Finite Group Databasebeta

← #34026989

Subgroups — #34026989

Order 18688.

868 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626672C211yesmaximal, characteristic
2#22626670C211yesmaximal, characteristic
3C2×#17989602C211yesmaximal, characteristic, complemented
4C2×D73⋊#108C211yesmaximal, characteristic, complemented
5#22626047C211yesmaximal, characteristic, complemented
6#22626046C211yesmaximal, characteristic, complemented
7#22625885C211yesmaximal, characteristic, complemented
8#22625885C211yesmaximal, characteristic, complemented
9#22625885C211yesmaximal, characteristic, complemented
10#22625884C211yesmaximal, characteristic, complemented
11#22625873C211yesmaximal, characteristic, complemented
12#22625812C211yesmaximal, characteristic, complemented
13#22625810C211yesmaximal, characteristic, complemented
14#22625751C211yesmaximal, characteristic, complemented
15#435×D73C211yesmaximal, characteristic
16C22×#11924038C2211yescharacteristic
17C2×D73⋊M16C2211yescharacteristic
18C2×D73⋊M16C2211yescharacteristic
19C2×D73⋊M16C2211yescharacteristic
20#17989622—21no—
21#17989620—21no—
22#17989619—21no—
23#17989619—21no—
24#17989618—21no—
25#17989617—21no—
26#17989615—21no—
27#17989614—21no—
28#17989602—24no—
29C2×#14556662C2211yescharacteristic
30C2×#14556662C2211yescharacteristic
31C2×#14556662C2211yescharacteristic
32C2×#14556662C2211yescharacteristic
33D73⋊#108—24no—
34C2×#14556661C2211yescharacteristic
35C2×#14556661C2211yescharacteristic
36C2×#14556661C2211yescharacteristic
37C2×#14556661C2211yescharacteristic
38C2×#14556661C2211yescharacteristic
39C2×#14556661C2211yescharacteristic
40#17989592C2211yescharacteristic
41#17989591C2211yescharacteristic
42#17989558C2211yescharacteristic
43#17989558C2211yescharacteristic
44#17989558C2211yescharacteristic
45#17989558C2211yescharacteristic
46C4×#11924038C2211yescharacteristic
47C4×#11924038C2211yescharacteristic
48#17989463C2211yescharacteristic
49#17989463C2211yescharacteristic
50#17989463C2211yescharacteristic
51#17989463C2211yescharacteristic
52#17989463C2211yescharacteristic
53#17989463C2211yescharacteristic
54C2×M16×D73C2211yescharacteristic
55C22×C8×D73C2211yescharacteristic
56C4×D4×D73C2211yescharacteristic
57#17988661C411yescharacteristic
58#17988660C411yescharacteristic
59#17988659C411yescharacteristic
60#17988658C411yescharacteristic
61#17988657C411yescharacteristic
62#17988656C411yescharacteristic
63#17988655C411yescharacteristic
64C4⋊C8×D73C2211yescharacteristic
65C22⋊C8×D73C2211yescharacteristic
66C22⋊C8×D73C2211yescharacteristic
67#97×D73C2211yescharacteristic
68#435×C73C411yescharacteristic
69C2×#11924038—22no—
70C2×#11924038—21no—
71C2×#11924038—41no—
72C2×#11924038C2311yescharacteristic
73C2×#11924038C2311yescharacteristic
74C2×#11924038C2311yescharacteristic
75C2×#11924038C2311yescharacteristic
76C2×#11924038C2311yescharacteristic
77C2×#11924038C2311yescharacteristic
78C2×#11924038C2311yescharacteristic
79C2×#11924038C2311yescharacteristic
80D73⋊M16—22no—
