Finite Group Databasebeta

← C2×#22572666 #31734380

Subgroups — C2×#22572666 #31734380

Order 17152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864103C211yesmaximal, characteristic
2C2×#16864086C211yesmaximal, characteristic
3#22572666C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863732C211yesmaximal, characteristic, complemented
6C2×#16863738C211yesmaximal, characteristic, complemented
7C2×#16863727C211yesmaximal, characteristic, complemented
8C2×#16863727C211yesmaximal, characteristic, complemented
9C2×#16863704C211yesmaximal, characteristic, complemented
10C2×#16863682C211yesmaximal, characteristic, complemented
11C2×#16863654C211yesmaximal, characteristic, complemented
12C2×#16863637C211yesmaximal, characteristic, complemented
13C2×#16863504C211yesmaximal, characteristic, complemented
14C2×#16863438C211yesmaximal, characteristic, complemented
15C22×#14523975C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic
17C22×Dic268C2211yescharacteristic
18#16864103—24no—
19#16864103C2218yes—
20#16864086—24no—
21#16864086C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524036—21no—
24C2×#14524035C2211yescharacteristic
25C2×#14524034—21no—
26C2×#14524033—21no—
27C2×#14524024—21no—
28C2×#14524022C2211yescharacteristic
29C2×#14524022C2211yescharacteristic
30C2×#14524022C2211yescharacteristic
31C2×#14524022C2211yescharacteristic
32C2×#14524020—21no—
33C2×#14524020—21no—
34C2×C4×Dic134C2211yescharacteristic
35C2×C4×Dic134C2211yescharacteristic
36C2×D4×Dic67—21no—
37C2×#14524002C2211yescharacteristic
38C2×#14523999—21no—
39C22×C4⋊Dic67C2211yescharacteristic
40C22×C4⋊Dic67C2211yescharacteristic
41C22×C4⋊Dic67C2211yescharacteristic
42#16863805C2218yescomplemented
43#16863738C2218yescomplemented
44#16863732C2218yescomplemented
45#16863727C2218yescomplemented
46#16863727C2218yescomplemented
47#16863704C2218yescomplemented
48#16863682C2218yescomplemented
49#16863654C2218yescomplemented
50#16863637C2218yescomplemented
51#16863504C2218yescomplemented
52#16863438C2218yescomplemented
53C2×#14523977C2211yescharacteristic
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523975C2211yescharacteristic
57C2×#14523975C2211yescharacteristic
58C2×#14523975C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
60C2×#14523975C2211yescharacteristic
61C2×#14523975C2211yescharacteristic
62C2×#14523975C2218yescomplemented
63C2×#14523968C2211yescharacteristic
64C2×#14523968C2211yescharacteristic
65C2×#14523968C2211yescharacteristic
66C2×#14523968C2211yescharacteristic
67C2×#14523968C2211yescharacteristic
68C2×#14523968C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C23×C8×C67C2211yescharacteristic
71C2×C4×D4×C67C2211yescharacteristic
72#435×C67C2218yes—
73C2×C4⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×Dic134C2311yescharacteristic
80C23×Dic67—21no—
81C23×Dic67—21no—
82C23×Dic67—21no—
83C2×Dic268—24no—
84C2×Dic268C2314yes—
85#14524043—22no—
86#14524043C2314yes—
87#14524036—28no—
88#14524035—22no—
89#14524035C2314yes—
90#14524034—28no—
91#14524033—28no—
92#14524024—28no—
93#14524022—22no—
94#14524022—22no—
95#14524022—22no—
96#14524022—22no—
97#14524022C2314yes—
98#14524022C2314yes—
