Finite Group Databasebeta

← C67×#14095 #30693346

Subgroups — C67×#14095 #30693346

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C67C211yesmaximal, characteristic
2C2×#390×C67C211yesmaximal, characteristic
3C2×#387×C67C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C67C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
6C67×#1441C211yesmaximal, characteristic, complemented
7C67×#1439C211yesmaximal, characteristic, complemented
8C67×#1439C211yesmaximal, characteristic, complemented
9C67×#1438C211yesmaximal, characteristic
10C67×#1437C211yesmaximal, characteristic, complemented
11C67×#1437C211yesmaximal, characteristic, complemented
12C67×#1437C211yesmaximal, characteristic, complemented
13C67×#1437C211yesmaximal, characteristic, complemented
14C67×#1436C211yesmaximal, characteristic, complemented
15C67×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C67C2211yescharacteristic
17C24×C4×C67C2211yescharacteristic
18C2×#123×C67—24no—
19C2×#123×C67—24no—
20C2×#123×C67C418yescomplemented
21C22×C4⋊C4×C67C2211yescharacteristic
22C22×C4⋊C4×C67C2211yescharacteristic
23C22×C4⋊C4×C67C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C67C2211yescharacteristic
32C22×C22⋊C4×C67C2211yescharacteristic
33C22×C22⋊C4×C67C2211yescharacteristic
34C22×C22⋊C4×C67C2211yescharacteristic
35C22×C22⋊C4×C67C2211yescharacteristic
36C22×C42×C67C2211yescharacteristic
37C22×C42×C67C2211yescharacteristic
38C22×C42×C67C2211yescharacteristic
39C22×C42×C67C2211yescharacteristic
40#390×C67—24no—
41#387×C67—24no—
42C4×C4⋊C4×C67—24no—
43C4×C22⋊C4×C67—24no—
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
56C2×#95×C67C2211yescharacteristic
57C2×#95×C67C2211yescharacteristic
58C25×C67C2311yescharacteristic
59C25×C67C2311yescharacteristic
60C22×D4×C67—22no—
61C22×D4×C67—22no—
62C22×D4×C67—22no—
63C22×D4×C67—22no—
64C22×D4×C67—41no—
65C22×D4×C67—41no—
66C22×D4×C67C2×C414yes—
67C23×C4×C67—22no—
68C23×C4×C67—22no—
69C23×C4×C67—22no—
70C23×C4×C67—22no—
71C23×C4×C67—41no—
72C23×C4×C67—41no—
73C23×C4×C67C2×C414yes—
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
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87#123×C67—232no—
88C2×C4⋊C4×C67—22no—
89C2×C4⋊C4×C67—22no—
90C2×C4⋊C4×C67—22no—
91C2×C4⋊C4×C67—22no—
92C2×C4⋊C4×C67—22no—
93C2×C4⋊C4×C67—22no—
94C2×C4⋊C4×C67—22no—
95C2×C4⋊C4×C67—41no—
96C2×C4⋊C4×C67C2×C414yes—
97C2×C4⋊C4×C67C2×C414yes—
98C2×C4⋊C4×C67D414yes—
99C2×C4⋊C4×C67D414yes—
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—22no—
111C2×C22⋊C4×C67—22no—
112C2×C22⋊C4×C67—22no—
113C2×C22⋊C4×C67—22no—
114C2×C22⋊C4×C67—22no—
115C2×C22⋊C4×C67—22no—
116C2×C22⋊C4×C67—22no—
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—41no—
124C2×C22⋊C4×C67—41no—
125C2×C22⋊C4×C67—41no—
126C2×C22⋊C4×C67—41no—
127C2×C22⋊C4×C67—41no—
128C2×C22⋊C4×C67—41no—
129C2×C22⋊C4×C67C2×C414yes—
130C2×C22⋊C4×C67C2×C414yes—
131C2×C22⋊C4×C67C2×C414yes—
132C2×C22⋊C4×C67D414yes—
133C2×C42×C67—22no—
134C2×C42×C67—22no—
135C2×C42×C67—22no—
136C2×C42×C67—22no—
137C2×C42×C67—22no—
138C2×C42×C67—22no—
139C2×C42×C67—22no—
140C2×C42×C67—22no—
141C2×C42×C67—22no—
142C2×C42×C67—41no—
143C2×C42×C67—41no—
144C2×C42×C67—41no—
145#95×C67—22no—
146#95×C67—22no—
147#95×C67—22no—
148#95×C67—22no—
149#95×C67—22no—
150#95×C67—22no—
151#95×C67—22no—
152#95×C67—22no—
153#95×C67—22no—
154#95×C67—22no—
155#95×C67—41no—
156#95×C67—41no—
157#95×C67—41no—
158#95×C67—41no—