81D73⋊M16—22no—
82D73⋊M16—22no—
83D73⋊M16—41no—
84D73⋊M16—41no—
85D73⋊M16—41no—
86C2×#11924037—21no—
87C2×#11924037—21no—
88C2×#11924037—21no—
89C2×#11924036—21no—
90C2×#11924036—21no—
91C2×#11924036—21no—
92C22×#10596833—21no—
93#14556662—22no—
94#14556662—22no—
95#14556662—41no—
96#14556662D414yescomplemented
97#14556661—22no—
98#14556661—22no—
99#14556661—22no—
100#14556661—22no—
101#14556661—22no—
102#14556661—41no—
103#14556658—21no—
104#14556658—21no—
105C4⋊#10596833—21no—
106C4⋊#10596833—21no—
107#14556648—21no—
108#14556648—21no—
109#14556648—21no—
110#14556648—21no—
111C22⋊#10596833—21no—
112C22⋊#10596833—21no—
113C22⋊#10596833—21no—
114C22⋊#10596833—21no—
115#14556646—21no—
116#14556646—21no—
117C4×#10596833—21no—
118C4×#10596833—21no—
119C2×D4×D73Q811yescharacteristic
120C22×C4×D73C2311yescharacteristic
121C22×C4×D73C2311yescharacteristic
122C2×#11924012C2×C411yescharacteristic
123C2×#11924011C2×C411yescharacteristic
124C2×#11924011C2×C411yescharacteristic
125M16×D73—22no—
126M16×D73—22no—
127C22×#10596831C2×C411yescharacteristic
128C2×C8×D73—22no—
129C2×C8×D73—22no—
130C2×C8×D73C2×C411yescharacteristic
131C2×C8×D73C2×C411yescharacteristic
132C2×C8×D73C2311yescharacteristic
133C2×C8×D73C2311yescharacteristic
134C2×C8×D73C2311yescharacteristic
135C2×C8×D73C2311yescharacteristic
136C4×D292C2×C411yescharacteristic
137D4×Dic73D411yescharacteristic
138#14556553D411yescharacteristic
139C4×C22⋊D73C2×C411yescharacteristic
140C4×C22⋊D73C2×C411yescharacteristic
141#14556551D411yescharacteristic
142#14556551D411yescharacteristic
143C4⋊C4×D73Q811yescharacteristic
144C22⋊C4×D73Q811yescharacteristic
145C22⋊C4×D73Q811yescharacteristic
146C42×D73C2311yescharacteristic
147C4⋊#10596831C2×C411yescharacteristic
148#14556520C2×C411yescharacteristic
149#14556520C2×C411yescharacteristic
150C22⋊#10596831C2×C411yescharacteristic
151C22⋊#10596831C2×C411yescharacteristic
152#14556503C2×C411yescharacteristic
153#14556503C2×C411yescharacteristic
154#14556503C2×C411yescharacteristic
155#14556503C2×C411yescharacteristic
156#14556502C2×C411yescharacteristic
157#14556501C2×C411yescharacteristic
158#14556501C2×C411yescharacteristic
159C2×M16×C73C2×C411yescharacteristic
160C22×C8×C73C2×C411yescharacteristic
161C4×D4×C73C2×C411yescharacteristic
162C4⋊C8×C73C2×C411yescharacteristic
163C22⋊C8×C73C2×C411yescharacteristic
164C22⋊C8×C73C2×C411yescharacteristic
165#97×C73C2×C411yescharacteristic
166#11924038—21no—
167#11924038—21no—
168#11924038—21no—
169#11924038—21no—
170#11924038—21no—
171#11924038—21no—
172#11924038—21no—
173#11924038—21no—
174#11924038—21no—
175#11924038—21no—
176#11924038—21no—
177#11924038—21no—
178#11924038—21no—
179#11924038—21no—
180#11924038—42no—
181#11924038C2×D412yes—
182#11924038C2×D412yes—
183#11924037—42no—
184#11924037—42no—
185#11924037—42no—
186#11924036—42no—
187#11924036—42no—
188#11924036—42no—
189C2×#10596833—21no—
190C2×#10596833—21no—
191C2×#10596833—21no—
192C2×#10596833—21no—
193C2×#10596833—21no—
