Finite Group Databasebeta

← #33091132

Subgroups — #33091132

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988648C211yesmaximal, characteristic, complemented
2#22612287C211yesmaximal, characteristic, complemented
3#22610884C211yesmaximal, characteristic, complemented
4#22610880C211yesmaximal, characteristic, complemented
5#22610864C211yesmaximal, characteristic, complemented
6#22610864C211yesmaximal, characteristic, complemented
7#22610254C211yesmaximal, characteristic
8#22610249C211yesmaximal, characteristic
9#22610244C211yesmaximal, characteristic, complemented
10#22610239C211yesmaximal, characteristic, complemented
11#22609761C211yesmaximal, characteristic, complemented
12#22609756C211yesmaximal, characteristic, complemented
13C4×#14556515C211yesmaximal, characteristic, complemented
14C4×#14556512C211yesmaximal, characteristic, complemented
15C2×#542×C73C211yesmaximal, characteristic
16C2×#14556550C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18#17988648—24no—
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×#14556515C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556515C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556512C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×#14556502C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C4⋊C4×Dic73—21no—
34C4⋊C4×Dic73—21no—
35C4×C4⋊Dic73C2211yescharacteristic
36C4×C4⋊Dic73C2211yescharacteristic
37C4×C4⋊Dic73C2211yescharacteristic
38C4×C4⋊Dic73C2211yescharacteristic
39C22⋊C4×Dic73—21no—
40C22⋊C4×Dic73—21no—
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#542×C73—24no—
50#542×C73C418yescomplemented
51C2×C4⋊Q8×C73C2211yescharacteristic
52C2×#126×C73—21no—
53C2×#124×C73—21no—
54C2×#124×C73C2211yescharacteristic
55C2×#123×C73—21no—
56C2×C22⋊Q8×C73—21no—
57C2×C22⋊Q8×C73C2211yescharacteristic
58C2×#121×C73C2211yescharacteristic
59C2×C4×Q8×C73C2211yescharacteristic
60C2×C4×D4×C73C2211yescharacteristic
61C2×#117×C73C2211yescharacteristic
62C23×Dic73—21no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67#14556550—22no—
68#14556550—22no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C22⋊Dic73—21no—
77C2×C4×Dic73—21no—
78C2×C4×Dic73—21no—
79C2×C4×Dic73—21no—
80C2×C4×Dic73—21no—
81C2×C4×Dic73—21no—
82C4⋊#10596831—22no—
83C4⋊#10596831—22no—
84#14556515—22no—
85#14556515—22no—
86#14556515—22no—
87#14556515—22no—
88#14556512—22no—
89#14556512—22no—
90#14556512—22no—
91#14556512—22no—
92C22⋊#10596831—22no—
93C22⋊#10596831—22no—
94#14556502—22no—
95C4×#10596831—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100C22×Q8×C73—21no—
101C22×Q8×C73C2311yescharacteristic
102C22×D4×C73—21no—
103C22×D4×C73C2311yescharacteristic
104C23×C4×C73—21no—
105C23×C4×C73C2311yescharacteristic
106C4⋊Q8×C73—22no—
107C4⋊Q8×C73C2×C414yescomplemented
108#126×C73—28no—
109#124×C73—28no—
110#124×C73—22no—
111#124×C73C2×C414yescomplemented
112#123×C73—28no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—28no—
115C22⋊Q8×C73C2×C414yes—
116#121×C73—22no—
117#121×C73C2×C414yes—
118C4×Q8×C73—22no—
119C4×Q8×C73C2×C414yescomplemented
120C4×D4×C73—22no—
121C4×D4×C73C2×C414yescomplemented
122#117×C73C2×C414yes—
123#117×C73D414yes—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73D411yescharacteristic
