Finite Group Databasebeta

← #33106748

Subgroups — #33106748

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#22619147C211yesmaximal, characteristic
2C2×#17988701C211yesmaximal, characteristic, complemented
3#22618658C211yesmaximal, characteristic, complemented
4C22×#14556519C211yesmaximal, characteristic, complemented
5#22618381C211yesmaximal, characteristic, complemented
6#22610816C211yesmaximal, characteristic, complemented
7#22610636C211yesmaximal, characteristic, complemented
8#22610577C211yesmaximal, characteristic, complemented
9#22610256C211yesmaximal, characteristic, complemented
10#22610255C211yesmaximal, characteristic, complemented
11#22610207C211yesmaximal, characteristic, complemented
12#22610135C211yesmaximal, characteristic, complemented
13#22609765C211yesmaximal, characteristic, complemented
14C4×C22⋊#10596831C211yesmaximal, characteristic, complemented
15C73×#1896C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556611C2211yescharacteristic
19C2×#14556599C2211yescharacteristic
20C2×#14556599C2211yescharacteristic
21C2×#14556598C2211yescharacteristic, complemented
22C22×#11924012C2211yescharacteristic
23#17988747C411yescharacteristic, complemented
24#17988747C411yescharacteristic, complemented
25#17988742C411yescharacteristic, complemented
26#17988737C411yescharacteristic, complemented
27#17988730C411yescharacteristic, complemented
28#17988730C411yescharacteristic, complemented
29#17988725C411yescharacteristic, complemented
30#17988720C411yescharacteristic, complemented
31#17988701—24no—
32#17988665—21no—
33#17988659—21no—
34#17988659—21no—
35D4×#10596831—21no—
36C2×#14556526C2211yescharacteristic, complemented
37C2×#14556526C2211yescharacteristic, complemented
38#17988614C2211yescharacteristic, complemented
39C2×#14556519—24no—
40C2×#14556519C2211yescharacteristic
41C2×#14556519C2211yescharacteristic
42C2×#14556519C2211yescharacteristic
43C2×#14556519C2211yescharacteristic
44#17988581C2211yescharacteristic
45#17988581C2211yescharacteristic
46#17988555C2211yescharacteristic
47#17988555C2211yescharacteristic
48#17988554C2211yescharacteristic, complemented
49#17988552—21no—
50#17988552—21no—
51#17988549—21no—
52C2×C22⋊#10596831C2211yescharacteristic
53C2×C22⋊#10596831C2211yescharacteristic
54C22⋊C8×D73—21no—
55#17988543C2211yescharacteristic, complemented
56C2×C4×#10596831C2211yescharacteristic, complemented
57C2×C4×#10596831C2211yescharacteristic, complemented
58#17988351C2211yescharacteristic, complemented
59#17988351C2211yescharacteristic, complemented
60#17988342C2211yescharacteristic, complemented
61#17988342C2211yescharacteristic, complemented
62#525×C73C2211yescharacteristic
63C22×C42×C73C2211yescharacteristic
64C2×#104×C73C2211yescharacteristic, complemented
65C2×#104×C73C2211yescharacteristic, complemented
66#407×C73C2211yescharacteristic
67#339×C73C2211yescharacteristic, complemented
68#339×C73C2211yescharacteristic, complemented
69C2×#11924028—22no—
70C2×#11924028—22no—
71C2×#11924028—21no—
72C2×#11924028—21no—
73C2×#11924028—41no—
74C2×#11924028—41no—
75C2×#11924028C2×C411yescharacteristic
76C2×#11924028C2×C411yescharacteristic
77C2×#11924028C2311yescharacteristic
