Finite Group Databasebeta

← #33102364

Subgroups — #33102364

Order 18688.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989294C211yesmaximal, characteristic
2#22612860C211yesmaximal, characteristic
3#22610904C211yesmaximal, characteristic, complemented
4#22610882C211yesmaximal, characteristic, complemented
5#22610364C211yesmaximal, characteristic, complemented
6#22610354C211yesmaximal, characteristic, complemented
7#22610241C211yesmaximal, characteristic, complemented
8#22610236C211yesmaximal, characteristic, complemented
9#22610022C211yesmaximal, characteristic, complemented
10#22610018C211yesmaximal, characteristic, complemented
11#22609947C211yesmaximal, characteristic, complemented
12#22609762C211yesmaximal, characteristic, complemented
13#22609651C211yesmaximal, characteristic, complemented
14C2×#17988350C211yesmaximal, characteristic, complemented
15C2×#435×C73C211yesmaximal, characteristic
16#17989294—24no—
17#17989294C418yescomplemented
18C2×#14556591C2211yescharacteristic
19C2×#14556582—21no—
20C2×#14556570C2211yescharacteristic
21C2×#14556570C2211yescharacteristic
22C2×#14556568—21no—
23C2×#14556568—21no—
24C2×C4×Dic146C2211yescharacteristic
25C2×D4×Dic73—21no—
26C2×#14556550C2211yescharacteristic
27C22×C4⋊Dic73C2211yescharacteristic
28C22×C4⋊Dic73C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30C2×#14556516C2211yescharacteristic
31C2×#14556516C2211yescharacteristic
32C2×#14556516C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34#17988480—21no—
35#17988473—21no—
36#17988467—21no—
37#17988453C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988447C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41C22⋊C4×Dic73—21no—
42#17988350C2211yescharacteristic
43#17988350C2211yescharacteristic
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988350C2211yescharacteristic
54C22×M16×C73C2211yescharacteristic
55C23×C8×C73C2211yescharacteristic
56C2×C4×D4×C73C2211yescharacteristic
57#435×C73—24no—
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×Dic146C2311yescharacteristic
64C23×Dic73—21no—
65C23×Dic73—21no—
66C23×Dic73—21no—
67#14556591—22no—
68#14556591C2×C414yescomplemented
69#14556582—28no—
70#14556570—22no—
71#14556570—22no—
72#14556570C2×C414yes—
73#14556570C2×C414yescomplemented
74#14556568—28no—
75#14556568—28no—
76C4×Dic146—22no—
77C4×Dic146C2×C414yescomplemented
78D4×Dic73—28no—
79#14556550—22no—
80#14556550—41no—
81C2×C4⋊Dic73—22no—
82C2×C4⋊Dic73—21no—
83C2×C4⋊Dic73—22no—
84C2×C4⋊Dic73—22no—
85C2×C4⋊Dic73—21no—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73—41no—
89C2×C4⋊Dic73C2×C414yes—
90C2×C4⋊Dic73C2×C414yescomplemented
91C2×C4⋊Dic73C2311yescharacteristic
92C2×C4⋊Dic73C2311yescharacteristic
93C2×C4⋊Dic73C2311yescharacteristic
94C2×C4⋊Dic73C2311yescharacteristic
95C2×C4⋊Dic73C2311yescharacteristic
96C2×C4⋊Dic73C2311yescharacteristic
97C2×C4⋊Dic73C2311yescharacteristic
98C2×#11924007—21no—
99C2×#11924007—21no—
100C2×#11924007—21no—
101C2×C22⋊Dic73—21no—
102C2×C22⋊Dic73—21no—
103C2×C22⋊Dic73—21no—
104C2×C22⋊Dic73—21no—
105C2×C22⋊Dic73—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73—21no—
108C2×C4×Dic73—21no—
109#14556516—22no—
110#14556516—22no—
111#14556516—41no—
112#14556516—41no—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118C22×D4×C73D411yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C2×M16×C73—22no—
122C2×M16×C73—22no—
123C2×M16×C73—41no—
124C22×C8×C73—22no—
125C22×C8×C73—22no—
126C22×C8×C73—41no—
