Finite Group Databasebeta

← #33106432

Subgroups — #33106432

Order 18688.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988749C211yesmaximal, characteristic
2C2×#17988692C211yesmaximal, characteristic, complemented
3C2×#17988588C211yesmaximal, characteristic
4#22612934C211yesmaximal, characteristic, complemented
5#22610784C211yesmaximal, characteristic, complemented
6#22610631C211yesmaximal, characteristic, complemented
7#22610555C211yesmaximal, characteristic, complemented
8#22610362C211yesmaximal, characteristic, complemented
9#22610289C211yesmaximal, characteristic, complemented
10#22610272C211yesmaximal, characteristic, complemented
11#22610199C211yesmaximal, characteristic, complemented
12#22610123C211yesmaximal, characteristic, complemented
13C4×#14556515C211yesmaximal, characteristic, complemented
14#22609715C211yesmaximal, characteristic, complemented
15C73×#2341C211yesmaximal, characteristic
16C22×#11924018C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C2×#14556570C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22#17988749C418yescomplemented
23#17988692—24no—
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26#17988588—24no—
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×#14556514C2211yescharacteristic
31C2×#14556514C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988493C2211yescharacteristic
39#17988485C2211yescharacteristic
40#17988484—21no—
41#17988474—21no—
42#17988459—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44C22⋊C4×Dic73—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C22×#41×C73C2211yescharacteristic
52C2×C4×Q8×C73C2211yescharacteristic
53C2×C4×Q8×C73C2211yescharacteristic
54#390×C73—21no—
55#390×C73—21no—
56#390×C73C2211yescharacteristic
57#390×C73C2211yescharacteristic
58#380×C73—21no—
59#380×C73C2211yescharacteristic
60C4×C22⋊C4×C73—21no—
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C23×Dic73—21no—
64C2×#11924018—22no—
65C2×#11924018—22no—
66C2×#11924018C2×C414yescomplemented
67C2×#11924016—41no—
68C2×#11924016—41no—
69C2×#11924016C2×C414yescomplemented
70C2×#11924012—22no—
71C2×#11924012—22no—
72C2×#11924012—41no—
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77#14556570—22no—
78#14556570C2×C414yes—
79C4×Dic146—22no—
80C4×Dic146—41no—
81C2×C4⋊Dic73—22no—
82C2×C4⋊Dic73—21no—
83C2×C4⋊Dic73—41no—
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×C22⋊Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93#14556522—22no—
94#14556522—41no—
95#14556515—22no—
96#14556515C2×C414yescomplemented
97#14556515D414yes—
98#14556514—22no—
99#14556514—41no—
100#14556512—22no—
101#14556512—22no—
102#14556512C2×C414yescomplemented
103C22⋊#10596831C2×C414yes—
104#14556502—22no—
105C4×#10596831—41no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C2×#41×C73—22no—
111C2×#41×C73—22no—
112C2×#41×C73—22no—
113C2×#41×C73—41no—
114C2×#41×C73—41no—
115C2×#41×C73C2×C414yes—
116C22×Q8×C73C2311yescharacteristic
117C22×D4×C73—21no—
118C22×D4×C73C2311yescharacteristic
119C23×C4×C73—21no—
120C23×C4×C73C2311yescharacteristic
121C4×Q8×C73—22no—
122C4×Q8×C73—22no—
123C4×Q8×C73—41no—
124C4×Q8×C73—41no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C42×C73—21no—
137C2×C42×C73—21no—
138C2×C42×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140#95×C73—21no—
141#95×C73D411yescharacteristic
142#95×C73D411yescharacteristic
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146C22×C412yes—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—42no—
154C22×Dic73—42no—
155C22×Dic73—81no—
156#11924018—28no—
157#11924016—44no—
158#11924012—44no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C22×C412yes—
169C2×#10596831C22×C412yes—
170C2×#10596831C2×D412yes—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—42no—
176C4⋊Dic73C22×C412yes—
177C4⋊Dic73C2×D412yes—
178#11924007—24no—
179#11924007—42no—
180#11924007—81no—
181C22⋊Dic73—24no—
182C4×Dic73—42no—
183C4×Dic73—81no—
184C24×C73—21no—
185C24×C73C2×D411yescharacteristic
186#41×C73—28no—
187#41×C73—44no—
188#41×C73—44no—
189#41×C73—44no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73C22×C412yes—
194C2×Q8×C73C2×D412yes—
195C2×Q8×C73#4112yes—
196C2×D4×C73—24no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—42no—
