Finite Group Databasebeta

← #33057290

Subgroups — #33057290

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#22618998C211yesmaximal, characteristic, complemented
2#22618966C211yesmaximal, characteristic, complemented
3#22608845C211yesmaximal, characteristic, complemented
4#22608816C211yesmaximal, characteristic, complemented
5#22608796C211yesmaximal, characteristic, complemented
6#22608796C211yesmaximal, characteristic, complemented
7#22608761C211yesmaximal, characteristic, complemented
8#22608761C211yesmaximal, characteristic, complemented
9#22608755C211yesmaximal, characteristic, complemented
10D8×#10596831C211yesmaximal, characteristic, complemented
11#22608711C211yesmaximal, characteristic, complemented
12#22608400C211yesmaximal, characteristic, complemented
13#22608322C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#3100C211yesmaximal, characteristic
16#17988665—21no—
17#17988665C2211yescharacteristic
18#17988665C2211yescharacteristic
19#17988665C2211yescharacteristic, complemented
20#17988665C2211yescharacteristic, complemented
21#17988659—21no—
22#17988659—21no—
23D4×#10596831—21no—
24D4×#10596831C2211yescharacteristic
25D4×#10596831C2211yescharacteristic
26D4×#10596831C2211yescharacteristic, complemented
27D4×#10596831C2211yescharacteristic, complemented
28#17988644C2211yescharacteristic
29#17988640C2211yescharacteristic
30#17988640C2211yescharacteristic
31#17988640C2211yescharacteristic
32#17988554—21no—
33#17988554—21no—
34#17988551—21no—
35C2×C22⋊#10596831—21no—
36#17988340C2211yescharacteristic, complemented
37#17988340C2211yescharacteristic, complemented
38#17988338C2211yescharacteristic, complemented
39#17988338C2211yescharacteristic, complemented
40D4⋊#10596831C2211yescharacteristic
41D4⋊#10596831C2211yescharacteristic
42D4⋊#10596831C2211yescharacteristic
43D4⋊#10596831C2211yescharacteristic
44D4⋊#10596831C2211yescharacteristic, complemented
45D4⋊#10596831C2211yescharacteristic, complemented
46D4⋊#10596831C2211yescharacteristic, complemented
47D4⋊#10596831C2211yescharacteristic, complemented
48#17988309C2211yescharacteristic, complemented
49#17988309C2211yescharacteristic, complemented
50#17988308C2211yescharacteristic, complemented
51C8×#10596831C2211yescharacteristic, complemented
52#532×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54#480×C73C411yescharacteristic
55#480×C73C411yescharacteristic
56#474×C73C411yescharacteristic
57#474×C73C411yescharacteristic
58#459×C73C411yescharacteristic
59#459×C73C411yescharacteristic
60#447×C73C411yescharacteristic
61#447×C73C411yescharacteristic
62C4×D8×C73C2211yescharacteristic
63C4×D8×C73C2211yescharacteristic
64C4×D8×C73C2211yescharacteristic
65C4×D8×C73C2211yescharacteristic
66#431×C73C2211yescharacteristic
67C2×#11924012—21no—
68C2×#11924012—21no—
69C2×#11924012—21no—
70C2×#11924012—21no—
71C22×#10596831—21no—
72C22×#10596831—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C4⋊#10596831—21no—
76C4⋊#10596831D411yescharacteristic
77C4⋊#10596831D411yescharacteristic
78C4⋊#10596831C2311yescharacteristic
79C4⋊#10596831C2311yescharacteristic
80C4⋊#10596831C2311yescharacteristic
81C4⋊#10596831C2311yescharacteristic
82C22⋊#10596831—21no—
83C22⋊#10596831—21no—
84C22⋊#10596831—21no—
85C22⋊#10596831—21no—
86C22⋊#10596831—21no—
87C22⋊#10596831—21no—
88C22⋊#10596831—21no—
89C22⋊#10596831—21no—
90C22⋊#10596831—21no—
91C22⋊#10596831—21no—
92C22⋊#10596831—21no—
93C22⋊#10596831D411yescharacteristic
94C22⋊#10596831D411yescharacteristic
95#14556502—21no—
96C4×#10596831—21no—
