Finite Group Databasebeta

← C4×#16863627 #30862316

Subgroups — C4×#16863627 #30862316

Order 17152.

1138 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863627C211yesmaximal, characteristic
2C2×C4×#11761615C211yesmaximal, characteristic, complemented
3C22×C4×C67⋊C8C211yesmaximal, characteristic, complemented
4C4×#14524017C211yesmaximal, characteristic
5#22561066C211yesmaximal, characteristic, complemented
6#22560934C211yesmaximal, characteristic, complemented
7#22560891C211yesmaximal, characteristic, complemented
8#22560888C211yesmaximal, characteristic, complemented
9#22560635C211yesmaximal, characteristic
10#22560633C211yesmaximal, characteristic, complemented
11#22560232C211yesmaximal, characteristic, complemented
12C4×#14523974C211yesmaximal, characteristic, complemented
13C4×#14523967C211yesmaximal, characteristic, complemented
14C4×#14523963C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C67C211yesmaximal, characteristic, complemented
16C22×#11761615C2211yescharacteristic
17C23×C67⋊C8C2211yescharacteristic
18C23×C67⋊C8C2211yescharacteristic
19C2×#14524017C2211yescharacteristic
20C2×C4×D268C2211yescharacteristic
21C2×C4×C22⋊D67—21no—
22#16863627C418yesdirect product factor
23C4×#11761615—24no—
24C2×#14523974C2211yescharacteristic
25C2×#14523974C2211yescharacteristic
26C2×#14523974C2211yescharacteristic
27C2×#14523967C2211yescharacteristic
28C2×#14523967C2211yescharacteristic
29C2×#14523967C2211yescharacteristic
30C2×#14523963C2211yescharacteristic
31C2×#14523963C2211yescharacteristic
32C2×#14523963C2211yescharacteristic
33C2×C4×C67⋊C8—24no—
34C2×C4×C67⋊C8C2211yescharacteristic
35C2×C4×C67⋊C8C2211yescharacteristic
36C2×C4×C67⋊C8C2211yescharacteristic
37C2×C4×C67⋊C8C2211yescharacteristic
38#16863298C2211yescharacteristic
39#16863294C2211yescharacteristic
40#16863287—21no—
41#16863275—21no—
42#16863256C2211yescharacteristic
43C4×C4⋊Dic67C2211yescharacteristic
44C4×(C2×D67)⋊C4—21no—
45#16863158C2211yescharacteristic
46#16863158C2211yescharacteristic
47#16863158C2211yescharacteristic
48#16863158C2211yescharacteristic
49#16863158C2211yescharacteristic
50#16863158C2211yescharacteristic
51C2×C22⋊Q8×C67C2211yescharacteristic
52C2×C4×Q8×C67C2211yescharacteristic
53C22×C42×C67C2211yescharacteristic
54#391×C67C2211yescharacteristic
55#389×C67C2211yescharacteristic
56#387×C67—21no—
57#385×C67—21no—
58#380×C67C2211yescharacteristic
59C4×C4⋊C4×C67—21no—
60C4×C4⋊C4×C67C2211yescharacteristic
61C4×C22⋊C4×C67—21no—
62C22×D268C2311yescharacteristic
63C22×C22⋊D67—21no—
64C22×C4×D67—21no—
65C2×#11761615—22no—
66C2×#11761615—22no—
67C2×#11761615C2×C414yescomplemented
68C22×C67⋊C8—22no—
69C22×C67⋊C8—22no—
70C22×C67⋊C8—22no—
71C22×C67⋊C8—22no—
72C22×C67⋊C8—22no—
73C22×C67⋊C8C2×C414yescomplemented