78C2×#11924028C2311yescharacteristic
79C22×Dic146C2×C411yescharacteristic
80C22×D292C2×C411yescharacteristic
81C22×C22⋊D73—21no—
82C22×C4×D73—21no—
83#14556611—22no—
84#14556611—22no—
85#14556611—41no—
86#14556611—41no—
87C2×#11924018C2×C411yescharacteristic, complemented
88C2×#11924018C2×C411yescharacteristic, complemented
89C2×#11924016C2×C411yescharacteristic, complemented
90C2×#11924016C2×C411yescharacteristic, complemented
91C2×#11924015C2×C411yescharacteristic, complemented
92C2×#11924015C2×C411yescharacteristic, complemented
93C2×#11924013C2×C411yescharacteristic, complemented
94C2×#11924013C2×C411yescharacteristic, complemented
95#14556599—22no—
96#14556599—22no—
97#14556599—41no—
98#14556599—41no—
99#14556598—22no—
100#14556598—41no—
101C2×#11924012—21no—
102C2×#11924012—22no—
103C2×#11924012—21no—
104C2×#11924012—41no—
105C2×#11924012C2311yescharacteristic
106C2×#11924012C2311yescharacteristic
107C2×#11924011—21no—
108C2×#11924011—21no—
109C22×#10596831—21no—
110C22×#10596831—21no—
111C22×#10596831C2311yescharacteristic
112C22×#10596831C2311yescharacteristic
113C22×#10596831C2311yescharacteristic
114C22×#10596831C2311yescharacteristic
115C2×C8×D73—21no—
116C2×C8×D73—21no—
117#14556526—22no—
118#14556526—41no—
119C4⋊#10596831—21no—
120C4⋊#10596831—21no—
121#14556519—22no—
122#14556519—22no—
123#14556519—22no—
124#14556519D414yescomplemented
125#14556514C2×C411yescharacteristic, complemented
126#14556514C2×C411yescharacteristic, complemented
127#14556514C2×C411yescharacteristic, complemented
128#14556514C2×C411yescharacteristic, complemented
129#14556511C2×C411yescharacteristic, complemented
130#14556511C2×C411yescharacteristic, complemented
131#14556511C2×C411yescharacteristic, complemented
132#14556511C2×C411yescharacteristic, complemented
133C22⋊#10596831—21no—
134C22⋊#10596831—21no—
135C22⋊#10596831C2×C411yescharacteristic
136C22⋊#10596831C2×C411yescharacteristic
137C22⋊#10596831C2×C411yescharacteristic
138C22⋊#10596831C2×C411yescharacteristic
139C22⋊#10596831D411yescharacteristic
140C22⋊#10596831D411yescharacteristic
141C22⋊#10596831D411yescharacteristic
142C22⋊#10596831D411yescharacteristic
143#14556503—21no—
144#14556503—21no—
145#14556503—21no—
146#14556503—21no—
147#14556502—21no—
148C4×#10596831—21no—
149C4×#10596831—22no—
150C4×#10596831—41no—
151C2×#41×C73C2311yescharacteristic
152C23×C4×C73—21no—
153C23×C4×C73C2311yescharacteristic
154C2×M16×C73C2311yescharacteristic
155C2×M16×C73C2311yescharacteristic
156#123×C73—21no—
157C22⋊Q8×C73C2×C411yescharacteristic
158C22⋊Q8×C73C2×C411yescharacteristic
159#121×C73C2×C411yescharacteristic
160#121×C73C2×C411yescharacteristic
161#120×C73—21no—
162C4×D4×C73—21no—
163C4×D4×C73—21no—
164#117×C73C2311yescharacteristic
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—41no—
172C22⋊C8×C73—21no—
173C22⋊C8×C73—21no—
174C23×D73—21no—
175#11924028—21no—
176#11924028—21no—
177#11924028—21no—
178#11924028—21no—
179#11924028—21no—
180#11924028—21no—
181#11924028—22no—
182#11924028—22no—
183#11924028—41no—
184#11924028—41no—
185#11924028—42no—
186#11924028—42no—
187#11924028—42no—
188#11924028—42no—
189#11924028C2×D412yes—
190#11924028#4112yes—
