Finite Group Databasebeta

← #33106751

Subgroups — #33106751

Order 18688.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 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#22610816C211yesmaximal, characteristic, complemented
6#22610632C211yesmaximal, characteristic, complemented
7#22610582C211yesmaximal, characteristic, complemented
8#22610374C211yesmaximal, characteristic, complemented
9#22610256C211yesmaximal, characteristic, complemented
10#22610255C211yesmaximal, characteristic, complemented
11#22610204C211yesmaximal, characteristic, complemented
12#22610136C211yesmaximal, characteristic, complemented
13#22609769C211yesmaximal, characteristic, complemented
14C4×C22⋊#10596831C211yesmaximal, characteristic, complemented
15C22×#104×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×C4×#10596831C2211yescharacteristic, 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
63C22×C42×C73C2211yescharacteristic
64C2×#104×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, complemented
75C2×#11924018C2×C411yescharacteristic, complemented
76C2×#11924016C2×C411yescharacteristic, complemented
77C2×#11924016C2×C411yescharacteristic, complemented
78C2×#11924015C2×C411yescharacteristic, complemented
79C2×#11924015C2×C411yescharacteristic, complemented
80C2×#11924013C2×C411yescharacteristic, complemented
81C2×#11924013C2×C411yescharacteristic, complemented
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, complemented
116#14556515C2×C411yescharacteristic, complemented
117#14556515C2×C411yescharacteristic, complemented
118#14556515C2×C411yescharacteristic, complemented
119#14556512C2×C411yescharacteristic, complemented
120#14556512C2×C411yescharacteristic, complemented
121#14556512C2×C411yescharacteristic, complemented
122#14556512C2×C411yescharacteristic, complemented
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#14556501—21no—
140C4×#10596831—22no—
141C4×#10596831—41no—
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×C73—21no—
158C23×C4×C73C2311yescharacteristic
159C2×M16×C73—21no—
160C2×M16×C73—22no—
161C2×M16×C73—41no—
162C2×M16×C73C2311yescharacteristic
163C2×M16×C73C2311yescharacteristic
164C22×C8×C73—21no—
165C2×C42×C73—22no—
166C2×C42×C73—21no—
167C2×C42×C73—41no—
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—24no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—42no—
277C22×C4×C73—42no—
278C22×C4×C73—42no—
279C22×C4×C73—42no—
280C22×C4×C73C22×C411yescharacteristic
281C22×C4×C73C22×C411yescharacteristic
282C22×C4×C73C2×D411yescharacteristic
283C22×C4×C73C2×D411yescharacteristic
284C22×C4×C73#4111yescharacteristic
285C22×C4×C73C2411yescharacteristic
286M16×C73—21no—
287M16×C73—21no—
288M16×C73—21no—
289M16×C73—42no—
290M16×C73C2×D412yes—
291C2×C8×C73—21no—
292C2×C8×C73—21no—
293C2×C8×C73—42no—
294C42×C73—21no—
295C42×C73—21no—
296C42×C73—21no—
297C42×C73—42no—
298C42×C73C2×D412yes—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—22no—
303C23×C73—21no—
304C23×C73—41no—
305C23×C73—42no—
306C23×C73—42no—
307C23×C73—81no—
308C23×C73C4×D411yescharacteristic
309C23×C73C4×D411yescharacteristic
310C23×C73C2×#4111yescharacteristic
311C22×D73—21no—
312Q8×C73—21no—
313Q8×C73—21no—
314Q8×C73—21no—
315Q8×C73—42no—
316Q8×C73C4×D412yes—
317D4×C73—22no—
318D4×C73—22no—
319D4×C73—21no—
320D4×C73—21no—
321D4×C73—21no—
322D4×C73—42no—
323D4×C73—42no—
324D4×C73—42no—
325D4×C73—41no—
326D4×C73—41no—