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×C67—21no—
179C24×C67—21no—
180C24×C67—21no—
181C24×C67—21no—
182C24×C67—21no—
183C24×C67—21no—
184C24×C67—21no—
185C24×C67C22×C412yes—
186C24×C67C22×C412yes—
187C24×C67C2×D412yes—
188C24×C67#4112yes—
189C24×C67C2411yescharacteristic
190C2×D4×C67—28no—
191C2×D4×C67—28no—
192C2×D4×C67—44no—
193C2×D4×C67—44no—
194C2×D4×C67—44no—
195C2×D4×C67—44no—
196C2×D4×C67—44no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
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—28no—
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—28no—
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—21no—
266C22×C4×C67—21no—
267C22×C4×C67—21no—
268C22×C4×C67—21no—
269C22×C4×C67—21no—
270C22×C4×C67—21no—
271C22×C4×C67—44no—
272C22×C4×C67—44no—
273C22×C4×C67—44no—
274C22×C4×C67—44no—
275C22×C4×C67—44no—
276C22×C4×C67C22×C412yes—
277C22×C4×C67C22×C412yes—
278C22×C4×C67C22×C412yes—
279C22×C4×C67C22×C412yes—
280C22×C4×C67C22×C412yes—
281C22×C4×C67C2×D412yes—
282C22×C4×C67C2×D412yes—
283C22×C4×C67C2×D412yes—
284C22×C4×C67C2×D412yes—
285C22×C4×C67C2×D412yes—
286C22×C4×C67C2×D412yes—
287C22×C4×C67C2×D412yes—
288C22×C4×C67C2×D412yes—
289C22×C4×C67#4112yes—
290C22×C4×C67#4112yes—
291C22×C4×C67#4112yes—
292C22×C4×C67#4112yes—
293C22×C4×C67#4112yes—
294C22×C4×C67#4112yes—
295C4⋊C4×C67—28no—
296C4⋊C4×C67—28no—
297C4⋊C4×C67—44no—
298C4⋊C4×C67C22⋊C4116yescomplemented
299C22⋊C4×C67—28no—
300C22⋊C4×C67—28no—
301C22⋊C4×C67—28no—
302C22⋊C4×C67—28no—
303C22⋊C4×C67—28no—
304C22⋊C4×C67—44no—
305C22⋊C4×C67—44no—
306C22⋊C4×C67—44no—
307C22⋊C4×C67—44no—
308C22⋊C4×C67—44no—
309C22⋊C4×C67—44no—
310C42×C67—28no—
311C42×C67—44no—
312C42×C67—44no—
313C42×C67—44no—
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—22no—
331C23×C67—22no—
332C23×C67—22no—
333C23×C67—22no—
334C23×C67—22no—
335C23×C67—22no—
336C23×C67—22no—
337C23×C67—22no—
338C23×C67—22no—
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—41no—
375C23×C67—41no—
376C23×C67—41no—
377C23×C67—41no—
378C23×C67—41no—
379C23×C67—41no—
380C23×C67—41no—
381C23×C67—41no—
382C23×C67—41no—
383C23×C67C4×D414yes—
384C23×C67C23×C411yescharacteristic
385C23×C67C22×D411yescharacteristic
386C23×C67C22×D411yescharacteristic
387C23×C67C22×D411yescharacteristic
388C23×C67C2×#4111yescharacteristic
389C23×C67C2×#4111yescharacteristic
390C23×C67C2×#4111yescharacteristic
391C23×C67C2×#4111yescharacteristic
392C23×C67C2×#4111yescharacteristic
393C23×C67C2×#4111yescharacteristic
394C23×C67C2×#4111yescharacteristic
395C23×C67H(5,𝔽2)11yescharacteristic
396C23×C67H(5,𝔽2)11yescharacteristic
397C23×C67H(5,𝔽2)11yescharacteristic
398C23×C672−1+411yescharacteristic
399D4×C67—416no—
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—22no—
434C2×C4×C67—22no—
435C2×C4×C67—22no—
436C2×C4×C67—22no—
437C2×C4×C67—22no—
438C2×C4×C67—22no—
439C2×C4×C67—22no—
440C2×C4×C67—22no—
441C2×C4×C67—22no—
442C2×C4×C67—22no—
443C2×C4×C67—22no—
444C2×C4×C67—22no—
445C2×C4×C67—416no—
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×C67—41no—
481C2×C4×C67—41no—
482C2×C4×C67—41no—
483C2×C4×C67—41no—
484C2×C4×C67—41no—
485C2×C4×C67—41no—
486C2×C4×C67—41no—
487C2×C4×C67—41no—
488C2×C4×C67C2×C22⋊C414yes—
489C2×C4×C67C2×C22⋊C414yes—
490C2×C4×C67C2×C22⋊C414yes—
491C2×C4×C67#12314yescomplemented
492C22×C67—24no—
493C22×C67—24no—
494C22×C67—24no—
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—42no—
506C22×C67—42no—