191C2×Dic146—22no—
192C2×Dic146—21no—
193C2×Dic146—41no—
194C2×Dic146C22×C411yescharacteristic
195C2×Dic146C22×C411yescharacteristic
196C2×D292—22no—
197C2×D292—21no—
198C2×D292—41no—
199C2×D292C22×C411yescharacteristic
200C2×D292C22×C411yescharacteristic
201C2×C22⋊D73—21no—
202C2×C22⋊D73—21no—
203C2×C22⋊D73—21no—
204C2×C22⋊D73—21no—
205C2×C22⋊D73—42no—
206C2×C22⋊D73—42no—
207C22×Dic73—21no—
208C2×C4×D73—21no—
209C2×C4×D73—21no—
210C2×C4×D73—21no—
211C2×C4×D73—21no—
212C2×C4×D73—42no—
213C2×C4×D73—42no—
214#11924018—22no—
215#11924018—41no—
216#11924016—22no—
217#11924016—41no—
218#11924015—22no—
219#11924015—41no—
220#11924013—22no—
221#11924013—41no—
222#11924012—21no—
223#11924012—21no—
224#11924012—21no—
225#11924012—42no—
226#11924012—42no—
227#11924012C2×D412yes—
228#11924011—42no—
229#11924011—42no—
230C2×#10596831—21no—
231C2×#10596831—21no—
232C2×#10596831—21no—
233C2×#10596831—21no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831—21no—
237C2×#10596831—21no—
238C2×#10596831—21no—
239C2×#10596831—21no—
240C2×#10596831—42no—
241C2×#10596831—42no—
242C2×#10596831C22×C411yescharacteristic
243C2×#10596831C22×C411yescharacteristic
244C2×#10596831C22×C411yescharacteristic
245C2×#10596831C22×C411yescharacteristic
246C2×#10596831C2×D411yescharacteristic
247C2×#10596831C2×D411yescharacteristic
248C2×#10596831C2×D411yescharacteristic
249C2×#10596831C2×D411yescharacteristic
250C8×D73—42no—
251C8×D73—42no—
252C24×C73#4111yescharacteristic
253#41×C73—21no—
254#41×C73—21no—
255#41×C73—21no—
256#41×C73—21no—
257C2×Q8×C73C22×C411yescharacteristic
258C2×D4×C73—21no—
259C2×D4×C73—21no—
260C2×D4×C73—21no—
261C2×D4×C73C22×C411yescharacteristic
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—24no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—42no—
271C22×C4×C73—42no—
272C22×C4×C73C22×C411yescharacteristic
273C22×C4×C73C22×C411yescharacteristic
274C22×C4×C73C2×D411yescharacteristic
275C22×C4×C73C2×D411yescharacteristic
276C22×C4×C73#4111yescharacteristic
277C22×C4×C73C2411yescharacteristic
278M16×C73—21no—
279M16×C73—21no—
280M16×C73—21no—
281M16×C73—21no—
282C2×C8×C73—21no—
283C2×C8×C73—21no—
284C4⋊C4×C73—21no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73C22×C411yescharacteristic
287C4⋊C4×C73C22×C411yescharacteristic
288C22⋊C4×C73—21no—
289C22⋊C4×C73—21no—
290C22⋊C4×C73—21no—
291C22⋊C4×C73—21no—
292C22⋊C4×C73—21no—
293C42×C73—21no—
294C42×C73—21no—
295C42×C73—21no—
296C42×C73—21no—
297C42×C73—42no—
298C42×C73C2×D412yes—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—22no—
302C23×C73—21no—
303C23×C73—41no—
304C23×C73C4×D411yescharacteristic
305C23×C73C4×D411yescharacteristic
306C23×C73C2×#4111yescharacteristic
307C22×D73—21no—
308C22×D73—21no—
309C22×D73—42no—
310C22×D73—42no—
311C22×D73—81no—
312Q8×C73—21no—
313Q8×C73—21no—
314D4×C73—21no—
315D4×C73—21no—
316D4×C73—41no—
317D4×C73—41no—
318D4×C73—42no—
319D4×C73—81no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
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—22no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—48no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73C4×D411yescharacteristic
