Finite Group Databasebeta

← C67×#24662 #30703913

Subgroups — C67×#24662 #30703913

Order 17152.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C67C211yesmaximal, characteristic, complemented
2C2×#433×C67C211yesmaximal, characteristic, complemented
3C67×#2619C211yesmaximal, characteristic, complemented
4C67×#2324C211yesmaximal, characteristic, complemented
5C67×#2034C211yesmaximal, characteristic, complemented
6C67×#2033C211yesmaximal, characteristic, complemented
7C67×#1999C211yesmaximal, characteristic, complemented
8C67×#1999C211yesmaximal, characteristic, complemented
9C67×#1982C211yesmaximal, characteristic, complemented
10C67×#1972C211yesmaximal, characteristic, complemented
11C67×#1970C211yesmaximal, characteristic, complemented
12C67×#1949C211yesmaximal, characteristic, complemented
13C67×#1936C211yesmaximal, characteristic, complemented
14C67×#1934C211yesmaximal, characteristic, complemented
15C67×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C67C2211yescharacteristic
17C22×D8×C67C2211yescharacteristic
18C2×#127×C67C2211yescharacteristic
19C2×#121×C67C2211yescharacteristic
20C2×#121×C67C2211yescharacteristic
21C2×#121×C67C2211yescharacteristic
22C2×C4×D4×C67C2211yescharacteristic
23C2×#117×C67C2211yescharacteristic
24#459×C67—24no—
25#433×C67—24no—
26C2×#107×C67C2211yescharacteristic
27C2×#106×C67C2211yescharacteristic
28C2×C4⋊C8×C67C2211yescharacteristic
29C2×C4⋊C8×C67C2211yescharacteristic
30C2×#102×C67C2211yescharacteristic
31C2×#102×C67C2211yescharacteristic
32C2×#102×C67C2211yescharacteristic
33C2×#102×C67C2211yescharacteristic
34C2×#102×C67C2211yescharacteristic
35C2×#102×C67C2211yescharacteristic
36C2×#102×C67C2211yescharacteristic
37C2×#102×C67C2211yescharacteristic
38C2×C22⋊C8×C67C2211yescharacteristic
39C2×C22⋊C8×C67C2211yescharacteristic
40C2×#97×C67C2211yescharacteristic
41C2×C4×C8×C67C2211yescharacteristic
42#394×C67—21no—
43#394×C67—21no—
44#392×C67—21no—
45#392×C67—21no—
46#390×C67—21no—
47#390×C67C2211yescharacteristic
48#390×C67C2211yescharacteristic
49#390×C67C2211yescharacteristic
50#389×C67C2211yescharacteristic
51#388×C67—21no—
52#386×C67—21no—
53#385×C67—21no—
54#382×C67C2211yescharacteristic
55#380×C67C2211yescharacteristic
56C4×C4⋊C4×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61C22×D4×C67—21no—
62C22×D4×C67—21no—
63C22×D4×C67—21no—
64C22×D4×C67—21no—
65C22×D4×C67—21no—
66C22×D4×C67C2311yescharacteristic
67C22×D4×C67C2311yescharacteristic
68C22×D4×C67C2311yescharacteristic
69C23×C4×C67—21no—
70C23×C4×C67C2311yescharacteristic
71C2×D8×C67—22no—
72C2×D8×C67—22no—
73C2×D8×C67—22no—
74C2×D8×C67—22no—
75C2×D8×C67—41no—
76C2×D8×C67—41no—
77C22×C8×C67C2311yescharacteristic
78C22×C8×C67C2311yescharacteristic
79C22×C8×C67C2311yescharacteristic
80C22×C8×C67C2311yescharacteristic
81#127×C67—22no—
82#127×C67—22no—
83#121×C67—22no—
84#121×C67—22no—
85#121×C67—41no—
86#121×C67—41no—
87#121×C67—41no—
88#121×C67—41no—
89C4×D4×C67—22no—
90C4×D4×C67—22no—
91#117×C67—22no—
92#117×C67—22no—
93C2×C4⋊C4×C67—21no—
94C2×C4⋊C4×C67D411yescharacteristic
95C2×C4⋊C4×C67D411yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67C2311yescharacteristic
