Finite Group Databasebeta

← #33106766

Subgroups — #33106766

Order 18688.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619149C211yesmaximal, characteristic
2C2×#17988701C211yesmaximal, characteristic, complemented
3#22618656C211yesmaximal, characteristic, complemented
4#22618380C211yesmaximal, characteristic, complemented
5#22610821C211yesmaximal, characteristic, complemented
6#22610632C211yesmaximal, characteristic, complemented
7#22610582C211yesmaximal, characteristic, complemented
8#22610379C211yesmaximal, characteristic, complemented
9#22610256C211yesmaximal, characteristic, complemented
10#22610255C211yesmaximal, characteristic, complemented
11#22610204C211yesmaximal, characteristic, complemented
12#22610136C211yesmaximal, characteristic, complemented
13#22609776C211yesmaximal, characteristic, complemented
14#22609697C211yesmaximal, characteristic, complemented
15C2×#421×C73C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556599C2211yescharacteristic, complemented
19C2×#14556598C2211yescharacteristic
20C2×#14556598C2211yescharacteristic
21#17989098C2211yescharacteristic
22#17988749C411yescharacteristic, complemented
23#17988749C411yescharacteristic, complemented
24#17988743C411yescharacteristic, complemented
25#17988738C411yescharacteristic, complemented
26#17988732C411yescharacteristic, complemented
27#17988732C411yescharacteristic, complemented
28#17988726C411yescharacteristic, complemented
29#17988721C411yescharacteristic, complemented
30#17988701—24no—
31#17988663—21no—
32#17988658—21no—
33#17988656—21no—
34C8×C22⋊D73—21no—
35C2×#14556526C2211yescharacteristic, complemented
36C2×#14556526C2211yescharacteristic, complemented
37#17988615C2211yescharacteristic, complemented
38C2×#14556519C2211yescharacteristic, complemented
39C2×#14556519C2211yescharacteristic, complemented
40#17988583C2211yescharacteristic
41#17988583C2211yescharacteristic
42#17988555C2211yescharacteristic, complemented
43#17988554—21no—
44#17988554—21no—
45#17988554C2211yescharacteristic
46#17988554C2211yescharacteristic
47#17988551—21no—
48#17988551C2211yescharacteristic
49C2×C22⋊#10596831—21no—
50C2×C22⋊#10596831C2211yescharacteristic
51C2×C22⋊#10596831C2211yescharacteristic
52#17988545C2211yescharacteristic, complemented
53C2×#14556502C2211yescharacteristic, complemented
54C2×C4×#10596831C2211yescharacteristic, complemented
55#17988351C2211yescharacteristic, complemented
56#17988351C2211yescharacteristic, complemented
57#17988347C2211yescharacteristic, complemented
58#17988347C2211yescharacteristic, complemented
59#17988342C2211yescharacteristic, complemented
60#17988342C2211yescharacteristic, complemented
61C22×#41×C73C2211yescharacteristic
62C22×M16×C73C2211yescharacteristic
63C2×#117×C73C2211yescharacteristic
64#421×C73—24no—
65C2×#104×C73C2211yescharacteristic
66C2×#104×C73C2211yescharacteristic
67C2×#104×C73C2211yescharacteristic
68C2×#104×C73C2211yescharacteristic
69C2×#11924028C2311yescharacteristic
70#14556611—22no—
71#14556611—22no—
72#14556611—41no—
73#14556611—41no—
74C2×#11924018C2×C411yescharacteristic
75C2×#11924018C2×C411yescharacteristic
76C2×#11924016C2×C411yescharacteristic