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C4×D4×C73C2×C414yes—
132C4×D4×C73D414yes—
133C2×C4⋊C4×C73D411yescharacteristic
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C42×C73C2311yescharacteristic
137C4⋊C8×C73—22no—
138C22⋊C8×C73—22no—
139C22⋊C8×C73—22no—
140#97×C73—22no—
141C2×Dic146—21no—
142C2×Dic146—21no—
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—24no—
147C2×Dic146—81no—
148C2×Dic146—81no—
149C2×Dic146C22×C412yes—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—24no—
156C22×Dic73—24no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—42no—
161C22×Dic73—42no—
162C22×Dic73—81no—
163C22×Dic73—81no—
164C22×Dic73—81no—
165C22×Dic73—81no—
166C22×Dic73—81no—
167C4⋊Dic73—24no—
168C4⋊Dic73—24no—
169C4⋊Dic73—24no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—42no—
181C4⋊Dic73C22×C412yes—
182C4⋊Dic73C22×C412yes—
183C4⋊Dic73C22×C412yes—
184C4⋊Dic73#4112yes—
185#11924007—24no—
186#11924007—24no—
187#11924007—24no—
188C22⋊Dic73—24no—
189C22⋊Dic73—24no—
190C22⋊Dic73—42no—
191C22⋊Dic73—42no—
192C22⋊Dic73—81no—
193C4×Dic73—24no—
194C4×Dic73—42no—
195C4×Dic73—81no—
196C24×C73C2×D411yescharacteristic
197C24×C73C2×D411yescharacteristic
198C2×D4×C73—22no—
199C2×D4×C73—22no—
200C2×D4×C73C22⋊C414yes—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73C22×C412yes—
210C22×C4×C73C22×C412yes—
211C22×C4×C73C2×D412yes—
212C22×C4×C73C2×D412yes—
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2411yescharacteristic
218M16×C73—44no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—44no—
231C2×C8×C73#4112yes—
232C4⋊C4×C73C22⋊C414yes—
233C22⋊C4×C73C22⋊C414yes—
234C22⋊C4×C73C22⋊C414yes—
235C42×C73C22×C412yes—
236C42×C73C2×D412yes—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73C2×C22⋊C412yes—
248C23×C73C2×C22⋊C412yes—
249C23×C73#13712yes—
250C23×C73#13712yes—
251C23×C73C22×D411yescharacteristic
252D4×C73—28no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73C2×C22⋊C412yes—
270C2×C4×C73C2×C22⋊C412yes—
271C2×C4×C73C2×C22⋊C412yes—
272C2×C4×C73C2×C22⋊C412yes—
273C2×C4×C73C23×C411yescharacteristic
274C2×C4×C73C22×D411yescharacteristic
275C2×C4×C73C2×#4111yescharacteristic
276C2×C4×C73C2×#4111yescharacteristic
277C2×C4×C73H(5,𝔽2)11yescharacteristic
278C2×C4×C732−1+411yescharacteristic
279C2×Dic73—22no—
280C2×Dic73—22no—
281C2×Dic73—22no—
282C2×Dic73—22no—
283C2×Dic73—22no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286C2×Dic73—41no—
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—84no—
304C2×Dic73—84no—
305C2×Dic73—84no—
306Dic146—22no—
307Dic146—22no—
308Dic146—41no—
309Dic146—41no—
310Dic146—84no—
311C8×C73—22no—
312C8×C73—41no—
313C8×C73—41no—
314C8×C73—41no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73#41914yes—
329C22×C73C22×C22⋊C411yescharacteristic
330C22×C73#54611yescharacteristic
331C22×C73#54711yescharacteristic
332C22×C73C2×#13711yescharacteristic
333C22×C73C2×#13711yescharacteristic
334C22×C73#57611yescharacteristic
335C22×C73#57711yescharacteristic
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—22no—
339C4×C73—22no—
340C4×C73C4×#4111yescharacteristic
341C4×C73#52011yescharacteristic
342C4×C73#54611yescharacteristic
343C4×C73#54711yescharacteristic
344Dic73—42no—
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348Dic73—42no—
349Dic73—81no—
350Dic73—81no—
351Dic73—81no—
352#22497—731nomaximal, Sylow
353C2×C73—24no—
354C2×C73—42no—
355C2×C73#233911yescharacteristic
356C2×C73C2×#41911yescharacteristic
357C2×C73#289711yescharacteristic
358C2×C73#331411yescharacteristic
