Finite Group Databasebeta

← C2×#22572756 #31734476

Subgroups — C2×#22572756 #31734476

Order 17152.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864116C211yesmaximal, characteristic, complemented
2C2×#16864092C211yesmaximal, characteristic
3#22572756C2116yesmaximal, direct product factor
4C2×#16863805C211yesmaximal, characteristic, complemented
5C2×#16863738C211yesmaximal, characteristic, complemented
6C2×#16863721C211yesmaximal, characteristic, complemented
7C2×#16863721C211yesmaximal, characteristic, complemented
8C2×#16863727C211yesmaximal, characteristic, complemented
9C2×#16863704C211yesmaximal, characteristic, complemented
10C2×#16863687C211yesmaximal, characteristic, complemented
11C2×#16863642C211yesmaximal, characteristic, complemented
12C2×#16863625C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic, complemented
14C2×#16863438C211yesmaximal, characteristic, complemented
15C2×#16863434C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic, complemented
17C22×#11761617C2211yescharacteristic
18#16864116—24no—
19#16864116C2218yescomplemented
20#16864092—24no—
21#16864092C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524038—21no—
24C2×#14524036—21no—
25C2×#14524036—21no—
26C2×#14524035C2211yescharacteristic
27C2×#14524030—21no—
28C2×#14524025—21no—
29C2×#14524022C2211yescharacteristic
30C2×#14524022C2211yescharacteristic
31C2×#14524017C2211yescharacteristic
32C2×#14524017C2211yescharacteristic
33C2×#14524015—21no—
34C2×C4×Dic134C2211yescharacteristic
35C2×#14524008—21no—
36C2×C4×D268C2211yescharacteristic
37C2×(C22⋊D67)⋊C4—21no—
38C2×#14524002C2211yescharacteristic
39C2×#14524002C2211yescharacteristic
40C2×#14524002C2211yescharacteristic
41C22×C4⋊Dic67C2211yescharacteristic
42#16863805C2218yescomplemented
43#16863738C2218yescomplemented
44#16863727C2218yescomplemented
45#16863721C2218yescomplemented
46#16863721C2218yescomplemented
47#16863704C2218yescomplemented
48#16863687C2218yescomplemented
49#16863642C2218yescomplemented
50#16863625C2218yescomplemented
51#16863498C2218yescomplemented
52#16863438C2218yescomplemented
53#16863434C2218yescomplemented
54C2×#14523977C2211yescharacteristic
55C2×#14523977C2211yescharacteristic
56C2×#14523977C2211yescharacteristic
57C2×#14523977C2211yescharacteristic
58C2×#14523975C2211yescharacteristic
59C2×#14523975C2211yescharacteristic
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
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×D268C2311yescharacteristic
80C22×C22⋊D67—21no—
81C22×C22⋊D67—21no—
82C23×Dic67—21no—
83C22×C4×D67—21no—
84C2×#11761617—24no—
85C2×#11761617C2314yes—
86#14524043—22no—
87#14524043C2314yes—
88#14524038—28no—
89#14524036—28no—
90#14524036—28no—
91#14524035—22no—
92#14524035C2314yes—
93#14524030—28no—
94#14524025—28no—
95#14524022—22no—
96#14524022—22no—
97#14524022C2314yes—
98#14524022C2314yes—
99#14524017—22no—
100#14524017—22no—
101#14524017C2314yes—
102#14524017C2314yes—
103#14524015—28no—
104C4×Dic134—22no—
105C4×Dic134C2314yes—
106#14524008—28no—
107C4×D268—22no—
108C4×D268C2314yes—
109(C22⋊D67)⋊C4—28no—
110#14524002—22no—
111#14524002—22no—