98C2×C4⋊C4×C67C2311yescharacteristic
99C2×C4⋊C4×C67C2311yescharacteristic
100C2×C4⋊C4×C67C2311yescharacteristic
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67—21no—
104C2×C22⋊C4×C67—21no—
105C2×C22⋊C4×C67—21no—
106C2×C22⋊C4×C67—21no—
107C2×C22⋊C4×C67—21no—
108C2×C22⋊C4×C67—21no—
109C2×C22⋊C4×C67—21no—
110C2×C22⋊C4×C67—21no—
111C2×C22⋊C4×C67—21no—
112C2×C22⋊C4×C67D411yescharacteristic
113C2×C22⋊C4×C67D411yescharacteristic
114C2×C42×C67—21no—
115C2×C42×C67C2311yescharacteristic
116C2×C42×C67C2311yescharacteristic
117#107×C67—41no—
118#106×C67—41no—
119C4⋊C8×C67—22no—
120C4⋊C8×C67D414yescomplemented
121#102×C67—22no—
122#102×C67—22no—
123#102×C67—22no—
124#102×C67—22no—
125#102×C67—41no—
126#102×C67—41no—
127#102×C67—41no—
128#102×C67—41no—
129C22⋊C8×C67—22no—
130C22⋊C8×C67—22no—
131#97×C67—22no—
132C4×C8×C67—22no—
133#95×C67—21no—
134#95×C67—21no—
135#95×C67—21no—
136#95×C67—21no—
137#95×C67—21no—
138C24×C67—21no—
139C24×C67—21no—
140C24×C67—21no—
141C24×C67C2×D411yescharacteristic
142C2×D4×C67—24no—
143C2×D4×C67—21no—
144C2×D4×C67—21no—
145C2×D4×C67—21no—
146C2×D4×C67—21no—
147C2×D4×C67—21no—
148C2×D4×C67—21no—
149C2×D4×C67—21no—
150C2×D4×C67—21no—
151C2×D4×C67—21no—
152C2×D4×C67—21no—
153C2×D4×C67—21no—
154C2×D4×C67—21no—
155C2×D4×C67—21no—
156C2×D4×C67—21no—
157C2×D4×C67—21no—
158C2×D4×C67—21no—
159C2×D4×C67—21no—
160C2×D4×C67—42no—
161C2×D4×C67—42no—
162C2×D4×C67—42no—
163C2×D4×C67—42no—
164C2×D4×C67—81no—
165C2×D4×C67—81no—
166C2×D4×C67—81no—
167C2×D4×C67—81no—
168C2×D4×C67—81no—
169C2×D4×C67—81no—
170C2×D4×C67—81no—
171C2×D4×C67—81no—
172C2×D4×C67—81no—
173C2×D4×C67—81no—
174C2×D4×C67#4112yes—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—21no—
178C22×C4×C67—21no—
179C22×C4×C67—21no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—21no—
183C22×C4×C67—21no—
184C22×C4×C67—21no—
185C22×C4×C67—21no—
186C22×C4×C67—42no—
187C22×C4×C67—81no—
188C22×C4×C67—81no—
189C22×C4×C67C2×D411yescharacteristic
190C22×C4×C67C2×D411yescharacteristic
191C22×C4×C67C2×D411yescharacteristic
192C22×C4×C67C2×D411yescharacteristic
193C22×C4×C67C2×D411yescharacteristic
194C22×C4×C67C2411yescharacteristic
195D8×C67—44no—
196D8×C67—44no—
197C2×C8×C67—21no—
198C2×C8×C67—21no—
199C2×C8×C67—21no—
200C2×C8×C67—21no—
201C2×C8×C67—21no—
202C2×C8×C67—21no—
203C2×C8×C67—21no—
204C2×C8×C67—21no—
205C2×C8×C67—21no—
206C2×C8×C67—21no—
207C2×C8×C67C2×D412yes—
208C2×C8×C67C2×D412yes—
209C4⋊C4×C67—22no—
210C4⋊C4×C67—22no—
211C4⋊C4×C67—21no—
212C4⋊C4×C67—21no—
213C4⋊C4×C67—21no—
214C4⋊C4×C67—21no—
215C4⋊C4×C67—21no—
216C4⋊C4×C67—21no—
217C4⋊C4×C67—21no—
218C4⋊C4×C67—21no—
219C4⋊C4×C67—21no—
220C4⋊C4×C67—81no—
221C4⋊C4×C67#4112yes—
222C22⋊C4×C67—24no—
223C22⋊C4×C67—22no—
224C22⋊C4×C67—22no—
225C22⋊C4×C67—42no—
226C22⋊C4×C67—42no—
227C22⋊C4×C67—42no—
228C22⋊C4×C67—81no—
229C22⋊C4×C67—81no—
230C22⋊C4×C67—81no—
231C22⋊C4×C67—81no—
232C22⋊C4×C67—81no—
233C22⋊C4×C67—81no—
234C22⋊C4×C67—81no—
235C42×C67—21no—
236C42×C67—21no—
237C42×C67—81no—
238C42×C67C2×D412yes—
239C42×C67#4112yes—
240C23×C67—21no—
241C23×C67—22no—
242C23×C67—21no—
243C23×C67—21no—
244C23×C67—21no—
245C23×C67—21no—