359C2×C73#331611yescharacteristic
360C2×C73#334411yescharacteristic
361C2×C73#334611yescharacteristic
362C2×#554—731no—
363C2×#435D7311yescharacteristic
364#2352—731no—
365#1993—731no—
366#1988—731no—
367#1894—731no—
368#1892—731no—
369#1873—731no—
370#1872—731no—
371#1824—731no—
372#1823—731no—
373#1805—731no—
374#1763—731no—
375#1736—731no—
376C2×#340—731no—
377C73#2249711yescharacteristic, complemented, Sylow
378C22×M16C2×D7311yescharacteristic
379C23×C8C2×D7311yescharacteristic
380#554—738no—
381#554—1464no—
382C2×C4⋊Q8—731no—
383C2×#125—1461no—
384C2×C22⋊Q8—731no—
385C2×C22⋊Q8—731no—
386C2×C22⋊Q8—1461no—
387C2×C22⋊Q8—1461no—
388C2×C4×Q8—731no—
389C2×C4×D4—1461no—
390C2×C4×D4C2×D7311yescharacteristic
391C2×#117—731no—
392C22×C4⋊C4—731no—
393C22×C4⋊C4—731no—
394C22×C4⋊C4—731no—
395#435—24no—
396C2×C4⋊C8C2×D7311yescharacteristic
397C2×#103—731no—
398C2×#103—731no—
399C2×#103—731no—
400C2×#103—731no—
401C2×C22⋊C8C2×D7311yescharacteristic
402C2×C22⋊C8C2×D7311yescharacteristic
403C2×#97C2×D7311yescharacteristic
404#388—1461no—
405#387—1461no—
406#386—1461no—
407#382—731no—
408#380—731no—
409#380—731no—
410C4×C4⋊C4—731no—
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—
420#340—731no—
421#340—731no—
422#340—731no—
423#340—731no—
424C22×Q8—731no—
425C22×Q8—1461no—
426C22×D4D29211yescharacteristic
427C23×C4—1461no—
428C23×C4—1461no—
429C23×C4—1461no—
430C23×C4C22×D7311yescharacteristic
431C23×C4C22×D7311yescharacteristic
432C2×M16—22no—
433C2×M16—22no—
434C2×M16—41no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8C22×D7311yescharacteristic
439C22×C8C22×D7311yescharacteristic
440C22×C8C22×D7311yescharacteristic
441C22×C8C22×D7311yescharacteristic
442C4⋊Q8—734no—
443C4⋊Q8—1462no—
444#125—1468no—
445C22⋊Q8—734no—
446C22⋊Q8—734no—
447C22⋊Q8—1462no—
448C22⋊Q8—1462no—
449C22⋊Q8—1468no—
450C22⋊Q8—1468no—
451C4×Q8—734no—
452C4×Q8—1462no—
453C4×D4—1468no—
454C4×D4C4×D7314yes—
455C4×D4C22⋊D7314yes—
456#117—2921no—
457#117—1462no—
458C2×C4⋊C4—2921no—
459C2×C4⋊C4—734no—
460C2×C4⋊C4—734no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—1461no—
469C2×C4⋊C4—1462no—
470C2×C4⋊C4—1462no—
471C2×C4⋊C4—1462no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4—1461no—
478C2×C4⋊C4D29211yescharacteristic
479C2×C22⋊C4—1461no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4D29211yescharacteristic
485C2×C22⋊C4D29211yescharacteristic
486C2×C42—1461no—
487C2×C42—1461no—
488C2×C42—1461no—
489C2×C42C22×D7311yescharacteristic
490C4⋊C8—22no—
491#103—2921no—
492#103—2921no—
493#103—1462no—
494#103—1462no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497#97—22no—
498#95—1461no—
499#95—1461no—
500#95—1461no—
501#95—1461no—
502#95—1461no—
503C24C2×D29211yescharacteristic
504C24C2×D29211yescharacteristic
505C2×Q8—5841no—
506C2×Q8—5841no—
507C2×Q8—732no—
508C2×Q8—1461no—
509C2×Q8—1461no—
510C2×Q8—1461no—
511C2×Q8—1461no—
512C2×Q8—1464no—
513C2×Q8—1461no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4#1192400514yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—2922no—
526C22×C4—2922no—
527C22×C4—5841no—
528C22×C4—5841no—
529C22×C4—5841no—
530C22×C4—5841no—
531C22×C4—5841no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4—1461no—
535C22×C4—1461no—
536C22×C4—1461no—
537C22×C4—1461no—
538C22×C4—1461no—
539C22×C4—1461no—
540C22×C4—1464no—
541C22×C4—1464no—
542C22×C4C2×C4×D7312yes—
543C22×C4C2×C4×D7312yes—
544C22×C4C2×C22⋊D7312yes—
545C22×C4C2×C22⋊D7312yes—
546C22×C4C2×D29211yescharacteristic