74C22×C67⋊C8C2311yescharacteristic
75C22×C67⋊C8C2311yescharacteristic
76C22×C67⋊C8C2311yescharacteristic
77C22×C67⋊C8C2311yescharacteristic
78#14524017—22no—
79#14524017C2×C414yes—
80C4×D268—22no—
81C4×D268—22no—
82C4×C22⋊D67—44no—
83C2×C4⋊Dic67C2311yescharacteristic
84C2×C4⋊Dic67C2311yescharacteristic
85C2×C4⋊Dic67C2311yescharacteristic
86C2×Dic67⋊C4—21no—
87C2×C22⋊Dic67—21no—
88C2×(C2×D67)⋊C4—21no—
89C2×(C2×D67)⋊C4—21no—
90C2×(C2×D67)⋊C4—21no—
91C2×(C2×D67)⋊C4—21no—
92C2×C4×Dic67—21no—
93#14523974—22no—
94#14523974—22no—
95#14523974C2×C414yescomplemented
96#14523967—22no—
97#14523967—22no—
98#14523967C2×C414yescomplemented
99#14523963—22no—
100#14523963—22no—
101#14523963C2×C414yescomplemented
102C4×C67⋊C8—22no—
103C4×C67⋊C8—22no—
104C4×C67⋊C8—22no—
105C4×C67⋊C8D414yescomplemented
106C67⋊#95—21no—
107C67⋊#95—21no—
108C67⋊#95—21no—
109C22×Q8×C67C2311yescharacteristic
110C23×C4×C67D411yescharacteristic
111C23×C4×C67D411yescharacteristic
112C23×C4×C67C2311yescharacteristic
113C22⋊Q8×C67—22no—
114C22⋊Q8×C67C2×C414yescomplemented
115C4×Q8×C67—22no—
116C4×Q8×C67—22no—
117C2×C4⋊C4×C67—21no—
118C2×C4⋊C4×C67—21no—
119C2×C4⋊C4×C67—21no—
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C4⋊C4×C67C2311yescharacteristic
122C2×C4⋊C4×C67C2311yescharacteristic
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C42×C67—22no—
126C2×C42×C67—22no—
127C2×C42×C67—21no—
128C2×C42×C67—21no—
129C2×C42×C67D411yescharacteristic
130C2×C42×C67D411yescharacteristic
131C2×C42×C67C2311yescharacteristic
132C2×C42×C67C2311yescharacteristic
133#95×C67—21no—
134#95×C67—21no—
135#95×C67—21no—
136#95×C67—21no—
137#95×C67—21no—
138C23×D67—21no—
139C2×D268—21no—
140C2×D268—21no—
141C2×D268—21no—
142C2×D268—21no—
143C2×D268—21no—
144C2×D268C22×C412yes—
145C2×C22⋊D67—24no—
146C2×C22⋊D67—42no—
147C2×C22⋊D67—42no—
148C22×Dic67—21no—
149C22×Dic67—21no—
150C22×Dic67—21no—
151C2×C4×D67—42no—
152C2×C4×D67—42no—
153C2×C4×D67—42no—
154#11761615—28no—
155C2×C67⋊C8—28no—
156C2×C67⋊C8—21no—
157C2×C67⋊C8—21no—
158C2×C67⋊C8—21no—
159C2×C67⋊C8—21no—
160C2×C67⋊C8—21no—
161C2×C67⋊C8—21no—
162C2×C67⋊C8—28no—
163C2×C67⋊C8C22×C412yes—
164C2×C67⋊C8C22×C412yes—
165C2×C67⋊C8C2×D412yes—
166C2×C67⋊C8C2×D412yes—
167C2×C67⋊C8#4112yes—
168C2×C67⋊C8#4112yes—
169C4⋊Dic67—21no—
170C4⋊Dic67—21no—
171C4⋊Dic67—21no—
172C4⋊Dic67—21no—
173C4⋊Dic67—21no—
174C4⋊Dic67C22×C412yes—
175Dic67⋊C4—42no—
176C22⋊Dic67—42no—
177(C2×D67)⋊C4—24no—
178(C2×D67)⋊C4—42no—
179(C2×D67)⋊C4—42no—
180(C2×D67)⋊C4—42no—
181C4×Dic67—42no—
182C24×C67C2×D411yescharacteristic
183C2×Q8×C67—21no—
184C2×Q8×C67—21no—
185C2×Q8×C67—21no—
186C2×Q8×C67—21no—
187C2×Q8×C67—21no—
188C2×Q8×C67C22×C412yes—
189C22×C4×C67—22no—
190C22×C4×C67—22no—
191C22×C4×C67—22no—
192C22×C4×C67—22no—
