Finite Group Databasebeta

← C2×#22622293 #33964413

Subgroups — C2×#22622293 #33964413

Order 18688.

1866 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989277C211yesmaximal, characteristic
2#22622293C2116yesmaximal, direct product factor
3C2×#17988986C211yesmaximal, characteristic, complemented
4C2×#17988928C211yesmaximal, characteristic, complemented
5C2×#17988925C211yesmaximal, characteristic, complemented
6C2×#17988917C211yesmaximal, characteristic, complemented
7C2×#17988915C211yesmaximal, characteristic, complemented
8C2×#17988894C211yesmaximal, characteristic, complemented
9C2×#17988891C211yesmaximal, characteristic, complemented
10C2×#17988826C211yesmaximal, characteristic, complemented
11C2×#17988826C211yesmaximal, characteristic, complemented
12C2×C4×#11924018C211yesmaximal, characteristic, complemented
13C2×D4×#10596831C211yesmaximal, characteristic
14C2×#17988623C211yesmaximal, characteristic, complemented
15C22×#14556524C211yesmaximal, characteristic, complemented
16C2×#552×C73C211yesmaximal, characteristic
17C22×#11924018C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20#17989277—24no—
21#17989277C2218yes—
22C2×#14556584—21no—
23C2×#14556583C2211yescharacteristic
24C2×#14556581—21no—
25C2×#14556572—21no—
26C2×#14556570C2211yescharacteristic
27C2×#14556570C2211yescharacteristic
28C2×C4×Dic146C2211yescharacteristic
29C2×#14556550C2211yescharacteristic
30C2×#14556547—21no—
31C22×C4⋊Dic73C2211yescharacteristic
32#17988986C2218yescomplemented
33#17988928C2218yescomplemented
34#17988925C2218yescomplemented
35#17988917C2218yescomplemented
36#17988915C2218yescomplemented
37#17988894C2218yescomplemented
38#17988891C2218yescomplemented
39#17988826C2218yescomplemented
40#17988826C2218yescomplemented
41C4×#11924018C2218yescomplemented
42D4×#10596831C2218yes—
43#17988623C2218yescomplemented
44C2×#14556524C2211yescharacteristic
45C2×#14556524C2211yescharacteristic
46C2×#14556524C2211yescharacteristic
47C2×#14556524C2211yescharacteristic
48C2×#14556524C2211yescharacteristic
49C2×#14556524C2218yescomplemented
50C2×#14556522C2211yescharacteristic
51C2×#14556522C2211yescharacteristic
52C2×#14556522C2211yescharacteristic
53C2×#14556522C2211yescharacteristic
54C2×C4⋊#10596831C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556515C2211yescharacteristic
58C2×#14556514C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×C22⋊#10596831C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#552×C73—24no—
65#552×C73C2218yes—
66C2×#126×C73—21no—
67C2×#125×C73—21no—
68C2×#125×C73C2211yescharacteristic
69C2×#123×C73—21no—
70C2×C22⋊Q8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×D4×C73C2211yescharacteristic
74C2×#117×C73—21no—
75C2×#117×C73C2211yescharacteristic
76C22×C4⋊C4×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C23×Dic73—21no—
79C2×#11924018—24no—
80C2×#11924018C2314yes—
81C22×#10596831—24no—
82C22×#10596831—24no—
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2314yes—
87C22×#10596831C2314yes—
88C22×#10596831C2311yescharacteristic
89#14556584—28no—
90#14556583—22no—
91#14556583C2314yes—
92#14556581—28no—
93#14556572—28no—
94#14556570—22no—
