Finite Group Databasebeta

← #34023355

Subgroups — #34023355

Order 18688.

848 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989639C211yesmaximal, characteristic, complemented
2C2×#17989616C211yesmaximal, characteristic
3#22626101C211yesmaximal, characteristic, complemented
4#22626054C211yesmaximal, characteristic
5#22626006C211yesmaximal, characteristic, complemented
6#22626004C211yesmaximal, characteristic, complemented
7#22626002C211yesmaximal, characteristic, complemented
8#22626000C211yesmaximal, characteristic, complemented
9#22625849C211yesmaximal, characteristic, complemented
10#22625672C211yesmaximal, characteristic, complemented
11#22625672C211yesmaximal, characteristic, complemented
12#22625668C211yesmaximal, characteristic, complemented
13C22⋊C4×#10596833C211yesmaximal, characteristic, complemented
14#22625588C211yesmaximal, characteristic, complemented
15#22613216C211yesmaximal, characteristic
16C22×#11924038C2211yescharacteristic
17C23×#10596833C2211yescharacteristic
18#17989639—24no—
19#17989616—24no—
20C2×#14556658C2211yescharacteristic
21C2×#14556658C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×#14556646C2211yescharacteristic
31C2×#14556646C2211yescharacteristic
32C2×#14556646C2211yescharacteristic
33C2×#14556646C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36C2×C4×#10596833C2211yescharacteristic
37C2×C4×#10596833C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556556C2211yescharacteristic
47C2×#14556551C2211yescharacteristic
48#17988528C411yescharacteristic
49#17988528C411yescharacteristic
50#17988513C411yescharacteristic
51#17988502C411yescharacteristic
52#17988502C411yescharacteristic
53#17988500C411yescharacteristic
54#17988499C411yescharacteristic
55C22⋊C4×Dic73C2211yescharacteristic
56C22⋊C4×Dic73C2211yescharacteristic
57#17988434C2211yescharacteristic
58#17988434C2211yescharacteristic
59#17988432C2211yescharacteristic
60#397×C73C411yescharacteristic
61C2×#11924038—22no—
62C2×#11924038—22no—
63C2×#11924038—22no—
64C22×#10596833—22no—
65C22×#10596833—22no—
66C22×#10596833—22no—
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75#14556658—22no—
76#14556658—22no—
77C4⋊#10596833—22no—
78C4⋊#10596833—22no—
79#14556648—22no—
80#14556648—22no—
81#14556648—22no—
82C22⋊#10596833—22no—
83C22⋊#10596833—22no—
84C22⋊#10596833—22no—
85#14556646—22no—
86#14556646—22no—
87#14556646—22no—
88#14556646D414yes—
89C4×#10596833—22no—
90C4×#10596833—22no—
91C4×#10596833—22no—
92C4×#10596833—22no—
93C22×Dic146C2×C411yescharacteristic
94C22×C22⋊D73C2×C411yescharacteristic
95C23×Dic73C2311yescharacteristic
96C22×C4×D73C2311yescharacteristic
97#14556556—22no—
98#14556556—22no—
99#14556551—22no—
100#14556551—22no—
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×C22⋊Dic73C2×C411yescharacteristic
105C2×C22⋊Dic73C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×#11924005C2×C411yescharacteristic
108C2×#11924005C2×C411yescharacteristic
109C2×#11924005C2×C411yescharacteristic
110C2×#11924005C2×C411yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#11924038—44no—
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—21no—
150C2×#10596833—21no—
151C2×#10596833—44no—
152C2×#10596833C2×D412yes—
153C2×#10596833C2×D412yes—
154C2×#10596833#4112yes—
155C2×#10596833#4112yes—
156C2×#10596833#4112yes—
157C2×#10596833#4112yes—
158C23×D73C22×C411yescharacteristic
159C2×Dic146—22no—
160C2×Dic146—22no—
161C2×Dic146—41no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—22no—
164C2×C22⋊D73—41no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73C22×C411yescharacteristic
172C22×Dic73C22×C411yescharacteristic
173C22×Dic73C22×C411yescharacteristic
174C22×Dic73C22×C411yescharacteristic
175C22×Dic73C22×C411yescharacteristic
176C22×Dic73C22×C411yescharacteristic
177C22×Dic73C2411yescharacteristic
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—21no—
184#11924007—22no—
185#11924007—22no—
186#11924007—22no—
187C22⋊Dic73—22no—
188C22⋊Dic73—41no—
189#11924005—22no—
190#11924005—22no—
191#11924005—41no—
192#11924005—41no—
193#11924005—41no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C4×Dic73C2×D412yes—
