Finite Group Databasebeta

← #33057294

Subgroups — #33057294

Order 18688.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619927C211yesmaximal, characteristic
2#22618998C211yesmaximal, characteristic, complemented
3#22618968C211yesmaximal, characteristic, complemented
4#22608842C211yesmaximal, characteristic, complemented
5#22608813C211yesmaximal, characteristic, complemented
6#22608798C211yesmaximal, characteristic, complemented
7#22608792C211yesmaximal, characteristic, complemented
8#22608763C211yesmaximal, characteristic, complemented
9#22608757C211yesmaximal, characteristic, complemented
10#22608752C211yesmaximal, characteristic, complemented
11#22608723C211yesmaximal, characteristic, complemented
12#22608712C211yesmaximal, characteristic, complemented
13#22608323C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1496C211yesmaximal, characteristic, complemented
16C2×C4×D292C2211yescharacteristic
17#17988898C411yescharacteristic
18#17988898C411yescharacteristic
19#17988864C411yescharacteristic
20#17988864C411yescharacteristic
21#17988779C411yescharacteristic
22#17988779C411yescharacteristic
23#17988720C411yescharacteristic
24#17988720C411yescharacteristic
25C4×#11924013C2211yescharacteristic
26C4×#11924013C2211yescharacteristic
27C4×#11924013C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29#17988665—21no—
30#17988665C2211yescharacteristic, complemented
31#17988665C2211yescharacteristic, complemented
32#17988664C2211yescharacteristic
33#17988664C2211yescharacteristic
34#17988660—21no—
35#17988660—21no—
36D4×#10596831—21no—
37D4×#10596831C2211yescharacteristic, complemented
38D4×#10596831C2211yescharacteristic, complemented
39#17988652C2211yescharacteristic
40#17988652C2211yescharacteristic
41#17988640C2211yescharacteristic
42#17988640C2211yescharacteristic
43#17988640C2211yescharacteristic
44#17988554—21no—
45#17988554—21no—
46#17988549—21no—
47C22⋊C8×D73—21no—
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988337C2211yescharacteristic, complemented
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic, complemented
57#17988309C2211yescharacteristic, complemented
58#17988308C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60#532×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic, complemented
64D4⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic, complemented
66D4⋊C8×C73C2211yescharacteristic, complemented
67C22×D292C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924013C2×C411yescharacteristic
73C2×#11924012—21no—
74C2×#11924012—21no—
75C2×#11924011—21no—
76C2×#11924011—21no—
77C22×#10596831—21no—
78C22×#10596831—21no—
79C2×C8×D73—21no—
80C2×C8×D73—21no—
81C4×D292—21no—
82C4×D292—21no—
83C4×D292C2×C411yescharacteristic
84C4×D292C2×C411yescharacteristic
85C4×D292C2311yescharacteristic
86C4×D292C2311yescharacteristic
87C2×C4⋊Dic73C2×C411yescharacteristic
88C2×#11924005—21no—
89#14556524C2×C411yescharacteristic
90#14556524C2×C411yescharacteristic
91#14556524C2×C411yescharacteristic
92#14556524C2×C411yescharacteristic
93C4⋊#10596831C2×C411yescharacteristic
94C4⋊#10596831C2×C411yescharacteristic
95C4⋊#10596831D411yescharacteristic
96C4⋊#10596831D411yescharacteristic
97C4⋊#10596831C2311yescharacteristic
98C4⋊#10596831C2311yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556512C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104#14556511C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831—21no—