95#14556570—22no—
96#14556570C2314yes—
97#14556570C2314yes—
98C4×Dic146—22no—
99C4×Dic146C2314yes—
100#14556550—22no—
101#14556550C2314yes—
102#14556547—28no—
103C2×C4⋊Dic73—22no—
104C2×C4⋊Dic73—21no—
105C2×C4⋊Dic73C2311yescharacteristic
106C2×C4⋊Dic73C2311yescharacteristic
107C2×C4⋊Dic73C2311yescharacteristic
108C2×C4⋊Dic73C2314yes—
109C2×#11924007—21no—
110C2×#11924007—21no—
111C2×#11924007—21no—
112C2×#11924007—21no—
113C2×#11924007—21no—
114C2×C22⋊Dic73—21no—
115C2×C22⋊Dic73—21no—
116C2×C22⋊Dic73—21no—
117C2×C4×Dic73—21no—
118C2×C4×Dic73—21no—
119#14556524C2314yes—
120#14556524C2314yes—
121#14556524C2314yes—
122#14556524C2314yes—
123#14556524C2314yes—
124#14556522C2314yes—
125#14556522C2314yes—
126#14556522C2314yes—
127#14556522C2314yes—
128C4⋊#10596831C2314yes—
129#14556515C2314yes—
130#14556515C2314yes—
131#14556515C2314yes—
132#14556514C2314yes—
133#14556514C2314yes—
134#14556514C2314yes—
135C22⋊#10596831C2314yes—
136C22⋊#10596831C2314yes—
137C4×#10596831C2314yes—
138C22×Q8×C73C2311yescharacteristic
139C22×D4×C73D411yescharacteristic
140C23×C4×C73—21no—
141C23×C4×C73C2311yescharacteristic
142C23×C4×C73C2311yescharacteristic
143#126×C73—28no—
144#125×C73—28no—
145#125×C73—22no—
146#125×C73C2314yes—
147#123×C73—28no—
148C22⋊Q8×C73—22no—
149C22⋊Q8×C73—22no—
150C22⋊Q8×C73C2314yes—
151C22⋊Q8×C73C2314yes—
152C4×Q8×C73—22no—
153C4×Q8×C73C2314yes—
154C4×D4×C73D414yes—
155C4×D4×C73C2314yes—
156#117×C73—22no—
157#117×C73—28no—
158#117×C73C2314yes—
159C2×C4⋊C4×C73—21no—
160C2×C4⋊C4×C73—22no—
161C2×C4⋊C4×C73—21no—
162C2×C4⋊C4×C73—21no—
163C2×C4⋊C4×C73—21no—
164C2×C4⋊C4×C73—21no—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73D411yescharacteristic
167C2×C4⋊C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2314yes—
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C22⋊C4×C73D411yescharacteristic
175C2×C22⋊C4×C73D411yescharacteristic
176C2×C42×C73—21no—
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179C2×Dic146—22no—
180C2×Dic146—22no—
181C2×Dic146—21no—
182C2×Dic146C2412yes—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—24no—
188C22×Dic73—44no—
189#11924018—28no—
190C2×#10596831—22no—
191C2×#10596831—22no—
192C2×#10596831—22no—
193C2×#10596831—28no—
194C2×#10596831—28no—
195C2×#10596831#4114yes—
196C2×#10596831C2412yes—
197C2×#10596831C2412yes—
198C2×#10596831C2412yes—
199C2×#10596831C2412yes—
200C4⋊Dic73—21no—
201C4⋊Dic73—21no—
202C4⋊Dic73—24no—
203C4⋊Dic73—21no—
204C4⋊Dic73C2412yes—
205C4⋊Dic73C2412yes—
206C4⋊Dic73C2412yes—
207#11924007—24no—
208#11924007—24no—
209#11924007—24no—
210#11924007—24no—
211#11924007—24no—
212C22⋊Dic73—24no—
213C22⋊Dic73—24no—
214C22⋊Dic73—24no—
215C4×Dic73—24no—
216C4×Dic73—24no—
217C24×C73C2×D411yescharacteristic
218C24×C73C2×D411yescharacteristic
219C2×Q8×C73—21no—
220C2×Q8×C73—22no—
221C2×Q8×C73—22no—
222C2×Q8×C73C2412yes—
223C2×D4×C73—24no—
224C2×D4×C73C2×D414yes—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—24no—
234C22×C4×C73—44no—
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2×D411yescharacteristic
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×D412yes—
240C22×C4×C73C2×D412yes—
241C22×C4×C73C2412yes—