246C23×C67—21no—
247C23×C67—21no—
248C23×C67—41no—
249C23×C67—41no—
250C23×C67—41no—
251C23×C67—41no—
252C23×C67—41no—
253C23×C67—41no—
254C23×C67—41no—
255C23×C67—41no—
256C23×C67—41no—
257C23×C67—41no—
258C23×C67—41no—
259C23×C67—41no—
260C23×C67—41no—
261C23×C67—41no—
262C23×C67—41no—
263C23×C67—41no—
264C23×C67—41no—
265C23×C67—41no—
266C23×C67—41no—
267C23×C67—41no—
268C23×C67C22×D411yescharacteristic
269D4×C67—22no—
270D4×C67—22no—
271D4×C67—41no—
272D4×C67—41no—
273D4×C67—41no—
274D4×C67—41no—
275D4×C67—41no—
276D4×C67—41no—
277D4×C67—41no—
278D4×C67—41no—
279D4×C67—41no—
280D4×C67—41no—
281D4×C67—84no—
282D4×C67—84no—
283D4×C67—84no—
284D4×C67—84no—
285D4×C67—84no—
286C2×C4×C67—21no—
287C2×C4×C67—21no—
288C2×C4×C67—21no—
289C2×C4×C67—21no—
290C2×C4×C67—21no—
291C2×C4×C67—21no—
292C2×C4×C67—21no—
293C2×C4×C67—21no—
294C2×C4×C67—22no—
295C2×C4×C67—21no—
296C2×C4×C67—21no—
297C2×C4×C67—21no—
298C2×C4×C67—21no—
299C2×C4×C67—21no—
300C2×C4×C67—41no—
301C2×C4×C67—41no—
302C2×C4×C67—41no—
303C2×C4×C67—41no—
304C2×C4×C67—41no—
305C2×C4×C67—41no—
306C2×C4×C67—41no—
307C2×C4×C67—41no—
308C2×C4×C67—41no—
309C2×C4×C67—41no—
310C2×C4×C67—41no—
311C2×C4×C67—41no—
312C2×C4×C67—41no—
313C2×C4×C67—41no—
314C2×C4×C67—41no—
315C2×C4×C67—41no—
316C2×C4×C67—41no—
317C2×C4×C67—41no—
318C2×C4×C67—84no—
319C2×C4×C67#12112yes—
320C2×C4×C67#12112yes—
321C2×C4×C67C22×D411yescharacteristic
322C2×C4×C67C2×#4111yescharacteristic
323C2×C4×C67C2×#4111yescharacteristic
324C2×C4×C67C2×#4111yescharacteristic
325C2×C4×C67H(5,𝔽2)11yescharacteristic
326C2×C4×C67H(5,𝔽2)11yescharacteristic
327C8×C67—22no—
328C8×C67—22no—
329C8×C67—41no—
330C8×C67—41no—
331C22×C67—41no—
332C22×C67—42no—
333C22×C67—41no—
334C22×C67—42no—
335C22×C67—41no—
336C22×C67—42no—
337C22×C67—41no—
338C22×C67—41no—
339C22×C67—41no—
340C22×C67—41no—
341C22×C67—81no—
342C22×C67—81no—
343C22×C67—81no—
344C22×C67—81no—
345C22×C67—81no—
346C22×C67—81no—
347C22×C67—81no—
348C22×C67—81no—
349C22×C67—81no—
350C22×C67—81no—
351C22×C67—81no—
352C22×C67—81no—
353C22×C67—81no—
354C22×C67—81no—
355C22×C67—81no—
356C22×C67—81no—
357C22×C67—81no—
358C22×C67—81no—
359C22×C67C2×#12111yescharacteristic
360C22×C67#52511yescharacteristic
361C22×C67#53511yescharacteristic
362C22×C67#57611yescharacteristic
363C22×C67#57611yescharacteristic
364C22×C67#57611yescharacteristic
365C22×C67#57711yescharacteristic
366C4×C67—22no—
367C4×C67—22no—
368C4×C67—42no—
369C4×C67—41no—
370C4×C67—41no—
371C4×C67—41no—
372C4×C67—81no—
373C4×C67—81no—
374C4×C67—81no—
375C4×C67—81no—
376C4×C67#54611yescharacteristic
377C4×C67#55011yescharacteristic
378C4×C67#55311yescharacteristic
379C4×C67#55511yescharacteristic
380#24662C6711yesmaximal, characteristic, direct product factor, Sylow
381C2×C67—81no—
382C2×C67—82no—
383C2×C67—161no—
384C2×C67—161no—
385C2×C67#241411yescharacteristic
386C2×C67#305811yescharacteristic
387C2×C67#306211yescharacteristic
388C2×C67#311911yescharacteristic
389C2×C67#312211yescharacteristic
390C2×C67#322011yescharacteristic
391C2×C67#322411yescharacteristic
392C2×#459C2×C6711yescharacteristic, complemented
393C2×#433C2×C6711yescharacteristic, complemented
