Finite Group Databasebeta

← #33108528

Subgroups — #33108528

Order 18688.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619509C211yesmaximal, characteristic
2C2×#17988702C211yesmaximal, characteristic, complemented
3#22618652C211yesmaximal, characteristic, complemented
4C22×#14556526C211yesmaximal, characteristic, complemented
5#22610818C211yesmaximal, characteristic, complemented
6#22610676C211yesmaximal, characteristic, complemented
7#22610579C211yesmaximal, characteristic, complemented
8#22610576C211yesmaximal, characteristic, complemented
9#22610234C211yesmaximal, characteristic, complemented
10#22610233C211yesmaximal, characteristic, complemented
11#22610206C211yesmaximal, characteristic, complemented
12#22610205C211yesmaximal, characteristic, complemented
13#22609811C211yesmaximal, characteristic, complemented
14#22609705C211yesmaximal, characteristic, complemented
15C73×#2933C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556597C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20#17989098C2211yescharacteristic
21#17988826C411yescharacteristic, complemented
22#17988826C411yescharacteristic, complemented
23#17988821C411yescharacteristic, complemented
24#17988821C411yescharacteristic, complemented
25#17988818C411yescharacteristic, complemented
26#17988818C411yescharacteristic, complemented
27#17988814C411yescharacteristic, complemented
28#17988814C411yescharacteristic, complemented
29#17988702—24no—
30#17988662—21no—
31#17988661—21no—
32#17988655—21no—
33#17988650—21no—
34C2×#14556526—24no—
35C2×#14556526C2211yescharacteristic
36C2×#14556526C2211yescharacteristic
37C2×#14556526C2211yescharacteristic
38C2×#14556526C2211yescharacteristic
39#17988623C2211yescharacteristic
40#17988613C2211yescharacteristic
41C2×#14556518C2211yescharacteristic
42C2×#14556518C2211yescharacteristic
43C2×#14556517C2211yescharacteristic
44C2×#14556517C2211yescharacteristic
45#17988583C2211yescharacteristic
46#17988581C2211yescharacteristic
47#17988553C2211yescharacteristic
48#17988542C2211yescharacteristic
49C2×C8×Dic73C2211yescharacteristic
50C2×C8×Dic73C2211yescharacteristic
51C4×C22⋊Dic73C2211yescharacteristic
52#17988348C2211yescharacteristic
53#17988348C2211yescharacteristic
54#17988346C2211yescharacteristic
55#17988346C2211yescharacteristic
56#17988341C2211yescharacteristic
57#17988341C2211yescharacteristic
58C2×#131×C73C2211yescharacteristic
59C22×M16×C73C2211yescharacteristic
60#525×C73C2211yescharacteristic
61#436×C73—21no—
62#435×C73—21no—
63#435×C73—21no—
64C8×D4×C73—21no—
65#424×C73C2211yescharacteristic
66#408×C73C2211yescharacteristic
67C2×C22⋊C8×C73C2211yescharacteristic
68#405×C73C2211yescharacteristic
69C2×#11924028C2311yescharacteristic
70#14556611—22no—
71#14556611—22no—
72C2×#11924018C2×C411yescharacteristic
73C2×#11924016C2×C411yescharacteristic
74C2×#11924015C2×C411yescharacteristic
75C2×#11924013C2×C411yescharacteristic
76#14556597—22no—
77#14556597—41no—
78C2×#11924012—22no—
79C2×#11924012—21no—
80C2×#11924012—41no—
81C2×#11924012C2311yescharacteristic
82C2×#11924012C2311yescharacteristic
83C2×#11924011—21no—
84C22×#10596831—22no—
85C22×#10596831—22no—
86C22×#10596831—21no—
87C22×#10596831C2×C411yescharacteristic
88C22×#10596831C2×C411yescharacteristic
89C22×#10596831C2×C411yescharacteristic
90C22×#10596831C2×C411yescharacteristic
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93C2×C8×D73—21no—
94#14556574—21no—
95#14556570C2×C411yescharacteristic