77C2×#11924016C2×C411yescharacteristic
78C2×#11924015C2×C411yescharacteristic
79C2×#11924015C2×C411yescharacteristic
80C2×#11924013C2×C411yescharacteristic
81C2×#11924013C2×C411yescharacteristic
82#14556599—22no—
83#14556599—41no—
84#14556598—22no—
85#14556598—22no—
86#14556598—41no—
87#14556598—41no—
88C2×#11924012—21no—
89C2×#11924012—21no—
90C2×#11924012C2311yescharacteristic
91C2×#11924012C2311yescharacteristic
92C2×#11924011—21no—
93C22×#10596831—21no—
94C22×#10596831—21no—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99C2×C8×D73—21no—
100#14556574—21no—
101#14556570C2×C411yescharacteristic
102#14556570C2×C411yescharacteristic
103#14556565C2×C411yescharacteristic
104#14556565C2×C411yescharacteristic
105#14556560—21no—
106C4×C22⋊D73—21no—
107C4×C22⋊D73—21no—
108#14556550C2311yescharacteristic
109#14556526—22no—
110#14556526—41no—
111#14556520—21no—
112#14556520—21no—
113#14556519—22no—
114#14556519—41no—
115#14556515C2×C411yescharacteristic
116#14556515C2×C411yescharacteristic
117#14556515C2×C411yescharacteristic
118#14556515C2×C411yescharacteristic
119#14556512C2×C411yescharacteristic
120#14556512C2×C411yescharacteristic
121#14556512C2×C411yescharacteristic
122#14556512C2×C411yescharacteristic
123C22⋊#10596831—21no—
124C22⋊#10596831—21no—
125C22⋊#10596831—21no—
126C22⋊#10596831—21no—
127C22⋊#10596831—21no—
128C22⋊#10596831—21no—
129C22⋊#10596831C2×C411yescharacteristic
130C22⋊#10596831C2×C411yescharacteristic
131C22⋊#10596831C2×C411yescharacteristic
132C22⋊#10596831C2×C411yescharacteristic
133C22⋊#10596831D411yescharacteristic
134C22⋊#10596831D411yescharacteristic
135C22⋊#10596831D411yescharacteristic
136C22⋊#10596831D411yescharacteristic
137#14556503—21no—
138#14556503—21no—
139#14556502—41no—
140#14556501—21no—
141C4×#10596831—22no—
142C8×Dic73—21no—
143C2×#41×C73—21no—
144C2×#41×C73—21no—
145C2×#41×C73—22no—
146C2×#41×C73—22no—
147C2×#41×C73—41no—
148C2×#41×C73—41no—
149C2×#41×C73C2×C411yescharacteristic
150C2×#41×C73C2×C411yescharacteristic
151C2×#41×C73C2311yescharacteristic
152C2×#41×C73C2311yescharacteristic
153C22×Q8×C73C2×C411yescharacteristic
154C22×D4×C73—21no—
155C22×D4×C73C2×C411yescharacteristic
156C23×C4×C73—21no—
157C23×C4×C73C2311yescharacteristic
158C2×M16×C73—21no—
159C2×M16×C73—22no—
160C2×M16×C73—41no—
161C2×M16×C73C2311yescharacteristic
162C2×M16×C73C2311yescharacteristic
163C22×C8×C73—21no—
164#117×C73—22no—
165#117×C73—41no—
166C2×C4⋊C4×C73—21no—
167C2×C22⋊C4×C73—21no—
168C2×C42×C73C2311yescharacteristic
169C2×C42×C73C2311yescharacteristic
170#104×C73—22no—
171#104×C73—22no—
172#104×C73—22no—
173#104×C73D414yescomplemented
174#11924028—21no—
175#11924028—21no—
176#11924028—21no—
177#11924028—21no—
178C2×Dic146C22×C411yescharacteristic
179C2×D292C22×C411yescharacteristic
180C2×C22⋊D73—21no—
181C2×C22⋊D73—21no—
182C2×C22⋊D73—21no—
183C2×C4×D73—21no—
184#11924018—22no—
185#11924018—41no—
186#11924016—22no—
187#11924016—41no—
188#11924015—22no—
189#11924015—41no—
190#11924013—22no—
191#11924013—41no—
192#11924012—21no—
193#11924012—21no—
194#11924012—21no—
195#11924012—21no—
196#11924012—42no—
197#11924012—42no—