128C2×C4⋊C4×C73D411yescharacteristic
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73D411yescharacteristic
137C2×C22⋊C4×C73D411yescharacteristic
138C2×C42×C73—21no—
139C2×C42×C73C2311yescharacteristic
140C2×C42×C73C2311yescharacteristic
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—24no—
146C22×Dic73—81no—
147C22×Dic73—81no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C4⋊Dic73—24no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73#4112yes—
166C4⋊Dic73#4112yes—
167C4⋊Dic73#4112yes—
168C4⋊Dic73#4112yes—
169C22⋊Dic73—24no—
170C4×Dic73—24no—
171C4×Dic73—81no—
172C4×Dic73—81no—
173C4×Dic73—81no—
174C4×Dic73—81no—
175C24×C73—21no—
176C24×C73C2×D411yescharacteristic
177C2×Q8×C73—24no—
178C2×Q8×C73—21no—
179C2×Q8×C73—21no—
180C2×Q8×C73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—81no—
184C2×Q8×C73—81no—
185C2×Q8×C73C22×C412yes—
186C2×D4×C73—24no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73C22×C412yes—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—24no—
203C22×C4×C73—81no—
204C22×C4×C73—81no—
205C22×C4×C73C22×C412yes—
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D412yes—
212C22×C4×C73C2411yescharacteristic
213C4⋊C4×C73—24no—
214C4⋊C4×C73—24no—
215C4⋊C4×C73—24no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73C22⋊C414yes—
219C4⋊C4×C73C22⋊C414yes—
220C4⋊C4×C73C22×C412yes—
221C4⋊C4×C73C22×C412yes—
222C22⋊C4×C73—24no—
223C22⋊C4×C73—24no—
224C22⋊C4×C73—24no—
225C22⋊C4×C73—24no—
226C22⋊C4×C73—24no—
227C22⋊C4×C73C22⋊C414yes—
228C22⋊C4×C73C22⋊C414yes—
229C42×C73—24no—
230C42×C73C22×C412yes—
231C42×C73C22×C412yes—
232C42×C73C2×D412yes—
233C42×C73C2×D412yes—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—22no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73C2×C22⋊C412yes—
248C23×C73C22×D411yescharacteristic
249Q8×C73—22no—
250Q8×C73—22no—
251Q8×C73—41no—
252Q8×C73—41no—
253Q8×C73—84no—
254D4×C73—22no—
255D4×C73—22no—
256D4×C73—41no—
257D4×C73—41no—
258D4×C73—84no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—84no—
283C2×C4×C73C2×C22⋊C412yes—
284C2×C4×C73C2×C22⋊C412yes—
285C2×C4×C73C2×C22⋊C412yes—
286C2×C4×C73C2×C22⋊C412yes—
287C2×C4×C73C2×C22⋊C412yes—
288C2×C4×C73C23×C411yescharacteristic
289C2×C4×C73C22×D411yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—84no—
307#10596831—41no—
308#10596831—41no—
309#10596831—41no—
310#10596831—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—42no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73C22×C22⋊C411yescharacteristic
326C22×C73#52511yescharacteristic
327C22×C73#52511yescharacteristic
328C22×C73#57611yescharacteristic
329C22×C73#57711yescharacteristic
330C22×C73#57711yescharacteristic
331C22×C73#57811yescharacteristic
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73C4×#4111yescharacteristic
341C4×C73C4×#4111yescharacteristic
342C4×C73#53211yescharacteristic
343C4×C73#53211yescharacteristic
344Dic73—42no—
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348#21397—731nomaximal, Sylow
349C2×C73—42no—
350C2×C73—82no—
351C2×C73#229711yescharacteristic
352C2×C73#289711yescharacteristic
353C2×C73#289811yescharacteristic
354C2×C73#311811yescharacteristic
355C2×C73#312111yescharacteristic
356C2×C73#312411yescharacteristic
357C2×C73#312511yescharacteristic