242C22×C4×C73C2412yes—
243C22×C4×C73C2411yescharacteristic
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—24no—
247C4⋊C4×C73—24no—
248C4⋊C4×C73—24no—
249C4⋊C4×C73—24no—
250C4⋊C4×C73—24no—
251C4⋊C4×C73—24no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73C2×D414yes—
254C4⋊C4×C73C2412yes—
255C4⋊C4×C73C2412yes—
256C4⋊C4×C73C2412yes—
257C22⋊C4×C73—24no—
258C22⋊C4×C73—24no—
259C22⋊C4×C73—24no—
260C22⋊C4×C73C2×D414yes—
261C22⋊C4×C73C2×D414yes—
262C42×C73—24no—
263C42×C73—24no—
264C42×C73C2×D412yes—
265C42×C73C2412yes—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73#13514yes—
272C23×C73C22×D412yes—
273C23×C73C22×D412yes—
274C23×C73C22×D411yescharacteristic
275Q8×C73—22no—
276Q8×C73—22no—
277Q8×C73—42no—
278D4×C73—28no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—24no—
284C2×C4×C73—24no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—42no—
294C2×C4×C73—48no—
295C2×C4×C73—42no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73C22×D412yes—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D412yes—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4112yes—
304C2×C4×C732−1+412yes—
305C2×C4×C73C2511yescharacteristic
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—42no—
311C2×Dic73—48no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315Dic146—22no—
316Dic146—22no—
317Dic146—42no—
318#10596831—22no—
319#10596831—22no—
320#10596831—22no—
321#10596831C2×#4114yes—
322C22×C73—28no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—44no—
329C22×C73#54712yes—
330C22×C73C2×#13514yes—
331C22×C73C2×#13512yes—
332C22×C73#57812yes—
333C22×C73C23×D411yescharacteristic
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73#54712yes—
343C4×C73C22×#4111yescharacteristic
344C4×C73C2×2−1+411yescharacteristic
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348Dic73—42no—
349C2×#3336—731nomaximal, Sylow
350C2×C73—24no—
351C2×C73—42no—
352C2×C73#333614yescomplemented
353C2×C73C2×#54711yescharacteristic
354C2×C73C22×#13511yescharacteristic
355C2×C73C2×#57811yescharacteristic
356C2×#552—731no—
357C2×#552D7311yescharacteristic
358#3336—7316no—
359C2×#499—731no—
360C2×#485—731no—
361C2×#485—731no—
362C2×#483—731no—
363C2×#483—731no—
364C2×#479—731no—
365C2×#479—731no—
366C2×#467—731no—
367C2×#467—731no—
368C2×C4×Q16—731no—
369C2×C8×D4—731no—
370C2×#427—731no—
371C22×#107—731no—
372C73C2×#333611yescharacteristic, complemented, Sylow
373C22×Q16—731no—
374C23×C8—731no—
375C23×C8—731no—
376#552—24no—
377#552—738no—
378#552—1464no—
379#552C2×D7318yes—
380C2×#126—21no—
381C2×#126—1461no—
382C2×#125—21no—
383C2×#125—731no—
384C2×#125—1461no—
385C2×#125C2×D7311yescharacteristic
386C2×#123—21no—
387C2×#123—1461no—
388C2×C22⋊Q8—731no—
389C2×C22⋊Q8—731no—
390C2×C22⋊Q8C2×D7311yescharacteristic
391C2×C22⋊Q8C2×D7311yescharacteristic
392C2×C4×Q8—731no—
393C2×C4×Q8C2×D7311yescharacteristic
394C2×C4×D4C2×D7311yescharacteristic
395C2×#117—21no—
396C2×#117—731no—
397C2×#117—1461no—
398C2×#117C2×D7311yescharacteristic
399C22×C4⋊C4—731no—
400C22×C4⋊C4C2×D7311yescharacteristic
401#499—738no—
402#485—738no—
403#485—738no—
404#483—738no—
405#483—738no—
406#479—738no—
407#479—738no—