194C2×#10596833—21no—
195C2×#10596833—21no—
196C2×#10596833—21no—
197C2×#10596833—42no—
198C23×D73C2×Q811yescharacteristic
199C23×D73C2×Q811yescharacteristic
200C2×D292C4⋊C411yescharacteristic
201C2×C22⋊D73C4⋊C411yescharacteristic
202C2×C22⋊D73C4⋊C411yescharacteristic
203D4×D73—42no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C2×C4×D73—21no—
207C2×C4×D73—21no—
208C2×C4×D73—21no—
209C2×C4×D73—21no—
210C2×C4×D73—21no—
211C2×C4×D73—21no—
212C2×C4×D73—21no—
213C2×C4×D73—21no—
214C2×C4×D73C22×C411yescharacteristic
215C2×C4×D73C22×C411yescharacteristic
216C2×C4×D73C2×D411yescharacteristic
217C2×C4×D73C2×D411yescharacteristic
218C2×C4×D73C2×Q811yescharacteristic
219C2×C4×D73C2×Q811yescharacteristic
220C2×C4×D73C2×Q811yescharacteristic
221C2×C4×D73C2×Q811yescharacteristic
222C2×C4×D73C2411yescharacteristic
223#11924012—22no—
224#11924011—22no—
225#11924011—22no—
226C2×#10596831—22no—
227C2×#10596831C22×C411yescharacteristic
228C2×#10596831C22×C411yescharacteristic
229C2×#10596831C22×C411yescharacteristic
230C2×#10596831C22×C411yescharacteristic
231C8×D73—21no—
232C8×D73—21no—
233C8×D73—21no—
234C8×D73—21no—
235C8×D73—21no—
236C8×D73—21no—
237C8×D73—22no—
238C8×D73—22no—
239C8×D73C2×D412yes—
240C8×D73#4112yes—
241C4⋊Dic73C4⋊C411yescharacteristic
242#11924007C4⋊C411yescharacteristic
243#11924007C4⋊C411yescharacteristic
244C22⋊Dic73C4⋊C411yescharacteristic
245C22⋊Dic73C4⋊C411yescharacteristic
246#11924005C4⋊C411yescharacteristic
247#11924005C4⋊C411yescharacteristic
248#11924005C4⋊C411yescharacteristic
249#11924005C4⋊C411yescharacteristic
250C4×Dic73C22×C411yescharacteristic
251C4×Dic73C2×D411yescharacteristic
252C4×Dic73C2×D411yescharacteristic
253C2×D4×C73C4⋊C411yescharacteristic
254C22×C4×C73C22×C411yescharacteristic
255C22×C4×C73C22×C411yescharacteristic
256M16×C73—22no—
257C2×C8×C73—22no—
258C2×C8×C73C22×C411yescharacteristic
259C2×C8×C73C22×C411yescharacteristic
260C2×C8×C73C22×C411yescharacteristic
261C2×C8×C73C22×C411yescharacteristic
262C4⋊C4×C73C4⋊C411yescharacteristic
263C22⋊C4×C73C4⋊C411yescharacteristic
264C22⋊C4×C73C4⋊C411yescharacteristic
265C42×C73C22×C411yescharacteristic
266C23×C73C2×C4⋊C411yescharacteristic
267C23×C73C2×C4⋊C411yescharacteristic
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—22no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—41no—
274C22×D73—41no—
275C22×D73—41no—
276C22×D73C2×C4⋊C411yescharacteristic
277C22×D73C2×C4⋊C411yescharacteristic
278C22×D73C22×Q811yescharacteristic
279D4×C73—41no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73C2×C4⋊C411yescharacteristic
285C2×C4×C73C2×C4⋊C411yescharacteristic
286C2×C4×C73C2×C4⋊C411yescharacteristic
287C2×C4×C73C2×C4⋊C411yescharacteristic
288C2×C4×C73C23×C411yescharacteristic
289C22⋊D73—22no—
290C22⋊D73—41no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73C2×C4⋊C411yescharacteristic
296C2×Dic73C2×C4⋊C411yescharacteristic
297C2×Dic73C2×C4⋊C411yescharacteristic
298C2×Dic73C2×C4⋊C411yescharacteristic
299C2×Dic73C22×D411yescharacteristic
