Finite Group Databasebeta

← C2×#22572651 #31734364

Subgroups — C2×#22572651 #31734364

Order 17152.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864086C211yesmaximal, characteristic, complemented
2C2×#16864050C211yesmaximal, characteristic
3#22572651C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863732C211yesmaximal, characteristic, complemented
6C2×#16863721C211yesmaximal, characteristic, complemented
7C2×#16863727C211yesmaximal, characteristic, complemented
8C2×#16863710C211yesmaximal, characteristic, complemented
9C2×#16863692C211yesmaximal, characteristic, complemented
10C2×#16863697C211yesmaximal, characteristic, complemented
11C2×#16863642C211yesmaximal, characteristic, complemented
12C2×#16863625C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic, complemented
14C2×#16863438C211yesmaximal, characteristic, complemented
15C22×#14523977C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic, complemented
17C22×#11761627—21no—
18C22×#11761617C2211yescharacteristic
19#16864086—24no—
20#16864086C2218yescomplemented
21#16864050—24no—
22#16864050C2218yes—
23C2×#14524043C2211yescharacteristic
24C2×#14524036—21no—
25C2×#14524035C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524027—21no—
28C2×#14524027—21no—
29C2×#14524024—21no—
30C2×#14524023—21no—
31C2×#14524022C2211yescharacteristic
32C2×#14524022C2211yescharacteristic
33C2×#14524017C2211yescharacteristic
34C2×#14524017C2211yescharacteristic
35C2×C4×Dic134C2211yescharacteristic
36C2×C4×D268C2211yescharacteristic
37C2×#14524002C2211yescharacteristic
38C2×#14523999—21no—
39C22×C4⋊Dic67C2211yescharacteristic
40C22×C4⋊Dic67C2211yescharacteristic
41C22×C4⋊Dic67C2211yescharacteristic
42#16863805C2218yescomplemented
43#16863732C2218yescomplemented
44#16863727C2218yescomplemented
45#16863721C2218yescomplemented
46#16863710C2218yescomplemented
47#16863697C2218yescomplemented
48#16863692C2218yescomplemented
49#16863642C2218yescomplemented
50#16863625C2218yescomplemented
51#16863498C2218yescomplemented
52#16863438C2218yescomplemented
53C2×#14523977C2211yescharacteristic
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523977C2211yescharacteristic
57C2×#14523977C2211yescharacteristic
58C2×#14523977C2211yescharacteristic
59C2×#14523977C2218yescomplemented
60C2×#14523975C2211yescharacteristic
61C2×#14523975C2211yescharacteristic
62C2×#14523975C2211yescharacteristic
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523968C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71C2×C4×D4×C67C2211yescharacteristic
72#435×C67C2218yescomplemented
73C2×C4⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C2×#11761627—28no—
78C2×#11761627—48no—
79C22×Dic134—21no—
80C22×Dic134C2311yescharacteristic
81C22×D268C2311yescharacteristic
82C22×C22⋊D67—21no—
83C22×C22⋊D67—21no—
84C23×Dic67—21no—
85C23×Dic67—21no—
86C23×Dic67—21no—