343C2×C4×C73C4×D411yescharacteristic
344C2×C4×C73C23×C411yescharacteristic
345C2×C4×C73C22×D411yescharacteristic
346C2×C4×C73C22×D411yescharacteristic
347C2×C4×C73C2×#4111yescharacteristic
348C2×C4×C73H(5,𝔽2)11yescharacteristic
349C2×C4×C73H(5,𝔽2)11yescharacteristic
350C22⋊D73—22no—
351C22⋊D73—22no—
352C22⋊D73—42no—
353C22⋊D73—42no—
354C22⋊D73—41no—
355C22⋊D73—41no—
356C2×Dic73—21no—
357C2×Dic73—21no—
358C2×Dic73—42no—
359D292—21no—
360D292—21no—
361D292—21no—
362D292—42no—
363D292C4×D412yes—
364C4×D73—22no—
365C4×D73—22no—
366C4×D73—42no—
367C4×D73—42no—
368C4×D73—41no—
369C4×D73—41no—
370Dic146—21no—
371Dic146—21no—
372Dic146—21no—
373Dic146—42no—
374Dic146C4×D412yes—
375C8×C73—41no—
376C8×C73—41no—
377#10596831—21no—
378#10596831—21no—
379#10596831—21no—
380#10596831—21no—
381#10596831—21no—
382#10596831—21no—
383#10596831—22no—
384#10596831—21no—
385#10596831—21no—
386#10596831—41no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—21no—
393C22×C73—21no—
394C22×C73—42no—
395C22×C73—42no—
396C22×C73—41no—
397C22×C73—41no—
398C22×C73—41no—
399C22×C73#44312yescomplemented
400C22×C73C2×C4×D411yescharacteristic
401C22×C73#54611yescharacteristic
402C22×C73#55111yescharacteristic
403C2×D73—22no—
404C2×D73—41no—
405C2×D73—41no—
406C2×D73—41no—
407C2×D73—41no—
408C2×D73—41no—
409C2×D73—84no—
410C4×C73—24no—
411C4×C73—21no—
412C4×C73—21no—
413C4×C73—42no—
414C4×C73—41no—
415C4×C73—41no—
416C4×C73—41no—
417C4×C73C2×C4×D411yescharacteristic
418C4×C73#51811yescharacteristic
419C4×C73D4211yescharacteristic
420C4×C73#54611yescharacteristic
421Dic73—22no—
422Dic73—41no—
423#22888—731nomaximal, Sylow
424C2×C73—21no—
425C2×C73—22no—
426C2×C73—21no—
427C2×C73—41no—
428C2×C73—81no—
429C2×C73#235811yescharacteristic
430C2×C73C2×#44311yescharacteristic
431C2×C73#295611yescharacteristic
432D73—42no—
433D73—81no—
434#3002—731no—
435C2×#443—731no—
436#2933—731no—
437C22×#104—731no—
438#2880—731no—
439#1974—731no—
440#1937—731no—
441#1929—731no—
442#1896D7311yescharacteristic, complemented
443#1876—731no—
444#1876—731no—
445#1866—731no—
446#1855—731no—
447#1764—731no—
448C4×C22⋊C8—731no—
449C73#2288811yescharacteristic, complemented, Sylow
450C22×#41—731no—
451C2×#135—731no—
452C2×#135—731no—
453C2×#131—731no—
454C2×#131—731no—
455C2×#131—731no—
456C22×M16—731no—
457#525C2×D7311yescharacteristic
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—731no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104—731no—
479C2×#104—1464no—
480C2×#104C2×D7311yescharacteristic, complemented
481C2×#104C2×D7311yescharacteristic, complemented
482#416—731no—
483#416—731no—
484#408—731no—
485#408—731no—
486#408—731no—
487#408—1461no—
488#408—1461no—
489#407—1461no—
490#407C2×D7311yescharacteristic
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#339C2×D7311yescharacteristic, complemented
500#339C2×D7311yescharacteristic, complemented
501#336—731no—
502#336—731no—
503C2×#41—2921no—
504C2×#41—2921no—
505C2×#41—731no—
506C2×#41—731no—
507C2×#41—731no—
508C2×#41—731no—
509C2×#41—1462no—
510C2×#41—1462no—
511C2×#41—1461no—
512C2×#41—1461no—
513C2×#41C22×D7311yescharacteristic
514C22×Q8—731no—
515C22×D4—731no—
516C22×D4—1461no—