203C2×D4×C73—42no—
204C2×D4×C73C22×C412yes—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—24no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73C22×C412yes—
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73#4112yes—
222C22×C4×C73C2411yescharacteristic
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—42no—
228C4⋊C4×C73—42no—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—41no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—81no—
234C22⋊C4×C73—81no—
235C22⋊C4×C73—81no—
236C42×C73—21no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—21no—
240C42×C73—42no—
241C42×C73—42no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—22no—
260Q8×C73C4×D414yes—
261D4×C73—22no—
262D4×C73—22no—
263D4×C73—48no—
264D4×C73—41no—
265D4×C73—41no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—48no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73C4×D412yes—
294C2×C4×C73#13712yes—
295C2×C4×C73C23×C411yescharacteristic
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—84no—
314Dic146—22no—
315Dic146—22no—
316Dic146—41no—
317Dic146—41no—
318#10596831—22no—
319#10596831—22no—
320#10596831—22no—
321#10596831—41no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—42no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73C2×C4×D411yescharacteristic
337C22×C73D4211yescharacteristic
338C22×C73#54611yescharacteristic
339C22×C73C2×#13711yescharacteristic
340C22×C73#57511yescharacteristic
341C22×C73#57711yescharacteristic
342C22×C73#57711yescharacteristic
343C4×C73—22no—
344C4×C73—24no—
345C4×C73—22no—
346C4×C73—41no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—81no—
350C4×C73—81no—
351C4×C73C2×C4×D411yescharacteristic
352C4×C73#51811yescharacteristic
353C4×C73#54611yescharacteristic
354C4×C73#55111yescharacteristic
355Dic73—42no—
356Dic73—42no—
357Dic73—42no—
358Dic73—81no—
359#22867—731nomaximal, Sylow
360C2×C73—42no—
361C2×C73—82no—
362C2×C73#235811yescharacteristic
363C2×C73C4×#13711yescharacteristic
364C2×C73#295211yescharacteristic
365C2×C73#327511yescharacteristic
366C2×C73#327811yescharacteristic
367C2×C73#331611yescharacteristic
368C2×C73#331711yescharacteristic
369C2×#452—731no—
370C2×#441—731no—
371C2×#417—731no—
372#2360—731no—
373#2341D7311yescharacteristic
374#1968—731no—
375#1936—731no—
376#1926—731no—
377#1894—731no—
378#1880—731no—
379#1878—731no—
380#1865—731no—
381#1853—731no—
382C4×#103—731no—
383#1753—731no—
384C73#2286711yescharacteristic, complemented, Sylow
385C22×#41C2×D7311yescharacteristic
386C22×Q16—731no—
387C22×SD16—731no—
388C22×M16—731no—
389C2×C22⋊Q8—731no—
390C2×C4×Q8—731no—
391C2×C4×Q8C2×D7311yescharacteristic
392C2×C4×Q8C2×D7311yescharacteristic
393C22×C4⋊C4—731no—
394#452—738no—
395#441—1464no—
396C2×#106—731no—
397C2×#106—731no—
398#417—1464no—
399C2×#103—731no—
400C2×#103—731no—
401C2×#103—731no—
402C2×#103—731no—
403C2×#103—731no—
404C2×#102—731no—
405C2×#102—731no—
406C2×#102—731no—
407C2×C22⋊C8—731no—
408C2×#97—731no—
409C2×C4×C8—731no—
410#391—731no—
411#390—21no—
412#390—21no—
413#390C2×D7311yescharacteristic
414#390C2×D7311yescharacteristic
415#389—731no—
416#389—1461no—
417#387—1461no—
418#385—1461no—
419#380—21no—
420#380C2×D7311yescharacteristic
421C4×C4⋊C4—731no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—1461no—
424C4×C22⋊C4C2×D7311yescharacteristic
425#340—731no—
426#340—731no—
427#340—731no—
428#340—731no—
429#336—731no—
430#336—731no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41C4×D7314yes—
437C22×Q8—731no—
438C22×Q8C22×D7311yescharacteristic
439C22×D4—21no—
440C22×D4C22×D7311yescharacteristic
441C23×C4—21no—
442C23×C4—1461no—
443C23×C4C22×D7311yescharacteristic
444C2×Q16—734no—
445C2×Q16—1462no—
446C2×Q16—1462no—
447C2×SD16—2921no—
448C2×SD16—2921no—
449C2×SD16—734no—
450C2×M16—2921no—
451C2×M16—1462no—
452C2×M16—1462no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8—731no—
456C22×C8—731no—
457C22⋊Q8—734no—
458C22⋊Q8—1462no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—41no—
462C4×Q8—41no—
463C4×Q8—2921no—
464C4×Q8—1462no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—2921no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1462no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C4⋊C4C22×D7311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4C22⋊D7311yescharacteristic