99#14524022C2314yes—
100#14524022C2314yes—
101#14524020—28no—
102#14524020—28no—
103C4×Dic134—22no—
104C4×Dic134—22no—
105C4×Dic134C2314yes—
106C4×Dic134C2314yes—
107D4×Dic67—28no—
108#14524002—22no—
109#14524002C2314yes—
110#14523999—28no—
111C2×C4⋊Dic67—22no—
112C2×C4⋊Dic67—22no—
113C2×C4⋊Dic67—22no—
114C2×C4⋊Dic67—21no—
115C2×C4⋊Dic67—21no—
116C2×C4⋊Dic67—21no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67C2314yes—
119C2×C4⋊Dic67C2311yescharacteristic
120C2×C4⋊Dic67C2314yes—
121C2×C4⋊Dic67C2314yes—
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×C4⋊Dic67C2311yescharacteristic
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×Dic67⋊C4—21no—
132C2×Dic67⋊C4—21no—
133C2×Dic67⋊C4—21no—
134C2×Dic67⋊C4—21no—
135C2×C22⋊Dic67—21no—
136C2×C22⋊Dic67—21no—
137C2×C22⋊Dic67—21no—
138C2×C22⋊Dic67—21no—
139C2×C22⋊Dic67—21no—
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67—21no—
143#14523977C2314yes—
144#14523977C2314yes—
145#14523977C2314yes—
146#14523975C2314yes—
147#14523975C2314yes—
148#14523975C2314yes—
149#14523975C2314yes—
150#14523975C2314yes—
151#14523975C2314yes—
152#14523968C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523968C2314yes—
157#14523968C2314yes—
158C22×D4×C67D411yescharacteristic
159C23×C4×C67C2311yescharacteristic
160C23×C4×C67C2311yescharacteristic
161C2×M16×C67—24no—
162C2×M16×C67C2314yes—
163C22×C8×C67—24no—
164C22×C8×C67C2314yes—
165C22×C8×C67C2311yescharacteristic
166C22×C8×C67C2311yescharacteristic
167C22×C8×C67C2311yescharacteristic
168C22×C8×C67C2311yescharacteristic
169C4×D4×C67D414yes—
170C4×D4×C67C2314yes—
171C2×C4⋊C4×C67D411yescharacteristic
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C42×C67C2311yescharacteristic
175C4⋊C8×C67C2314yes—
176C22⋊C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178#97×C67C2314yes—
179C2×Dic134—22no—
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—22no—
183C2×Dic134—21no—
184C2×Dic134—21no—
185C2×Dic134—24no—
186C2×Dic134—82no—
187C2×Dic134C2412yes—
188C2×Dic134C2412yes—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—24no—
198C22×Dic67—24no—
199C22×Dic67—24no—
200C22×Dic67—44no—
201C22×Dic67—82no—
202C22×Dic67—82no—
203Dic268—28no—
204C4⋊Dic67—21no—
205C4⋊Dic67—21no—
206C4⋊Dic67—24no—
207C4⋊Dic67—24no—
208C4⋊Dic67—21no—
209C4⋊Dic67—21no—
210C4⋊Dic67—21no—
211C4⋊Dic67—24no—
212C4⋊Dic67—24no—
213C4⋊Dic67—21no—
214C4⋊Dic67C2412yes—
215C4⋊Dic67C2412yes—
216C4⋊Dic67C2412yes—
217C4⋊Dic67C2412yes—
218C4⋊Dic67C2412yes—
219C4⋊Dic67C2412yes—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4—24no—
226Dic67⋊C4—24no—
227Dic67⋊C4—24no—
228C22⋊Dic67—24no—
229C22⋊Dic67—24no—
230C22⋊Dic67—24no—
231C22⋊Dic67—24no—
232C22⋊Dic67—24no—
233C4×Dic67—24no—
234C4×Dic67—24no—
235C4×Dic67—24no—
236C24×C67C2×D411yescharacteristic
237C24×C67C2×D411yescharacteristic
238C2×D4×C67—24no—
239C2×D4×C67C2×D414yes—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D412yes—
249C22×C4×C67C2×D412yes—
250C22×C4×C67C2412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2411yescharacteristic
253M16×C67—28no—
254C2×C8×C67—22no—
255C2×C8×C67—22no—
256C2×C8×C67—22no—
257C2×C8×C67—28no—
258C2×C8×C67#4114yes—
259C2×C8×C67C2412yes—