358C2×#542D7311yescharacteristic
359C2×#433—731no—
360#2274—731no—
361#1988—731no—
362#1987—731no—
363#1983—731no—
364#1983—731no—
365#1875—731no—
366#1874—731no—
367#1873—731no—
368#1872—731no—
369#1763—731no—
370#1762—731no—
371C4×#103—731no—
372C4×#102—731no—
373C73#2139711yescharacteristic, complemented, Sylow
374#542—24no—
375#542Dic7318yescomplemented
376C2×C4⋊Q8C2×D7311yescharacteristic
377C2×#126—21no—
378C2×#124—21no—
379C2×#124C2×D7311yescharacteristic
380C2×#123—21no—
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8C2×D7311yescharacteristic
383C2×#121C2×D7311yescharacteristic
384C2×C4×Q8C2×D7311yescharacteristic
385C2×C4×D4C2×D7311yescharacteristic
386C2×#117—731no—
387C2×#117C2×D7311yescharacteristic
388C22×C4⋊C4—731no—
389#433—1464no—
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×#103—731no—
393C2×#103—731no—
394C2×#103—731no—
395C2×#103—731no—
396C2×#102—731no—
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×#97—731no—
403C2×C4×C8—731no—
404C4×C4⋊C4—731no—
405C4×C4⋊C4—731no—
406C4×C4⋊C4—731no—
407C4×C4⋊C4—731no—
408C4×C4⋊C4—1461no—
409C4×C4⋊C4—1461no—
410C4×C22⋊C4—1461no—
411C4×C22⋊C4—1461no—
412#340—731no—
413#340—731no—
414#340—731no—
415#340—731no—
416#340—731no—
417#340—731no—
418#340—731no—
419#340—731no—
420C22×Q8—21no—
421C22×Q8C22×D7311yescharacteristic
422C22×D4—21no—
423C22×D4C22×D7311yescharacteristic
424C23×C4—21no—
425C23×C4—1461no—
426C23×C4C22×D7311yescharacteristic
427C22×C8—731no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—731no—
431C4⋊Q8—22no—
432C4⋊Q8C2×Dic7314yescomplemented
433#126—28no—
434#124—28no—
435#124—22no—
436#124C2×Dic7314yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440C22⋊Q8C2×Dic7314yes—
441#121—22no—
442#121C2×Dic7314yes—
443C4×Q8—22no—
444C4×Q8C2×Dic7314yescomplemented
445C4×D4—22no—
446C4×D4C2×Dic7314yescomplemented
447#117—1462no—
448#117—1462no—
449#117C2×Dic7314yes—
450#117C22⋊D7314yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—731no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4—1462no—
459C2×C4⋊C4—1462no—
460C2×C4⋊C4—1461no—
461C2×C4⋊C4C22⋊D7311yescharacteristic
462C2×C4⋊C4C22⋊D7311yescharacteristic
463C2×C4⋊C4C22×D7311yescharacteristic
464C2×C4⋊C4C22×D7311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4C22⋊D7311yescharacteristic
472C2×C22⋊C4C22⋊D7311yescharacteristic
473C2×C42—21no—
474C2×C42—1461no—
475C2×C42—1461no—
476C2×C42—1461no—
477C2×C42—1461no—
478C2×C42—1461no—
479C2×C42C22×D7311yescharacteristic
480C2×C42C22×D7311yescharacteristic
481C4⋊C8—1462no—
482C4⋊C8—1462no—
483#103—1462no—
484#103—1462no—
485#103—1462no—
486#103—1462no—
487#102—1462no—
488#102—1462no—
489#102—1462no—
490#102—1462no—
491C22⋊C8—1462no—
492C22⋊C8—1462no—
493#97—1462no—
494C4×C8—1462no—
495#95—1461no—
496#95—1461no—
497#95—1461no—
498#95—1461no—
499C24—21no—
500C24C2×C22⋊D7311yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×Dic7312yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×Dic7312yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—5841no—
530C22×C4—5841no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4—1461no—
535C22×C4—1464no—
536C22×C4C22×Dic7312yes—
537C22×C4C2×C22⋊D7311yescharacteristic
538C22×C4C2×C22⋊D7311yescharacteristic
539C22×C4C2×C22⋊D7311yescharacteristic