96#14556570C2×C411yescharacteristic
97#14556565C2×C411yescharacteristic
98#14556565C2×C411yescharacteristic
99#14556560—21no—
100C4×C22⋊D73—21no—
101C4×C22⋊D73—21no—
102#14556550C2311yescharacteristic
103C2×C22⋊Dic73—21no—
104C2×C4×Dic73C2311yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106#14556526—22no—
107#14556526—22no—
108#14556526—22no—
109#14556526D414yescomplemented
110#14556524C2×C411yescharacteristic
111#14556524C2×C411yescharacteristic
112#14556522C2×C411yescharacteristic
113#14556522C2×C411yescharacteristic
114#14556520—21no—
115#14556520—21no—
116#14556518—22no—
117#14556518—41no—
118#14556517—22no—
119#14556517—41no—
120#14556515C2×C411yescharacteristic
121#14556515C2×C411yescharacteristic
122#14556514C2×C411yescharacteristic
123#14556514C2×C411yescharacteristic
124#14556512C2×C411yescharacteristic
125#14556512C2×C411yescharacteristic
126#14556511C2×C411yescharacteristic
127#14556511C2×C411yescharacteristic
128#14556503—21no—
129#14556503—21no—
130#14556501—21no—
131C8×Dic73—22no—
132C8×Dic73—22no—
133C8×Dic73—21no—
134#14556498—21no—
135C2×#41×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137#131×C73—22no—
138#131×C73—41no—
139C2×M16×C73—21no—
140C2×M16×C73—21no—
141C2×M16×C73—22no—
142C2×M16×C73—41no—
143C2×M16×C73C2311yescharacteristic
144C2×M16×C73C2311yescharacteristic
145C22×C8×C73—21no—
146C22×C8×C73—21no—
147C22×C8×C73C2311yescharacteristic
148C22×C8×C73C2311yescharacteristic
149#123×C73—21no—
150C22⋊Q8×C73C2×C411yescharacteristic
151C22⋊Q8×C73C2×C411yescharacteristic
152#121×C73C2×C411yescharacteristic
153#121×C73C2×C411yescharacteristic
154#120×C73—21no—
155C4×D4×C73—21no—
156C4×D4×C73—21no—
157#117×C73C2311yescharacteristic
158C4⋊C8×C73—21no—
159C4⋊C8×C73—21no—
160C22⋊C8×C73—21no—
161C22⋊C8×C73—21no—
162C22⋊C8×C73D411yescharacteristic
163C22⋊C8×C73D411yescharacteristic
164C22⋊C8×C73D411yescharacteristic
165C22⋊C8×C73D411yescharacteristic
166#97×C73—21no—
167C4×C8×C73—21no—
168#11924028—21no—
169#11924028—21no—
170#11924028—21no—
171#11924028—21no—
172C2×Dic146C22×C411yescharacteristic
173C2×D292C22×C411yescharacteristic
174C2×C22⋊D73—21no—
175C2×C22⋊D73—21no—
176C2×C22⋊D73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C2×C4×D73—21no—
180#11924018—22no—
181#11924016—22no—
182#11924015—22no—
183#11924013—22no—
184#11924012—21no—
185#11924012—21no—
186#11924012—21no—
187#11924012—42no—
188#11924012C2×D412yes—
189#11924011—42no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—22no—
194C2×#10596831—22no—
195C2×#10596831—22no—
196C2×#10596831—22no—
197C2×#10596831—21no—
198C2×#10596831—42no—
199C2×#10596831C22×C411yescharacteristic
200C2×#10596831C22×C411yescharacteristic
201C2×#10596831C22×C411yescharacteristic
202C2×#10596831C22×C411yescharacteristic
203C2×#10596831C2×D412yes—
204C2×#10596831#4112yes—
205C8×D73—42no—
206C4⋊Dic73C22×C411yescharacteristic
207C4⋊Dic73C22×C411yescharacteristic
208#11924007—21no—
209#11924007—21no—
210C22⋊Dic73—24no—
211C22⋊Dic73—21no—
212C22⋊Dic73—21no—
213C22⋊Dic73—21no—
214#11924005—21no—
215#11924005—21no—
216C4×Dic73—21no—
217C4×Dic73—21no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C24×C73#4111yescharacteristic
222#41×C73—21no—
223#41×C73—21no—
224#41×C73—21no—
225#41×C73—21no—
226C2×Q8×C73C22×C411yescharacteristic
227C2×D4×C73—21no—
228C2×D4×C73—21no—
229C2×D4×C73—21no—
230C2×D4×C73C22×C411yescharacteristic
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×D411yescharacteristic