517C23×C4—21no—
518C23×C4—1461no—
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—2921no—
539C2×M16—731no—
540C2×M16—731no—
541C2×M16—1461no—
542C2×M16—1461no—
543C2×M16—1462no—
544C2×M16—1461no—
545C2×M16—1461no—
546C2×M16C22×D7311yescharacteristic
547C2×M16C22×D7311yescharacteristic
548C22×C8—731no—
549C22×C8—731no—
550C22×C8—731no—
551C22×C8—731no—
552C22×C8—1461no—
553C22×C8—1461no—
554C22×C8—1461no—
555C22×C8—1461no—
556#123—21no—
557C22⋊Q8C4×D7311yescharacteristic
558C22⋊Q8C4×D7311yescharacteristic
559#121C4×D7311yescharacteristic
560#121C4×D7311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D7311yescharacteristic
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—41no—
576#104—734no—
577#104—1462no—
578#104—1462no—
579#104—1462no—
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—21no—
589C22⋊C8—21no—
590C22⋊C8—731no—
591C22⋊C8—731no—
592C22⋊C8—731no—
593C22⋊C8—731no—
594C22⋊C8—731no—
595C22⋊C8—731no—
596C22⋊C8—731no—
597C22⋊C8—731no—
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—1461no—
609C24#1192402711yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—2922no—
615#41—2922no—
616#41—2921no—
617#41—2921no—
618#41—2922no—
619#41—2922no—
620#41—732no—
621#41—732no—
622#41—1462no—
623#41—1462no—
624#41—1461no—
625#41—1461no—
626#41—1461no—
627#41—1461no—
628#41—1461no—
629#41—1461no—
630C2×Q8—2921no—
631C2×Q8—731no—
632C2×Q8—731no—
633C2×Q8—1462no—
634C2×Q8—1461no—
635C2×Q8C2×C4×D7311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—2921no—
640C2×D4—2922no—
641C2×D4—2922no—
642C2×D4—731no—
643C2×D4—731no—
644C2×D4—1462no—
645C2×D4—1461no—
646C2×D4—1461no—
647C2×D4—1461no—
648C2×D4—1461no—
649C2×D4—1461no—
650C2×D4C2×C4×D7311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—2922no—
662C22×C4—2922no—
663C22×C4—1461no—
664C22×C4—1461no—
665C22×C4—1461no—
666C22×C4—1461no—
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—21no—
686M16—2922no—
687M16—2922no—
688M16—2922no—
689M16—2922no—
690M16—732no—
691M16—1461no—
692M16—1461no—
693M16—1461no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—2922no—
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—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D7311yescharacteristic
721C4⋊C4C2×C4×D7311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42D4×D7312yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—2922no—
739C23—2922no—
740C23—5841no—
741C23—1461no—
742C23—1461no—
743C23#1455655111yescharacteristic
744C23#1455655111yescharacteristic
745C23C2×#1192402711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—2922no—
749Q8—732no—
750Q8—1461no—
751Q8—1461no—
752Q8—1461no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—2922no—
760D4—2922no—
761D4—2921no—
762D4—2921no—
763D4—2922no—
764D4—732no—
765D4—1462no—
766D4—1462no—
767D4—1461no—
768D4—1461no—
769D4—1461no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—2922no—
793C2×C4—2922no—
794C2×C4—2922no—
795C2×C4—2921no—
796C2×C4—2921no—
797C2×C4—1461no—
798C2×C4—1461no—
799C2×C4—1462no—
800C2×C4—1462no—
801C2×C4#1455655111yescharacteristic
802C2×C4#1455655111yescharacteristic
803C2×C4C22×C4×D7311yescharacteristic
804C2×C4C2×D4×D7311yescharacteristic