193C22×C4×C67—22no—
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×C67SD1614yescomplemented
203C22×C4×C67C22×C412yes—
204C22×C4×C67C2×D411yescharacteristic
205C22×C4×C67C2×D411yescharacteristic
206C22×C4×C67C2×D411yescharacteristic
207C22×C4×C67C2×D411yescharacteristic
208C22×C4×C67C2×D411yescharacteristic
209C22×C4×C67#4112yes—
210C22×C4×C67C2411yescharacteristic
211C4⋊C4×C67—24no—
212C4⋊C4×C67—21no—
213C4⋊C4×C67—21no—
214C4⋊C4×C67—21no—
215C4⋊C4×C67—21no—
216C4⋊C4×C67—21no—
217C4⋊C4×C67—42no—
218C4⋊C4×C67—42no—
219C4⋊C4×C67C22×C412yes—
220C22⋊C4×C67—24no—
221C22⋊C4×C67—42no—
222C42×C67—22no—
223C42×C67—22no—
224C42×C67—21no—
225C42×C67—21no—
226C42×C67—42no—
227C42×C67—42no—
228C42×C67C2×D412yes—
229C42×C67#4112yes—
230C23×C67—21no—
231C23×C67—21no—
232C23×C67—21no—
233C23×C67—21no—
234C23×C67C4×D412yes—
235C23×C67C2×SD1612yes—
236C23×C67#13512yes—
237C23×C67C22×D411yescharacteristic
238C22×D67—22no—
239C22×D67—41no—
240C22×D67—41no—
241C22×D67—41no—
242C22×D67—41no—
243C22×D67—41no—
244C22×D67—41no—
245Q8×C67—22no—
246Q8×C67—22no—
247Q8×C67—41no—
248Q8×C67—41no—
249C2×C4×C67—28no—
250C2×C4×C67—21no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—21no—
254C2×C4×C67—21no—
255C2×C4×C67—21no—
256C2×C4×C67—21no—
257C2×C4×C67—21no—
258C2×C4×C67—22no—
259C2×C4×C67—22no—
260C2×C4×C67—22no—
261C2×C4×C67—22no—
262C2×C4×C67—28no—
263C2×C4×C67—22no—
264C2×C4×C67—22no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—41no—
268C2×C4×C67—41no—
269C2×C4×C67—41no—
270C2×C4×C67—41no—
271C2×C4×C67—41no—
272C2×C4×C67—41no—
273C2×C4×C67—41no—
274C2×C4×C67—41no—
275C2×C4×C67C4×D412yes—
276C2×C4×C67#12112yes—
277C2×C4×C67#12112yes—
278C2×C4×C67C2×SD1612yes—
279C2×C4×C67C2×SD1612yes—
280C2×C4×C67#13512yes—
281C2×C4×C67#13512yes—
282C2×C4×C67C23×C411yescharacteristic
283C2×C4×C67C22×D411yescharacteristic
284C2×C4×C67C2×#4111yescharacteristic
285C2×C4×C67C2×#4111yescharacteristic
286C2×C4×C67C2×#4111yescharacteristic
287C2×C4×C67C2×#4111yescharacteristic
288C22⋊D67—48no—
289C2×Dic67—22no—
290C2×Dic67—41no—
291C2×Dic67—41no—
292C2×Dic67—41no—
293C2×Dic67—41no—
294C2×Dic67—41no—
295C2×Dic67—41no—
296C2×Dic67—41no—
297C2×Dic67—41no—
298D268—22no—
299D268—22no—
300D268—41no—
301D268—41no—
302C4×D67—84no—
303C67⋊C8—22no—
304C67⋊C8—22no—
305C67⋊C8—22no—
306C67⋊C8C4×D414yescomplemented
307C22×C67—22no—
308C22×C67—22no—
309C22×C67—22no—
310C22×C67—22no—
311C22×C67—22no—
312C22×C67—22no—
313C22×C67C4×SD1614yescomplemented
314C22×C67C2×C4×D411yescharacteristic
315C22×C67C2×#12111yescharacteristic
316C22×C67#53211yescharacteristic
317C22×C67C22×SD1611yescharacteristic
318C22×C67C2×#13511yescharacteristic
319C22×C67C2×#13511yescharacteristic
320C22×C67C2×#13511yescharacteristic
321C2×D67—42no—
322C2×D67—42no—