485C2×C22⋊C4C22⋊D7311yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—1461no—
489C2×C42—1461no—
490C2×C42C22×D7311yescharacteristic
491C2×C42C22×D7311yescharacteristic
492#106—2921no—
493#106—1462no—
494#103—2921no—
495#103—734no—
496#103—734no—
497#103—1462no—
498#103—1462no—
499#102—734no—
500#102—1462no—
501#102—1462no—
502C22⋊C8—734no—
503#97—1462no—
504C4×C8—2921no—
505#95—21no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95C22⋊D7311yescharacteristic
511#95C22⋊D7311yescharacteristic
512C24—21no—
513C24C2×C22⋊D7311yescharacteristic
514#41—28no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—732no—
522C2×Q8—1461no—
523C2×Q8—1461no—
524C2×Q8—1461no—
525C2×Q8—1461no—
526C2×Q8—1461no—
527C2×Q8C2×C4×D7312yes—
528C2×Q8D4×D7312yes—
529C2×Q8#1192402712yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D7312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—2922no—
550C22×C4—2922no—
551C22×C4—5841no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4C2×C4×D7312yes—
557C22×C4C2×C22⋊D7311yescharacteristic
558C22×C4C2×C22⋊D7311yescharacteristic
559C22×C4C2×C22⋊D7311yescharacteristic
560C22×C4C2×C22⋊D7311yescharacteristic
561C22×C4C2×C22⋊D7311yescharacteristic
562C22×C4#1192402812yes—
563C22×C4C23×D7311yescharacteristic
564Q16—1468no—
565SD16—2924no—
566M16—2924no—
567C2×C8—732no—
568C2×C8—732no—
569C2×C8—732no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—2922no—
586C4⋊C4—2922no—
587C4⋊C4—5841no—
588C4⋊C4—732no—
589C4⋊C4—732no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1464no—
593C4⋊C4—1461no—
594C4⋊C4—1461no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—1464no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42—42no—
609C42—2922no—
610C42—5841no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23C4×C22⋊D7312yes—
625C23C22×C22⋊D7311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—2921no—
630Q8—2921no—
631Q8—1462no—
632Q8—1462no—
633Q8#1455655114yes—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—5844no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4C4×C22⋊D7312yes—
680C2×C4#1455662112yes—
681C2×C4C22×C4×D7311yescharacteristic
682C2×C4C2×D4×D7311yescharacteristic
683C2×C4C2×#1192402711yescharacteristic
684C2×C4C2×#1192402811yescharacteristic
685C2×C4#1455663611yescharacteristic
686C2×C4#1455663611yescharacteristic
687C8—2921no—
688C8—1462no—
689C8—1462no—
690C8—1462no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×C4×C22⋊D7311yescharacteristic
706C22D4×C22⋊D7311yescharacteristic
707C22#1798923111yescharacteristic
708C22C2×#1455662111yescharacteristic
709C22#1798938511yescharacteristic
710C22#1798939511yescharacteristic
711C22#1798939811yescharacteristic
712C4—22no—
713C4—22no—
714C4—24no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—81no—
719C4—81no—
720C4—2922no—
721C4—2922no—
722C4—2922no—
723C4—5841no—
724C4C2×#1455655111yescharacteristic
725C4#1798906011yescharacteristic
726C4#1798922711yescharacteristic
727C4#1798926311yescharacteristic
728C2—42no—
729C2—82no—
730C2#2261291011yescharacteristic
731C2C4×#1455662111yescharacteristic
732C2#2261881211yescharacteristic
733C2#2262156311yescharacteristic
734C2#2262159711yescharacteristic
735C2#2262204211yescharacteristic
736C2#2262205711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2341C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenter#2341D73
hypocenterC73#22867
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#17988692C2semidirect
4. #22612934C2semidirect
5. #22610784C2semidirect
6. #22610631C2semidirect
7. #22610555C2semidirect
8. #22610362C2semidirect
9. #22610289C2semidirect
10. #22610272C2semidirect
11. #22610199C2semidirect
12. #22610123C2semidirect
13. C4×#14556515C2semidirect
14. #22609715C2semidirect
22. #17988749C4semidirect
66. C2×#11924018C2×C4semidirect
69. C2×#11924016C2×C4semidirect
96. #14556515C2×C4semidirect
102. #14556512C2×C4semidirect
384. C73#22867semidirect

Maximal subgroups

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

subgroupindex
C2×#179887492
C2×#179886922
C2×#179885882
#226129342
#226107842
#226106312
#226105552
#226103622
#226102892
#226102722
#226101992
#226101232
C4×#145565152
#226097152
C73×#23412
#2286773