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831C2×C411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120C4×#10596831—21no—
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C2×#41×C73—21no—
126C4⋊Q8×C73C2×C411yescharacteristic
127#127×C73C2×C411yescharacteristic
128#124×C73—21no—
129#121×C73—21no—
130#121×C73C2×C411yescharacteristic
131#121×C73C2×C411yescharacteristic
132C4×D4×C73—21no—
133C4×D4×C73C2311yescharacteristic
134C4×D4×C73C2311yescharacteristic
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145C2×D292—22no—
146C2×D292—21no—
147C2×D292—41no—
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C22×Dic73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—81no—
156C2×C4×D73—81no—
157#11924013—22no—
158#11924013—22no—
159#11924013—41no—
160#11924013—41no—
161#11924012—81no—
162#11924012—81no—
163#11924011—81no—
164#11924011—81no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—81no—
168C2×#10596831—81no—
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C2×D411yescharacteristic
174C2×#10596831C2×D411yescharacteristic
175C2×#10596831C2×D411yescharacteristic
176C2×#10596831C2×D411yescharacteristic
177C8×D73—81no—
178C8×D73—81no—
179C4⋊Dic73—21no—
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924005—21no—
183#11924005—21no—
184#11924005—21no—
185#11924005—21no—
186#41×C73—81no—
187#41×C73—81no—
188C2×Q8×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73C22×C411yescharacteristic
194C2×D4×C73C22×C411yescharacteristic
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73#4111yescharacteristic
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73C22×C411yescharacteristic
206C4⋊C4×C73C22×C411yescharacteristic
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C22⋊C4×C73—21no—
210C22⋊C4×C73—21no—
211C42×C73C22×C411yescharacteristic
212C42×C73C2×D411yescharacteristic
213C42×C73#4111yescharacteristic
214C42×C73C2411yescharacteristic
215C23×C73—21no—
216C23×C73—21no—
217C23×C73C4×D411yescharacteristic
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—42no—
221C22×D73—42no—
222C22×D73—81no—
223Q8×C73—81no—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—42no—
229D4×C73—81no—
230D4×C73—81no—
231D4×C73—81no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73C4×D411yescharacteristic
244C2×C4×C73C4×D411yescharacteristic
245C2×C4×C73C4×D411yescharacteristic
246C2×C4×C73C23×C411yescharacteristic
247C2×C4×C73C22×D411yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—81no—
252D292—21no—
253D292—21no—
254D292—21no—
255D292—42no—
256D292#13112yes—
257C4×D73—41no—
258C4×D73—41no—
259C4×D73—41no—
260C4×D73—41no—
261C4×D73—81no—
262C4×D73—81no—
263C8×C73—41no—
264C8×C73—41no—
265C8×C73—41no—
266C8×C73—41no—
267#10596831—21no—
268#10596831—21no—
269#10596831—21no—
270#10596831—21no—
271#10596831—21no—
272#10596831—21no—
273#10596831—21no—
274#10596831—21no—
275#10596831—41no—
276#10596831—41no—
277C22×C73—21no—
278C22×C73—21no—
279C22×C73—21no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73C2×C4×D411yescharacteristic
287C2×D73—22no—
288C2×D73—41no—
289C2×D73—41no—
290C2×D73—41no—
291C2×D73—41no—
292C2×D73—41no—
293C2×D73—84no—
294C4×C73—21no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73C2×#13111yescharacteristic
301C4×C73#56811yescharacteristic
302C4×C73#57611yescharacteristic
303C4×C73#57611yescharacteristic
304Dic73—41no—
305Dic73—41no—
306#18026—731nomaximal, Sylow
307C2×C73—41no—