547C22×C4C2×D29211yescharacteristic
548C22×C4C2×D29211yescharacteristic
549C22×C4C2×D29211yescharacteristic
550C22×C4C23×D7311yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8#1192402712yes—
565C4⋊C4—2922no—
566C4⋊C4—732no—
567C4⋊C4—732no—
568C4⋊C4—732no—
569C4⋊C4—732no—
570C4⋊C4—1461no—
571C4⋊C4—1461no—
572C4⋊C4—1461no—
573C4⋊C4—1461no—
574C4⋊C4—1461no—
575C4⋊C4—1461no—
576C4⋊C4—1464no—
577C4⋊C4—1464no—
578C4⋊C4—1464no—
579C4⋊C4—1464no—
580C4⋊C4—1464no—
581C4⋊C4—1464no—
582C4⋊C4—1461no—
583C4⋊C4—1461no—
584C4⋊C4—1461no—
585C4⋊C4—1461no—
586C4⋊C4#1192400514yes—
587C22⋊C4—2922no—
588C22⋊C4—2922no—
589C22⋊C4—5841no—
590C22⋊C4—1464no—
591C22⋊C4—1464no—
592C22⋊C4#1192400514yes—
593C22⋊C4#1192400514yes—
594C42—2922no—
595C42—5841no—
596C42—1464no—
597C42C2×C4×D7312yes—
598C42C2×C22⋊D7312yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×#1192400512yes—
610C23C2×#1192400512yes—
611C23#1455662412yes—
612C23#1455662412yes—
613C23C22×D29211yescharacteristic
614Q8—2921no—
615Q8—2921no—
616Q8—5844no—
617Q8—1462no—
618Q8—1462no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
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—2921no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—5844no—
656C2×C4—5844no—
657C2×C4—5844no—
658C2×C4—1462no—
659C2×C4—1462no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4C2×#1192400512yes—
664C2×C4C2×#1192400512yes—
665C2×C4C2×#1192400512yes—
666C2×C4C2×#1192400512yes—
667C2×C4C22×C4×D7311yescharacteristic
668C2×C4C22×C22⋊D7311yescharacteristic
669C2×C4#41×D7311yescharacteristic
670C2×C4C2×#1192402711yescharacteristic
671C2×C4#1455663611yescharacteristic
672C2×C4#1455663811yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1798859714yes—
691C22C22×#1192400511yescharacteristic
692C22#1798923211yescharacteristic
693C22#1798924111yescharacteristic
694C22C2×#1455662411yescharacteristic
695C22C2×#1455662411yescharacteristic
696C22#1798939211yescharacteristic
697C22#1798939911yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—2922no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—2922no—
707C4—5841no—
708C4—5841no—
709C4—5841no—
710C4C4×#1192402711yescharacteristic
711C4#1798906611yescharacteristic
712C4#1798923111yescharacteristic
713C4#1798923611yescharacteristic
714C2—24no—
715C2—42no—
716C2#2261275611yescharacteristic
717C2C2×#1798859711yescharacteristic
718C2#2261845811yescharacteristic
719C2#2262201411yescharacteristic
720C2#2262204411yescharacteristic
721C2#2262238811yescharacteristic
722C2#2262241811yescharacteristic
subgroupG/H
centerC23C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#435×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
cosocleC22×C4×C73C24
hypercenterC2×#435D73
hypocenterC73#22497
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #22610904C2semidirect
4. #22610882C2semidirect
5. #22610364C2semidirect
6. #22610354C2semidirect
7. #22610241C2semidirect
8. #22610236C2semidirect
9. #22610022C2semidirect
10. #22610018C2semidirect
11. #22609947C2semidirect
12. #22609762C2semidirect
13. #22609651C2semidirect
14. C2×#17988350C2semidirect
17. #17989294C4semidirect
68. #14556591C2×C4semidirect
73. #14556570C2×C4semidirect
77. C4×Dic146C2×C4semidirect
90. C2×C4⋊Dic73C2×C4semidirect
377. C73#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#179892942
#226128602
#226109042
#226108822
#226103642
#226103542
#226102412
#226102362
#226100222
#226100182
#226099472
#226097622
#226096512
C2×#179883502
C2×#435×C732
#2249773