112#14524002—22no—
113#14524002C2314yes—
114#14524002C2314yes—
115#14524002C2314yes—
116C2×C4⋊Dic67—22no—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67C2314yes—
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×C4⋊Dic67C2311yescharacteristic
125C2×C4⋊Dic67C2311yescharacteristic
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4—21no—
130C2×Dic67⋊C4—21no—
131C2×C22⋊Dic67—21no—
132C2×C22⋊Dic67—21no—
133C2×C22⋊Dic67—21no—
134C2×C22⋊Dic67—21no—
135C2×C22⋊Dic67—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4—21no—
139C2×C4×Dic67—21no—
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67—21no—
143#14523977C2314yes—
144#14523977C2314yes—
145#14523977C2314yes—
146#14523977C2314yes—
147#14523975C2314yes—
148#14523975C2314yes—
149#14523975C2314yes—
150#14523975C2314yes—
151#14523975C2314yes—
152#14523968C2314yes—
153#14523968C2314yes—
154#14523968C2314yes—
155#14523965C2314yes—
156#14523965C2314yes—
157#14523965C2314yes—
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—
179C23×D67—21no—
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—24no—
183C2×Dic134—21no—
184C2×Dic134—44no—
185C2×Dic134C2412yes—
186C2×D268—22no—
187C2×D268—22no—
188C2×D268—21no—
189C2×D268C2412yes—
190C2×C22⋊D67—24no—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—44no—
193C2×C22⋊D67—82no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67—21no—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—21no—
201C22×Dic67—24no—
202C22×Dic67—82no—
203C2×C4×D67—24no—
204C2×C4×D67—82no—
205#11761617—28no—
206C4⋊Dic67—21no—
207C4⋊Dic67—21no—
208C4⋊Dic67—24no—
209C4⋊Dic67—24no—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67—21no—
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—
225C22⋊Dic67—24no—
226C22⋊Dic67—24no—
227C22⋊Dic67—24no—
228C22⋊Dic67—24no—
229C22⋊Dic67—24no—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232(C2×D67)⋊C4—24no—
233C4×Dic67—24no—
234C4×Dic67—24no—
235C4×Dic67—24no—
236C4×Dic67—24no—
237C24×C67C2×D411yescharacteristic
238C24×C67C2×D411yescharacteristic
239C2×D4×C67—42no—
240C2×D4×C67C2×D414yes—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D412yes—
250C22×C4×C67C2×D412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2412yes—
253C22×C4×C67C2411yescharacteristic
254M16×C67—28no—
255C2×C8×C67—22no—
256C2×C8×C67—22no—
257C2×C8×C67—22no—
258C2×C8×C67—28no—
259C2×C8×C67#4114yes—
260C2×C8×C67C2412yes—
261C2×C8×C67C2412yes—
262C2×C8×C67C2412yes—
263C2×C8×C67C2412yes—
264C4⋊C4×C67C2×D414yes—
265C22⋊C4×C67C2×D414yes—
266C22⋊C4×C67C2×D414yes—
267C42×C67C2×D412yes—
268C42×C67C2412yes—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67C22×D412yes—
276C23×C67C22×D412yes—
277C23×C67C22×D411yescharacteristic
278C22×D67—22no—
279C22×D67—42no—
280C22×D67—42no—
281C22×D67—42no—
282D4×C67—44no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—24no—
288C2×C4×C67—24no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67C22×D412yes—
294C2×C4×C67C22×D412yes—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D412yes—
297C2×C4×C67C22×D411yescharacteristic
298C2×C4×C67C2×#4112yes—
299C2×C4×C672−1+412yes—