260C2×C8×C67C2412yes—
261C2×C8×C67C2412yes—
262C2×C8×C67C2412yes—
263C4⋊C4×C67C2×D414yes—
264C22⋊C4×C67C2×D414yes—
265C22⋊C4×C67C2×D414yes—
266C42×C67C2×D412yes—
267C42×C67C2412yes—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67#13714yes—
274C23×C67C22×D412yes—
275C23×C67C22×D412yes—
276C23×C67C22×D411yescharacteristic
277D4×C67—28no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—24no—
283C2×C4×C67—24no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67C22×D412yes—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D412yes—
291C2×C4×C67C22×D412yes—
292C2×C4×C67C22×D411yescharacteristic
293C2×C4×C67C2×#4112yes—
294C2×C4×C672−1+412yes—
295C2×C4×C67C2511yescharacteristic
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—42no—
305C2×Dic67—42no—
306C2×Dic67—48no—
307C2×Dic67—42no—
308C2×Dic67—42no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311C2×Dic67—42no—
312C2×Dic67—42no—
313C2×Dic67—84no—
314C2×Dic67—84no—
315Dic134—22no—
316Dic134—22no—
317Dic134—22no—
318Dic134—22no—
319Dic134—42no—
320Dic134—42no—
321Dic134—84no—
322C8×C67—22no—
323C8×C67—22no—
324C8×C67—22no—
325C8×C67C2×#4114yes—
326C22×C67—28no—
327C22×C67—22no—
328C22×C67—22no—
329C22×C67—22no—
330C22×C67—22no—
331C22×C67—22no—
332C22×C67—44no—
333C22×C67#54712yes—
334C22×C67C2×#13714yes—
335C22×C67C2×#13712yes—
336C22×C67#57712yes—
337C22×C67C23×D411yescharacteristic
338C4×C67—22no—
339C4×C67—22no—
340C4×C67—22no—
341C4×C67—22no—
342C4×C67#54712yes—
343C4×C67C22×#4111yescharacteristic
344C4×C67C2×2−1+411yescharacteristic
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352Dic67—42no—
353C2×#3344—671nomaximal, Sylow
354C2×C67—24no—
355C2×C67—42no—
356C2×C67#334414yescomplemented
357C2×C67C2×#54711yescharacteristic
358C2×C67C22×#13711yescharacteristic
359C2×C67C2×#57711yescharacteristic
360C2×#554—671no—
361C2×#552—671no—
362#3344—6716no—
363C2×#501—671no—
364C2×#484—671no—
365C2×#485—671no—
366C2×#483—671no—
367C2×#483—671no—
368C2×#479—671no—
369C2×#475—671no—
370C2×#470—671no—
371C2×#467—671no—
372C2×#441—671no—
373C2×#435D6711yescharacteristic
374C2×#428—671no—
375C22×#106—671no—
376C67C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—671no—
378C22×M16C2×D6711yescharacteristic
379C23×C8C2×D6711yescharacteristic
380#554—678no—
381#554—1344no—
382#552—678no—
383#552—1344no—
384C2×C4⋊Q8—671no—
385C2×#126—1341no—
386C2×#125—671no—
387C2×#125—1341no—
388C2×#125—1341no—
389C2×#123—1341no—
390C2×C22⋊Q8—671no—
391C2×C22⋊Q8—671no—
392C2×C22⋊Q8—671no—
393C2×C22⋊Q8—671no—
394C2×C22⋊Q8—1341no—
395C2×C22⋊Q8—1341no—
396C2×C4×Q8—671no—
397C2×C4×Q8—671no—
398C2×C4×D4—1341no—
399C2×C4×D4C2×D6711yescharacteristic
400C2×#117—671no—
401C2×#117—1341no—
402C22×C4⋊C4—671no—
403C22×C4⋊C4—671no—
404C22×C4⋊C4—671no—
405#501—678no—
406#485—678no—
407#484—678no—
408#483—678no—
409#483—678no—
410#479—678no—
411#475—678no—
412#470—678no—
413#467—678no—
414#441—678no—
415#435C2×D6718yes—
416#428—678no—
417C2×#107—671no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#106—671no—
421C2×#106—671no—
422C2×#106—671no—
423C2×#106—671no—
424C2×#106—678no—
425C2×#106—671no—
426C2×#106—671no—
427C2×C4⋊C8C2×D6711yescharacteristic