240C22×C4×C73#4111yescharacteristic
241C22×C4×C73C2411yescharacteristic
242M16×C73—21no—
243M16×C73—21no—
244M16×C73—21no—
245M16×C73—42no—
246M16×C73—42no—
247M16×C73C2×D412yes—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73—42no—
255C2×C8×C73—42no—
256C2×C8×C73C2×D411yescharacteristic
257C2×C8×C73C2×D411yescharacteristic
258C2×C8×C73C2×D411yescharacteristic
259C2×C8×C73C2×D411yescharacteristic
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73C22×C411yescharacteristic
263C4⋊C4×C73C22×C411yescharacteristic
264C22⋊C4×C73—21no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—21no—
267C22⋊C4×C73—21no—
268C22⋊C4×C73—21no—
269C42×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—22no—
273C23×C73—21no—
274C23×C73—41no—
275C23×C73C4×D411yescharacteristic
276C23×C73C4×D411yescharacteristic
277C23×C73C2×#4111yescharacteristic
278C22×D73—21no—
279Q8×C73—21no—
280Q8×C73—21no—
281D4×C73—21no—
282D4×C73—21no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—42no—
286D4×C73—81no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73C4×D411yescharacteristic
303C2×C4×C73C4×D411yescharacteristic
304C2×C4×C73C23×C411yescharacteristic
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C732−1+411yescharacteristic
310C22⋊D73—41no—
311C22⋊D73—41no—
312C22⋊D73—42no—
313C22⋊D73—81no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323D292—21no—
324D292—21no—
325C4×D73—41no—
326C4×D73—41no—
327Dic146—21no—
328Dic146—21no—
329C8×C73—21no—
330C8×C73—21no—
331C8×C73—22no—
332C8×C73—21no—
333C8×C73—21no—
334C8×C73—41no—
335#10596831—21no—
336#10596831—21no—
337#10596831—22no—
338#10596831—41no—
339#10596831C4×D412yes—
340#10596831C4×D412yes—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—21no—
346C22×C73—21no—
347C22×C73—21no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73#44312yescomplemented
354C22×C73C2×C4×D411yescharacteristic
355C22×C73#54811yescharacteristic
356C22×C73#55311yescharacteristic
357C2×D73—41no—
358C2×D73—41no—
359C2×D73—41no—
360C4×C73—21no—
361C4×C73—21no—
362C4×C73—41no—
363C4×C73—41no—
364C4×C73—41no—
365C4×C73C2×C4×D411yescharacteristic
366C4×C73#52011yescharacteristic
367C4×C73D4211yescharacteristic
368C4×C73#54711yescharacteristic
369Dic73—42no—
370Dic73—42no—
371Dic73—41no—
372Dic73—41no—
373Dic73—41no—
374#23018—731nomaximal, Sylow
375C2×C73—21no—
376C2×C73—21no—
377C2×C73—22no—
378C2×C73—41no—
379C2×C73—81no—
380C2×C73#236111yescharacteristic
381C2×C73C2×#44311yescharacteristic
382C2×C73#295711yescharacteristic
383D73—81no—
384#3050—731no—
385C2×#443—731no—
386#2933—731no—
387#2933D7311yescharacteristic, complemented
388C22×#108—731no—
389#1974—731no—
390#1945—731no—
391#1929—731no—
392#1929—731no—
393#1871—731no—
394#1871—731no—
395#1866—731no—
396#1866—731no—
397#1772—731no—
398C8×C22⋊C4—731no—
399C73#2301811yescharacteristic, complemented, Sylow
400C2×#135—731no—
401C2×#131—731no—
402C2×#131C2×D7311yescharacteristic
403C22×M16—731no—
404C22×M16C2×D7311yescharacteristic
405C23×C8—731no—
406#525—731no—
407#525C2×D7311yescharacteristic
408#467—731no—
409#467—731no—
410#466—731no—
411#466—731no—
412#465—731no—
413#465—731no—
414#465—731no—
415#465—731no—
416#443—1464no—
417#436—21no—
418#436—1461no—
419#435—21no—
420#435—21no—
421#435—1461no—
422#435—1461no—
423C8×D4—21no—
424C8×D4—1461no—
425C2×#108—731no—
426C2×#108—731no—
427C2×#108—731no—
428C2×#108—731no—
429C2×#108—1464no—
430#427—731no—
