Finite Group Databasebeta

← #34026039

Subgroups — #34026039

Order 18688.

738 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626105C211yesmaximal, characteristic, complemented
2#22626105C211yesmaximal, characteristic, complemented
3#22626007C211yesmaximal, characteristic, complemented
4#22626005C211yesmaximal, characteristic, complemented
5#22626002C211yesmaximal, characteristic, complemented
6#22626001C211yesmaximal, characteristic, complemented
7#22625906C211yesmaximal, characteristic
8#22625905C211yesmaximal, characteristic
9#22625876C211yesmaximal, characteristic, complemented
10#22625875C211yesmaximal, characteristic, complemented
11#22625860C211yesmaximal, characteristic, complemented
12#22625719C211yesmaximal, characteristic, complemented
13#22625669C211yesmaximal, characteristic, complemented
14#22625668C211yesmaximal, characteristic, complemented
15#22613213C211yesmaximal, characteristic
16C22×#11924036C2211yescharacteristic
17C23×#10596833C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×#14556648C2211yescharacteristic
23C2×#14556648C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×C22⋊#10596833C2211yescharacteristic
26C2×C22⋊#10596833C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×#14556646C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C2×C4×#10596833C2211yescharacteristic
32#17989453C2211yescharacteristic
33#17989453C2211yescharacteristic
34#17989453C2211yescharacteristic
35#17989453C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44C2×Q8×Dic73C2211yescharacteristic
45C2×#14556551C2211yescharacteristic
46#17988529C411yescharacteristic
47#17988529C411yescharacteristic
48#17988514C411yescharacteristic
49#17988512C411yescharacteristic
50#17988503C411yescharacteristic
51#17988503C411yescharacteristic
52#17988498C411yescharacteristic
53C22⋊C4×Dic73C2211yescharacteristic
54C22⋊C4×Dic73C2211yescharacteristic
55#17988434C2211yescharacteristic
56#17988434C2211yescharacteristic
57#17988432C2211yescharacteristic
58#393×C73C411yescharacteristic
59C2×#11924036—22no—
60C2×#11924036—41no—
61C2×#11924036—41no—
62C22×#10596833—22no—
63C22×#10596833—41no—
64C22×#10596833—41no—
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73#14556658—22no—
74#14556658—41no—
75#14556658—41no—
76C4⋊#10596833—22no—
77#14556648—22no—
78#14556648—41no—
79#14556648—41no—
80C22⋊#10596833—22no—
81C22⋊#10596833—41no—
82C22⋊#10596833—41no—
83#14556646—41no—
84#14556646—41no—
85#14556646—41no—
86C4×#10596833—41no—
87C22×C22⋊D73C2×C411yescharacteristic
88C23×Dic73C2311yescharacteristic
89C22×C4×D73C2311yescharacteristic
90Q8×Dic73—41no—
91Q8×Dic73—41no—
92#14556551—41no—
93#14556551—41no—
94C2×C4⋊Dic73C2×C411yescharacteristic
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×C4⋊Dic73C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×C22⋊Dic73C2×C411yescharacteristic
99C2×C22⋊Dic73C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C2×C4×Dic73C2311yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C22×Q8×C73C2×C411yescharacteristic
120C2×C22⋊C4×C73C2×C411yescharacteristic
121C2×C22⋊C4×C73C2×C411yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126#11924036—44no—
127C2×#10596833—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—21no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—44no—
150C2×#10596833#4112yes—
151C2×#10596833#4112yes—
152C23×D73C22×C411yescharacteristic
153C2×C22⋊D73—22no—
154C2×C22⋊D73—22no—
155C2×C22⋊D73—41no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C2411yescharacteristic
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C4⋊Dic73—41no—
176C4⋊Dic73—41no—
177C4⋊Dic73—41no—
178#11924007—41no—
179C22⋊Dic73—22no—
180C22⋊Dic73—22no—
181#11924005—22no—
182#11924005—22no—
183#11924005—41no—
184#11924005—41no—
185#11924005—41no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C24×C73C22×C411yescharacteristic
197C2×Q8×C73—41no—
198C2×Q8×C73—41no—
