Finite Group Databasebeta

← #33106752

Subgroups — #33106752

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×#17988702C211yesmaximal, characteristic, complemented
3C22×#14556517C211yesmaximal, characteristic, complemented
4#22618377C211yesmaximal, characteristic, complemented
5#22610818C211yesmaximal, characteristic, complemented
6#22610634C211yesmaximal, characteristic, complemented
7#22610579C211yesmaximal, characteristic, complemented
8#22610375C211yesmaximal, characteristic, complemented
9#22610261C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610205C211yesmaximal, characteristic, complemented
12#22610136C211yesmaximal, characteristic, complemented
13#22609770C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic73C211yesmaximal, characteristic, complemented
15C73×#2933C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556611C2211yescharacteristic
19C2×#14556597C2211yescharacteristic
20C2×#14556597C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22#17988747C411yescharacteristic, complemented
23#17988747C411yescharacteristic, complemented
24#17988742C411yescharacteristic, complemented
25#17988737C411yescharacteristic, complemented
26#17988730C411yescharacteristic, complemented
27#17988730C411yescharacteristic, complemented
28#17988725C411yescharacteristic, complemented
29#17988720C411yescharacteristic, complemented
30#17988702—24no—
31C2×#14556526C2211yescharacteristic, complemented
32C2×#14556526C2211yescharacteristic, complemented
33C2×#14556518C2211yescharacteristic, complemented
34C2×#14556518C2211yescharacteristic, complemented
35C2×#14556517—24no—
36C2×#14556517C2211yescharacteristic
37C2×#14556517C2211yescharacteristic
38C2×#14556517C2211yescharacteristic
39C2×#14556517C2211yescharacteristic
40#17988581C2211yescharacteristic
41#17988581C2211yescharacteristic
42#17988553C2211yescharacteristic
43#17988553C2211yescharacteristic
44#17988552—21no—
45#17988552—21no—
46#17988551C2211yescharacteristic
47#17988549—21no—
48C2×C22⋊#10596831C2211yescharacteristic
49C22⋊C8×D73—21no—
50C2×C8×Dic73C2211yescharacteristic, complemented
51C2×C8×Dic73C2211yescharacteristic, complemented
52#17988351C2211yescharacteristic, complemented
53#17988351C2211yescharacteristic, complemented
54#17988346C2211yescharacteristic, complemented
55#17988346C2211yescharacteristic, complemented
56#17988341C2211yescharacteristic, complemented
57#17988341C2211yescharacteristic, complemented
58C2×#131×C73C2211yescharacteristic, complemented
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, complemented
66#408×C73C2211yescharacteristic, complemented
67C2×C22⋊C8×C73C2211yescharacteristic
68#405×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—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84#14556611—22no—
85#14556611—22no—
86#14556611—41no—
87#14556611—41no—
88C2×#11924018C2×C411yescharacteristic, complemented
89C2×#11924018C2×C411yescharacteristic, complemented
90C2×#11924016C2×C411yescharacteristic, complemented
91C2×#11924016C2×C411yescharacteristic, complemented
92C2×#11924015C2×C411yescharacteristic, complemented
93C2×#11924015C2×C411yescharacteristic, complemented
94C2×#11924013C2×C411yescharacteristic, complemented
95C2×#11924013C2×C411yescharacteristic, complemented
96#14556597—22no—
97#14556597—22no—
98#14556597—41no—
99#14556597—41no—
100C2×#11924012C2311yescharacteristic
101C2×#11924012C2311yescharacteristic
102C2×#11924011—21no—
103C2×#11924011—21no—
104C22×#10596831C2311yescharacteristic
105C22×#10596831C2311yescharacteristic
106C2×C8×D73—21no—
107C2×C8×D73—21no—
108C2×C4×Dic73—22no—
109C2×C4×Dic73—21no—
110C2×C4×Dic73—41no—
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113#14556526—22no—
114#14556526—41no—
115#14556518—22no—
116#14556518—41no—
117#14556517—22no—
118#14556517—22no—
119#14556517—22no—
120#14556517D414yescomplemented
121#14556514C2×C411yescharacteristic, complemented
122#14556514C2×C411yescharacteristic, complemented