431#424—731no—
432#424C2×D7311yescharacteristic
433C2×#104—731no—
434C2×#104—731no—
435C2×#104—731no—
436C2×#104—731no—
437#416—731no—
438#416—731no—
439#408—731no—
440#408C2×D7311yescharacteristic
441C2×C22⋊C8C2×D7311yescharacteristic
442#405—731no—
443#405C2×D7311yescharacteristic
444C2×C4×C8—731no—
445C2×C4×C8—731no—
446C4×C22⋊C4—731no—
447#339—731no—
448#339—731no—
449#339—731no—
450#339—731no—
451#336—731no—
452#336—731no—
453C2×#41—731no—
454C2×#41C22×D7311yescharacteristic
455C23×C4C22×D7311yescharacteristic
456#135—1462no—
457#135—1462no—
458C2×Q16—731no—
459C2×SD16—731no—
460C2×SD16—731no—
461C2×D8—731no—
462#131—22no—
463#131—41no—
464#131—2921no—
465#131—1462no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—22no—
469C2×M16—41no—
470C2×M16—2921no—
471C2×M16—731no—
472C2×M16—731no—
473C2×M16—1462no—
474C2×M16—1461no—
475C2×M16—1461no—
476C2×M16C22×D7311yescharacteristic
477C2×M16C22×D7311yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—731no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—1461no—
487C22×C8—1461no—
488C22×C8—1462no—
489C22×C8—1462no—
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492#123—21no—
493#123—1461no—
494C22⋊Q8—731no—
495C22⋊Q8—731no—
496C22⋊Q8C4×D7311yescharacteristic
497C22⋊Q8C4×D7311yescharacteristic
498#121—731no—
499#121—731no—
500#121C4×D7311yescharacteristic
501#121C4×D7311yescharacteristic
502#120—21no—
503#120—1461no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—1461no—
507C4×D4—1461no—
508#117—731no—
509#117C22×D7311yescharacteristic
510C2×C22⋊C4—1461no—
511C2×C42—731no—
512C2×C42—731no—
513#108—734no—
514#108—1462no—
515#108—1462no—
516#108—1462no—
517#107—731no—
518#107—731no—
519#106—731no—
520#106—731no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8—1461no—
524C4⋊C8—1461no—
525#104—2921no—
526#104—2921no—
527#104—1462no—
528#104—1462no—
529#103—731no—
530#103—731no—
531#103—731no—
532#103—731no—
533#102—731no—
534#102—731no—
535#102—731no—
536#102—731no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—1461no—
540C22⋊C8—1461no—
541C22⋊C8C22⋊D7311yescharacteristic
542C22⋊C8C22⋊D7311yescharacteristic
543C22⋊C8C22⋊D7311yescharacteristic
544C22⋊C8C22⋊D7311yescharacteristic
545#97—21no—
546#97—1461no—
547C4×C8—21no—
548C4×C8—1462no—
549C4×C8—1462no—
550C4×C8—1461no—
551#95—1461no—
552C24#1192402811yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—1461no—
558#41—1461no—
559#41—1461no—
560#41—1461no—
561C2×Q8—731no—
562C2×Q8C2×C4×D7311yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—731no—
567C2×D4—1461no—
568C2×D4—1461no—
569C2×D4—1461no—
570C2×D4C2×C4×D7311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4C2×C4×D7311yescharacteristic
580C22×C4C2×C4×D7311yescharacteristic
581C22×C4C2×C22⋊D7311yescharacteristic
582C22×C4C2×C22⋊D7311yescharacteristic
583C22×C4#1192402811yescharacteristic
584C22×C4C23×D7311yescharacteristic
585Q16—1462no—
586SD16—1462no—
587SD16—1462no—
588D8—1462no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—42no—
594M16—2922no—
595M16—2922no—
596M16—732no—
597M16—1461no—
598M16—1461no—
599M16—1461no—
600M16D4×D7312yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—2922no—
610C2×C8—2922no—
611C2×C8—731no—
612C2×C8—731no—
613C2×C8—732no—
614C2×C8—732no—
615C2×C8—731no—
616C2×C8—731no—
617C2×C8—1461no—
618C2×C8—1462no—
619C2×C8—1462no—
620C2×C8—1462no—
621C2×C8—1462no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8C2×C22⋊D7311yescharacteristic