540C22×C4C2×C22⋊D7311yescharacteristic
541C22×C4C2×C22⋊D7311yescharacteristic
542C22×C4C2×C22⋊D7312yes—
543C22×C4C23×D7311yescharacteristic
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—732no—
562C4⋊C4—732no—
563C4⋊C4—732no—
564C4⋊C4—732no—
565C4⋊C4—1464no—
566C4⋊C4—1461no—
567C4⋊C4—1461no—
568C4⋊C4—1461no—
569C4⋊C4—1461no—
570C4⋊C4C22⋊Dic7314yes—
571C4⋊C4C22⋊Dic7314yes—
572C4⋊C4C22×Dic7312yes—
573C4⋊C4C22×Dic7312yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—1464no—
580C22⋊C4C22⋊Dic7314yes—
581C22⋊C4C22⋊Dic7314yes—
582C42—24no—
583C42—5841no—
584C42—5841no—
585C42—5841no—
586C42—5841no—
587C42—1464no—
588C42C22×Dic7312yes—
589C42C22×Dic7312yes—
590C42C2×C22⋊D7312yes—
591C42C2×C22⋊D7312yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊Dic7312yes—
606C23C22×C22⋊D7311yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—2921no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—2921no—
646C2×C4—2921no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—5844no—
650C2×C4—1462no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4C2×C22⋊Dic7312yes—
655C2×C4C2×C22⋊Dic7312yes—
656C2×C4C2×C22⋊Dic7312yes—
657C2×C4C2×C22⋊Dic7312yes—
658C2×C4C2×C22⋊Dic7312yes—
659C2×C4C23×Dic7311yescharacteristic
660C2×C4C22×C22⋊D7311yescharacteristic
661C2×C4#41×D7311yescharacteristic
662C2×C4#41×D7311yescharacteristic
663C2×C4#41×D7311yescharacteristic
664C2×C4#41×D7311yescharacteristic
665C8—2921no—
666C8—2921no—
667C8—2921no—
668C8—2921no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic7311yescharacteristic
684C22#1798909411yescharacteristic
685C22#1798909411yescharacteristic
686C22#1798939011yescharacteristic
687C22#1798939511yescharacteristic
688C22#1798939811yescharacteristic
689C22#1798940211yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2922no—
699C4—2922no—
700C4—2922no—
701C4—2922no—
702C4#41×Dic7311yescharacteristic
703C4#41×Dic7311yescharacteristic
704C4#1798913311yescharacteristic
705C4#1798913311yescharacteristic
706C2—42no—
707C2—82no—
708C2#2261242211yescharacteristic
709C2#2261845711yescharacteristic
710C2#2261846411yescharacteristic
711C2#2262010911yescharacteristic
712C2#2262015411yescharacteristic
713C2#2262018711yescharacteristic
714C2#2262020211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#542×C73C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#542D73
hypocenterC73#21397
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17988648C2semidirect
2. #22612287C2semidirect
3. #22610884C2semidirect
4. #22610880C2semidirect
5. #22610864C2semidirect
6. #22610864C2semidirect
9. #22610244C2semidirect
10. #22610239C2semidirect
11. #22609761C2semidirect
12. #22609756C2semidirect
13. C4×#14556515C2semidirect
14. C4×#14556512C2semidirect
50. #542×C73C4semidirect
107. C4⋊Q8×C73C2×C4semidirect
111. #124×C73C2×C4semidirect
119. C4×Q8×C73C2×C4semidirect
121. C4×D4×C73C2×C4semidirect
373. C73#21397semidirect
375. #542Dic73semidirect
432. C4⋊Q8C2×Dic73semidirect
436. #124C2×Dic73semidirect
444. C4×Q8C2×Dic73semidirect
446. C4×D4C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886482
#226122872
#226108842
#226108802
#226108642
#226102542
#226102492
#226102442
#226102392
#226097612
#226097562
C4×#145565152
C4×#145565122
C2×#542×C732
#2139773