300D292—22no—
301C4×D73—21no—
302C4×D73—21no—
303C4×D73—21no—
304C4×D73—21no—
305C4×D73—21no—
306C4×D73—21no—
307C4×D73—21no—
308C4×D73—21no—
309C4×D73—21no—
310C4×D73—21no—
311C4×D73—21no—
312C4×D73—21no—
313C4×D73—41no—
314C4×D73—41no—
315C4×D73C22×D411yescharacteristic
316C4×D73C2×#4111yescharacteristic
317C4×D73H(5,𝔽2)11yescharacteristic
318C4×D732−1+411yescharacteristic
319#10596833—22no—
320#10596833—22no—
321#10596833—41no—
322#10596833—41no—
323#10596833—41no—
324#10596833—41no—
325#10596833—41no—
326#10596833—41no—
327C8×C73—21no—
328C8×C73—21no—
329C8×C73—21no—
330C8×C73C4×D412yes—
331#10596831—21no—
332#10596831—21no—
333#10596831—21no—
334#10596831C4×D412yes—
335C22×C73—21no—
336C22×C73—21no—
337C22×C73—21no—
338C22×C73—21no—
339C22×C73—21no—
340C22×C73—21no—
341C22×C73C22×C4⋊C411yescharacteristic
342C2×D73—21no—
343C2×D73—21no—
344C2×D73—21no—
345C2×D73—21no—
346C2×D73—21no—
347C2×D73—21no—
348C2×D73—21no—
349C2×D73—42no—
350C2×D73—42no—
351C2×D73—81no—
352C2×D73—81no—
353C2×D73#43012yescomplemented
354C2×D73D4×Q811yescharacteristic
355C2×D73#55411yescharacteristic
356C4×C73—21no—
357C4×C73—21no—
358C4×C73—21no—
359C4×C73—21no—
360C4×C73C2×C4×D411yescharacteristic
361C4×C73#52011yescharacteristic
362Dic73—21no—
363Dic73—21no—
364Dic73—21no—
365Dic73—21no—
366Dic73D4211yescharacteristic
367Dic73#54711yescharacteristic
368#22668—731nomaximal, Sylow
369C2×C73—41no—
370C2×C73—41no—
371C2×C73D4×C4⋊C411yescharacteristic
372C2×C73C2×#43011yescharacteristic
373C2×C73#291611yescharacteristic
374D73—21no—
375D73—21no—
376D73—22no—
377D73—41no—
378D4×M16—731no—
379D4×M16—731no—
380C2×#435—731no—
381C2×#430—731no—
382C22×#108—731no—
383#1950—731no—
384#1950—731no—
385#1855—731no—
386#1855—731no—
387#1855—731no—
388#1855—731no—
389#1849—731no—
390#1811—731no—
391#1810—731no—
392#1778—731no—
393C73#2266811yescharacteristic, complemented, Sylow
394C22×M16—731no—
395C22×M16—731no—
396C22×M16—731no—
397C22×M16—731no—
398C22×M16—731no—
399C23×C8—731no—
400C2×C4×D4—731no—
401#436—1461no—
402#436—1461no—
403#435—731no—
404#435—731no—
405#435—731no—
406#435—731no—
407#435—731no—
408#435—731no—
409#435—731no—
410#435—1461no—
411#435—1461no—
412#435—1461no—
413#435—1461no—
414#435#6440811yescharacteristic
415C8×D4—1461no—
416C8×D4—1461no—
417#430—1464no—
418C2×#108—731no—
419C2×#108—731no—
420C2×#108—731no—
421C2×#108—731no—
422C2×#108—731no—
423C2×#108—731no—
424C2×#108—731no—
425C2×#108—731no—
426C2×#108—731no—
427C2×#108—731no—
428C2×#108—1464no—
429#423—731no—
430#423—731no—
431C2×C4⋊C8—731no—
432#407—731no—
433#407—731no—
434#407—731no—
435#407—731no—
436C2×C22⋊C8—731no—
437C2×C22⋊C8—731no—
438C4×M16—731no—
439C4×M16—731no—
440C2×#97—731no—
441#341—731no—
442#341—731no—
443#341—731no—
444#341—731no—
445#341—731no—
446#341—731no—
447C22×D4—731no—
448C23×C4—731no—
449C23×C4—731no—
450C2×M16—2921no—
451C2×M16—2921no—
452C2×M16—2921no—
453C2×M16—2921no—
454C2×M16—731no—
455C2×M16—731no—
456C2×M16—731no—
457C2×M16—731no—