626C2×C8C2×C22⋊D7311yescharacteristic
627C2×C8C2×C22⋊D7311yescharacteristic
628C2×C8C2×C22⋊D7311yescharacteristic
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—731no—
632C4⋊C4—731no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C4⋊C4C2×C4×D7311yescharacteristic
636C4⋊C4C2×C4×D7311yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—1464no—
643C22⋊C4—1461no—
644C22⋊C4—1461no—
645C22⋊C4—1461no—
646C22⋊C4—1461no—
647C22⋊C4—1461no—
648C42—21no—
649C42—1461no—
650C42—1461no—
651C42—1461no—
652C42—1461no—
653C42—1461no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—1461no—
660C23C4×C22⋊D7311yescharacteristic
661C23C4×C22⋊D7311yescharacteristic
662C23C2×#1192402811yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—1461no—
666Q8—1461no—
667D4—21no—
668D4—21no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—81no—
673D4—2922no—
674D4—2921no—
675D4—2921no—
676D4—5841no—
677D4—1461no—
678D4—1461no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—2921no—
695C2×C4—2921no—
696C2×C4—2921no—
697C2×C4—2921no—
698C2×C4—2921no—
699C2×C4—2921no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1461no—
703C2×C4—1461no—
704C2×C4—1461no—
705C2×C4C4×C22⋊D7311yescharacteristic
706C2×C4C4×C22⋊D7311yescharacteristic
707C2×C4C22×C4×D7311yescharacteristic
708C2×C4C2×D4×D7311yescharacteristic
709C2×C4C22×C22⋊D7311yescharacteristic
710C2×C4#41×D7311yescharacteristic
711C2×C4#1455663611yescharacteristic
712C2×C4#1455663811yescharacteristic
713C8—21no—
714C8—21no—
715C8—22no—
716C8—21no—
717C8—21no—
718C8—41no—
719C8—2921no—
720C8—732no—
721C8—732no—
722C8—1462no—
723C8—1461no—
724C8—1461no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—2921no—
738C22—2921no—
739C22—2921no—
740C22#1798870212yescomplemented
741C22C2×C4×C22⋊D7311yescharacteristic
742C22#1798924611yescharacteristic
743C22#1798928611yescharacteristic
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—2922no—
750C4—2922no—
751C4—2921no—
752C4—2921no—
753C4—2921no—
754C4C4×D4×D7311yescharacteristic
755C4#1798906611yescharacteristic
756C4D4×C22⋊D7311yescharacteristic
757C4#1798923611yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—5841no—
764C2#2261294811yescharacteristic
765C2C2×#1798870211yescharacteristic
766C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2933C2
socleC22×C73C2×C4×D4
prime radical#22619509C2
cosocleC22×C4×C73C24
hypercenter#2933D73
hypocenterC73#23018
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#17988702C2semidirect
3. #22618652C2semidirect
4. C22×#14556526C2semidirect
5. #22610818C2semidirect
6. #22610676C2semidirect
7. #22610579C2semidirect
8. #22610576C2semidirect
9. #22610234C2semidirect
10. #22610233C2semidirect
11. #22610206C2semidirect
12. #22610205C2semidirect
13. #22609811C2semidirect
14. #22609705C2semidirect
15. C73×#2933C2semidirect
21. #17988826C4semidirect
22. #17988826C4semidirect
23. #17988821C4semidirect
24. #17988821C4semidirect
25. #17988818C4semidirect
26. #17988818C4semidirect
27. #17988814C4semidirect
28. #17988814C4semidirect
109. #14556526D4semidirect
353. C22×C73#443semidirect
387. #2933D73semidirect
399. C73#23018semidirect
740. C22#17988702semidirect

Maximal subgroups

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

subgroupindex
#226195092
C2×#179887022
#226186522
C22×#145565262
#226108182
#226106762
#226105792
#226105762
#226102342
#226102332
#226102062
#226102052
#226098112
#226097052
C73×#29332
#2301873