323C2×D67—42no—
324C2×D67—81no—
325C2×D67—81no—
326C2×D67—81no—
327C2×D67—81no—
328C4×C67—22no—
329C4×C67—22no—
330C4×C67—22no—
331C4×C67—22no—
332C4×C67—42no—
333C4×C67—42no—
334C4×C67—81no—
335C4×C67—81no—
336C4×C67#46514yescomplemented
337C4×C67C2×C4×D411yescharacteristic
338C4×C67C4×#4111yescharacteristic
339C4×C67#52511yescharacteristic
340C4×C67#52911yescharacteristic
341Dic67—42no—
342Dic67—81no—
343Dic67—81no—
344C4×#465—671nomaximal, Sylow
345C2×C67—24no—
346C2×C67C4×#12111yescharacteristic
347C2×C67C2×C4×SD1611yescharacteristic
348C2×C67C4×#13511yescharacteristic
349C2×C67C2×#46511yescharacteristic
350C2×C67#305011yescharacteristic
351C2×C67#316711yescharacteristic
352C2×C67#316811yescharacteristic
353D67—82no—
354C2×#465—671no—
355C2×C4×SD16—671no—
356C22×C4×C8—671no—
357C4×C22⋊Q8D6711yescharacteristic, complemented
358C4×#121—671no—
359#1968—671no—
360#1941—671no—
361#1934—671no—
362#1933—671no—
363#1893—671no—
364#1892—671no—
365#1807—671no—
366C4×#106—671no—
367C4×#103—671no—
368C4×#102—671no—
369C67C4×#46511yescharacteristic, complemented, Sylow
370C22×SD16—671no—
371C23×C8—671no—
372C23×C8—671no—
373C2×C22⋊Q8C2×D6711yescharacteristic
374C2×#121—671no—
375C2×C4×Q8C2×D6711yescharacteristic
376C2×C4×D4—671no—
377C2×C4×D4—1341no—
378C22×C42C2×D6711yescharacteristic
379#465—678no—
380C4×SD16—1344no—
381C2×#106—671no—
382C2×#106—671no—
383C2×#106—671no—
384C2×#103—671no—
385C2×#103—671no—
386C2×#103—671no—
387C2×#102—671no—
388C2×#102—671no—
389C2×#102—671no—
390C2×C4×C8—671no—
391C2×C4×C8—671no—
392C2×C4×C8—671no—
393C2×C4×C8—671no—
394C2×C4×C8—1344no—
395#391C2×D6711yescharacteristic
396#390—671no—
397#389—671no—
398#389C2×D6711yescharacteristic
399#388—1341no—
400#387—21no—
401#386—1341no—
402#385—21no—
403#380—671no—
404#380C2×D6711yescharacteristic
405C4×C4⋊C4—21no—
406C4×C4⋊C4—671no—
407C4×C4⋊C4C2×D6711yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4—1341no—
410#340—671no—
411#340—671no—
412#340—671no—
413#340—671no—
414#340—671no—
415#340—671no—
416C22×Q8C22×D6711yescharacteristic
417C22×D4—671no—
418C22×D4—1341no—
419C23×C4—1341no—
420C23×C4C22⋊D6711yescharacteristic
421C23×C4C22⋊D6711yescharacteristic
422C23×C4C22×D6711yescharacteristic
423C2×SD16—674no—
424C2×SD16—1342no—
425C2×SD16—1342no—
426C22×C8—671no—
427C22×C8—674no—
428C22×C8—671no—
429C22×C8—671no—
430C22×C8—671no—
431C22×C8—1342no—
432C22×C8—1342no—
433C22×C8—1342no—
434C22×C8—1342no—
435C22×C8—1342no—
436C22⋊Q8—22no—
437C22⋊Q8C4×D6714yescomplemented
438#121—674no—
439#121—1342no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—2684no—
443C4×D4—1342no—
444C4×D4—1342no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—671no—
449C2×C4⋊C4—671no—
450C2×C4⋊C4—671no—
451C2×C4⋊C4—1341no—
