect
591. #1434C2×C67semidirect
592. C22⋊#95C2×C67semidirect
593. C4×#95C2×C67semidirect
594. C67#14034direct (N × H)
614. #390C4×C67semidirect
669. C2×C4⋊C4C2×C4×C67semidirect
701. C2×C22⋊C4C2×C4×C67semidirect
702. C2×C22⋊C4C2×C4×C67semidirect
714. C2×C42C2×C4×C67semidirect
730. #95D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#390×C672
C2×#388×C672
C2×#387×C672
C2×#386×C672
C2×C4×C22⋊C4×C672
C67×#14452
C67×#14402
C67×#14392
C67×#14382
C67×#14372
C67×#14342
C67×C22⋊#952
C4×#95×C672
#1403467