87C22×C4×D67—21no—
88C2×#11761617—24no—
89C2×#11761617C2314yes—
90#14524043—22no—
91#14524043C2314yes—
92#14524036—28no—
93#14524035—22no—
94#14524035C2314yes—
95#14524033—28no—
96#14524027—28no—
97#14524027—28no—
98#14524024—28no—
99#14524023—28no—
100#14524022—22no—
101#14524022—22no—
102#14524022C2314yes—
103#14524022C2314yes—
104#14524017—22no—
105#14524017—22no—
106#14524017C2314yes—
107#14524017C2314yes—
108C4×Dic134—22no—
109C4×Dic134C2314yes—
110C4×D268—22no—
111C4×D268C2314yes—
112#14524002—22no—
113#14524002C2314yes—
114#14523999—28no—
115C2×C4⋊Dic67—22no—
116C2×C4⋊Dic67—22no—
117C2×C4⋊Dic67—22no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67—21no—
122C2×C4⋊Dic67C2314yes—
123C2×C4⋊Dic67C2314yes—
124C2×C4⋊Dic67C2314yes—
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×C4⋊Dic67C2311yescharacteristic
128C2×C4⋊Dic67C2311yescharacteristic
129C2×C4⋊Dic67C2311yescharacteristic
130C2×C4⋊Dic67C2311yescharacteristic
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×Dic67⋊C4—21no—
136C2×C22⋊Dic67—21no—
137C2×C22⋊Dic67—21no—
138C2×C22⋊Dic67—21no—
139C2×(C2×D67)⋊C4—21no—
140C2×(C2×D67)⋊C4—21no—
141C2×(C2×D67)⋊C4—21no—
142C2×C4×Dic67—21no—
143C2×C4×Dic67—21no—
144#14523977C2314yes—
145#14523977C2314yes—
146#14523977C2314yes—
147#14523977C2314yes—
148#14523977C2314yes—
149#14523977C2314yes—
150#14523975C2314yes—
151#14523975C2314yes—
152#14523975C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523965C2314yes—
157#14523965C2314yes—
158#14523965C2314yes—
159C22×D4×C67D411yescharacteristic
160C23×C4×C67C2311yescharacteristic
161C23×C4×C67C2311yescharacteristic
162C2×M16×C67—24no—
163C2×M16×C67C2314yes—
164C22×C8×C67—24no—
165C22×C8×C67C2314yes—
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168C22×C8×C67C2311yescharacteristic
169C22×C8×C67C2311yescharacteristic
170C4×D4×C67D414yes—
171C4×D4×C67C2314yes—
172C2×C4⋊C4×C67D411yescharacteristic
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C22⋊C4×C67D411yescharacteristic
175C2×C42×C67C2311yescharacteristic
176C4⋊C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178C22⋊C8×C67C2314yes—
179#97×C67C2314yes—
180C23×D67—21no—
181#11761627—432no—
182C2×Dic134—22no—
183C2×Dic134—22no—
184C2×Dic134—21no—
185C2×Dic134—24no—
186C2×Dic134—44no—
187C2×Dic134C2412yes—
188C2×D268—22no—
189C2×D268—22no—
190C2×D268—21no—
191C2×D268C2412yes—
192C2×C22⋊D67—24no—
193C2×C22⋊D67—24no—
194C2×C22⋊D67—44no—
195C2×C22⋊D67—44no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—21no—
201C22×Dic67—21no—
202C22×Dic67—21no—
203C22×Dic67—24no—
204C22×Dic67—24no—
205C22×Dic67—24no—
206C22×Dic67—44no—
207C22×Dic67—44no—
208C22×Dic67—44no—
209C2×C4×D67—24no—
210C2×C4×D67—44no—
211#11761617—28no—
212C4⋊Dic67—21no—
213C4⋊Dic67—21no—
214C4⋊Dic67—21no—
215C4⋊Dic67—21no—
216C4⋊Dic67—21no—
217C4⋊Dic67—24no—
218C4⋊Dic67—24no—
219C4⋊Dic67—24no—