458C2×M16—731no—
459C2×M16—731no—
460C2×M16—731no—
461C2×M16—731no—
462C2×M16—731no—
463C2×M16—731no—
464C2×M16—731no—
465C2×M16—1462no—
466C2×M16—1462no—
467C2×M16—1462no—
468C2×M16—1462no—
469C2×M16—1462no—
470C2×M16—1462no—
471C2×M16—1461no—
472C2×M16—1461no—
473C2×M16—1461no—
474C2×M16—1461no—
475C2×M16C2×#6440811yescharacteristic
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—731no—
479C22×C8—731no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—1462no—
484C22×C8—1462no—
485C22×C8—1461no—
486C22×C8—1461no—
487C22×C8—1461no—
488C22×C8—1461no—
489C22×C8C2×#6440811yescharacteristic
490C4×D4—731no—
491C4×D4—731no—
492C4×D4—731no—
493C4×D4—731no—
494C4×D4—731no—
495C4×D4—731no—
496C4×D4—731no—
497C4×D4C2×#6440811yescharacteristic
498C2×C4⋊C4—731no—
499C2×C22⋊C4—731no—
500C2×C22⋊C4—731no—
501C2×C42—731no—
502#108—2921no—
503#108—2921no—
504#108—734no—
505#108—1462no—
506#108—1462no—
507#108—1462no—
508#108—1462no—
509#108—1462no—
510#108—1462no—
511#108—1462no—
512C4⋊C8—731no—
513C4⋊C8—731no—
514C4⋊C8—731no—
515C4⋊C8—1461no—
516C4⋊C8—1461no—
517C4⋊C8—1461no—
518C4⋊C8—1461no—
519C4⋊C8C2×#6440811yescharacteristic
520C22⋊C8—731no—
521C22⋊C8—731no—
522C22⋊C8—731no—
523C22⋊C8—731no—
524C22⋊C8—731no—
525C22⋊C8—731no—
526C22⋊C8—1461no—
527C22⋊C8—1461no—
528C22⋊C8—1461no—
529C22⋊C8—1461no—
530C22⋊C8—1461no—
531C22⋊C8—1461no—
532C22⋊C8—1461no—
533C22⋊C8—1461no—
534C22⋊C8C2×#6440811yescharacteristic
535C22⋊C8C2×#6440811yescharacteristic
536#97—731no—
537#97—731no—
538#97—731no—
539#97—1461no—
540#97—1461no—
541#97C2×#6440811yescharacteristic
542C4×C8—1461no—
543C4×C8—1461no—
544C24—731no—
545C24—731no—
546C2×D4—2922no—
547C2×D4—731no—
548C2×D4—731no—
549C2×D4—731no—
550C2×D4C4⋊#6440811yescharacteristic
551C22×C4—731no—
552C22×C4—731no—
553C22×C4—731no—
554C22×C4—731no—
555C22×C4—731no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—731no—
559C22×C4—731no—
560C22×C4—731no—
561C22×C4—731no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4C22×#6440811yescharacteristic
571C22×C4C22×#6440811yescharacteristic
572M16—22no—
573M16—2922no—
574M16—2922no—
575M16—2922no—
576M16—2922no—
577M16—732no—
578M16—732no—
579M16—1462no—
580M16—1461no—
581M16—1461no—
582M16—1461no—
583M16—1461no—
584M16—1461no—
585M16—1461no—
586M16—1461no—
587M16—1461no—
588M16—1461no—
589M16—1461no—
590M16—1461no—
591M16—1461no—
592M16—1462no—
593M16—1461no—
594M16—1461no—
595M16—1462no—
596C2×C8—22no—
597C2×C8—2922no—
598C2×C8—2922no—
599C2×C8—2922no—
600C2×C8—2922no—
601C2×C8—731no—
602C2×C8—732no—
603C2×C8—732no—
604C2×C8—731no—
605C2×C8—731no—
606C2×C8—731no—
607C2×C8—1462no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C2×C8—1461no—
618C2×C8—1461no—
619C2×C8—1461no—
620C2×C8—1462no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1462no—
624C2×C8C22×#6440811yescharacteristic
625C2×C8C22×#6440811yescharacteristic
626C2×C8C22×#6440811yescharacteristic
627C2×C8C22×#6440811yescharacteristic
628C4⋊C4—731no—
629C4⋊C4—731no—
630C4⋊C4—731no—