408#467—738no—
409#467—738no—
410C4×Q16—738no—
411C8×D4—738no—
412#427—738no—
413C2×#107—731no—
414C2×#107—731no—
415C2×#107—738no—
416C2×#107—731no—
417C2×#107—731no—
418C2×#107—731no—
419C2×#106—731no—
420C2×#106—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×C4⋊C8—731no—
424C2×#103—731no—
425C2×#103—731no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×C22⋊C8—731no—
431C2×C22⋊C8—731no—
432C2×C4×C8—731no—
433C22×Q8—731no—
434C22×Q8C22×D7311yescharacteristic
435C22×D4C22⋊D7311yescharacteristic
436C23×C4—21no—
437C23×C4—1461no—
438C23×C4C22×D7311yescharacteristic
439C23×C4C22×D7311yescharacteristic
440C2×Q16—734no—
441C2×Q16—1464no—
442C22×C8—731no—
443C22×C8—731no—
444C22×C8—731no—
445C22×C8—734no—
446C22×C8—734no—
447C22×C8—731no—
448C22×C8—1464no—
449C22×C8—1464no—
450#126—28no—
451#126—1468no—
452#125—28no—
453#125—22no—
454#125—734no—
455#125—1468no—
456#125—1462no—
457#125C22×D7314yes—
458#123—28no—
459#123—1468no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—734no—
463C22⋊Q8—734no—
464C22⋊Q8—1462no—
465C22⋊Q8—1462no—
466C22⋊Q8C22×D7314yes—
467C22⋊Q8C22×D7314yes—
468C4×Q8—22no—
469C4×Q8—734no—
470C4×Q8—1462no—
471C4×Q8C22×D7314yes—
472C4×D4C22⋊D7314yes—
473C4×D4C22×D7314yes—
474#117—22no—
475#117—28no—
476#117—734no—
477#117—1462no—
478#117—1468no—
479#117C22×D7314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—731no—
488C2×C4⋊C4—731no—
489C2×C4⋊C4—734no—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—1461no—
492C2×C4⋊C4—1462no—
493C2×C4⋊C4—1461no—
494C2×C4⋊C4—1461no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4C22⋊D7311yescharacteristic
499C2×C4⋊C4C22×D7311yescharacteristic
500C2×C4⋊C4C22×D7311yescharacteristic
501C2×C4⋊C4C22×D7314yes—
502C2×C4⋊C4C22×D7311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1461no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4C22⋊D7311yescharacteristic
510C2×C22⋊C4C22⋊D7311yescharacteristic
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—1461no—
514C2×C42—1461no—
515C2×C42C22×D7311yescharacteristic
516#107—734no—
517#107—734no—
518#107—734no—
519#107—734no—
520#107—734no—
521#106—734no—
522#106—734no—
523#106—734no—
524#106—734no—
525C4⋊C8—734no—
526#103—734no—
527#103—734no—
528#103—734no—
529#103—734no—
530#103—734no—
531#103—734no—
532C22⋊C8—734no—
533C22⋊C8—734no—
534C4×C8—734no—
535C24C2×C22⋊D7311yescharacteristic
536C24C2×C22⋊D7311yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—732no—
541C2×Q8—1462no—
542C2×Q8—1462no—
543C2×Q8—1461no—
544C2×Q8C23×D7312yes—
545C2×D4—24no—
546C2×D4C2×C22⋊D7314yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—44no—
557C22×C4—2924no—
558C22×C4—1464no—
559C22×C4—1461no—
560C22×C4—1461no—
561C22×C4—1461no—
562C22×C4—1461no—
563C22×C4C2×C22⋊D7312yes—
564C22×C4C2×C22⋊D7312yes—
565C22×C4C2×C22⋊D7311yescharacteristic
566C22×C4C2×C22⋊D7311yescharacteristic
567C22×C4C2×C22⋊D7311yescharacteristic
568C22×C4C2×C22⋊D7311yescharacteristic
569C22×C4C23×D7312yes—
570C22×C4C23×D7312yes—
571C22×C4C23×D7311yescharacteristic
572Q16—1468no—
573C2×C8—734no—
574C2×C8—732no—
575C2×C8—732no—
576C2×C8—732no—
577C2×C8—732no—
578C2×C8—1468no—
579C2×C8—1468no—