507C22×C67—42no—
508C22×C67—42no—
509C22×C67—42no—
510C22×C67—42no—
511C22×C67—42no—
512C22×C67—42no—
513C22×C67—42no—
514C22×C67—81no—
515C22×C67—81no—
516C22×C67—81no—
517C22×C67—81no—
518C22×C67—81no—
519C22×C67—81no—
520C22×C67—81no—
521C22×C67—81no—
522C22×C67C22×C22⋊C411yescharacteristic
523C22×C67C2×C4×D411yescharacteristic
524C22×C67C4×#4111yescharacteristic
525C22×C67C4×#4111yescharacteristic
526C22×C67C4×#4111yescharacteristic
527C22×C67#51811yescharacteristic
528C22×C67#52011yescharacteristic
529C22×C67C2×#12311yescharacteristic
530C22×C67#52511yescharacteristic
531C22×C67#52511yescharacteristic
532C22×C67#52511yescharacteristic
533C22×C67#52911yescharacteristic
534C22×C67#52911yescharacteristic
535C22×C67#53211yescharacteristic
536C22×C67#53211yescharacteristic
537C22×C67#53811yescharacteristic
538C22×C67#53911yescharacteristic
539C22×C67#54011yescharacteristic
540C22×C67#54211yescharacteristic
541C22×C67D4211yescharacteristic
542C22×C67D4211yescharacteristic
543C22×C67#54611yescharacteristic
544C22×C67#54611yescharacteristic
545C22×C67#54611yescharacteristic
546C22×C67#54711yescharacteristic
547C22×C67#54811yescharacteristic
548C22×C67#54811yescharacteristic
549C22×C67#55011yescharacteristic
550C22×C67#55011yescharacteristic
551C22×C67#55111yescharacteristic
552C22×C67#55111yescharacteristic
553C22×C67#55211yescharacteristic
554C22×C67#55311yescharacteristic
555C22×C67#55311yescharacteristic
556C22×C67#55911yescharacteristic
557C4×C67—24no—
558C4×C67—24no—
559C4×C67—24no—
560C4×C67—24no—
561C4×C67—42no—
562C4×C67—42no—
563C4×C67—42no—
564C4×C67—42no—
565C4×C67—42no—
566C4×C67—42no—
567C4×C67—42no—
568C4×C67—81no—
569C4×C67—81no—
570#14095C6711yesmaximal, characteristic, direct product factor, Sylow
571C2×C67—44no—
572C2×C67—82no—
573C2×C67#229711yescharacteristic
574C2×C67C4×#12311yescharacteristic
575C2×C67#233511yescharacteristic
576C2×C67D4×C22⋊C411yescharacteristic
577C2×C67#234111yescharacteristic
578C2×C67#235911yescharacteristic
579C2×C67#237411yescharacteristic
580C2×C67#244311yescharacteristic
581C2×C67#244511yescharacteristic
582C2×C67#245611yescharacteristic
583C2×C67#245811yescharacteristic
584C2×C67#246111yescharacteristic
585C2×C67#247111yescharacteristic
586C2×C67#255411yescharacteristic
587C2×C67#255811yescharacteristic
588C22×#123C2×C6711yescharacteristic
589C2×#390C2×C6711yescharacteristic
590C2×#387C2×C6711yescharacteristic, complemented
591C2×C4×C4⋊C4C2×C6711yescharacteristic, complemented
592C2×C4×C22⋊C4C2×C6711yescharacteristic, complemented
593#1441C2×C6711yescharacteristic, complemented
594#1439C2×C6711yescharacteristic, complemented
595#1439C2×C6711yescharacteristic, complemented
596#1438C2×C6711yescharacteristic
597#1437C2×C6711yescharacteristic, complemented
598#1437C2×C6711yescharacteristic, complemented
599#1437C2×C6711yescharacteristic, complemented
600#1437C2×C6711yescharacteristic, complemented
601#1436C2×C6711yescharacteristic, complemented
602C22⋊#95C2×C6711yescharacteristic, complemented
603C67#1409511yescharacteristic, direct product factor, Sylow
604C23×D4C22×C6711yescharacteristic
605C24×C4C22×C6711yescharacteristic
606C2×#123—24no—
607C2×#123—24no—
608C2×#123C4×C6718yescomplemented
609C22×C4⋊C4C22×C6711yescharacteristic
610C22×C4⋊C4C22×C6711yescharacteristic
611C22×C4⋊C4C22×C6711yescharacteristic
612C22×C4⋊C4C22×C6711yescharacteristic
613C22×C22⋊C4C22×C6711yescharacteristic