203C4×Dic73#4112yes—
204C24×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C4⋊C4×C73—22no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—22no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73#13112yes—
222C23×C73C23×C411yescharacteristic
223C22×D73—21no—
224C22×D73—21no—
225C22×D73—21no—
226C22×D73—21no—
227C22×D73—21no—
228C22×D73—21no—
229C22×D73—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—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73C4×D412yes—
248C22⋊D73—44no—
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—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73C4×D412yes—
270C2×Dic73#13112yes—
271C2×Dic73C22×D411yescharacteristic
272C2×Dic73C2×#4111yescharacteristic
273C2×Dic73C2×#4111yescharacteristic
274C2×Dic73C2×#4111yescharacteristic
275C2×Dic73C2×#4111yescharacteristic
276C2×Dic73C2×#4111yescharacteristic
277C4×D73—41no—
278C4×D73—41no—
279C4×D73—41no—
280C4×D73—41no—
281Dic146—44no—
282#10596833—22no—
283#10596833—22no—
284#10596833—22no—
285#10596833—41no—
286#10596833—41no—
287#10596833—41no—
288#10596833—41no—
289#10596833#12414yes—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73C2×C4×D411yescharacteristic
298C22×C73C4×#4111yescharacteristic
299C22×C73C4×#4111yescharacteristic
300C22×C73C2×#13111yescharacteristic
301C22×C73C2×#13111yescharacteristic
302C22×C73#56811yescharacteristic
303C22×C73#56811yescharacteristic
304C2×D73—41no—
305C2×D73—41no—
306C2×D73—41no—
307C2×D73—41no—
308C2×D73—41no—
309C2×D73—41no—
310C2×D73—41no—
311C4×C73—22no—
312C4×C73—41no—
313C4×C73—41no—
314C4×C73—41no—
315C4×C73—41no—
316C4×C73—41no—
317Dic73—22no—
318Dic73—22no—
319Dic73—41no—
320Dic73—41no—
321Dic73—41no—
322Dic73—41no—
323Dic73C2×#12411yescharacteristic
324Dic73#52911yescharacteristic
325Dic73#52911yescharacteristic
326Dic73#53211yescharacteristic
327#21637—731nomaximal, Sylow
328C2×C73—42no—
329C2×C73C4×#12411yescharacteristic
330C2×C73#293311yescharacteristic
331C2×C73#293311yescharacteristic
332C2×C73#296611yescharacteristic
333C2×C73#296711yescharacteristic
334C2×C73#296811yescharacteristic
335C2×C73#296911yescharacteristic
336D73—81no—
337C2×#446—731no—
338C2×#435—731no—
339#2398—731no—
340#1984—731no—
341#1954—731no—
342#1924—731no—
343#1924—731no—
344#1923—731no—
345#1923—731no—
346#1832—731no—
347#1753—731no—
348#1753—731no—
349#1752—731no—
350C8×C22⋊C4—731no—
351#1726—731no—
352C73#2163711yescharacteristic, complemented, Sylow
353C22×M16—731no—
354C23×C8—731no—
355C2×C4×Q8—731no—
356C2×C4×D4—731no—
357#446—1464no—
358#435—1464no—
359C2×C4⋊C8—731no—
360C2×C4⋊C8—731no—
361C2×C4⋊C8—731no—
362C2×C4⋊C8—731no—
363C2×C22⋊C8—731no—
364C2×C22⋊C8—731no—
365C2×C22⋊C8—731no—
366C2×C22⋊C8—731no—
367C2×C22⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×#97—731no—
370C2×#97—731no—
371C2×#97—731no—
372C2×#97—731no—
373C2×C4×C8—731no—
374C2×C4×C8—731no—
375C2×C4×C8—731no—
376C2×C4×C8—731no—
377#400—731no—
378#400—731no—
379#397—731no—
380#397#6440811yescharacteristic
381#394—731no—
382#394—731no—
383#393—731no—
384#393—731no—
385C4×C22⋊C4—731no—
386C4×C22⋊C4—731no—
387C4×C22⋊C4—731no—
388C4×C22⋊C4—731no—
389#376—731no—
390#336—731no—
391#336—731no—
392#336—731no—
393#336—731no—
394#336—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398C22×Q8—731no—
399C22×D4—731no—
400C23×C4—731no—
401C23×C4—731no—
402C2×M16—1462no—
403C2×M16—1462no—
404C2×M16—1462no—
405C22×C8—731no—
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411C22×C8—731no—
412C22×C8—731no—
413C22×C8—1462no—
414C22×C8—1462no—
415C22×C8—1462no—
416C4×Q8—1462no—
417C4×Q8—1462no—
418C4×D4—1462no—
419C4×D4—1462no—
420C2×C4⋊C4—731no—
421C2×C4⋊C4—731no—
422C2×C4⋊C4—731no—
423C2×C4⋊C4C2×#6440811yescharacteristic
424C2×C22⋊C4—731no—
425C2×C22⋊C4—731no—
426C2×C22⋊C4—731no—
427C2×C22⋊C4—731no—
428C2×C22⋊C4—731no—
429C2×C22⋊C4—731no—
430C2×C22⋊C4—731no—
431C2×C22⋊C4C2×#6440811yescharacteristic
432C2×C22⋊C4C2×#6440811yescharacteristic
433C2×C22⋊C4C2×#6440811yescharacteristic
434C2×C42—731no—
435C2×C42—731no—
436C2×C42—731no—
437C2×C42—731no—
438C2×C42—731no—
439C4⋊C8—1462no—