199C2×Q8×C73—41no—
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22⋊C4×C73—41no—
207C22⋊C4×C73—41no—
208C22⋊C4×C73—41no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73#13112yes—
216C23×C73C23×C411yescharacteristic
217C22×D73—21no—
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—21no—
221C22×D73—21no—
222C22×D73—21no—
223C22×D73#13112yes—
224Q8×C73—44no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
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—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C22⋊D73—44no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73C2×#4111yescharacteristic
267C2×Dic73C2×#4111yescharacteristic
268C2×Dic73H(5,𝔽2)11yescharacteristic
269C2×Dic73H(5,𝔽2)11yescharacteristic
270C2×Dic73H(5,𝔽2)11yescharacteristic
271C2×Dic732−1+411yescharacteristic
272C4×D73—41no—
273C4×D73—41no—
274C4×D73—41no—
275C4×D73—41no—
276#10596833—22no—
277#10596833—22no—
278#10596833—41no—
279#10596833—41no—
280#10596833—41no—
281#10596833—41no—
282#10596833—41no—
283#10596833—41no—
284C22×C73—22no—
285C22×C73—22no—
286C22×C73—22no—
287C22×C73—41no—
288C22×C73—41no—
289C22×C73—41no—
290C22×C73—41no—
291C22×C73C4×#4111yescharacteristic
292C22×C73#51811yescharacteristic
293C22×C73#52011yescharacteristic
294C22×C73C2×#13111yescharacteristic
295C22×C73C2×#13111yescharacteristic
296C22×C73#56811yescharacteristic
297C22×C73#56811yescharacteristic
298C2×D73—22no—
299C2×D73—22no—
300C2×D73—22no—
301C2×D73—41no—
302C2×D73—41no—
303C2×D73—41no—
304C2×D73—41no—
305C4×C73—41no—
306C4×C73—41no—
307C4×C73—41no—
308C4×C73—41no—
309C4×C73—41no—
310C4×C73—41no—
311Dic73—41no—
312Dic73—41no—
313Dic73—41no—
314Dic73—41no—
315Dic73—41no—
316Dic73—41no—
317Dic73#53811yescharacteristic
318Dic73#53811yescharacteristic
319Dic73#54211yescharacteristic
320Dic73#54211yescharacteristic
321#22396—731nomaximal, Sylow
322C2×C73—42no—
323C2×C73#233711yescharacteristic
324C2×C73#296811yescharacteristic
325C2×C73#296811yescharacteristic
326C2×C73#297711yescharacteristic
327C2×C73#297811yescharacteristic
328C2×C73#299211yescharacteristic
329C2×C73#299211yescharacteristic
330D73—42no—
331#2398—731no—
332#1985—731no—
333#1985—731no—
334#1924—731no—
335#1924—731no—
336#1923—731no—
337#1923—731no—
338#1869—731no—
339#1869—731no—
340#1850—731no—
341#1850—731no—
342#1840—731no—
343#1768—731no—
344#1752—731no—
345#1752—731no—
346C73#2239611yescharacteristic, complemented, Sylow
347C23×C8—731no—
348C23×C8—731no—
349C2×C4×Q8—731no—
350C2×C4×D4—731no—
351C2×C4⋊C8—731no—
352C2×C4⋊C8—731no—
353C2×C4⋊C8—731no—
354C2×C4⋊C8—731no—
355C2×C22⋊C8—731no—
356C2×C22⋊C8—731no—
357C2×C22⋊C8—731no—
358C2×C22⋊C8—731no—
359C2×C22⋊C8—731no—
360C2×C22⋊C8—731no—
361C2×#97—731no—
362C2×#97—731no—
363C2×#97—731no—
364C2×C4×C8—731no—
365#400—731no—
366#400—731no—
367#397—731no—
368#397—731no—
369#394—731no—
370#394—731no—
371#393—731no—
372#393#6440811yescharacteristic
373C4×C22⋊C4—731no—
374C4×C22⋊C4—731no—
375C4×C22⋊C4—731no—
376C4×C22⋊C4—731no—
377#376—731no—
378#336—731no—
379#336—731no—
380#336—731no—
381#336—731no—
382#336—731no—
383#336—731no—
384#336—731no—
385#336—731no—
386#336—731no—
387#336—731no—
388#336—731no—
389#336—731no—
390C22×Q8C2×#6440811yescharacteristic
391C22×D4—731no—
392C23×C4—731no—
393C23×C4—731no—
394C22×C8—2921no—
395C22×C8—2921no—
396C22×C8—2921no—
397C22×C8—2921no—
398C22×C8—731no—
399C22×C8—731no—
400C22×C8—731no—
401C22×C8—731no—
402C22×C8—731no—
403C22×C8—731no—
404C22×C8—731no—
405C22×C8—731no—
406C22×C8—1462no—
407C22×C8—1462no—
408C4×Q8—2921no—
409C4×Q8—2921no—
410C4×D4—2921no—
411C4×D4—2921no—
412C2×C4⋊C4—731no—
413C2×C4⋊C4—731no—
414C2×C4⋊C4—731no—
415C2×C4⋊C4—731no—
416C2×C22⋊C4—731no—
417C2×C22⋊C4—731no—
418C2×C22⋊C4—731no—
419C2×C22⋊C4—731no—
420C2×C22⋊C4—731no—
421C2×C22⋊C4—731no—
422C2×C22⋊C4—731no—
423C2×C22⋊C4C2×#6440811yescharacteristic
424C2×C22⋊C4C2×#6440811yescharacteristic
425C2×C22⋊C4C2×#6440811yescharacteristic