428C2×#103—671no—
429C2×#103—671no—
430C2×#103—671no—
431C2×#103—671no—
432C2×#103—671no—
433C2×#103—671no—
434C2×C22⋊C8C2×D6711yescharacteristic
435C2×C22⋊C8C2×D6711yescharacteristic
436C2×#97C2×D6711yescharacteristic
437C22×Q8—671no—
438C22×Q8—671no—
439C22×Q8—1341no—
440C22×D4D26811yescharacteristic
441C23×C4—1341no—
442C23×C4—1341no—
443C23×C4—1341no—
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C2×Q16—674no—
447C2×Q16—1344no—
448C2×M16—24no—
449C2×M16C22×D6714yes—
450C22×C8—24no—
451C22×C8C22×D6711yescharacteristic
452C22×C8C22×D6714yes—
453C22×C8C22×D6711yescharacteristic
454C22×C8C22×D6711yescharacteristic
455C22×C8C22×D6711yescharacteristic
456C4⋊Q8—674no—
457C4⋊Q8—1342no—
458#126—1348no—
459#125—674no—
460#125—1348no—
461#125—1348no—
462#125—1342no—
463#123—1348no—
464C22⋊Q8—674no—
465C22⋊Q8—674no—
466C22⋊Q8—674no—
467C22⋊Q8—674no—
468C22⋊Q8—1342no—
469C22⋊Q8—1342no—
470C22⋊Q8—1342no—
471C22⋊Q8—1342no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474C4×Q8—674no—
475C4×Q8—674no—
476C4×Q8—1342no—
477C4×Q8—1342no—
478C4×D4—1348no—
479C4×D4D26814yes—
480C4×D4C22×D6714yes—
481#117—674no—
482#117—1342no—
483#117—1348no—
484C2×C4⋊C4—671no—
485C2×C4⋊C4—671no—
486C2×C4⋊C4—671no—
487C2×C4⋊C4—671no—
488C2×C4⋊C4—671no—
489C2×C4⋊C4—674no—
490C2×C4⋊C4—674no—
491C2×C4⋊C4—674no—
492C2×C4⋊C4—671no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4—1341no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1342no—
497C2×C4⋊C4—1342no—
498C2×C4⋊C4—1342no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4—1341no—
505C2×C4⋊C4—1341no—
506C2×C4⋊C4—1341no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4D26811yescharacteristic
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4—1341no—
513C2×C22⋊C4—1341no—
514C2×C22⋊C4D26811yescharacteristic
515C2×C22⋊C4D26811yescharacteristic
516C2×C42—1341no—
517C2×C42—1341no—
518C2×C42—1341no—
519C2×C42C22×D6711yescharacteristic
520#107—674no—
521#107—674no—
522#107—674no—
523#106—674no—
524#106—674no—
525#106—674no—
526#106—674no—
527#106—674no—
528#106—674no—
529C4⋊C8C22×D6714yes—
530#103—674no—
531#103—674no—
532#103—674no—
533#103—674no—
534#103—674no—
535#103—674no—
536C22⋊C8C22×D6714yes—
537C22⋊C8C22×D6714yes—
538#97C22×D6714yes—
539C24C2×D26811yescharacteristic
540C24C2×D26811yescharacteristic
541C2×Q8—5362no—
542C2×Q8—672no—
543C2×Q8—672no—
544C2×Q8—1342no—
545C2×Q8—1342no—
546C2×Q8—1342no—
547C2×Q8—1342no—
548C2×Q8—1341no—
549C2×Q8—1341no—
550C2×Q8—1344no—
551C2×D4—24no—
552C2×D4C2×D26814yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—2684no—
558C22×C4—5362no—
559C22×C4—5362no—
560C22×C4—1344no—
561C22×C4—1341no—
562C22×C4—1341no—
563C22×C4—1341no—
564C22×C4—1341no—
565C22×C4—1341no—
566C22×C4—1341no—
567C22×C4—1341no—
568C22×C4—1341no—
569C22×C4—1344no—
570C22×C4—1344no—
571C22×C4C2×D26812yes—
572C22×C4C2×D26812yes—
573C22×C4C2×D26811yescharacteristic
574C22×C4C2×D26811yescharacteristic
575C22×C4C2×D26811yescharacteristic
576C22×C4C2×D26811yescharacteristic
577C22×C4C23×D6712yes—
578C22×C4C23×D6712yes—
579C22×C4C23×D6711yescharacteristic
580Q16—1348no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1176162714yes—
587C2×C8C23×D6712yes—