327D4×C73C4×D412yes—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—21no—
331C2×C4×C73—22no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—22no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—21no—
346C2×C4×C73—42no—
347C2×C4×C73—42no—
348C2×C4×C73—42no—
349C2×C4×C73—48no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73C4×D411yescharacteristic
355C2×C4×C73C4×D411yescharacteristic
356C2×C4×C73C23×C411yescharacteristic
357C2×C4×C73C22×D411yescharacteristic
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C2×#4111yescharacteristic
360C2×C4×C73H(5,𝔽2)11yescharacteristic
361C2×C4×C73H(5,𝔽2)11yescharacteristic
362C22⋊D73—41no—
363C22⋊D73—41no—
364C22⋊D73—42no—
365C22⋊D73—81no—
366C2×Dic73—21no—
367C2×Dic73—21no—
368C2×Dic73—21no—
369D292—21no—
370D292—21no—
371C4×D73—41no—
372C4×D73—41no—
373Dic146—21no—
374Dic146—21no—
375C8×C73—22no—
376C8×C73—41no—
377#10596831—21no—
378#10596831—21no—
379#10596831—21no—
380#10596831—21no—
381#10596831—21no—
382#10596831—21no—
383#10596831—21no—
384#10596831—21no—
385#10596831—41no—
386#10596831—41no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—22no—
393C22×C73—21no—
394C22×C73—21no—
395C22×C73—42no—
396C22×C73—42no—
397C22×C73—41no—
398C22×C73—41no—
399C22×C73—41no—
400C22×C73—41no—
401C22×C73—41no—
402C22×C73—84no—
403C22×C73#44312yescomplemented
404C22×C73C2×C4×D411yescharacteristic
405C22×C73#54611yescharacteristic
406C22×C73#55111yescharacteristic
407C2×D73—41no—
408C2×D73—41no—
409C2×D73—41no—
410C4×C73—24no—
411C4×C73—21no—
412C4×C73—21no—
413C4×C73—22no—
414C4×C73—42no—
415C4×C73—41no—
416C4×C73C2×C4×D411yescharacteristic
417C4×C73#51811yescharacteristic
418C4×C73D4211yescharacteristic
419C4×C73#54611yescharacteristic
420Dic73—41no—
421Dic73—41no—
422Dic73—41no—
423#22888—731nomaximal, Sylow
424C2×C73—21no—
425C2×C73—22no—
426C2×C73—21no—
427C2×C73—41no—
428C2×C73—42no—
429C2×C73—81no—
430C2×C73#235811yescharacteristic
431C2×C73C2×#44311yescharacteristic
432C2×C73#295611yescharacteristic
433D73—81no—
434#3002—731no—
435C2×#443—731no—
436#2933—731no—
437C22×#104D7311yescharacteristic, complemented
438#2880—731no—
439#1974—731no—
440#1937—731no—
441#1929—731no—
442#1896—731no—
443#1876—731no—
444#1876—731no—
445#1866—731no—
446#1855—731no—
447#1764—731no—
448C4×C22⋊C8—731no—
449C73#2288811yescharacteristic, complemented, Sylow
450C22×#41C2×D7311yescharacteristic
451C2×#135—731no—
452C2×#135—731no—
453C2×#131—731no—
454C2×#131—731no—
455C2×#131—731no—
456C22×M16C2×D7311yescharacteristic
457#525—731no—
458C22×C42C2×D7311yescharacteristic
459#452—731no—
460#452—731no—
461#451—731no—
462#450—731no—
463#449—731no—
464#449—731no—
465#448—731no—
466#447—731no—
467#443—1464no—
468#436—1461no—
469#435—1461no—
470#435—1461no—
471C8×D4—1461no—
472C2×#108—731no—
473C2×#108—731no—
474#424—731no—
475C2×#104—24no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104C2×D7311yescharacteristic
479C2×#104C2×D7311yescharacteristic
480C2×#104C2×D7311yescharacteristic
481C2×#104C2×D7311yescharacteristic
482#416—731no—
483#416—731no—
484#408—731no—
485#408—731no—
486#408—731no—
487#408—1461no—
488#408—1461no—
489#407—731no—
490#407—1461no—
491C2×C22⋊C8—731no—
492C2×C22⋊C8—731no—
493C2×C22⋊C8—1461no—
494#405—731no—
495C2×C4×C8—731no—
496C2×C4×C8—731no—
497#341—731no—
498#341—731no—
499#339—731no—
500#339—731no—
501#336—731no—
502#336—731no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—731no—