220C4⋊Dic67—24no—
221C4⋊Dic67—21no—
222C4⋊Dic67C2412yes—
223C4⋊Dic67C2412yes—
224C4⋊Dic67C2412yes—
225C4⋊Dic67C2412yes—
226C4⋊Dic67C2412yes—
227C4⋊Dic67C2412yes—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232Dic67⋊C4—24no—
233C22⋊Dic67—24no—
234C22⋊Dic67—24no—
235C22⋊Dic67—24no—
236(C2×D67)⋊C4—24no—
237(C2×D67)⋊C4—24no—
238(C2×D67)⋊C4—24no—
239C4×Dic67—24no—
240C4×Dic67—24no—
241C24×C67C2×D411yescharacteristic
242C24×C67C2×D411yescharacteristic
243C2×D4×C67—24no—
244C2×D4×C67C2×D414yes—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—22no—
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D412yes—
254C22×C4×C67C2×D412yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2412yes—
257C22×C4×C67C2411yescharacteristic
258M16×C67—28no—
259C2×C8×C67—22no—
260C2×C8×C67—22no—
261C2×C8×C67—22no—
262C2×C8×C67—28no—
263C2×C8×C67#4114yescomplemented
264C2×C8×C67C2412yes—
265C2×C8×C67C2412yes—
266C2×C8×C67C2412yes—
267C2×C8×C67C2412yes—
268C4⋊C4×C67C2×D414yes—
269C22⋊C4×C67C2×D414yes—
270C22⋊C4×C67C2×D414yes—
271C42×C67C2×D412yes—
272C42×C67C2412yes—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67AGL(1,ℤ/8)14yes—
279C23×C67C22×D412yes—
280C23×C67C22×D412yes—
281C23×C67C22×D411yescharacteristic
282C22×D67—22no—
283C22×D67—42no—
284C22×D67—42no—
285C22×D67—42no—
286D4×C67—28no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—24no—
292C2×C4×C67—24no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D412yes—
299C2×C4×C67C22×D412yes—
300C2×C4×C67C22×D412yes—
301C2×C4×C67C22×D411yescharacteristic
302C2×C4×C67C2×#4112yes—
303C2×C4×C672−1+412yes—
304C2×C4×C67C2511yescharacteristic
305C22⋊D67—48no—
306C22⋊D67—48no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—48no—
315C2×Dic67—42no—
316C2×Dic67—42no—
317C2×Dic67—48no—
318C2×Dic67—42no—
319C2×Dic67—42no—
320C2×Dic67—42no—
321C2×Dic67—42no—
322C2×Dic67—48no—
323C2×Dic67—42no—
324D268—22no—
325D268—22no—
326D268—42no—
327C4×D67—48no—
328Dic134—22no—
329Dic134—22no—
330Dic134—48no—
331Dic134—42no—
332C8×C67—22no—
333C8×C67—22no—
334C8×C67—22no—
335C8×C67C2×#4114yescomplemented
336C22×C67—28no—
337C22×C67—22no—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—22no—
341C22×C67—22no—
342C22×C67—44no—
343C22×C67#54712yes—
344C22×C67C2×AGL(1,ℤ/8)14yes—
345C22×C67C2×AGL(1,ℤ/8)12yes—
346C22×C67#57812yes—
347C22×C67C23×D411yescharacteristic
348C2×D67—42no—
349C2×D67—42no—
350C2×D67—42no—
351C2×D67—84no—
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—22no—
355C4×C67—22no—
356C4×C67#54712yes—
357C4×C67C22×#4111yescharacteristic
358C4×C67C2×2−1+411yescharacteristic
359Dic67—42no—
360Dic67—42no—
361Dic67—42no—
362Dic67—42no—
363Dic67—42no—
364Dic67—42no—
365Dic67—42no—
366C2×#3343—671nomaximal, Sylow
367C2×C67—24no—
368C2×C67—42no—
369C2×C67#334314yescomplemented
370C2×C67C2×#54711yescharacteristic