300C2×C4×C67C2511yescharacteristic
301C22⋊D67—48no—
302C22⋊D67—84no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—42no—
311C2×Dic67—42no—
312C2×Dic67—42no—
313C2×Dic67—42no—
314C2×Dic67—42no—
315C2×Dic67—42no—
316C2×Dic67—42no—
317C2×Dic67—84no—
318D268—22no—
319D268—22no—
320D268—42no—
321C4×D67—84no—
322Dic134—22no—
323Dic134—22no—
324Dic134—48no—
325Dic134—42no—
326C8×C67—22no—
327C8×C67—22no—
328C8×C67—22no—
329C8×C67C2×#4114yes—
330C22×C67—22no—
331C22×C67—22no—
332C22×C67—22no—
333C22×C67—22no—
334C22×C67—22no—
335C22×C67—22no—
336C22×C67—44no—
337C22×C67—44no—
338C22×C67#54712yes—
339C22×C67#57512yes—
340C22×C67#57712yes—
341C22×C67C23×D411yescharacteristic
342C2×D67—42no—
343C2×D67—42no—
344C2×D67—42no—
345C2×D67—84no—
346C4×C67—22no—
347C4×C67—22no—
348C4×C67—22no—
349C4×C67—22no—
350C4×C67#54712yes—
351C4×C67C22×#4111yescharacteristic
352C4×C67C2×2−1+411yescharacteristic
353Dic67—42no—
354Dic67—42no—
355Dic67—42no—
356Dic67—42no—
357Dic67—42no—
358Dic67—42no—
359Dic67—42no—
360C2×#3350—671nomaximal, Sylow
361C2×C67—42no—
362C2×C67—42no—
363C2×C67#335014yescomplemented
364C2×C67C2×#54711yescharacteristic
365C2×C67C2×#57511yescharacteristic
366C2×C67C2×#57711yescharacteristic
367D67—82no—
368C2×#556—671no—
369C2×#553—671no—
370#3350—6716no—
371C2×#501—671no—
372C2×#485—671no—
373C2×#482—671no—
374C2×#482—671no—
375C2×#483—671no—
376C2×#479—671no—
377C2×#476—671no—
378C2×#468—671no—
379C2×#465—671no—
380C2×#440—671no—
381C2×#435D6711yescharacteristic, complemented
382C2×#428—671no—
383C2×#427—671no—
384C67C2×#335011yescharacteristic, complemented, Sylow
385C22×SD16—671no—
386C22×M16C2×D6711yescharacteristic
387C23×C8C2×D6711yescharacteristic
388#556—678no—
389#556—1344no—
390#553—678no—
391#553—1344no—
392C2×C4⋊Q8—671no—
393C2×#126—1341no—
394C2×#126—1341no—
395C2×#126—1341no—
396C2×#125—671no—
397C2×#124—1341no—
398C2×#123—1341no—
399C2×C22⋊Q8—671no—
400C2×C22⋊Q8—671no—
401C2×#121—671no—
402C2×#121—671no—
403C2×#121—1341no—
404C2×C4×Q8—671no—
405C2×C4×Q8—1341no—
406C2×C4×D4—671no—
407C2×C4×D4—1341no—
408C2×C4×D4C2×D6711yescharacteristic
409C2×#117—671no—
410C2×#117—671no—
411C2×#117—671no—
412C22×C4⋊C4—671no—
413#501—678no—
414#485—678no—
415#483—678no—
416#482—678no—
417#482—678no—
418#479—678no—
419#476—678no—
420#468—678no—
421#465—678no—
422#440—678no—
423#435C2×D6718yescomplemented
424#428—678no—
425#427—678no—
426C2×#107—671no—
427C2×#107—671no—
428C2×#107—671no—
429C2×#107—671no—
430C2×#106—671no—
431C2×#106—671no—
432C2×#106—671no—
433C2×#106—671no—
434C2×#106—671no—
435C2×C4⋊C8C2×D6711yescharacteristic
436C2×#103—671no—
437C2×#103—671no—
438C2×#103—671no—
439C2×#102—671no—
440C2×#102—671no—
441C2×#102—671no—
442C2×C22⋊C8C2×D6711yescharacteristic
443C2×C22⋊C8C2×D6711yescharacteristic
444C2×#97C2×D6711yescharacteristic
445C22×Q8—671no—
446C22×Q8—1341no—
447C22×D4—671no—
448C22×D4—1341no—
449C22×D4—1341no—
450C22×D4D26811yescharacteristic
451C23×C4—1341no—
452C23×C4—1341no—
453C23×C4C22×D6711yescharacteristic
454C23×C4C22×D6711yescharacteristic
455C2×SD16—674no—
456C2×SD16—1344no—
457C2×M16—24no—
458C2×M16C22×D6714yes—