426C2×C42—731no—
427C2×C42—731no—
428C2×C42—731no—
429C2×C42—731no—
430C2×C42—731no—
431C4⋊C8—2921no—
432C4⋊C8—2921no—
433C4⋊C8—1462no—
434C4⋊C8—1462no—
435C22⋊C8—2921no—
436C22⋊C8—2921no—
437C22⋊C8—2921no—
438C22⋊C8—2921no—
439C22⋊C8—1462no—
440C22⋊C8—1462no—
441#97—2921no—
442#97—2921no—
443#97—2921no—
444C4×C8—2921no—
445#95—731no—
446#95—731no—
447#95—731no—
448#95—731no—
449#95—731no—
450#95—731no—
451#95—731no—
452#95—731no—
453#95—731no—
454#95C2×#6440811yescharacteristic
455#95C2×#6440811yescharacteristic
456#95C2×#6440811yescharacteristic
457C24—731no—
458C24C22×#6440811yescharacteristic
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×D4—2921no—
463C2×D4—1462no—
464C2×D4—1462no—
465C22×C4—731no—
466C22×C4—731no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—731no—
470C22×C4—731no—
471C22×C4—731no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4C22×#6440811yescharacteristic
485C22×C4C22×#6440811yescharacteristic
486C22×C4C22×#6440811yescharacteristic
487C22×C4C22×#6440811yescharacteristic
488C22×C4C22×#6440811yescharacteristic
489C22×C4C22×#6440811yescharacteristic
490C2×C8—2924no—
491C2×C8—2924no—
492C2×C8—732no—
493C2×C8—732no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C4⋊C4—2921no—
517C4⋊C4—2921no—
518C4⋊C4—2921no—
519C4⋊C4—2921no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—2921no—
524C22⋊C4—2921no—
525C22⋊C4—2921no—
526C22⋊C4—1462no—
527C22⋊C4—1462no—
528C22⋊C4—1462no—
529C22⋊C4—1462no—
530C42—1461no—
531C42—1461no—
532C42—1461no—
533C42—1461no—
534C42—1461no—
535C42—1461no—
536C42—1461no—
537C42—1461no—
538C42—1461no—
539C42—1461no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—732no—
547C23—1461no—
548C23—1461no—
549C23—1461no—
550C23—1461no—
551C23—1461no—
552C23—1461no—
553C23#1455667912yes—
554C23C23×#6440811yescharacteristic
555Q8—44no—
556D4—2924no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—731no—
584C2×C4—731no—
585C2×C4—731no—
586C2×C4—731no—
587C2×C4—731no—
588C2×C4—731no—
589C2×C4—1461no—
590C2×C4—1461no—
591C2×C4—1461no—
592C2×C4—1461no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4—1461no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C8—2921no—
608C8—2921no—
609C8—2921no—
610C8—2921no—
611C8—2921no—
612C8—2921no—
613C8—1462no—
614C8—1462no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—2921no—
623C22—2921no—
624C22—2921no—
625C22—2921no—
626C22—1462no—
627C22—1462no—
628C22—1462no—
629C22#41×#6440811yescharacteristic
630C22#1798965411yescharacteristic
631C22#1798965611yescharacteristic
632C22D73⋊#13111yescharacteristic
633C22C2×#1455667911yescharacteristic
634C22#1798966511yescharacteristic
635C22#1798966511yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—2921no—
643C4—2921no—
644C4—2921no—
645C4—2921no—
646C4—2921no—
647C4—2921no—
648C4—731no—
649C4—731no—
650C4—731no—
651C4—731no—
652C2—42no—
653C2—2922no—
654C2#2262643211yescharacteristic
655C2#2262675711yescharacteristic
656C2#2262675911yescharacteristic
657C2#2262680611yescharacteristic
658C2#2262680711yescharacteristic
659C2#2262686811yescharacteristic
660C2#2262687011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#393×C73C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×Dic73C24
hypercenter#393#64408
hypocenterC73#22396
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #22626105C2semidirect
2. #22626105C2semidirect
3. #22626007C2semidirect
4. #22626005C2semidirect
5. #22626002C2semidirect
6. #22626001C2semidirect
9. #22625876C2semidirect
10. #22625875C2semidirect
11. #22625860C2semidirect
12. #22625719C2semidirect
13. #22625669C2semidirect
14. #22625668C2semidirect
346. C73#22396semidirect

Maximal subgroups

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

subgroupindex
#226261052
#226260072
#226260052
#226260022
#226260012
#226259062
#226259052
#226258762
#226258752
#226258602
#226257192
#226256692
#226256682
#226132132
#2239673