371C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C67C2×#57811yescharacteristic
373D67—82no—
374C2×#552—671no—
375C2×#547—671no—
376#3343—6716no—
377C2×#501—671no—
378C2×#484—671no—
379C2×#482—671no—
380C2×#483—671no—
381C2×#480—671no—
382C2×#477—671no—
383C2×#478—671no—
384C2×#468—671no—
385C2×#465—671no—
386C2×#440—671no—
387C2×#435D6711yescharacteristic, complemented
388C2×#428—671no—
389C22×#107—671no—
390C67C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1341no—
392C22×SD16—671no—
393C22×M16C2×D6711yescharacteristic
394C23×C8C2×D6711yescharacteristic
395#552—678no—
396#552—1344no—
397#547—678no—
398#547—1344no—
399C2×C4⋊Q8—671no—
400C2×#126—1341no—
401C2×#125—671no—
402C2×#125—1341no—
403C2×#123—1341no—
404C2×#123—1341no—
405C2×#123—1341no—
406C2×C22⋊Q8—671no—
407C2×C22⋊Q8—671no—
408C2×C22⋊Q8—1341no—
409C2×#121—671no—
410C2×#121—671no—
411C2×C4×Q8—671no—
412C2×C4×D4—671no—
413C2×C4×D4C2×D6711yescharacteristic
414C2×#117—671no—
415C2×#117—1341no—
416C22×C4⋊C4—671no—
417C22×C4⋊C4—671no—
418C22×C4⋊C4—671no—
419#501—678no—
420#484—678no—
421#483—678no—
422#482—678no—
423#480—678no—
424#478—678no—
425#477—678no—
426#468—678no—
427#465—678no—
428#440—678no—
429#435C2×D6718yescomplemented
430#428—678no—
431C2×#107—671no—
432C2×#107—671no—
433C2×#107—671no—
434C2×#107—671no—
435C2×#107—678no—
436C2×#107—671no—
437C2×#107—671no—
438C2×#106—671no—
439C2×#106—671no—
440C2×#106—671no—
441C2×C4⋊C8C2×D6711yescharacteristic
442C2×#103—671no—
443C2×#103—671no—
444C2×#103—671no—
445C2×#102—671no—
446C2×#102—671no—
447C2×#102—671no—
448C2×C22⋊C8C2×D6711yescharacteristic
449C2×C22⋊C8C2×D6711yescharacteristic
450C2×#97C2×D6711yescharacteristic
451C2×#41—2688no—
452C2×#41—1348no—
453C22×Q8—671no—
454C22×Q8—1341no—
455C22×D4—671no—
456C22×D4—1341no—
457C22×D4—1341no—
458C22×D4D26811yescharacteristic
459C23×C4—1341no—
460C23×C4—1341no—
461C23×C4—1341no—
462C23×C4—1341no—
463C23×C4C22×D6711yescharacteristic
464C23×C4C22×D6711yescharacteristic
465C2×SD16—674no—
466C2×SD16—1344no—
467C2×M16—24no—
468C2×M16C22×D6714yes—
469C22×C8—24no—
470C22×C8C22×D6711yescharacteristic
471C22×C8C22×D6714yes—
472C22×C8C22×D6711yescharacteristic
473C22×C8C22×D6711yescharacteristic
474C22×C8C22×D6711yescharacteristic
475C4⋊Q8—674no—
476C4⋊Q8—1342no—
477#126—1348no—
478#125—674no—
479#125—1348no—
480#125—1342no—
481#123—1348no—
482#123—1348no—
483#123—1348no—
484C22⋊Q8—674no—
485C22⋊Q8—674no—
486C22⋊Q8—1342no—
487C22⋊Q8—1342no—
488C22⋊Q8—1348no—
489#121—674no—
490#121—674no—
491#121—1342no—
492#121—1342no—
493C4×Q8—674no—
494C4×Q8—1342no—
495C4×D4—674no—
496C4×D4—1342no—
497C4×D4D26814yes—
498C4×D4C22×D6714yes—
499#117—674no—
500#117—1342no—
501#117—1348no—
502C2×C4⋊C4—671no—
503C2×C4⋊C4—671no—
504C2×C4⋊C4—671no—
505C2×C4⋊C4—671no—
506C2×C4⋊C4—671no—
507C2×C4⋊C4—674no—
508C2×C4⋊C4—674no—
509C2×C4⋊C4—674no—
510C2×C4⋊C4—671no—