123#14556514C2×C411yescharacteristic, complemented
124#14556514C2×C411yescharacteristic, complemented
125#14556511C2×C411yescharacteristic, complemented
126#14556511C2×C411yescharacteristic, complemented
127#14556511C2×C411yescharacteristic, complemented
128#14556511C2×C411yescharacteristic, complemented
129C22⋊#10596831—21no—
130C22⋊#10596831—21no—
131C22⋊#10596831C2×C411yescharacteristic
132C22⋊#10596831C2×C411yescharacteristic
133C22⋊#10596831C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135#14556503—21no—
136#14556503—21no—
137#14556503—21no—
138#14556503—21no—
139C8×Dic73—22no—
140C8×Dic73—41no—
141C2×#41×C73C2311yescharacteristic
142C23×C4×C73C2311yescharacteristic
143#131×C73—22no—
144#131×C73—41no—
145C2×M16×C73—21no—
146C2×M16×C73—21no—
147C2×M16×C73—22no—
148C2×M16×C73—41no—
149C2×M16×C73C2311yescharacteristic
150C2×M16×C73C2311yescharacteristic
151C22×C8×C73—21no—
152C22×C8×C73—21no—
153C22×C8×C73C2311yescharacteristic
154C22×C8×C73C2311yescharacteristic
155#123×C73—21no—
156C22⋊Q8×C73C2×C411yescharacteristic
157C22⋊Q8×C73C2×C411yescharacteristic
158#121×C73C2×C411yescharacteristic
159#121×C73C2×C411yescharacteristic
160#120×C73—21no—
161C4×D4×C73—21no—
162C4×D4×C73—21no—
163#117×C73C2311yescharacteristic
164C4⋊C8×C73—21no—
165C4⋊C8×C73—21no—
166C22⋊C8×C73—21no—
167C22⋊C8×C73—21no—
168C22⋊C8×C73D411yescharacteristic
169C22⋊C8×C73D411yescharacteristic
170C22⋊C8×C73D411yescharacteristic
171C22⋊C8×C73D411yescharacteristic
172#97×C73—21no—
173C4×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—
208C22×Dic73—24no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—42no—
212C22×Dic73—42no—
213C2×C4×D73—21no—
214C2×C4×D73—21no—
215C2×C4×D73—21no—
216C2×C4×D73—21no—
217C2×C4×D73—42no—
218C2×C4×D73—42no—
219#11924018—22no—
220#11924018—41no—
221#11924016—22no—
222#11924016—41no—
223#11924015—22no—
224#11924015—41no—
225#11924013—22no—
226#11924013—41no—
227#11924012—21no—
228#11924012—21no—
229#11924012—21no—
230#11924012—21no—
231#11924011—42no—
232#11924011—42no—
233C2×#10596831—21no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831—21no—
237C2×#10596831—21no—
238C2×#10596831—21no—
239C2×#10596831C22×C411yescharacteristic
240C2×#10596831C22×C411yescharacteristic
241C2×#10596831C22×C411yescharacteristic
242C2×#10596831C22×C411yescharacteristic
243C8×D73—42no—
244C8×D73—42no—
245C4×Dic73—21no—
246C4×Dic73—21no—
247C4×Dic73—21no—
248C4×Dic73—42no—
249C4×Dic73C2×D412yes—
250C24×C73#4111yescharacteristic
251#41×C73—21no—
252#41×C73—21no—
253#41×C73—21no—
254#41×C73—21no—
255C2×Q8×C73C22×C411yescharacteristic
256C2×D4×C73—21no—
257C2×D4×C73—21no—
258C2×D4×C73—21no—
259C2×D4×C73C22×C411yescharacteristic
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73C22×C411yescharacteristic
266C22×C4×C73C22×C411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73#4111yescharacteristic
270C22×C4×C73C2411yescharacteristic
271M16×C73—21no—
272M16×C73—21no—
273M16×C73—21no—
274M16×C73—42no—
275M16×C73—42no—
276M16×C73C2×D412yes—
277C2×C8×C73—21no—
278C2×C8×C73—21no—
279C2×C8×C73—21no—
280C2×C8×C73—21no—
281C2×C8×C73—21no—
282C2×C8×C73—21no—
283C2×C8×C73—42no—
284C2×C8×C73—42no—
285C2×C8×C73C2×D411yescharacteristic
286C2×C8×C73C2×D411yescharacteristic
287C2×C8×C73C2×D411yescharacteristic
288C2×C8×C73C2×D411yescharacteristic
289C4⋊C4×C73—21no—
290C4⋊C4×C73—21no—
291C4⋊C4×C73C22×C411yescharacteristic
292C4⋊C4×C73C22×C411yescharacteristic
293C22⋊C4×C73—21no—
294C22⋊C4×C73—21no—
295C22⋊C4×C73—21no—
296C22⋊C4×C73—21no—
297C22⋊C4×C73—21no—
298C42×C73—21no—
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—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
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—41no—
334C2×C4×C73—41no—
335C2×C4×C73C4×D411yescharacteristic
336C2×C4×C73C4×D411yescharacteristic
337C2×C4×C73C23×C411yescharacteristic
338C2×C4×C73C22×D411yescharacteristic
339C2×C4×C73C22×D411yescharacteristic
340C2×C4×C73C2×#4111yescharacteristic
341C2×C4×C73H(5,𝔽2)11yescharacteristic