580C2×C8—1462no—
581C2×C8—1462no—
582C2×C8—1462no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—732no—
593C4⋊C4—732no—
594C4⋊C4—732no—
595C4⋊C4—1464no—
596C4⋊C4—1464no—
597C4⋊C4—1464no—
598C4⋊C4—1464no—
599C4⋊C4—1464no—
600C4⋊C4—1461no—
601C4⋊C4—1461no—
602C4⋊C4—1464no—
603C4⋊C4—1461no—
604C4⋊C4C2×C22⋊D7314yes—
605C4⋊C4C23×D7312yes—
606C4⋊C4C23×D7312yes—
607C4⋊C4C23×D7312yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—1464no—
612C22⋊C4—1464no—
613C22⋊C4—1464no—
614C22⋊C4C2×C22⋊D7314yes—
615C22⋊C4C2×C22⋊D7314yes—
616C42—24no—
617C42—24no—
618C42—1464no—
619C42—1464no—
620C42C2×C22⋊D7312yes—
621C42C23×D7312yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23#1455661114yes—
628C23C22×C22⋊D7312yes—
629C23C22×C22⋊D7312yes—
630C23C22×C22⋊D7311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—2922no—
635Q8—1462no—
636Q8—1462no—
637D4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—48no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—2922no—
658C2×C4—2922no—
659C2×C4—2928no—
660C2×C4—2922no—
661C2×C4—2922no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4C22×C22⋊D7312yes—
667C2×C4C22×C22⋊D7312yes—
668C2×C4C22×C22⋊D7312yes—
669C2×C4C22×C22⋊D7312yes—
670C2×C4C22×C22⋊D7311yescharacteristic
671C2×C4#41×D7312yes—
672C2×C4#1455663812yes—
673C2×C4C24×D7311yescharacteristic
674C8—734no—
675C8—1462no—
676C8—1462no—
677C8—1462no—
678C22—28no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22#1798923612yes—
686C22C2×#1455661114yes—
687C22C2×#1455661112yes—
688C22#1798940212yes—
689C22C23×C22⋊D7311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2922no—
699C4—2922no—
700C4—2922no—
701C4—2922no—
702C4#1798923612yes—
703C4C2×#41×D7311yescharacteristic
704C4C2×#1455663811yescharacteristic
705C2—24no—
706C2—42no—
707C2#2262229314yesdirect product factor
708C2C2×#1798923611yescharacteristic
709C2C22×#1455661111yescharacteristic
710C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#552×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
hypercenterC2×#552D73
hypocenterC73C2×#3336
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #22622293C2direct (N × H)
3. C2×#17988986C2semidirect
4. C2×#17988928C2semidirect
5. C2×#17988925C2semidirect
6. C2×#17988917C2semidirect
7. C2×#17988915C2semidirect
8. C2×#17988894C2semidirect
9. C2×#17988891C2semidirect
10. C2×#17988826C2semidirect
11. C2×#17988826C2semidirect
12. C2×C4×#11924018C2semidirect
14. C2×#17988623C2semidirect
15. C22×#14556524C2semidirect
32. #17988986C22semidirect
33. #17988928C22semidirect
34. #17988925C22semidirect
35. #17988917C22semidirect
36. #17988915C22semidirect
37. #17988894C22semidirect
38. #17988891C22semidirect
39. #17988826C22semidirect
40. #17988826C22semidirect
41. C4×#11924018C22semidirect
43. #17988623C22semidirect
49. C2×#14556524C22semidirect
352. C2×C73#3336semidirect
372. C73C2×#3336semidirect
707. C2#22622293direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892772
#226222932
C2×#179889862
C2×#179889282
C2×#179889252
C2×#179889172
C2×#179889152
C2×#179888942
C2×#179888912
C2×#179888262
C2×C4×#119240182
C2×D4×#105968312
C2×#179886232
C22×#145565242
C2×#552×C732
C2×#333673