308C2×C73—81no—
309C2×C73—81no—
310C2×C73#293311yescharacteristic
311C2×C73#294811yescharacteristic
312C2×C73#295511yescharacteristic
313D73—42no—
314D73—81no—
315#3100—731no—
316#2979—731no—
317#2974—731no—
318#1594—731no—
319#1589—731no—
320#1586—731no—
321#1586—731no—
322#1581—731no—
323#1581—731no—
324#1580—731no—
325C8×D8—731no—
326#1572—731no—
327#1496D7311yescharacteristic, complemented
328#1478—731no—
329#1454—731no—
330C73#1802611yescharacteristic, complemented, Sylow
331#532C2×D7311yescharacteristic
332C2×C4×D4—731no—
333#480—731no—
334#480—731no—
335#474—731no—
336#474—731no—
337#459—731no—
338#459—731no—
339#447—731no—
340#447—731no—
341C4×D8—731no—
342C4×D8—731no—
343C4×D8—731no—
344C4×D8—731no—
345#436—731no—
346#436—731no—
347#436—731no—
348#436—731no—
349#436—1461no—
350#435—1461no—
351#435—1461no—
352C8×D4—731no—
353C8×D4—731no—
354C8×D4—731no—
355C8×D4—731no—
356C8×D4—1461no—
357#432C2×D7311yescharacteristic
358#431—731no—
359#431—731no—
360#431—731no—
361#431C2×D7311yescharacteristic
362#408—1461no—
363#408—1461no—
364#407—1461no—
365C2×C22⋊C8—1461no—
366#335—731no—
367#335—731no—
368#334—731no—
369#334—731no—
370D4⋊C8—731no—
371D4⋊C8—731no—
372D4⋊C8—731no—
373D4⋊C8—731no—
374D4⋊C8C2×D7311yescharacteristic, complemented
375D4⋊C8C2×D7311yescharacteristic, complemented
376D4⋊C8C2×D7311yescharacteristic, complemented
377D4⋊C8C2×D7311yescharacteristic, complemented
378#322—731no—
379#322—731no—
380#322—731no—
381C82—731no—
382C2×#41—21no—
383C22×D4—731no—
384C23×C4—1461no—
385C2×D8—731no—
386C2×D8—731no—
387C2×D8—731no—
388C2×D8—731no—
389C2×M16—1461no—
390C2×M16—1461no—
391C2×M16—1461no—
392C2×M16—1461no—
393C22×C8—1461no—
394C22×C8—1461no—
395C22×C8—1461no—
396C22×C8—1461no—
397C4⋊Q8C4×D7311yescharacteristic
398#127C4×D7311yescharacteristic
399#124—21no—
400#121—21no—
401#121C4×D7311yescharacteristic
402#121C4×D7311yescharacteristic
403C4×D4—21no—
404C4×D4—731no—
405C4×D4—731no—
406C4×D4—731no—
407C4×D4—731no—
408C4×D4—1461no—
409C4×D4—1461no—
410C4×D4C22×D7311yescharacteristic
411C4×D4C22×D7311yescharacteristic
412C2×C4⋊C4—731no—
413C2×C22⋊C4—1461no—
414C2×C42C22×D7311yescharacteristic
415#107—731no—
416#107—731no—
417#107—731no—
418#107—731no—
419C4⋊C8—21no—
420C4⋊C8—731no—
421C4⋊C8—731no—
422C4⋊C8—731no—
423C4⋊C8—731no—
424C4⋊C8—731no—
425C4⋊C8—731no—
426C4⋊C8C22×D7311yescharacteristic
427C4⋊C8C22×D7311yescharacteristic
428#102—731no—
429#102—731no—
430#102—731no—
431#102—731no—
432#102—731no—
433#102—731no—
434#102—731no—
435#102—731no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—731no—
439C22⋊C8—731no—
440C22⋊C8—731no—
441C22⋊C8—731no—
442C22⋊C8—1461no—
443C22⋊C8—1461no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8—1461no—
448C22⋊C8—1461no—
449C22⋊C8—1461no—
450C22⋊C8—1461no—
451#97—21no—
452C4×C8—731no—
453C4×C8—731no—
454C4×C8—731no—
455C4×C8—731no—
456C4×C8—1461no—
457C4×C8C22×D7311yescharacteristic
458C4×C8C22×D7311yescharacteristic
459C24—1461no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—2921no—
468C2×D4—731no—
469C2×D4—731no—
470C2×D4—1462no—
471C2×D4—1461no—
472C2×D4C2×C4×D7311yescharacteristic
473C2×D4C2×C4×D7311yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—5841no—
477C22×C4—5841no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4C2×C4×D7311yescharacteristic
484C22×C4D4×D7311yescharacteristic
485C22×C4#1192402711yescharacteristic
486D8—2921no—
487D8—2921no—
488D8—1462no—