459C22×C8—24no—
460C22×C8C22×D6711yescharacteristic
461C22×C8C22×D6714yes—
462C22×C8C22×D6711yescharacteristic
463C22×C8C22×D6711yescharacteristic
464C22×C8C22×D6711yescharacteristic
465C4⋊Q8—674no—
466C4⋊Q8—1342no—
467#126—1348no—
468#126—1348no—
469#126—1348no—
470#125—674no—
471#125—1342no—
472#124—1348no—
473#123—1348no—
474C22⋊Q8—674no—
475C22⋊Q8—674no—
476C22⋊Q8—1342no—
477C22⋊Q8—1342no—
478#121—674no—
479#121—674no—
480#121—1348no—
481#121—1342no—
482#121—1342no—
483C4×Q8—674no—
484C4×Q8—1348no—
485C4×Q8—1342no—
486C4×D4—674no—
487C4×D4—1348no—
488C4×D4—1342no—
489C4×D4D26814yes—
490C4×D4C22×D6714yes—
491#117—674no—
492#117—674no—
493#117—674no—
494#117—1342no—
495#117—1342no—
496#117—1342no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—671no—
499C2×C4⋊C4—674no—
500C2×C4⋊C4—671no—
501C2×C4⋊C4—671no—
502C2×C4⋊C4—671no—
503C2×C4⋊C4—671no—
504C2×C4⋊C4—1341no—
505C2×C4⋊C4—1342no—
506C2×C4⋊C4—1341no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1341no—
510C2×C4⋊C4—1341no—
511C2×C4⋊C4—1341no—
512C2×C4⋊C4D26811yescharacteristic
513C2×C22⋊C4—1341no—
514C2×C22⋊C4—1341no—
515C2×C22⋊C4—1341no—
516C2×C22⋊C4—1341no—
517C2×C22⋊C4—1341no—
518C2×C22⋊C4—1341no—
519C2×C22⋊C4—1341no—
520C2×C22⋊C4—1341no—
521C2×C22⋊C4D26811yescharacteristic
522C2×C22⋊C4D26811yescharacteristic
523C2×C42—1341no—
524C2×C42—1341no—
525C2×C42—1341no—
526C2×C42—1341no—
527C2×C42C22×D6711yescharacteristic
528#107—674no—
529#107—674no—
530#107—674no—
531#107—674no—
532#106—674no—
533#106—674no—
534#106—674no—
535#106—674no—
536#106—674no—
537C4⋊C8C22×D6714yes—
538#103—674no—
539#103—674no—
540#103—674no—
541#102—674no—
542#102—674no—
543#102—674no—
544C22⋊C8C22×D6714yes—
545C22⋊C8C22×D6714yes—
546#97C22×D6714yes—
547C24—1341no—
548C24C2×D26811yescharacteristic
549C24C2×D26811yescharacteristic
550C2×Q8—2684no—
551C2×Q8—672no—
552C2×Q8—1342no—
553C2×Q8—1342no—
554C2×Q8—1341no—
555C2×Q8—1344no—
556C2×D4—42no—
557C2×D4—2684no—
558C2×D4—5362no—
559C2×D4—672no—
560C2×D4—1344no—
561C2×D4—1344no—
562C2×D4—1341no—
563C2×D4—1342no—
564C2×D4—1342no—
565C2×D4C2×D26814yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—5362no—
571C22×C4—5362no—
572C22×C4—1341no—
573C22×C4—1341no—
574C22×C4—1341no—
575C22×C4—1341no—
576C22×C4—1341no—
577C22×C4—1341no—
578C22×C4—1341no—
579C22×C4—1344no—
580C22×C4—1344no—
581C22×C4C2×D26812yes—
582C22×C4C2×D26812yes—
583C22×C4C2×D26811yescharacteristic
584C22×C4C2×D26811yescharacteristic
585C22×C4C2×D26811yescharacteristic
586C22×C4C2×D26811yescharacteristic
587C22×C4C23×D6712yes—
588C22×C4C23×D6712yes—
589C22×C4C23×D6711yescharacteristic
590SD16—1348no—
591M16—28no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8#1176162714yes—
597C2×C8C23×D6712yes—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C2×C8C23×D6712yes—
601C4⋊C4—672no—
602C4⋊C4—672no—
603C4⋊C4—672no—
604C4⋊C4—672no—
605C4⋊C4—672no—
606C4⋊C4—672no—
607C4⋊C4—1341no—
608C4⋊C4—1341no—
609C4⋊C4—1344no—
610C4⋊C4—1341no—
611C4⋊C4—1341no—
612C4⋊C4—1341no—
613C4⋊C4—1341no—
614C4⋊C4—1344no—
615C4⋊C4—1344no—
616C4⋊C4—1344no—
617C4⋊C4—1344no—
618C4⋊C4—1344no—
619C4⋊C4—1344no—
620C4⋊C4C2×D26814yes—