614C22×C22⋊C4C22×C6711yescharacteristic
615C22×C22⋊C4C22×C6711yescharacteristic
616C22×C22⋊C4C22×C6711yescharacteristic
617C22×C22⋊C4C22×C6711yescharacteristic
618C22×C22⋊C4C22×C6711yescharacteristic
619C22×C22⋊C4C22×C6711yescharacteristic
620C22×C22⋊C4C22×C6711yescharacteristic
621C22×C22⋊C4C22×C6711yescharacteristic
622C22×C22⋊C4C22×C6711yescharacteristic
623C22×C22⋊C4C22×C6711yescharacteristic
624C22×C42C22×C6711yescharacteristic
625C22×C42C22×C6711yescharacteristic
626C22×C42C22×C6711yescharacteristic
627C22×C42C22×C6711yescharacteristic
628#390—24no—
629#387—24no—
630C4×C4⋊C4—24no—
631C4×C22⋊C4—24no—
632C2×#95C22×C6711yescharacteristic
633C2×#95C22×C6711yescharacteristic
634C2×#95C22×C6711yescharacteristic
635C2×#95C22×C6711yescharacteristic
636C2×#95C22×C6711yescharacteristic
637C2×#95C22×C6711yescharacteristic
638C2×#95C22×C6711yescharacteristic
639C2×#95C22×C6711yescharacteristic
640C2×#95C22×C6711yescharacteristic
641C2×#95C22×C6711yescharacteristic
642C2×#95C22×C6711yescharacteristic
643C2×#95C22×C6711yescharacteristic
644C2×#95C22×C6711yescharacteristic
645C2×#95C22×C6711yescharacteristic
646C25C23×C6711yescharacteristic
647C25C23×C6711yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C6714yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C6714yes—
662C23×C4C23×C6711yescharacteristic
663C23×C4C23×C6711yescharacteristic
664C23×C4C23×C6711yescharacteristic
665C23×C4C23×C6711yescharacteristic
666C23×C4C23×C6711yescharacteristic
667C23×C4C23×C6711yescharacteristic
668C23×C4C23×C6711yescharacteristic
669C23×C4C23×C6711yescharacteristic
670C23×C4C23×C6711yescharacteristic
671C23×C4C23×C6711yescharacteristic
672C23×C4C23×C6711yescharacteristic
673C23×C4C23×C6711yescharacteristic
674C23×C4C23×C6711yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C6714yes—
685C2×C4⋊C4C2×C4×C6714yes—
686C2×C4⋊C4D4×C6714yes—
687C2×C4⋊C4D4×C6714yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C6714yes—
718C2×C22⋊C4C2×C4×C6714yes—
719C2×C22⋊C4C2×C4×C6714yes—
720C2×C22⋊C4D4×C6714yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C6712yes—
774C24C22×C4×C6712yes—
775C24C2×D4×C6712yes—
776C24#41×C6712yes—
777C24C24×C6711yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
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—28no—
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—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C6712yes—
865C22×C4C22×C4×C6712yes—
866C22×C4C22×C4×C6712yes—
867C22×C4C22×C4×C6712yes—
868C22×C4C22×C4×C6712yes—
869C22×C4C2×D4×C6712yes—
870C22×C4C2×D4×C6712yes—
871C22×C4C2×D4×C6712yes—
872C22×C4C2×D4×C6712yes—
873C22×C4C2×D4×C6712yes—
874C22×C4C2×D4×C6712yes—
875C22×C4C2×D4×C6712yes—
876C22×C4C2×D4×C6712yes—
877C22×C4#41×C6712yes—
878C22×C4#41×C6712yes—
879C22×C4#41×C6712yes—
880C22×C4#41×C6712yes—
881C22×C4#41×C6712yes—
882C22×C4#41×C6712yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C67116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C6714yes—
972C23C23×C4×C6711yescharacteristic
973C23C22×D4×C6711yescharacteristic
974C23C22×D4×C6711yescharacteristic
975C23C22×D4×C6711yescharacteristic
976C23C2×#41×C6711yescharacteristic
977C23C2×#41×C6711yescharacteristic
978C23C2×#41×C6711yescharacteristic
979C23C2×#41×C6711yescharacteristic
980C23C2×#41×C6711yescharacteristic
981C23C2×#41×C6711yescharacteristic
982C23C2×#41×C6711yescharacteristic
983C23H(5,𝔽2)×C6711yescharacteristic