394#2619C2×C6711yescharacteristic, complemented
395#2324C2×C6711yescharacteristic, complemented
396#2034C2×C6711yescharacteristic, complemented
397#2033C2×C6711yescharacteristic, complemented
398#1999C2×C6711yescharacteristic, complemented
399#1999C2×C6711yescharacteristic, complemented
400#1982C2×C6711yescharacteristic, complemented
401#1972C2×C6711yescharacteristic, complemented
402#1970C2×C6711yescharacteristic, complemented
403#1949C2×C6711yescharacteristic, complemented
404#1936C2×C6711yescharacteristic, complemented
405#1934C2×C6711yescharacteristic, complemented
406#1804C2×C6711yescharacteristic, complemented
407C67#2466211yescharacteristic, direct product factor, Sylow
408C22×D8C22×C6711yescharacteristic
409C22×D8C22×C6711yescharacteristic
410C2×#127C22×C6711yescharacteristic
411C2×#121C22×C6711yescharacteristic
412C2×#121C22×C6711yescharacteristic
413C2×#121C22×C6711yescharacteristic
414C2×C4×D4C22×C6711yescharacteristic
415C2×#117C22×C6711yescharacteristic
416#459—24no—
417#433—24no—
418C2×#107C22×C6711yescharacteristic
419C2×#106C22×C6711yescharacteristic
420C2×C4⋊C8C22×C6711yescharacteristic
421C2×C4⋊C8C22×C6711yescharacteristic
422C2×#102C22×C6711yescharacteristic
423C2×#102C22×C6711yescharacteristic
424C2×#102C22×C6711yescharacteristic
425C2×#102C22×C6711yescharacteristic
426C2×#102C22×C6711yescharacteristic
427C2×#102C22×C6711yescharacteristic
428C2×#102C22×C6711yescharacteristic
429C2×#102C22×C6711yescharacteristic
430C2×C22⋊C8C22×C6711yescharacteristic
431C2×C22⋊C8C22×C6711yescharacteristic
432C2×#97C22×C6711yescharacteristic
433C2×C4×C8C22×C6711yescharacteristic
434#394—21no—
435#394—21no—
436#392—21no—
437#392—21no—
438#390—21no—
439#390C22×C6711yescharacteristic
440#390C22×C6711yescharacteristic
441#390C22×C6711yescharacteristic
442#389C22×C6711yescharacteristic
443#388—21no—
444#386—21no—
445#385—21no—
446#382C22×C6711yescharacteristic
447#380C22×C6711yescharacteristic
448C4×C4⋊C4C22×C6711yescharacteristic
449#340C22×C6711yescharacteristic
450#340C22×C6711yescharacteristic
451#340C22×C6711yescharacteristic
452#340C22×C6711yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C6711yescharacteristic
459C22×D4C23×C6711yescharacteristic
460C22×D4C23×C6711yescharacteristic
461C23×C4—21no—
462C23×C4C23×C6711yescharacteristic
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C22×C8C23×C6711yescharacteristic
470C22×C8C23×C6711yescharacteristic
471C22×C8C23×C6711yescharacteristic
472C22×C8C23×C6711yescharacteristic
473#127—22no—
474#127—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—41no—
479#121—41no—
480#121—41no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C6711yescharacteristic
487C2×C4⋊C4D4×C6711yescharacteristic
488C2×C4⋊C4C23×C6711yescharacteristic
489C2×C4⋊C4C23×C6711yescharacteristic
490C2×C4⋊C4C23×C6711yescharacteristic
491C2×C4⋊C4C23×C6711yescharacteristic
492C2×C4⋊C4C23×C6711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C6711yescharacteristic
505C2×C22⋊C4D4×C6711yescharacteristic
506C2×C42—21no—
507C2×C42C23×C6711yescharacteristic
508C2×C42C23×C6711yescharacteristic
509#107—41no—
510#106—41no—
511C4⋊C8—22no—