342C2×C4×C73H(5,𝔽2)11yescharacteristic
343C22⋊D73—22no—
344C22⋊D73—22no—
345C22⋊D73—42no—
346C22⋊D73—42no—
347C22⋊D73—41no—
348C22⋊D73—41no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—21no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—21no—
355C2×Dic73—42no—
356C2×Dic73—48no—
357C2×Dic73—41no—
358C2×Dic73—41no—
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—21no—
376C8×C73—21no—
377C8×C73—22no—
378C8×C73—21no—
379C8×C73—21no—
380C8×C73—41no—
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—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—21no—
411C4×C73—21no—
412C4×C73—41no—
413C4×C73—41no—
414C4×C73—41no—
415C4×C73C2×C4×D411yescharacteristic
416C4×C73#51811yescharacteristic
417C4×C73D4211yescharacteristic
418C4×C73#54611yescharacteristic
419Dic73—24no—
420Dic73—22no—
421Dic73—42no—
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#2933D7311yescharacteristic, complemented
437C22×#104—731no—
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×#41—731no—
451C2×#135—731no—
452C2×#135—731no—
453C2×#131—731no—
454C2×#131—731no—
455C2×#131C2×D7311yescharacteristic, complemented
456C22×M16C2×D7311yescharacteristic
457#525C2×D7311yescharacteristic
458C22×C42—731no—
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—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108—731no—
473C2×#108—731no—
474#424C2×D7311yescharacteristic, complemented
475C2×#104—731no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104—731no—
479C2×#104—731no—
480C2×#104—731no—
481C2×#104—1464no—
482#416—731no—
483#416—731no—
484#408—731no—
485#408—731no—
486#408—1461no—
487#408—1461no—
488#408C2×D7311yescharacteristic, complemented
489#407—731no—
490#407—1461no—
491C2×C22⋊C8—731no—
492C2×C22⋊C8—1461no—
493C2×C22⋊C8C2×D7311yescharacteristic
494#405C2×D7311yescharacteristic, complemented
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—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—1461no—
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—22no—
533#131—41no—
534#131—2921no—
535#131—2921no—
536#131—1462no—
537#131—1462no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—731no—
543C2×M16—731no—
544C2×M16—1461no—
545C2×M16—1461no—
546C2×M16C22×D7311yescharacteristic
547C2×M16C22×D7311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—731no—
551C22×C8—731no—
552C22×C8—1461no—
553C22×C8—1461no—
554C22×C8C22×D7311yescharacteristic
555C22×C8C22×D7311yescharacteristic
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—2921no—
566C2×C42—731no—
567C2×C42—731no—
568C2×C42—1461no—
569C2×C42—1462no—
570#108—2921no—
571#108—1462no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—2921no—
575#104—734no—
576#104—1462no—
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—1461no—
595C22⋊C8—1461no—
596C22⋊C8—1461no—
597C22⋊C8—1461no—
598C22⋊C8—1461no—
599C22⋊C8—1461no—
600C22⋊C8C22⋊D7311yescharacteristic
601C22⋊C8C22⋊D7311yescharacteristic
602C22⋊C8C22⋊D7311yescharacteristic
603C22⋊C8C22⋊D7311yescharacteristic
604#97—21no—
605C4×C8—21no—
606C4×C8—2921no—
607C4×C8—1462no—
608C24—1461no—
609C24#1192402811yescharacteristic
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—2922no—
657C22×C4—2922no—
658C22×C4—2922no—
659C22×C4—2922no—
660C22×C4—1464no—
661C22×C4—1461no—
662C22×C4—1461no—
663C22×C4—1461no—
664C22×C4—1461no—
665C22×C4—1461no—
666C22×C4—1461no—
667C22×C4—1461no—
668C22×C4C2×C4×D7311yescharacteristic
669C22×C4C2×C4×D7311yescharacteristic
670C22×C4C2×C22⋊D7311yescharacteristic
671C22×C4C2×C22⋊D7311yescharacteristic
672C22×C4#1192402811yescharacteristic
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—42no—
687M16—2922no—
688M16—2922no—
689M16—1461no—
690M16—1461no—
691M16—1461no—
692M16—1461no—
693M16D4×D7312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—2922no—
703C2×C8—2922no—
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×C8C2×C22⋊D7311yescharacteristic
715C2×C8C2×C22⋊D7311yescharacteristic
716C2×C8C2×C22⋊D7311yescharacteristic