198#11924011—42no—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831—21no—
205C2×#10596831—21no—
206C2×#10596831—21no—
207C2×#10596831—21no—
208C2×#10596831—21no—
209C2×#10596831—42no—
210C2×#10596831—42no—
211C2×#10596831C22×C411yescharacteristic
212C2×#10596831C22×C411yescharacteristic
213C2×#10596831C22×C411yescharacteristic
214C2×#10596831C22×C411yescharacteristic
215C2×#10596831C2×D411yescharacteristic
216C2×#10596831C2×D411yescharacteristic
217C2×#10596831C2×D411yescharacteristic
218C2×#10596831C2×D411yescharacteristic
219C8×D73—42no—
220C4⋊Dic73C22×C411yescharacteristic
221C4⋊Dic73C22×C411yescharacteristic
222#11924007—21no—
223#11924007—21no—
224C22⋊Dic73—21no—
225C22⋊Dic73—21no—
226C22⋊Dic73—21no—
227#11924005—21no—
228#11924005—21no—
229C4×Dic73—21no—
230C24×C73—21no—
231C24×C73#4111yescharacteristic
232#41×C73—21no—
233#41×C73—21no—
234#41×C73—22no—
235#41×C73—22no—
236#41×C73—21no—
237#41×C73—21no—
238#41×C73—21no—
239#41×C73—21no—
240#41×C73—42no—
241#41×C73—42no—
242#41×C73—41no—
243#41×C73—41no—
244#41×C73—42no—
245#41×C73—42no—
246#41×C73C2×D412yes—
247#41×C73#4112yes—
248C2×Q8×C73—21no—
249C2×Q8×C73—22no—
250C2×Q8×C73—41no—
251C2×Q8×C73C22×C411yescharacteristic
252C2×Q8×C73C22×C411yescharacteristic
253C2×D4×C73—21no—
254C2×D4×C73—22no—
255C2×D4×C73—21no—
256C2×D4×C73—21no—
257C2×D4×C73—21no—
258C2×D4×C73—21no—
259C2×D4×C73—41no—
260C2×D4×C73—42no—
261C2×D4×C73—42no—
262C2×D4×C73C22×C411yescharacteristic
263C2×D4×C73C22×C411yescharacteristic
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—42no—
276C22×C4×C73—42no—
277C22×C4×C73C22×C411yescharacteristic
278C22×C4×C73C22×C411yescharacteristic
279C22×C4×C73C2×D411yescharacteristic
280C22×C4×C73C2×D411yescharacteristic
281C22×C4×C73#4111yescharacteristic
282C22×C4×C73C2411yescharacteristic
283M16×C73—21no—
284M16×C73—21no—
285M16×C73—21no—
286M16×C73—42no—
287M16×C73C2×D412yes—
288C2×C8×C73—21no—
289C2×C8×C73—21no—
290C2×C8×C73—42no—
291C4⋊C4×C73—42no—
292C22⋊C4×C73—42no—
293C42×C73—21no—
294C42×C73—21no—
295C42×C73—21no—
296C42×C73C2×D412yes—
297C23×C73—21no—
298C23×C73—21no—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—42no—
304C23×C73—42no—
305C23×C73—81no—
306C23×C73C4×D411yescharacteristic
307C23×C73C4×D411yescharacteristic
308C23×C73C2×#4111yescharacteristic
309C22×D73—21no—
310Q8×C73—21no—
311Q8×C73—21no—
312Q8×C73—21no—
313Q8×C73—42no—
314Q8×C73C4×D412yes—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—21no—
318D4×C73—21no—
319D4×C73—21no—
320D4×C73—42no—
321D4×C73—42no—
322D4×C73—42no—
323D4×C73—41no—
324D4×C73—41no—
325D4×C73C4×D412yes—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—22no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—22no—
339C2×C4×C73—21no—
340C2×C4×C73—22no—
341C2×C4×C73—42no—
342C2×C4×C73—42no—
343C2×C4×C73—42no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73C4×D411yescharacteristic
352C2×C4×C73C4×D411yescharacteristic
353C2×C4×C73C23×C411yescharacteristic
354C2×C4×C73C22×D411yescharacteristic
355C2×C4×C73C22×D411yescharacteristic
356C2×C4×C73C2×#4111yescharacteristic
357C2×C4×C73H(5,𝔽2)11yescharacteristic
358C2×C4×C73H(5,𝔽2)11yescharacteristic
359C22⋊D73—42no—
360C22⋊D73—41no—