631C4⋊C4C4⋊#6440811yescharacteristic
632C22⋊C4—731no—
633C22⋊C4—731no—
634C22⋊C4—731no—
635C22⋊C4—731no—
636C22⋊C4—731no—
637C22⋊C4—731no—
638C22⋊C4C4⋊#6440811yescharacteristic
639C22⋊C4C4⋊#6440811yescharacteristic
640C42—731no—
641C42—731no—
642C42—731no—
643C42C22×#6440811yescharacteristic
644C23—2921no—
645C23—2921no—
646C23—2921no—
647C23—731no—
648C23—731no—
649C23—731no—
650C23—1461no—
651C23—1461no—
652C23—1462no—
653C23—1461no—
654C23—1461no—
655C23C2×C4⋊#6440811yescharacteristic
656C23C2×C4⋊#6440811yescharacteristic
657D4—41no—
658D4—2921no—
659D4—1462no—
660D4—1462no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—731no—
668C2×C4—731no—
669C2×C4—731no—
670C2×C4—731no—
671C2×C4—731no—
672C2×C4—731no—
673C2×C4—731no—
674C2×C4—731no—
675C2×C4—731no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1461no—
679C2×C4—1461no—
680C2×C4—1461no—
681C2×C4—1461no—
682C2×C4—1461no—
683C2×C4—1461no—
684C2×C4—1461no—
685C2×C4—1461no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4C2×C4⋊#6440811yescharacteristic
693C2×C4C2×C4⋊#6440811yescharacteristic
694C2×C4C2×C4⋊#6440811yescharacteristic
695C2×C4C2×C4⋊#6440811yescharacteristic
696C2×C4C23×#6440811yescharacteristic
697C8—21no—
698C8—21no—
699C8—21no—
700C8—2921no—
701C8—2921no—
702C8—2921no—
703C8—2921no—
704C8—2921no—
705C8—2921no—
706C8—732no—
707C8—1462no—
708C8—1462no—
709C8—1461no—
710C8—1461no—
711C8—1461no—
712C8D4×#6440812yes—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—2922no—
720C22—2922no—
721C22—5841no—
722C22—5841no—
723C22—732no—
724C22—731no—
725C22—731no—
726C22—1461no—
727C22—1461no—
728C22—1461no—
729C22—1461no—
730C22—1461no—
731C22—1461no—
732C22—1461no—
733C22C22×C4⋊#6440811yescharacteristic
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—731no—
739C4—731no—
740C4—1461no—
741C4—1461no—
742C4—1461no—
743C4—1461no—
744C4C2×D4×#6440811yescharacteristic
745C4#1798965611yescharacteristic
746C2—41no—
747C2—41no—
748C2—2921no—
749C2—1461no—
750C2—1461no—
751C2—1462no—
752C2D4×C4⋊#6440811yescharacteristic
753C2D73⋊#43011yescharacteristic
754C2#2262659211yescharacteristic
subgroupG/H
centerC22C22×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#435×C73C4
socleC22×C73C22×C4⋊C4
prime radicalC2×D4×D73Q8
cosocleC2×C4×D73C24
hypercenter#435#64408
hypocenterC73#22668
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. C2×#17989602C2semidirect
4. C2×D73⋊#108C2semidirect
5. #22626047C2semidirect
6. #22626046C2semidirect
7. #22625885C2semidirect
8. #22625885C2semidirect
9. #22625885C2semidirect
10. #22625884C2semidirect
11. #22625873C2semidirect
12. #22625812C2semidirect
13. #22625810C2semidirect
14. #22625751C2semidirect
96. #14556662D4semidirect
353. C2×D73#430semidirect
393. C73#22668semidirect

Maximal subgroups

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

subgroupindex
#226266722
#226266702
C2×#179896022
C2×D73⋊#1082
#226260472
#226260462
#226258852
#226258842
#226258732
#226258122
#226258102
#226257512
#435×D732
#2266873