717C2×C8C2×C22⋊D7311yescharacteristic
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—2922no—
729C42—732no—
730C42—1461no—
731C42—1461no—
732C42—1461no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—2922no—
739C23—2922no—
740C23—5841no—
741C23—1461no—
742C23—1461no—
743C23C4×C22⋊D7311yescharacteristic
744C23C4×C22⋊D7311yescharacteristic
745C23C2×#1192402811yescharacteristic
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—21no—
771C2×C4—21no—
772C2×C4—21no—
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—41no—
784C2×C4—41no—
785C2×C4—2922no—
786C2×C4—2922no—
787C2×C4—2921no—
788C2×C4—2921no—
789C2×C4—2922no—
790C2×C4—2928no—
791C2×C4—2921no—
792C2×C4—2921no—
793C2×C4—1462no—
794C2×C4—1461no—
795C2×C4—1462no—
796C2×C4—1462no—
797C2×C4—1462no—
798C2×C4—1461no—
799C2×C4—1462no—
800C2×C4—1462no—
801C2×C4C4×C22⋊D7311yescharacteristic
802C2×C4C4×C22⋊D7311yescharacteristic
803C2×C4C22×C4×D7311yescharacteristic
804C2×C4C2×D4×D7311yescharacteristic
805C2×C4C22×C22⋊D7311yescharacteristic
806C2×C4#41×D7311yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663711yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—2921no—
816C8—2921no—
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#1798870212yescomplemented
841C22C2×C4×C22⋊D7311yescharacteristic
842C22#1798923311yescharacteristic
843C22#1798926611yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—2922no—
850C4—2921no—
851C4—1464no—
852C4—1462no—
853C4C4×D4×D7311yescharacteristic
854C4#1798905911yescharacteristic
855C4D4×C22⋊D7311yescharacteristic
856C4#1798922511yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—2922no—
863C2—5841no—
864C2#2261290811yescharacteristic
865C2C2×#1798870211yescharacteristic
866C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2933C2
socleC22×C73C2×C4×D4
prime radical#22619147C2
cosocleC22×C4×C73C24
hypercenter#2933D73
hypocenterC73#22888
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. C22×#14556517C2semidirect
4. #22618377C2semidirect
5. #22610818C2semidirect
6. #22610634C2semidirect
7. #22610579C2semidirect
8. #22610375C2semidirect
9. #22610261C2semidirect
10. #22610258C2semidirect
11. #22610205C2semidirect
12. #22610136C2semidirect
13. #22609770C2semidirect
14. C22⋊C8×Dic73C2semidirect
15. C73×#2933C2semidirect
22. #17988747C4semidirect
23. #17988747C4semidirect
24. #17988742C4semidirect
25. #17988737C4semidirect
26. #17988730C4semidirect
27. #17988730C4semidirect
28. #17988725C4semidirect
29. #17988720C4semidirect
31. C2×#14556526C22semidirect
32. C2×#14556526C22semidirect
33. C2×#14556518C22semidirect
34. C2×#14556518C22semidirect
50. C2×C8×Dic73C22semidirect
51. C2×C8×Dic73C22semidirect
52. #17988351C22semidirect
53. #17988351C22semidirect
54. #17988346C22semidirect
55. #17988346C22semidirect
56. #17988341C22semidirect
57. #17988341C22semidirect
58. C2×#131×C73C22semidirect
65. #424×C73C22semidirect
66. #408×C73C22semidirect
68. #405×C73C22semidirect
88. C2×#11924018C2×C4semidirect
89. C2×#11924018C2×C4semidirect
90. C2×#11924016C2×C4semidirect
91. C2×#11924016C2×C4semidirect
92. C2×#11924015C2×C4semidirect
93. C2×#11924015C2×C4semidirect
94. C2×#11924013C2×C4semidirect
95. C2×#11924013C2×C4semidirect
120. #14556517D4semidirect
121. #14556514C2×C4semidirect
122. #14556514C2×C4semidirect
123. #14556514C2×C4semidirect
124. #14556514C2×C4semidirect
125. #14556511C2×C4semidirect
126. #14556511C2×C4semidirect
127. #14556511C2×C4semidirect
128. #14556511C2×C4semidirect
399. C22×C73#443semidirect
436. #2933D73semidirect
449. C73#22888semidirect
455. C2×#131C2×D73semidirect
474. #424C2×D73semidirect
488. #408C2×D73semidirect
494. #405C2×D73semidirect
840. C22#17988702semidirect

Maximal subgroups

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

subgroupindex
#226191472
C2×#179887022
C22×#145565172
#226183772
#226108182
#226106342
#226105792
#226103752
#226102612
#226102582
#226102052
#226101362
#226097702
C22⋊C8×Dic732
C73×#29332
#2288873