97C4×#10596831C2311yescharacteristic
98C4×#10596831C2311yescharacteristic
99C4×#10596831C2311yescharacteristic
100C4×#10596831C2311yescharacteristic
101C2×#41×C73—21no—
102C22×D4×C73C2×C411yescharacteristic
103C23×C4×C73—21no—
104C2×D8×C73C2×C411yescharacteristic
105C2×D8×C73C2×C411yescharacteristic
106C2×D8×C73C2×C411yescharacteristic
107C2×D8×C73C2×C411yescharacteristic
108C4⋊Q8×C73C2×C411yescharacteristic
109#127×C73C2×C411yescharacteristic
110#124×C73—21no—
111#121×C73—21no—
112#121×C73C2×C411yescharacteristic
113#121×C73C2×C411yescharacteristic
114C4×D4×C73—21no—
115C4×D4×C73—21no—
116C4×D4×C73—21no—
117C4×D4×C73C2×C411yescharacteristic
118C4×D4×C73C2×C411yescharacteristic
119C4×D4×C73C2311yescharacteristic
120C4×D4×C73C2311yescharacteristic
121C4×D4×C73C2311yescharacteristic
122C4×D4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2×C411yescharacteristic
124C2×C22⋊C4×C73—21no—
125C2×C42×C73C2311yescharacteristic
126#107×C73C2×C411yescharacteristic
127#107×C73C2×C411yescharacteristic
128#107×C73C2×C411yescharacteristic
129#107×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132#102×C73C2×C411yescharacteristic
133#102×C73C2×C411yescharacteristic
134#102×C73C2×C411yescharacteristic
135#102×C73C2×C411yescharacteristic
136#102×C73C2×C411yescharacteristic
137#102×C73C2×C411yescharacteristic
138#102×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141C22⋊C8×C73C2×C411yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924012—81no—
145#11924012—81no—
146#11924012—81no—
147#11924012—81no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—81no—
155C2×#10596831—81no—
156C2×#10596831—81no—
157C2×#10596831—81no—
158C2×#10596831C2×D411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C24×C73—21no—
163#41×C73—81no—
164#41×C73—81no—
165C2×Q8×C73—21no—
166C2×D4×C73—22no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—41no—
173C2×D4×C73C22×C411yescharacteristic
174C2×D4×C73C22×C411yescharacteristic
175C2×D4×C73C22×C411yescharacteristic
176C2×D4×C73C22×C411yescharacteristic
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—81no—
185C22×C4×C73—81no—
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73#4111yescharacteristic
189D8×C73—22no—
190D8×C73—22no—
191D8×C73—41no—
192D8×C73—41no—
193C2×C8×C73C22×C411yescharacteristic
194C2×C8×C73C22×C411yescharacteristic
195C2×C8×C73C22×C411yescharacteristic
196C2×C8×C73C22×C411yescharacteristic
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C22×C411yescharacteristic
200C4⋊C4×C73C22×C411yescharacteristic
201C4⋊C4×C73C22×C411yescharacteristic
202C4⋊C4×C73C22×C411yescharacteristic
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
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×C73—21no—
218C23×C73—21no—
219C23×C73—42no—
220C23×C73—42no—
221C23×C73—81no—
222C23×C73C4×D411yescharacteristic
223Q8×C73—81no—
224D4×C73—21no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—21no—
228D4×C73—21no—
229D4×C73—21no—
230D4×C73—21no—
231D4×C73—42no—
232D4×C73—42no—
233D4×C73—81no—
234D4×C73—81no—
235D4×C73—81no—
236D4×C73#13112yes—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—81no—
255C2×C4×C73—81no—
256C2×C4×C73—81no—
257C2×C4×C73C4×D411yescharacteristic
258C2×C4×C73C4×D411yescharacteristic
259C2×C4×C73C4×D411yescharacteristic
260C2×C4×C73C23×C411yescharacteristic
261C2×C4×C73C22×D411yescharacteristic
262C2×C4×C73C2×#4111yescharacteristic
263C8×C73—21no—
264C8×C73—21no—
265C8×C73—21no—
266C8×C73—21no—
267#10596831—21no—
268#10596831—21no—
269#10596831—21no—
270#10596831—21no—
271#10596831—41no—