621C22⋊C4—1344no—
622C22⋊C4—1344no—
623C22⋊C4—1344no—
624C22⋊C4—1344no—
625C22⋊C4—1344no—
626C22⋊C4—1344no—
627C22⋊C4—1344no—
628C22⋊C4—1344no—
629C22⋊C4C2×D26814yes—
630C22⋊C4C2×D26814yes—
631C42—1344no—
632C42—1344no—
633C42—1344no—
634C42—1344no—
635C42C2×D26812yes—
636C42C23×D6712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—2682no—
644C23—2682no—
645C23—2682no—
646C23—1342no—
647C23C22×D26812yes—
648C23C22×D26812yes—
649C23C22×D26811yescharacteristic
650Q8—2688no—
651Q8—2682no—
652Q8—1342no—
653Q8—1342no—
654D4—44no—
655D4—2688no—
656D4—2682no—
657D4—5364no—
658D4—1342no—
659D4—1342no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—2682no—
671C2×C4—2682no—
672C2×C4—2682no—
673C2×C4—2682no—
674C2×C4—2682no—
675C2×C4—2682no—
676C2×C4—2682no—
677C2×C4—5364no—
678C2×C4—5364no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4—1342no—
685C2×C4—1342no—
686C2×C4C22×D26812yes—
687C2×C4C22×D26812yes—
688C2×C4C22×D26812yes—
689C2×C4C22×D26812yes—
690C2×C4C22×D26811yescharacteristic
691C2×C4C2×#1176162712yes—
692C2×C4#1452409012yes—
693C2×C4C24×D6711yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1176162714yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—2682no—
707C22—2682no—
708C22—2682no—
709C22—5364no—
710C22#1686405012yes—
711C22#1686419612yes—
712C22#1686420812yes—
713C22C23×D26811yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—2682no—
719C4—2682no—
720C4—2682no—
721C4—2682no—
722C4—2682no—
723C4—2682no—
724C4—2682no—
725C4#1686405012yes—
726C4C22×#1176162711yescharacteristic
727C4C2×#1452409011yescharacteristic
728C2—42no—
729C2—42no—
730C2—5362no—
731C2#2257275614yesdirect product factor
732C2C2×#1686405011yescharacteristic
733C2C2×#1686419611yescharacteristic
734C2C2×#1686420811yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864092C2
hypercenterC2×#435D67
hypocenterC67C2×#3350
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×#16864116C2semidirect
3. #22572756C2direct (N × H)
4. C2×#16863805C2semidirect
5. C2×#16863738C2semidirect
6. C2×#16863721C2semidirect
7. C2×#16863721C2semidirect
8. C2×#16863727C2semidirect
9. C2×#16863704C2semidirect
10. C2×#16863687C2semidirect
11. C2×#16863642C2semidirect
12. C2×#16863625C2semidirect
13. C2×#16863498C2semidirect
14. C2×#16863438C2semidirect
15. C2×#16863434C2semidirect
16. C2×#435×C67C2semidirect
19. #16864116C22semidirect
42. #16863805C22semidirect
43. #16863738C22semidirect
44. #16863727C22semidirect
45. #16863721C22semidirect
46. #16863721C22semidirect
47. #16863704C22semidirect
48. #16863687C22semidirect
49. #16863642C22semidirect
50. #16863625C22semidirect
51. #16863498C22semidirect
52. #16863438C22semidirect
53. #16863434C22semidirect
72. #435×C67C22semidirect
363. C2×C67#3350semidirect
381. C2×#435D67semidirect
384. C67C2×#3350semidirect
423. #435C2×D67semidirect
731. C2#22572756direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641162
C2×#168640922
#225727562
C2×#168638052
C2×#168637382
C2×#168637212
C2×#168637272
C2×#168637042
C2×#168636872
C2×#168636422
C2×#168636252
C2×#168634982
C2×#168634382
C2×#168634342
C2×#435×C672
C2×#335067