452C2×C4⋊C4C22×D6711yescharacteristic
453C2×C4⋊C4C22×D6711yescharacteristic
454C2×C4⋊C4C22×D6711yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1341no—
458C2×C22⋊C4—1341no—
459C2×C22⋊C4—1341no—
460C2×C22⋊C4—1341no—
461C2×C22⋊C4—1341no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—1341no—
467C2×C42C22⋊D6711yescharacteristic
468C2×C42C22⋊D6711yescharacteristic
469C2×C42C22×D6711yescharacteristic
470C2×C42C22×D6711yescharacteristic
471#106—674no—
472#106—1342no—
473#106—1342no—
474#103—674no—
475#103—1342no—
476#103—1342no—
477#102—674no—
478#102—1342no—
479#102—1342no—
480C4×C8—674no—
481C4×C8—1342no—
482C4×C8—1342no—
483C4×C8—1342no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—1341no—
490#95—1341no—
491#95—1341no—
492C24—1341no—
493C24C2×C22⋊D6711yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D6712yes—
500C2×D4—2682no—
501C2×D4—2682no—
502C2×D4—672no—
503C2×D4—1344no—
504C2×D4—1341no—
505C2×D4—1341no—
506C2×D4—1341no—
507C2×D4—1341no—
508C2×D4—1341no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—2682no—
523C22×C4—2682no—
524C22×C4—2682no—
525C22×C4—1341no—
526C22×C4—1341no—
527C22×C4—1341no—
528C22×C4#1176161514yescomplemented
529C22×C4C2×C4×D6712yes—
530C22×C4C2×C22⋊D6711yescharacteristic
531C22×C4C2×C22⋊D6711yescharacteristic
532C22×C4C2×C22⋊D6711yescharacteristic
533C22×C4C2×C22⋊D6711yescharacteristic
534C22×C4C2×C22⋊D6711yescharacteristic
535C22×C4#1176162812yes—
536C22×C4C23×D6711yescharacteristic
537SD16—1348no—
538C2×C8—672no—
539C2×C8—672no—
540C2×C8—672no—
541C2×C8—672no—
542C2×C8—672no—
543C2×C8—672no—
544C2×C8—1348no—
545C2×C8—1348no—
546C2×C8—1341no—
547C2×C8—1341no—
548C2×C8—1341no—
549C2×C8—1341no—
550C2×C8—1341no—
551C2×C8—1341no—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—2682no—
561C4⋊C4—672no—
562C4⋊C4—1341no—
563C4⋊C4—1341no—
564C4⋊C4—1341no—
565C4⋊C4—1341no—
566C4⋊C4—1341no—
567C4⋊C4C2×C4×D6712yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—2682no—
571C22⋊C4—2682no—
572C22⋊C4—2682no—
573C22⋊C4—2682no—
574C22⋊C4—1344no—
575C42—22no—
576C42—22no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—2682no—
582C42D4×D6712yes—
583C42#1176162712yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—2681no—
589C23—2681no—
590C23—2681no—
591C23—2681no—
592C23—2681no—
593C23—2681no—
594C23—1342no—
595C23C4×C22⋊D6712yes—
596C23C2×#1176161512yes—
597C23#1452406312yes—
598C23C22×C22⋊D6711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—2688no—
604D4—2681no—
605D4—2681no—
606D4—1342no—
607D4—1342no—
608C2×C4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—2681no—
635C2×C4—2681no—
636C2×C4—2681no—
637C2×C4—2681no—
638C2×C4—2681no—
639C2×C4—2681no—
640C2×C4—2681no—
641C2×C4—2681no—
642C2×C4—5364no—
643C2×C4—1342no—