510C2×#41C4×D7311yescharacteristic
511C2×#41C4×D7311yescharacteristic
512C2×#41C22×D7311yescharacteristic
513C2×#41C22×D7311yescharacteristic
514C22×Q8C4×D7311yescharacteristic
515C22×D4—21no—
516C22×D4C4×D7311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D7311yescharacteristic
520#135—2921no—
521#135—2921no—
522#135—1462no—
523#135—1462no—
524C2×Q16—731no—
525C2×Q16—731no—
526C2×SD16—731no—
527C2×SD16—731no—
528C2×SD16—731no—
529C2×SD16—731no—
530C2×D8—731no—
531C2×D8—731no—
532#131—2921no—
533#131—2921no—
534#131—2921no—
535#131—1462no—
536#131—1462no—
537#131—1462no—
538C2×M16—21no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—731no—
542C2×M16—731no—
543C2×M16—1461no—
544C2×M16—1461no—
545C2×M16—1461no—
546C2×M16C22×D7311yescharacteristic
547C2×M16C22×D7311yescharacteristic
548C22×C8—21no—
549C22×C8—731no—
550C22×C8—731no—
551C22×C8—731no—
552C22×C8—731no—
553C22×C8—1461no—
554C22×C8—1461no—
555C22×C8—1461no—
556#123—1461no—
557C22⋊Q8—731no—
558C22⋊Q8—731no—
559#121—731no—
560#121—731no—
561#120—1461no—
562C4×D4—1461no—
563C4×D4—1461no—
564#117—731no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D7311yescharacteristic
569C2×C42C22×D7311yescharacteristic
570#108—2921no—
571#108—1462no—
572C4⋊C8—1461no—
573C4⋊C8—1461no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—2921no—
578#104—1462no—
579#104C22⋊D7314yescomplemented
580#103—731no—
581#103—731no—
582#103—731no—
583#103—731no—
584#102—731no—
585#102—731no—
586#102—731no—
587#102—731no—
588C22⋊C8—731no—
589C22⋊C8—731no—
590C22⋊C8—731no—
591C22⋊C8—731no—
592C22⋊C8—731no—
593C22⋊C8—731no—
594C22⋊C8—731no—
595C22⋊C8—731no—
596C22⋊C8—1461no—
597C22⋊C8—1461no—
598C22⋊C8—1461no—
599C22⋊C8—1461no—
600C22⋊C8—1461no—
601C22⋊C8—1461no—
602C22⋊C8—1461no—
603C22⋊C8—1461no—
604#97—1461no—
605C4×C8—2921no—
606C4×C8—1461no—
607C4×C8—1462no—
608C24—21no—
609C24#1192402711yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41—1461no—
625#41—1461no—
626#41—1461no—
627#41—1461no—
628#41C2×C22⋊D7312yes—
629#41#1192402812yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—731no—
634C2×Q8C2×C4×D7311yescharacteristic
635C2×Q8C2×C4×D7311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—731no—
646C2×D4—1461no—
647C2×D4—1461no—
648C2×D4—1461no—
649C2×D4C2×C4×D7311yescharacteristic
650C2×D4C2×C4×D7311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1461no—
668C22×C4C2×C4×D7311yescharacteristic
669C22×C4C2×C4×D7311yescharacteristic
670C22×C4D4×D7311yescharacteristic
671C22×C4D4×D7311yescharacteristic
672C22×C4#1192402711yescharacteristic
673C22×C4C23×D7311yescharacteristic
674Q16—2921no—
675Q16—1462no—
676SD16—2921no—
677SD16—2921no—
678SD16—1462no—
679SD16—1462no—
680D8—2921no—
681D8—1462no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—2922no—
687M16—2922no—
688M16—2922no—
689M16—1461no—
690M16—1461no—
691M16—1461no—
692M16—1461no—
693M16C2×C22⋊D7312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—2922no—
698C2×C8—2922no—
699C2×C8—2922no—
700C2×C8—731no—
701C2×C8—731no—
702C2×C8—731no—
703C2×C8—731no—
704C2×C8—731no—
705C2×C8—731no—
706C2×C8—731no—
707C2×C8—731no—
708C2×C8—1461no—
709C2×C8—1461no—
710C2×C8—1461no—
711C2×C8—1461no—
712C2×C8—1461no—
713C2×C8—1461no—
714C2×C8—1461no—
715C2×C8—1461no—
716C2×C8—1461no—
717C2×C8—1461no—
718C4⋊C4—731no—
719C4⋊C4—731no—
720C4⋊C4—1461no—
721C4⋊C4—1461no—
722C22⋊C4—1461no—
723C22⋊C4—1461no—