588C2×C8C23×D6712yes—
589C2×C8C23×D6712yes—
590C2×C8C23×D6712yes—
591C4⋊C4—672no—
592C4⋊C4—672no—
593C4⋊C4—672no—
594C4⋊C4—672no—
595C4⋊C4—672no—
596C4⋊C4—672no—
597C4⋊C4—1341no—
598C4⋊C4—1341no—
599C4⋊C4—1344no—
600C4⋊C4—1344no—
601C4⋊C4—1341no—
602C4⋊C4—1341no—
603C4⋊C4—1341no—
604C4⋊C4—1344no—
605C4⋊C4—1341no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4—1344no—
615C4⋊C4C2×D26814yes—
616C22⋊C4—1344no—
617C22⋊C4—1344no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4—1344no—
621C22⋊C4C2×D26814yes—
622C22⋊C4C2×D26814yes—
623C42—1344no—
624C42—1344no—
625C42—1344no—
626C42C2×D26812yes—
627C42C23×D6712yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1452407614yes—
634C23C22×D26812yes—
635C23C22×D26812yes—
636C23C22×D26811yescharacteristic
637Q8—2682no—
638Q8—2682no—
639Q8—5364no—
640Q8—1342no—
641Q8—1342no—
642Q8—1342no—
643Q8—1342no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—2682no—
656C2×C4—2682no—
657C2×C4—2688no—
658C2×C4—2682no—
659C2×C4—2682no—
660C2×C4—2682no—
661C2×C4—2682no—
662C2×C4—2682no—
663C2×C4—2682no—
664C2×C4—5364no—
665C2×C4—5364no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4C22×D26812yes—
675C2×C4C22×D26812yes—
676C2×C4C22×D26812yes—
677C2×C4C22×D26812yes—
678C2×C4C22×D26811yescharacteristic
679C2×C4C2×#1176162712yes—
680C2×C4#1452409012yes—
681C2×C4C24×D6711yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1176162714yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1686405012yes—
694C22C2×#1452407614yes—
695C22C2×#1452407612yes—
696C22#1686420812yes—
697C22C23×D26811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—2682no—
703C4—2682no—
704C4—2682no—
705C4—2682no—
706C4—2682no—
707C4—2682no—
708C4—2682no—
709C4—2682no—
710C4#1686405012yes—
711C4C22×#1176162711yescharacteristic
712C4C2×#1452409011yescharacteristic
713C2—24no—
714C2—42no—
715C2#2257266614yesdirect product factor
716C2C2×#1686405011yescharacteristic
717C2C22×#1452407611yescharacteristic
718C2C2×#1686420811yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
hypercenterC2×#435D67
hypocenterC67C2×#3344
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
3. #22572666C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863732C2semidirect
6. C2×#16863738C2semidirect
7. C2×#16863727C2semidirect
8. C2×#16863727C2semidirect
9. C2×#16863704C2semidirect
10. C2×#16863682C2semidirect
11. C2×#16863654C2semidirect
12. C2×#16863637C2semidirect
13. C2×#16863504C2semidirect
14. C2×#16863438C2semidirect
15. C22×#14523975C2semidirect
42. #16863805C22semidirect
43. #16863738C22semidirect
44. #16863732C22semidirect
45. #16863727C22semidirect
46. #16863727C22semidirect
47. #16863704C22semidirect
48. #16863682C22semidirect
49. #16863654C22semidirect
50. #16863637C22semidirect
51. #16863504C22semidirect
52. #16863438C22semidirect
62. C2×#14523975C22semidirect
356. C2×C67#3344semidirect
376. C67C2×#3344semidirect
715. C2#22572666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641032
C2×#168640862
#225726662
C2×#168638052
C2×#168637322
C2×#168637382
C2×#168637272
C2×#168637042
C2×#168636822
C2×#168636542
C2×#168636372
C2×#168635042
C2×#168634382
C22×#145239752
C2×#435×C672
C2×#334467