644C2×C4C4×C22⋊D6712yes—
645C2×C4#1452401512yes—
646C2×C4#1452401512yes—
647C2×C4C2×#1176161512yes—
648C2×C4C2×#1176161512yes—
649C2×C4#1452406312yes—
650C2×C4#1452406312yes—
651C2×C4C22×C4×D6711yescharacteristic
652C2×C4C2×D4×D6711yescharacteristic
653C2×C4#41×D6711yescharacteristic
654C2×C4#41×D6711yescharacteristic
655C2×C4C2×#1176162711yescharacteristic
656C2×C4C2×#1176162811yescharacteristic
657C8—674no—
658C8—1342no—
659C8—1342no—
660C8—1342no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—2682no—
668C22—2682no—
669C22—2682no—
670C22—5361no—
671C22—5361no—
672C22—5361no—
673C22—5361no—
674C22C4×#1176161514yescomplemented
675C22C2×C4×C22⋊D6711yescharacteristic
676C22C2×#1452401511yescharacteristic
677C22#1686394211yescharacteristic
678C22C22×#1176161511yescharacteristic
679C22C2×#1452406311yescharacteristic
680C22C2×#1452406311yescharacteristic
681C22C2×#1452406311yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—2682no—
691C4—5361no—
692C4—5361no—
693C4#1686362714yesdirect product factor
694C4C4×D4×D6711yescharacteristic
695C4C4×#1176162711yescharacteristic
696C4#1686390511yescharacteristic
697C4#1686392611yescharacteristic
698C2—24no—
699C2—5362no—
700C2C4×#1452401511yescharacteristic
701C2C2×C4×#1176161511yescharacteristic
702C2C4×#1452406311yescharacteristic
703C2C2×#1686362711yescharacteristic
704C2#2256978711yescharacteristic
705C2#2257076911yescharacteristic
706C2#2257077311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC4×C22⋊Q8×C67C2
socleC23×C67C22×D4
prime radicalC2×#14524017C22
cosocleC22×C4×C67C24
hypercenterC4×C22⋊Q8D67
hypocenterC67C4×#465
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11761615C2semidirect
3. C22×C4×C67⋊C8C2semidirect
5. #22561066C2semidirect
6. #22560934C2semidirect
7. #22560891C2semidirect
8. #22560888C2semidirect
10. #22560633C2semidirect
11. #22560232C2semidirect
12. C4×#14523974C2semidirect
13. C4×#14523967C2semidirect
14. C4×#14523963C2semidirect
15. C4×C22⋊Q8×C67C2semidirect
22. #16863627C4direct (N × H)
67. C2×#11761615C2×C4semidirect
73. C22×C67⋊C8C2×C4semidirect
95. #14523974C2×C4semidirect
98. #14523967C2×C4semidirect
101. #14523963C2×C4semidirect
105. C4×C67⋊C8D4semidirect
114. C22⋊Q8×C67C2×C4semidirect
202. C22×C4×C67SD16semidirect
306. C67⋊C8C4×D4semidirect
313. C22×C67C4×SD16semidirect
336. C4×C67#465semidirect
357. C4×C22⋊Q8D67semidirect
369. C67C4×#465semidirect
437. C22⋊Q8C4×D67semidirect
528. C22×C4#11761615semidirect
674. C22C4×#11761615semidirect
693. C4#16863627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168636272
C2×C4×#117616152
C22×C4×C67⋊C82
C4×#145240172
#225610662
#225609342
#225608912
#225608882
#225606352
#225606332
#225602322
C4×#145239742
C4×#145239672
C4×#145239632
C4×C22⋊Q8×C672
C4×#46567