511C2×C4⋊C4—1341no—
512C2×C4⋊C4—1341no—
513C2×C4⋊C4—1341no—
514C2×C4⋊C4—1342no—
515C2×C4⋊C4—1342no—
516C2×C4⋊C4—1342no—
517C2×C4⋊C4—1341no—
518C2×C4⋊C4—1341no—
519C2×C4⋊C4—1341no—
520C2×C4⋊C4—1341no—
521C2×C4⋊C4—1341no—
522C2×C4⋊C4—1341no—
523C2×C4⋊C4D26811yescharacteristic
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4—1341no—
527C2×C22⋊C4—1341no—
528C2×C22⋊C4—1341no—
529C2×C22⋊C4—1341no—
530C2×C22⋊C4D26811yescharacteristic
531C2×C22⋊C4D26811yescharacteristic
532C2×C42—1341no—
533C2×C42—1341no—
534C2×C42C22×D6711yescharacteristic
535#107—674no—
536#107—674no—
537#107—674no—
538#107—674no—
539#107—674no—
540#107—674no—
541#106—674no—
542#106—674no—
543#106—674no—
544C4⋊C8C22×D6714yes—
545#103—674no—
546#103—674no—
547#103—674no—
548#102—674no—
549#102—674no—
550#102—674no—
551C22⋊C8C22×D6714yes—
552C22⋊C8C22×D6714yes—
553#97C22×D6714yes—
554C24—1341no—
555C24C2×D26811yescharacteristic
556C24C2×D26811yescharacteristic
557#41—26832no—
558C2×Q8—2684no—
559C2×Q8—672no—
560C2×Q8—1342no—
561C2×Q8—1342no—
562C2×Q8—1341no—
563C2×Q8—1344no—
564C2×D4—24no—
565C2×D4—2684no—
566C2×D4—2684no—
567C2×D4—672no—
568C2×D4—1344no—
569C2×D4—1344no—
570C2×D4—1341no—
571C2×D4—1342no—
572C2×D4—1342no—
573C2×D4C2×D26814yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—2684no—
579C22×C4—2684no—
580C22×C4—2684no—
581C22×C4—2684no—
582C22×C4—1344no—
583C22×C4—1344no—
584C22×C4—1344no—
585C22×C4—1341no—
586C22×C4—1341no—
587C22×C4—1341no—
588C22×C4—1341no—
589C22×C4—1341no—
590C22×C4—1341no—
591C22×C4—1341no—
592C22×C4—1344no—
593C22×C4C2×D26812yes—
594C22×C4C2×D26812yes—
595C22×C4C2×D26811yescharacteristic
596C22×C4C2×D26811yescharacteristic
597C22×C4C2×D26811yescharacteristic
598C22×C4C2×D26811yescharacteristic
599C22×C4C23×D6712yes—
600C22×C4C23×D6712yes—
601C22×C4C23×D6711yescharacteristic
602SD16—1348no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1176162714yescomplemented
609C2×C8C23×D6712yes—
610C2×C8C23×D6712yes—
611C2×C8C23×D6712yes—
612C2×C8C23×D6712yes—
613C4⋊C4—672no—
614C4⋊C4—672no—
615C4⋊C4—672no—
616C4⋊C4—672no—
617C4⋊C4—672no—
618C4⋊C4—672no—
619C4⋊C4—1341no—
620C4⋊C4—1341no—
621C4⋊C4—1341no—
622C4⋊C4—1341no—
623C4⋊C4—1344no—
624C4⋊C4—1344no—
625C4⋊C4—1341no—
626C4⋊C4—1344no—
627C4⋊C4—1341no—
628C4⋊C4—1344no—
629C4⋊C4—1344no—
630C4⋊C4—1344no—
631C4⋊C4—1344no—
632C4⋊C4—1344no—
633C4⋊C4—1344no—
634C4⋊C4C2×D26814yes—
635C22⋊C4—1344no—
636C22⋊C4—1344no—
637C22⋊C4—1344no—
638C22⋊C4—1344no—
639C22⋊C4—1344no—
640C22⋊C4—1344no—
641C22⋊C4C2×D26814yes—
642C22⋊C4C2×D26814yes—
643C42—1344no—
644C42—1344no—
645C42C2×D26812yes—
646C42C23×D6712yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2682no—
653C23—2682no—
654C23—2682no—
655C23—1342no—
656C23#1452407114yes—
657C23C22×D26812yes—
658C23C22×D26812yes—
659C23C22×D26811yescharacteristic
660Q8—2688no—
661Q8—2682no—
662Q8—1342no—