984C23H(5,𝔽2)×C6711yescharacteristic
985C23H(5,𝔽2)×C6711yescharacteristic
986C232−1+4×C6711yescharacteristic
987D4—416no—
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—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
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×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C6714yes—
1077C2×C4C2×C22⋊C4×C6714yes—
1078C2×C4C2×C22⋊C4×C6714yes—
1079C2×C4#123×C6714yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C6711yescharacteristic
1111C22C2×C4×D4×C6711yescharacteristic
1112C22C4×#41×C6711yescharacteristic
1113C22C4×#41×C6711yescharacteristic
1114C22C4×#41×C6711yescharacteristic
1115C22#518×C6711yescharacteristic
1116C22#520×C6711yescharacteristic
1117C22C2×#123×C6711yescharacteristic
1118C22#525×C6711yescharacteristic
1119C22#525×C6711yescharacteristic
1120C22#525×C6711yescharacteristic
1121C22#529×C6711yescharacteristic
1122C22#529×C6711yescharacteristic
1123C22#532×C6711yescharacteristic
1124C22#532×C6711yescharacteristic
1125C22#538×C6711yescharacteristic
1126C22#539×C6711yescharacteristic
1127C22#540×C6711yescharacteristic
1128C22#542×C6711yescharacteristic
1129C22D42×C6711yescharacteristic
1130C22D42×C6711yescharacteristic
1131C22#546×C6711yescharacteristic
1132C22#546×C6711yescharacteristic
1133C22#546×C6711yescharacteristic
1134C22#547×C6711yescharacteristic
1135C22#548×C6711yescharacteristic
1136C22#548×C6711yescharacteristic
1137C22#550×C6711yescharacteristic
1138C22#550×C6711yescharacteristic
1139C22#551×C6711yescharacteristic
1140C22#551×C6711yescharacteristic
1141C22#552×C6711yescharacteristic
1142C22#553×C6711yescharacteristic
1143C22#553×C6711yescharacteristic
1144C22#559×C6711yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C67×#229711yescharacteristic
1161C2C4×#123×C6711yescharacteristic
1162C2C67×#233511yescharacteristic
1163C2D4×C22⋊C4×C6711yescharacteristic
1164C2C67×#234111yescharacteristic
1165C2C67×#235911yescharacteristic
1166C2C67×#237411yescharacteristic
1167C2C67×#244311yescharacteristic
1168C2C67×#244511yescharacteristic
1169C2C67×#245611yescharacteristic
1170C2C67×#245811yescharacteristic
1171C2C67×#246111yescharacteristic
1172C2C67×#247111yescharacteristic
1173C2C67×#255411yescharacteristic
1174C2C67×#255811yescharacteristic
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
3. C2×#387×C67C2semidirect
4. C2×C4×C4⋊C4×C67C2semidirect
5. C2×C4×C22⋊C4×C67C2semidirect
6. C67×#1441C2semidirect
7. C67×#1439C2semidirect
8. C67×#1439C2semidirect
10. C67×#1437C2semidirect
11. C67×#1437C2semidirect
12. C67×#1437C2semidirect
13. C67×#1437C2semidirect
14. C67×#1436C2semidirect
15. C67×C22⋊#95C2semidirect
20. C2×#123×C67C4semidirect
298. C4⋊C4×C67C22⋊C4semidirect
491. C2×C4×C67#123semidirect
570. #14095C67direct (N × H)
590. C2×#387C2×C67semidirect
591. C2×C4×C4⋊C4C2×C67semidirect
592. C2×C4×C22⋊C4C2×C67semidirect
593. #1441C2×C67semidirect
594. #1439C2×C67semidirect
595. #1439C2×C67semidirect
597. #1437C2×C67semidirect
598. #1437C2×C67semidirect
599. #1437C2×C67semidirect
600. #1437C2×C67semidirect
601. #1436C2×C67semidirect
602. C22⋊#95C2×C67semidirect
603. C67#14095direct (N × H)
608. C2×#123C4×C67semidirect
886. C4⋊C4C22⋊C4×C67semidirect
1079. C2×C4#123×C67semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C672
C2×#390×C672
C2×#387×C672
C2×C4×C4⋊C4×C672
C2×C4×C22⋊C4×C672
C67×#14412
C67×#14392
C67×#14382
C67×#14372
C67×#14362
C67×C22⋊#952
#1409567