272#10596831—41no—
273#10596831—41no—
274#10596831—41no—
275#10596831—41no—
276#10596831—41no—
277C22×C73—21no—
278C22×C73—22no—
279C22×C73—21no—
280C22×C73—21no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73—41no—
287C22×C73—41no—
288C22×C73—41no—
289C22×C73—41no—
290C22×C73—41no—
291C22×C73—41no—
292C22×C73—84no—
293C22×C73C2×C4×D411yescharacteristic
294C4×C73—21no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73C2×#13111yescharacteristic
303C4×C73#56811yescharacteristic
304C4×C73#57611yescharacteristic
305C4×C73#57611yescharacteristic
306#18026—731nomaximal, Sylow
307C2×C73—41no—
308C2×C73—42no—
309C2×C73—81no—
310C2×C73—81no—
311C2×C73—81no—
312C2×C73#293311yescharacteristic
313C2×C73#294811yescharacteristic
314C2×C73#295511yescharacteristic
315#3100D7311yescharacteristic
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#1496—731no—
328#1478—731no—
329#1454—731no—
330C73#1802611yescharacteristic, complemented, Sylow
331#532C2×D7311yescharacteristic
332C2×C4×D4C2×D7311yescharacteristic
333#480Dic7311yescharacteristic
334#480Dic7311yescharacteristic
335#474Dic7311yescharacteristic
336#474Dic7311yescharacteristic
337#459Dic7311yescharacteristic
338#459Dic7311yescharacteristic
339#447Dic7311yescharacteristic
340#447Dic7311yescharacteristic
341C4×D8C2×D7311yescharacteristic
342C4×D8C2×D7311yescharacteristic
343C4×D8C2×D7311yescharacteristic
344C4×D8C2×D7311yescharacteristic
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#432—731no—
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⋊C8—731no—
375D4⋊C8—731no—
376D4⋊C8—731no—
377D4⋊C8—731no—
378#322—731no—
379#322—731no—
380#322—731no—
381C82—731no—
382C2×#41—21no—
383C22×D4C2×Dic7311yescharacteristic
384C23×C4—21no—
385C2×D8C2×Dic7311yescharacteristic
386C2×D8C2×Dic7311yescharacteristic
387C2×D8C2×Dic7311yescharacteristic
388C2×D8C2×Dic7311yescharacteristic
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⋊Q8C2×Dic7311yescharacteristic
398#127C2×Dic7311yescharacteristic
399#124—21no—
400#121—21no—
401#121C2×Dic7311yescharacteristic
402#121C2×Dic7311yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C2×Dic7311yescharacteristic
407C4×D4C2×Dic7311yescharacteristic
408C4×D4C22×D7311yescharacteristic
409C4×D4C22×D7311yescharacteristic
410C4×D4C22×D7311yescharacteristic
411C4×D4C22×D7311yescharacteristic
412C2×C4⋊C4C2×Dic7311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C42C22×D7311yescharacteristic
415#107C2×Dic7311yescharacteristic
416#107C2×Dic7311yescharacteristic
417#107C2×Dic7311yescharacteristic
418#107C2×Dic7311yescharacteristic
419C4⋊C8—731no—
420C4⋊C8—731no—
421C4⋊C8—731no—
422C4⋊C8—731no—
423C4⋊C8—731no—
424C4⋊C8—731no—
425C4⋊C8—1461no—
426C4⋊C8C2×Dic7311yescharacteristic
427C4⋊C8C2×Dic7311yescharacteristic
428#102C2×Dic7311yescharacteristic
429#102C2×Dic7311yescharacteristic
430#102C2×Dic7311yescharacteristic
431#102C2×Dic7311yescharacteristic
432#102C2×Dic7311yescharacteristic
433#102C2×Dic7311yescharacteristic
434#102C2×Dic7311yescharacteristic
435#102C2×Dic7311yescharacteristic
436C22⋊C8—731no—
437C22⋊C8—731no—
438C22⋊C8—1461no—
439C22⋊C8—1461no—
440C22⋊C8—1461no—
441C22⋊C8—1461no—
442C22⋊C8—1461no—
443C22⋊C8—1461no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8—1461no—
448C22⋊C8—1461no—
449C22⋊C8C2×Dic7311yescharacteristic
450C22⋊C8C2×Dic7311yescharacteristic
451#97—1461no—
452C4×C8—731no—
453C4×C8—731no—
454C4×C8—731no—
455C4×C8—731no—
456C4×C8—1461no—
457C4×C8C22×D7311yescharacteristic
458C4×C8C22×D7311yescharacteristic
459C24—21no—
460#41—81no—