663Q8—1342no—
664D4—28no—
665D4—2688no—
666D4—2688no—
667D4—2682no—
668D4—1342no—
669D4—1342no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—2688no—
681C2×C4—2688no—
682C2×C4—2682no—
683C2×C4—2682no—
684C2×C4—2682no—
685C2×C4—2682no—
686C2×C4—2688no—
687C2×C4—2688no—
688C2×C4—2682no—
689C2×C4—2682no—
690C2×C4—2682no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4—1342no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4—1342no—
697C2×C4—1342no—
698C2×C4C22×D26812yes—
699C2×C4C22×D26812yes—
700C2×C4C22×D26812yes—
701C2×C4C22×D26812yes—
702C2×C4C22×D26811yescharacteristic
703C2×C4C2×#1176162712yes—
704C2×C4#1452409012yes—
705C2×C4C24×D6711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1176162714yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—2682no—
718C22—2682no—
719C22—2682no—
720C22—5364no—
721C22#1686405012yes—
722C22C2×#1452407114yes—
723C22C2×#1452407112yes—
724C22#1686421312yes—
725C22C23×D26811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—2682no—
731C4—2682no—
732C4—2682no—
733C4—2682no—
734C4—2682no—
735C4—2682no—
736C4—2682no—
737C4#1686405012yes—
738C4C22×#1176162711yescharacteristic
739C4C2×#1452409011yescharacteristic
740C2—24no—
741C2—42no—
742C2—5362no—
743C2#2257265114yesdirect product factor
744C2C2×#1686405011yescharacteristic
745C2C22×#1452407111yescharacteristic
746C2C2×#1686421311yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864050C2
hypercenterC2×#435D67
hypocenterC67C2×#3343
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16864086C2semidirect
3. #22572651C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863732C2semidirect
6. C2×#16863721C2semidirect
7. C2×#16863727C2semidirect
8. C2×#16863710C2semidirect
9. C2×#16863692C2semidirect
10. C2×#16863697C2semidirect
11. C2×#16863642C2semidirect
12. C2×#16863625C2semidirect
13. C2×#16863498C2semidirect
14. C2×#16863438C2semidirect
15. C22×#14523977C2semidirect
16. C2×#435×C67C2semidirect
20. #16864086C22semidirect
42. #16863805C22semidirect
43. #16863732C22semidirect
44. #16863727C22semidirect
45. #16863721C22semidirect
46. #16863710C22semidirect
47. #16863697C22semidirect
48. #16863692C22semidirect
49. #16863642C22semidirect
50. #16863625C22semidirect
51. #16863498C22semidirect
52. #16863438C22semidirect
59. C2×#14523977C22semidirect
72. #435×C67C22semidirect
263. C2×C8×C67#41semidirect
335. C8×C67C2×#41semidirect
369. C2×C67#3343semidirect
387. C2×#435D67semidirect
390. C67C2×#3343semidirect
429. #435C2×D67semidirect
608. C2×C8#11761627semidirect
709. C8C2×#11761627semidirect
743. C2#22572651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640862
C2×#168640502
#225726512
C2×#168638052
C2×#168637322
C2×#168637212
C2×#168637272
C2×#168637102
C2×#168636922
C2×#168636972
C2×#168636422
C2×#168636252
C2×#168634982
C2×#168634382
C22×#145239772
C2×#435×C672
C2×#334367