724C22⋊C4—1461no—
725C22⋊C4—1461no—
726C22⋊C4—1461no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1461no—
732C42C2×C22⋊D7312yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—1461no—
743C23#1455655111yescharacteristic
744C23#1455655111yescharacteristic
745C23C2×#1192402711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—1461no—
751Q8—1461no—
752Q8C4×C22⋊D7312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—2922no—
764D4—2921no—
765D4—2921no—
766D4—5841no—
767D4—1461no—
768D4—1461no—
769D4C4×C22⋊D7312yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—2921no—
797C2×C4—2921no—
798C2×C4—1461no—
799C2×C4—1461no—
800C2×C4—1461no—
801C2×C4#1455655111yescharacteristic
802C2×C4#1455655111yescharacteristic
803C2×C4C22×C4×D7311yescharacteristic
804C2×C4C2×D4×D7311yescharacteristic
805C2×C4C22×C22⋊D7311yescharacteristic
806C2×C4C2×#1192402811yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663611yescharacteristic
809C8—22no—
810C8—41no—
811C8—2921no—
812C8—2921no—
813C8—1461no—
814C8—1461no—
815C8—1461no—
816C8—1461no—
817C8—1461no—
818C8—1461no—
819C8—1461no—
820C8—1461no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—2921no—
838C22—2921no—
839C22—2921no—
840C22#1798870112yescomplemented
841C22C2×#1455655111yescharacteristic
842C22#1798923111yescharacteristic
843C22#1798926311yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—2921no—
851C4—2921no—
852C4—2921no—
853C4C2×C4×C22⋊D7311yescharacteristic
854C4#1798906011yescharacteristic
855C4D4×C22⋊D7311yescharacteristic
856C4#1798922711yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—5841no—
864C2#2261291011yescharacteristic
865C2C2×#1798870111yescharacteristic
866C2#2261883711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC22×#104×C73C2
socleC22×C73C2×C4×D4
prime radical#22619149C2
cosocleC22×C4×C73C24
hypercenterC22×#104D73
hypocenterC73#22888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#17988701C2semidirect
3. #22618656C2semidirect
4. #22618380C2semidirect
5. #22610816C2semidirect
6. #22610632C2semidirect
7. #22610582C2semidirect
8. #22610374C2semidirect
9. #22610256C2semidirect
10. #22610255C2semidirect
11. #22610204C2semidirect
12. #22610136C2semidirect
13. #22609769C2semidirect
14. C4×C22⋊#10596831C2semidirect
15. C22×#104×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×C4×#10596831C22semidirect
54. C2×C4×#10596831C22semidirect
55. #17988351C22semidirect
56. #17988351C22semidirect
57. #17988347C22semidirect
58. #17988347C22semidirect
59. #17988342C22semidirect
60. #17988342C22semidirect
74. C2×#11924018C2×C4semidirect
75. C2×#11924018C2×C4semidirect
76. C2×#11924016C2×C4semidirect
77. C2×#11924016C2×C4semidirect
78. C2×#11924015C2×C4semidirect
79. C2×#11924015C2×C4semidirect
80. C2×#11924013C2×C4semidirect
81. C2×#11924013C2×C4semidirect
115. #14556515C2×C4semidirect
116. #14556515C2×C4semidirect
117. #14556515C2×C4semidirect
118. #14556515C2×C4semidirect
119. #14556512C2×C4semidirect
120. #14556512C2×C4semidirect
121. #14556512C2×C4semidirect
122. #14556512C2×C4semidirect
173. #104×C73D4semidirect
403. C22×C73#443semidirect
437. C22×#104D73semidirect
449. C73#22888semidirect
579. #104C22⋊D73semidirect
840. C22#17988701semidirect

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
#226108162
#226106322
#226105822
#226103742
#226102562
#226102552
#226102042
#226101362
#226097692
C4×C22⋊#105968312
C22×#104×C732
#2288873