361C22⋊D73—41no—
362C22⋊D73—81no—
363C2×Dic73—21no—
364C2×Dic73—21no—
365C2×Dic73—21no—
366D292—21no—
367D292—21no—
368C4×D73—41no—
369C4×D73—41no—
370Dic146—21no—
371Dic146—21no—
372C8×C73—22no—
373C8×C73—41no—
374#10596831—21no—
375#10596831—21no—
376#10596831—21no—
377#10596831—21no—
378#10596831—21no—
379#10596831—21no—
380#10596831—21no—
381#10596831—21no—
382#10596831—41no—
383#10596831—41no—
384C22×C73—21no—
385C22×C73—21no—
386C22×C73—21no—
387C22×C73—21no—
388C22×C73—22no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—21no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73—41no—
396C22×C73—41no—
397C22×C73—41no—
398C22×C73—81no—
399C22×C73—81no—
400C22×C73—84no—
401C22×C73C2×C4×D411yescharacteristic
402C22×C73#54611yescharacteristic
403C22×C73#55111yescharacteristic
404C2×D73—41no—
405C2×D73—41no—
406C2×D73—41no—
407C4×C73—21no—
408C4×C73—21no—
409C4×C73—22no—
410C4×C73—42no—
411C4×C73—41no—
412C4×C73—81no—
413C4×C73C2×C4×D411yescharacteristic
414C4×C73#51811yescharacteristic
415C4×C73D4211yescharacteristic
416C4×C73#54611yescharacteristic
417Dic73—41no—
418Dic73—41no—
419Dic73—41no—
420#22889—731nomaximal, Sylow
421C2×C73—21no—
422C2×C73—21no—
423C2×C73—41no—
424C2×C73—41no—
425C2×C73—42no—
426C2×C73—81no—
427C2×C73#235811yescharacteristic
428C2×C73#295511yescharacteristic
429C2×C73#295711yescharacteristic
430D73—81no—
431#3002—731no—
432C2×#443—731no—
433#2933—731no—
434C2×#421D7311yescharacteristic, complemented
435#2880—731no—
436#1975—731no—
437#1937—731no—
438#1929—731no—
439#1897—731no—
440#1876—731no—
441#1876—731no—
442#1866—731no—
443#1855—731no—
444#1765—731no—
445#1750—731no—
446C73#2288911yescharacteristic, complemented, Sylow
447C22×#41C2×D7311yescharacteristic
448C2×#135—731no—
449C2×#135—731no—
450C2×#131—731no—
451C2×#131—731no—
452C2×#131—731no—
453C22×M16C2×D7311yescharacteristic
454#525—731no—
455C2×#117C2×D7311yescharacteristic
456#452—731no—
457#452—731no—
458#451—731no—
459#450—731no—
460#449—731no—
461#449—731no—
462#448—731no—
463#447—731no—
464#443—1464no—
465#436—1461no—
466#435—1461no—
467#435—1461no—
468C8×D4—1461no—
469C2×#108—731no—
470C2×#108—731no—
471#424—731no—
472#421—24no—
473C2×#104—731no—
474C2×#104—731no—
475C2×#104C2×D7311yescharacteristic
476C2×#104C2×D7311yescharacteristic
477C2×#104C2×D7311yescharacteristic
478C2×#104C2×D7311yescharacteristic
479#416—731no—
480#416—731no—
481#408—731no—
482#408—731no—
483#408—731no—
484#408—1461no—
485#408—1461no—
486#407—731no—
487#407—1461no—
488C2×C22⋊C8—731no—
489C2×C22⋊C8—731no—
490C2×C22⋊C8—1461no—
491#405—731no—
492C2×#97—731no—
493C2×C4×C8—731no—
494#341—731no—
495#341—731no—
496#339—731no—
497#339—731no—
498#336—731no—
499#336—731no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—731no—
507C2×#41C4×D7311yescharacteristic
508C2×#41C4×D7311yescharacteristic
509C2×#41C22×D7311yescharacteristic
510C2×#41C22×D7311yescharacteristic
511C22×Q8C4×D7311yescharacteristic
512C22×D4—21no—
513C22×D4C4×D7311yescharacteristic
514C23×C4—21no—
515C23×C4C22×D7311yescharacteristic
516#135—2921no—
517#135—2921no—
518#135—1462no—
519#135—1462no—
520C2×Q16—731no—
521C2×Q16—731no—
522C2×SD16—731no—