489D8—1462no—
490M16—5841no—
491M16—5841no—
492M16—5841no—
493M16—5841no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—5841no—
499C2×C8—5841no—
500C2×C8—5841no—
501C2×C8—5841no—
502C2×C8—731no—
503C2×C8—731no—
504C2×C8—731no—
505C2×C8—731no—
506C2×C8—731no—
507C2×C8—731no—
508C2×C8—731no—
509C2×C8—731no—
510C2×C8—1461no—
511C2×C8—1461no—
512C4⋊C4—21no—
513C4⋊C4—731no—
514C4⋊C4—731no—
515C4⋊C4—1461no—
516C4⋊C4C2×C4×D7311yescharacteristic
517C4⋊C4C2×C4×D7311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—1461no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42C2×C4×D7311yescharacteristic
527C42D4×D7311yescharacteristic
528C42#1192402711yescharacteristic
529C42C23×D7311yescharacteristic
530C23—21no—
531C23—21no—
532C23—2922no—
533C23—2922no—
534C23—5841no—
535C23—1461no—
536C23—1461no—
537C23#1455655111yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—42no—
544D4—81no—
545D4—81no—
546D4—81no—
547D4—2922no—
548D4—732no—
549D4—1461no—
550D4—1461no—
551D4—1461no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—5841no—
568C2×C4—5841no—
569C2×C4—5841no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4#1455655111yescharacteristic
573C2×C4#1455655111yescharacteristic
574C2×C4#1455655111yescharacteristic
575C2×C4C22×C4×D7311yescharacteristic
576C2×C4C2×D4×D7311yescharacteristic
577C2×C4C2×#1192402711yescharacteristic
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—2921no—
583C8—2921no—
584C8—1461no—
585C8—1461no—
586C8—1461no—
587C8—1461no—
588C8—1461no—
589C8—1461no—
590C8—1461no—
591C8—1461no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—2921no—
602C22—2921no—
603C22—2921no—
604C22—2921no—
605C22—2921no—
606C22—5844no—
607C22—1462no—
608C22C2×#1455655111yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—2921no—
616C4—2921no—
617C4#131×D7311yescharacteristic
618C4#1798935211yescharacteristic
619C4#1798939111yescharacteristic
620C4#1798939111yescharacteristic
621C2—41no—
622C2—81no—
623C2—81no—
624C2—2922no—
625C2—5841no—
626C2#2261866111yescharacteristic
627C2#2261877911yescharacteristic
628C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1496C2
socleC22×C73C2×C4×D4
prime radical#22619927C2
cosocleC42×C73C24
hypercenter#1496D73
hypocenterC73#18026
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #22618998C2semidirect
3. #22618968C2semidirect
4. #22608842C2semidirect
5. #22608813C2semidirect
6. #22608798C2semidirect
7. #22608792C2semidirect
8. #22608763C2semidirect
9. #22608757C2semidirect
10. #22608752C2semidirect
11. #22608723C2semidirect
12. #22608712C2semidirect
13. #22608323C2semidirect
14. #22608231C2semidirect
15. C73×#1496C2semidirect
30. #17988665C22semidirect
31. #17988665C22semidirect
37. D4×#10596831C22semidirect
38. D4×#10596831C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988337C22semidirect
51. #17988337C22semidirect
56. #17988309C22semidirect
57. #17988309C22semidirect
58. #17988308C22semidirect
59. C8×#10596831C22semidirect
63. D4⋊C8×C73C22semidirect
64. D4⋊C8×C73C22semidirect
65. D4⋊C8×C73C22semidirect
66. D4⋊C8×C73C22semidirect
327. #1496D73semidirect
330. C73#18026semidirect
374. D4⋊C8C2×D73semidirect
375. D4⋊C8C2×D73semidirect
376. D4⋊C8C2×D73semidirect
377. D4⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199272
#226189982
#226189682
#226088422
#226088132
#226087982
#226087922
#226087632
#226087572
#226087522
#226087232
#226087122
#226083232
#226082312
C73×#14962
#1802673