512C4⋊C8D4×C6714yescomplemented
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524C4×C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×D4×C6711yescharacteristic
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4#41×C6712yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C6711yescharacteristic
582C22×C4C2×D4×C6711yescharacteristic
583C22×C4C2×D4×C6711yescharacteristic
584C22×C4C2×D4×C6711yescharacteristic
585C22×C4C2×D4×C6711yescharacteristic
586C22×C4C24×C6711yescharacteristic
587D8—44no—
588D8—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8C2×D4×C6712yes—
600C2×C8C2×D4×C6712yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4#41×C6712yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—81no—
630C42C2×D4×C6712yes—
631C42#41×C6712yes—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×D4×C6711yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4#121×C6712yes—
712C2×C4#121×C6712yes—
713C2×C4C22×D4×C6711yescharacteristic
714C2×C4C2×#41×C6711yescharacteristic
715C2×C4C2×#41×C6711yescharacteristic
716C2×C4C2×#41×C6711yescharacteristic
717C2×C4H(5,𝔽2)×C6711yescharacteristic
718C2×C4H(5,𝔽2)×C6711yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#121×C6711yescharacteristic
752C22#525×C6711yescharacteristic
753C22#535×C6711yescharacteristic
754C22#576×C6711yescharacteristic
755C22#576×C6711yescharacteristic
756C22#576×C6711yescharacteristic
757C22#577×C6711yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—42no—
763C4—41no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4#546×C6711yescharacteristic
769C4#550×C6711yescharacteristic
770C4#553×C6711yescharacteristic
771C4#555×C6711yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2C67×#241411yescharacteristic
777C2C67×#305811yescharacteristic
778C2C67×#306211yescharacteristic
779C2C67×#311911yescharacteristic
780C2C67×#312211yescharacteristic
781C2C67×#322011yescharacteristic
782C2C67×#322411yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×#117×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C67C2semidirect
2. C2×#433×C67C2semidirect
3. C67×#2619C2semidirect
4. C67×#2324C2semidirect
5. C67×#2034C2semidirect
6. C67×#2033C2semidirect
7. C67×#1999C2semidirect
8. C67×#1999C2semidirect
9. C67×#1982C2semidirect
10. C67×#1972C2semidirect
11. C67×#1970C2semidirect
12. C67×#1949C2semidirect
13. C67×#1936C2semidirect
14. C67×#1934C2semidirect
15. C67×#1804C2semidirect
120. C4⋊C8×C67D4semidirect
380. #24662C67direct (N × H)
392. C2×#459C2×C67semidirect
393. C2×#433C2×C67semidirect
394. #2619C2×C67semidirect
395. #2324C2×C67semidirect
396. #2034C2×C67semidirect
397. #2033C2×C67semidirect
398. #1999C2×C67semidirect
399. #1999C2×C67semidirect
400. #1982C2×C67semidirect
401. #1972C2×C67semidirect
402. #1970C2×C67semidirect
403. #1949C2×C67semidirect
404. #1936C2×C67semidirect
405. #1934C2×C67semidirect
406. #1804C2×C67semidirect
407. C67#24662direct (N × H)
512. C4⋊C8D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C672
C2×#433×C672
C67×#26192
C67×#23242
C67×#20342
C67×#20332
C67×#19992
C67×#19822
C67×#19722
C67×#19702
C67×#19492
C67×#19362
C67×#19342
C67×#18042
#2466267