461#41—81no—
462C2×Q8—21no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4C22×Dic7311yescharacteristic
471C2×D4C22×Dic7311yescharacteristic
472C2×D4C22×Dic7311yescharacteristic
473C2×D4C22×Dic7311yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4C22×Dic7311yescharacteristic
484C22×C4D4×D7311yescharacteristic
485C22×C4#1192402711yescharacteristic
486D8—22no—
487D8—22no—
488D8—41no—
489D8—41no—
490M16—5841no—
491M16—5841no—
492M16—5841no—
493M16—5841no—
494C2×C8—5841no—
495C2×C8—5841no—
496C2×C8—5841no—
497C2×C8—5841no—
498C2×C8—731no—
499C2×C8—731no—
500C2×C8—731no—
501C2×C8—731no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8C22×Dic7311yescharacteristic
509C2×C8C22×Dic7311yescharacteristic
510C2×C8C22×Dic7311yescharacteristic
511C2×C8C22×Dic7311yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4C22×Dic7311yescharacteristic
515C4⋊C4C22×Dic7311yescharacteristic
516C4⋊C4C22×Dic7311yescharacteristic
517C4⋊C4C22×Dic7311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C42C22×Dic7311yescharacteristic
527C42D4×D7311yescharacteristic
528C42#1192402711yescharacteristic
529C42C23×D7311yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—42no—
535C23—42no—
536C23—81no—
537C23D4×Dic7311yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—42no—
547D4—42no—
548D4—81no—
549D4—81no—
550D4—81no—
551D4#1455659812yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4D4×Dic7311yescharacteristic
573C2×C4D4×Dic7311yescharacteristic
574C2×C4D4×Dic7311yescharacteristic
575C2×C4C23×Dic7311yescharacteristic
576C2×C4C2×D4×D7311yescharacteristic
577C2×C4C2×#1192402711yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—2921no—
583C8—2921no—
584C8—2921no—
585C8—2921no—
586C8—2921no—
587C8—2921no—
588C8—1461no—
589C8—1461no—
590C8—1461no—
591C8—1461no—
592C22—21no—
593C22—22no—
594C22—21no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—84no—
608C22C2×D4×Dic7311yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4C2×#1455659811yescharacteristic
618C4#1798935411yescharacteristic
619C4#1798938811yescharacteristic
620C4#1798938811yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—81no—
625C2—81no—
626C2#2261865811yescharacteristic
627C2#2261878311yescharacteristic
628C2#2261883411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
Fitting, prime radicalC73×#3100C2
socleC22×C73C2×C4×D4
cosocleC42×C73C24
hypercenter#3100D73
hypocenterC73#18026
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #22618998C2semidirect
2. #22618966C2semidirect
3. #22608845C2semidirect
4. #22608816C2semidirect
5. #22608796C2semidirect
6. #22608796C2semidirect
7. #22608761C2semidirect
8. #22608761C2semidirect
9. #22608755C2semidirect
10. D8×#10596831C2semidirect
11. #22608711C2semidirect
12. #22608400C2semidirect
13. #22608322C2semidirect
14. #22608231C2semidirect
19. #17988665C22semidirect
20. #17988665C22semidirect
26. D4×#10596831C22semidirect
27. D4×#10596831C22semidirect
36. #17988340C22semidirect
37. #17988340C22semidirect
38. #17988338C22semidirect
39. #17988338C22semidirect
44. D4⋊#10596831C22semidirect
45. D4⋊#10596831C22semidirect
46. D4⋊#10596831C22semidirect
47. D4⋊#10596831C22semidirect
48. #17988309C22semidirect
49. #17988309C22semidirect
50. #17988308C22semidirect
51. C8×#10596831C22semidirect
330. C73#18026semidirect

Maximal subgroups

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

subgroupindex
#226189982
#226189662
#226088452
#226088162
#226087962
#226087612
#226087552
D8×#105968312
#226087112
#226084002
#226083222
#226082312
C73×#31002
#1802673