523C2×SD16—731no—
524C2×SD16—731no—
525C2×SD16—731no—
526C2×D8—731no—
527C2×D8—731no—
528#131—2921no—
529#131—2921no—
530#131—2921no—
531#131—1462no—
532#131—1462no—
533#131—1462no—
534C2×M16—21no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—731no—
538C2×M16—731no—
539C2×M16—1461no—
540C2×M16—1461no—
541C2×M16—1461no—
542C2×M16C22×D7311yescharacteristic
543C2×M16C22×D7311yescharacteristic
544C22×C8—21no—
545C22×C8—731no—
546C22×C8—731no—
547C22×C8—731no—
548C22×C8—731no—
549C22×C8—1461no—
550C22×C8—1461no—
551C22×C8—1461no—
552#123—1461no—
553C22⋊Q8—731no—
554C22⋊Q8—731no—
555#121—731no—
556#121—731no—
557#120—1461no—
558C4×D4—1461no—
559C4×D4—1461no—
560#117—22no—
561#117—41no—
562#117—731no—
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D7311yescharacteristic
566C2×C42C22×D7311yescharacteristic
567#108—2921no—
568#108—1462no—
569C4⋊C8—1461no—
570C4⋊C8—1461no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—2921no—
575#104—1462no—
576#104C22⋊D7314yescomplemented
577#103—731no—
578#103—731no—
579#103—731no—
580#103—731no—
581#102—731no—
582#102—731no—
583#102—731no—
584#102—731no—
585C22⋊C8—731no—
586C22⋊C8—731no—
587C22⋊C8—731no—
588C22⋊C8—731no—
589C22⋊C8—731no—
590C22⋊C8—731no—
591C22⋊C8—731no—
592C22⋊C8—731no—
593C22⋊C8—1461no—
594C22⋊C8—1461no—
595C22⋊C8—1461no—
596C22⋊C8—1461no—
597C22⋊C8—1461no—
598C22⋊C8—1461no—
599C22⋊C8—1461no—
600C22⋊C8—1461no—
601#97—2921no—
602#97—1461no—
603C4×C8—1461no—
604C4×C8—1462no—
605C24—21no—
606C24#1192402711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1461no—
622#41—1461no—
623#41—1461no—
624#41—1461no—
625#41C2×C22⋊D7312yes—
626#41#1192402812yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—731no—
631C2×Q8C2×C4×D7311yescharacteristic
632C2×Q8C2×C4×D7311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—731no—
643C2×D4—1461no—
644C2×D4—1461no—
645C2×D4—1461no—
646C2×D4C2×C4×D7311yescharacteristic
647C2×D4C2×C4×D7311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—1461no—
662C22×C4C2×C4×D7311yescharacteristic
663C22×C4C2×C4×D7311yescharacteristic
664C22×C4D4×D7311yescharacteristic
665C22×C4D4×D7311yescharacteristic
666C22×C4#1192402711yescharacteristic
667C22×C4C23×D7311yescharacteristic
668Q16—2921no—
669Q16—1462no—
670SD16—2921no—
671SD16—2921no—
672SD16—1462no—
673SD16—1462no—
674D8—2921no—
675D8—1462no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—42no—
680M16—2922no—
681M16—2922no—
682M16—2922no—
683M16—1461no—
684M16—1461no—
685M16—1461no—
686M16—1461no—
687M16C2×C22⋊D7312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—42no—
691C2×C8—2922no—
692C2×C8—2922no—
693C2×C8—2922no—
694C2×C8—731no—
695C2×C8—731no—
696C2×C8—731no—
697C2×C8—731no—
698C2×C8—731no—
699C2×C8—731no—
700C2×C8—731no—
701C2×C8—731no—
702C2×C8—1461no—
703C2×C8—1461no—
704C2×C8—1461no—
705C2×C8—1461no—
706C2×C8—1461no—
707C2×C8—1461no—
708C2×C8—1461no—
709C2×C8—1461no—
710C2×C8—1461no—
711C2×C8—1461no—
712C4⋊C4—42no—
713C4⋊C4—731no—
714C4⋊C4—731no—
715C4⋊C4—1461no—
716C4⋊C4—1461no—
717C22⋊C4—42no—
718C22⋊C4—1461no—
719C22⋊C4—1461no—
720C22⋊C4—1461no—
721C22⋊C4—1461no—
722C22⋊C4—1461no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—1461no—