440C4⋊C8—1462no—
441C4⋊C8—1462no—
442C4⋊C8—1462no—
443C22⋊C8—1462no—
444C22⋊C8—1462no—
445C22⋊C8—1462no—
446C22⋊C8—1462no—
447C22⋊C8—1462no—
448C22⋊C8—1462no—
449#97—734no—
450#97—1462no—
451#97—1462no—
452#97—1462no—
453C4×C8—1462no—
454C4×C8—1462no—
455C4×C8—1462no—
456C4×C8—1462no—
457#95—731no—
458#95—731no—
459#95—731no—
460#95—731no—
461#95—731no—
462#95—731no—
463#95—731no—
464#95—731no—
465#95—731no—
466#95C2×#6440811yescharacteristic
467#95C2×#6440811yescharacteristic
468#95C2×#6440811yescharacteristic
469C24—731no—
470C24C22×#6440811yescharacteristic
471C2×Q8—2921no—
472C2×Q8—1462no—
473C2×Q8—1462no—
474C2×D4—2921no—
475C2×D4—1462no—
476C2×D4—1462no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—731no—
482C22×C4—731no—
483C22×C4—731no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1461no—
495C22×C4—1461no—
496C22×C4C22×#6440811yescharacteristic
497C22×C4C22×#6440811yescharacteristic
498C22×C4C22×#6440811yescharacteristic
499C22×C4C22×#6440811yescharacteristic
500C22×C4C22×#6440811yescharacteristic
501C22×C4C22×#6440811yescharacteristic
502M16—2924no—
503C2×C8—2924no—
504C2×C8—732no—
505C2×C8—732no—
506C2×C8—732no—
507C2×C8—732no—
508C2×C8—732no—
509C2×C8—732no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C2×C8—1461no—
527C2×C8—1461no—
528C4⋊C4—22no—
529C4⋊C4—1462no—
530C4⋊C4—1462no—
531C4⋊C4—1462no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—2921no—
536C22⋊C4—2921no—
537C22⋊C4—2921no—
538C22⋊C4—2921no—
539C22⋊C4—1462no—
540C22⋊C4—1462no—
541C22⋊C4—1462no—
542C42—732no—
543C42—732no—
544C42—1461no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42—1461no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—1461no—
559C23—1461no—
560C23—1461no—
561C23—1461no—
562C23—1461no—
563C23—1461no—
564C23—1461no—
565C23#1455667812yes—
566C23C23×#6440811yescharacteristic
567Q8—2924no—
568D4—2924no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—2921no—
587C2×C4—2921no—
588C2×C4—2921no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—2921no—
592C2×C4—2921no—
593C2×C4—2921no—
594C2×C4—731no—
595C2×C4—731no—
596C2×C4—731no—
597C2×C4—731no—
598C2×C4—731no—
599C2×C4—731no—
600C2×C4—732no—
601C2×C4—732no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1461no—
611C2×C4—1461no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4D4×#6440812yes—
619C8—2921no—
620C8—2921no—
621C8—2921no—
622C8—2921no—
623C8—734no—
624C8—1462no—
625C8—1462no—
626C8—1462no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—2921no—
635C22—2921no—
636C22—2921no—
637C22—2921no—
638C22—2921no—
639C22—2921no—
640C22—2921no—
641C22C2×D4×#6440811yescharacteristic
642C22#41×#6440811yescharacteristic
643C22#41×#6440811yescharacteristic
644C22C2×#1455667811yescharacteristic
645C22D73⋊#13111yescharacteristic
646C22#1798966611yescharacteristic
647C22#1798966611yescharacteristic
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—2921no—
655C4—2921no—
656C4—2921no—
657C4—2921no—
658C4—731no—
659C4—731no—
660C4—731no—
661C4—731no—
662C4—1462no—
663C4—1462no—
664C2—42no—
665C2—5841no—
666C2#124×#6440811yescharacteristic
667C2#2262666111yescharacteristic
668C2#2262666511yescharacteristic
669C2#2262674611yescharacteristic
670C2#2262675411yescharacteristic
671C2#2262675811yescharacteristic
672C2#2262676611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#397×C73C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×Dic73C24
hypercenter#397#64408
hypocenterC73#21637
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#17989639C2semidirect
3. #22626101C2semidirect
5. #22626006C2semidirect
6. #22626004C2semidirect
7. #22626002C2semidirect
8. #22626000C2semidirect
9. #22625849C2semidirect
10. #22625672C2semidirect
11. #22625672C2semidirect
12. #22625668C2semidirect
13. C22⋊C4×#10596833C2semidirect
14. #22625588C2semidirect
352. C73#21637semidirect

Maximal subgroups

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

subgroupindex
C2×#179896392
C2×#179896162
#226261012
#226260542
#226260062
#226260042
#226260022
#226260002
#226258492
#226256722
#226256682
C22⋊C4×#105968332
#226255882
#226132162
#2163773