805C2×C4C2×D4×D7311yescharacteristic
806C2×C4#41×D7311yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663711yescharacteristic
809C8—41no—
810C8—41no—
811C8—2921no—
812C8—1461no—
813C8—1462no—
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—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—2921no—
834C22—2921no—
835C22—2921no—
836C22—2921no—
837C22—2921no—
838C22—5844no—
839C22—1462no—
840C22#1798870112yescomplemented
841C22C2×#1455655111yescharacteristic
842C22#1798922411yescharacteristic
843C22#1798926011yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—2921no—
852C4—1462no—
853C4C4×D4×D7311yescharacteristic
854C4#1798905911yescharacteristic
855C4#1798922111yescharacteristic
856C4#1798922611yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—2922no—
863C2—5841no—
864C2#2261291111yescharacteristic
865C2C2×#1798870111yescharacteristic
866C2#2261883711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1896C2
socleC22×C73C2×C4×D4
prime radical#22619147C2
cosocleC22×C4×C73C24
hypercenter#1896D73
hypocenterC73#22888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#17988701C2semidirect
3. #22618658C2semidirect
4. C22×#14556519C2semidirect
5. #22618381C2semidirect
6. #22610816C2semidirect
7. #22610636C2semidirect
8. #22610577C2semidirect
9. #22610256C2semidirect
10. #22610255C2semidirect
11. #22610207C2semidirect
12. #22610135C2semidirect
13. #22609765C2semidirect
14. C4×C22⋊#10596831C2semidirect
15. C73×#1896C2semidirect
21. C2×#14556598C22semidirect
23. #17988747C4semidirect
24. #17988747C4semidirect
25. #17988742C4semidirect
26. #17988737C4semidirect
27. #17988730C4semidirect
28. #17988730C4semidirect
29. #17988725C4semidirect
30. #17988720C4semidirect
36. C2×#14556526C22semidirect
37. C2×#14556526C22semidirect
38. #17988614C22semidirect
48. #17988554C22semidirect
55. #17988543C22semidirect
56. C2×C4×#10596831C22semidirect
57. C2×C4×#10596831C22semidirect
58. #17988351C22semidirect
59. #17988351C22semidirect
60. #17988342C22semidirect
61. #17988342C22semidirect
64. C2×#104×C73C22semidirect
65. C2×#104×C73C22semidirect
67. #339×C73C22semidirect
68. #339×C73C22semidirect
87. C2×#11924018C2×C4semidirect
88. C2×#11924018C2×C4semidirect
89. C2×#11924016C2×C4semidirect
90. C2×#11924016C2×C4semidirect
91. C2×#11924015C2×C4semidirect
92. C2×#11924015C2×C4semidirect
93. C2×#11924013C2×C4semidirect
94. C2×#11924013C2×C4semidirect
124. #14556519D4semidirect
125. #14556514C2×C4semidirect
126. #14556514C2×C4semidirect
127. #14556514C2×C4semidirect
128. #14556514C2×C4semidirect
129. #14556511C2×C4semidirect
130. #14556511C2×C4semidirect
131. #14556511C2×C4semidirect
132. #14556511C2×C4semidirect
399. C22×C73#443semidirect
442. #1896D73semidirect
449. C73#22888semidirect
480. C2×#104C2×D73semidirect
481. C2×#104C2×D73semidirect
499. #339C2×D73semidirect
500. #339C2×D73semidirect
840. C22#17988701semidirect

Maximal subgroups

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

subgroupindex
#226191472
C2×#179887012
#226186582
C22×#145565192
#226183812
#226108162
#226106362
#226105772
#226102562
#226102552
#226102072
#226101352
#226097652
C4×C22⋊#105968312
C73×#18962
#2288873