727C42C2×C22⋊D7312yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1461no—
738C23#1455655111yescharacteristic
739C23#1455655111yescharacteristic
740C23C2×#1192402711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1461no—
746Q8—1461no—
747Q8C4×C22⋊D7312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—2922no—
759D4—2921no—
760D4—2921no—
761D4—5841no—
762D4—1461no—
763D4—1461no—
764D4C4×C22⋊D7312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—2921no—
791C2×C4—2921no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1461no—
795C2×C4#1455655111yescharacteristic
796C2×C4#1455655111yescharacteristic
797C2×C4C22×C4×D7311yescharacteristic
798C2×C4C2×D4×D7311yescharacteristic
799C2×C4C22×C22⋊D7311yescharacteristic
800C2×C4C2×#1192402811yescharacteristic
801C2×C4#1455663611yescharacteristic
802C2×C4#1455663611yescharacteristic
803C8—22no—
804C8—41no—
805C8—2921no—
806C8—2921no—
807C8—1461no—
808C8—1461no—
809C8—1461no—
810C8—1461no—
811C8—1461no—
812C8—1461no—
813C8—1461no—
814C8—1461no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2921no—
833C22—2921no—
834C22—2921no—
835C22C2×#1455655111yescharacteristic
836C22#1798923111yescharacteristic
837C22#1798926311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—2921no—
845C4—2921no—
846C4—2921no—
847C4C2×C4×C22⋊D7311yescharacteristic
848C4#1798906011yescharacteristic
849C4D4×C22⋊D7311yescharacteristic
850C4#1798922711yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—5841no—
858C2#2261291011yescharacteristic
859C2#2261883011yescharacteristic
860C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#421×C73C2
socleC22×C73C2×C4×D4
prime radical#22619149C2
cosocleC22×C4×C73C24
hypercenterC2×#421D73
hypocenterC73#22889
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#17988701C2semidirect
3. #22618656C2semidirect
4. #22618380C2semidirect
5. #22610821C2semidirect
6. #22610632C2semidirect
7. #22610582C2semidirect
8. #22610379C2semidirect
9. #22610256C2semidirect
10. #22610255C2semidirect
11. #22610204C2semidirect
12. #22610136C2semidirect
13. #22609776C2semidirect
14. #22609697C2semidirect
15. C2×#421×C73C2semidirect
18. C2×#14556599C22semidirect
22. #17988749C4semidirect
23. #17988749C4semidirect
24. #17988743C4semidirect
25. #17988738C4semidirect
26. #17988732C4semidirect
27. #17988732C4semidirect
28. #17988726C4semidirect
29. #17988721C4semidirect
35. C2×#14556526C22semidirect
36. C2×#14556526C22semidirect
37. #17988615C22semidirect
38. C2×#14556519C22semidirect
39. C2×#14556519C22semidirect
42. #17988555C22semidirect
52. #17988545C22semidirect
53. C2×#14556502C22semidirect
54. C2×C4×#10596831C22semidirect
55. #17988351C22semidirect
56. #17988351C22semidirect
57. #17988347C22semidirect
58. #17988347C22semidirect
59. #17988342C22semidirect
60. #17988342C22semidirect
173. #104×C73D4semidirect
434. C2×#421D73semidirect
446. C73#22889semidirect
576. #104C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226191492
C2×#179887012
#226186562
#226183802
#226108212
#226106322
#226105822
#226103792
#226102562
#226102552
#226102042
#226101362
#226097762
#226096972
C2×#421×C732
#2288973