Finite Group Databasebeta

← #33057127

Subgroups — #33057127

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618951C211yesmaximal, characteristic
2#22618880C211yesmaximal, characteristic, complemented
3#22608834C211yesmaximal, characteristic, complemented
4#22608822C211yesmaximal, characteristic, complemented
5#22608810C211yesmaximal, characteristic, complemented
6#22608803C211yesmaximal, characteristic, complemented
7#22608782C211yesmaximal, characteristic, complemented
8#22608775C211yesmaximal, characteristic, complemented
9#22608750C211yesmaximal, characteristic, complemented
10Q16×#10596831C211yesmaximal, characteristic, complemented
11#22608716C211yesmaximal, characteristic, complemented
12#22608404C211yesmaximal, characteristic, complemented
13#22608318C211yesmaximal, characteristic
14#22608226C211yesmaximal, characteristic, complemented
15C73×#3107C211yesmaximal, characteristic
16#17988718—21no—
17#17988718—21no—
18#17988718C2211yescharacteristic
19#17988718C2211yescharacteristic
20Q8×#10596831C2211yescharacteristic
21Q8×#10596831C2211yescharacteristic
22Q8×#10596831C2211yescharacteristic
23Q8×#10596831C2211yescharacteristic
24#17988665—21no—
25#17988665—21no—
26#17988665C2211yescharacteristic
27#17988665C2211yescharacteristic
28#17988644—21no—
29#17988644C2211yescharacteristic
30#17988640C2211yescharacteristic
31#17988614—21no—
32C2×C4⋊#10596831C2211yescharacteristic
33#17988543—21no—
34C4×#11924012—21no—
35C4×#11924012C2211yescharacteristic
36#17988340C2211yescharacteristic
37#17988340C2211yescharacteristic
38#17988338C2211yescharacteristic
39#17988338C2211yescharacteristic
40Q8⋊#10596831C2211yescharacteristic
41Q8⋊#10596831C2211yescharacteristic
42Q8⋊#10596831C2211yescharacteristic
43Q8⋊#10596831C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48#17988309C2211yescharacteristic
49#17988309C2211yescharacteristic
50#17988308C2211yescharacteristic
51C8×#10596831C2211yescharacteristic
52#533×C73C2211yescharacteristic
53C4×#41×C73C2211yescharacteristic
54#485×C73C411yescharacteristic
55#485×C73C411yescharacteristic
56#475×C73C411yescharacteristic
57#474×C73C411yescharacteristic
58#462×C73C411yescharacteristic
59#461×C73C411yescharacteristic
60#452×C73C411yescharacteristic
61#452×C73C411yescharacteristic
62C4×Q16×C73C2211yescharacteristic
63C4×Q16×C73C2211yescharacteristic
64C4×SD16×C73C2211yescharacteristic
65C4×SD16×C73C2211yescharacteristic
66#431×C73C2211yescharacteristic
67C2×#11924012—21no—
68C2×#11924012—21no—
69C2×#11924012D411yescharacteristic
70C2×#11924012D411yescharacteristic
71C22×#10596831—21no—
72C4⋊#10596831—21no—
73C4⋊#10596831—21no—
74C4⋊#10596831—21no—
75C4⋊#10596831—21no—
76C4⋊#10596831—21no—
77C4⋊#10596831—21no—
78C4⋊#10596831—21no—
79C4⋊#10596831—21no—
80C4⋊#10596831C2311yescharacteristic
81C4⋊#10596831C2311yescharacteristic
82C4⋊#10596831C2311yescharacteristic
83C4⋊#10596831C2311yescharacteristic
84C22⋊#10596831—21no—
85C22⋊#10596831—21no—
86C22⋊#10596831—21no—
87C22⋊#10596831—21no—
88#14556502—21no—
89#14556502—21no—
90#14556502—21no—
91#14556502D411yescharacteristic
92#14556502D411yescharacteristic
93C4×#10596831—21no—
94C4×#10596831—21no—
95C4×#10596831—21no—
96C4×#10596831—21no—
97C4×#10596831C2311yescharacteristic
98C4×#10596831C2311yescharacteristic
99C4×#10596831C2311yescharacteristic
100C4×#10596831C2311yescharacteristic
101C2×#41×C73C2×C411yescharacteristic
102C2×Q16×C73C2×C411yescharacteristic
103C2×Q16×C73C2×C411yescharacteristic
104C2×SD16×C73C2×C411yescharacteristic
105C2×SD16×C73C2×C411yescharacteristic
106C4⋊Q8×C73C2×C411yescharacteristic
107C4⋊Q8×C73C2×C411yescharacteristic
108#125×C73—21no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73C2×C411yescharacteristic
111C22⋊Q8×C73C2×C411yescharacteristic
112C4×Q8×C73—21no—
113C4×Q8×C73C2×C411yescharacteristic
114C4×Q8×C73C2311yescharacteristic
115C4×Q8×C73C2311yescharacteristic
116C4×Q8×C73C2311yescharacteristic
117C4×D4×C73—21no—
118C4×D4×C73—21no—
119C4×D4×C73C2×C411yescharacteristic
120C4×D4×C73C2311yescharacteristic
121#117×C73—21no—
122#117×C73—21no—
123#117×C73C2×C411yescharacteristic
124C2×C42×C73—21no—
125C2×C42×C73C2311yescharacteristic
126#107×C73C2×C411yescharacteristic
127#107×C73C2×C411yescharacteristic
128#106×C73C2×C411yescharacteristic
129#106×C73C2×C411yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132#103×C73C2×C411yescharacteristic
133#103×C73C2×C411yescharacteristic
134#103×C73C2×C411yescharacteristic
135#103×C73C2×C411yescharacteristic
136#103×C73C2×C411yescharacteristic
137#103×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—22no—
145#11924012—41no—
146#11924012—42no—
147#11924012—42no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—42no—
155C2×#10596831C2×D411yescharacteristic
156C2×#10596831C2×D411yescharacteristic
157C2×#10596831C2×D411yescharacteristic
158C2×#10596831C2×D411yescharacteristic
159#41×C73—22no—
160#41×C73—41no—
161C2×Q8×C73—21no—
162C2×Q8×C73C22×C411yescharacteristic
163C2×Q8×C73C22×C411yescharacteristic
164C2×Q8×C73C22×C411yescharacteristic
165C2×D4×C73—21no—
166C2×D4×C73C22×C411yescharacteristic
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73#4111yescharacteristic
173Q16×C73—22no—
174Q16×C73—22no—
175SD16×C73—41no—
176SD16×C73—41no—
177C2×C8×C73C22×C411yescharacteristic
178C2×C8×C73C22×C411yescharacteristic
179C2×C8×C73C22×C411yescharacteristic
180C2×C8×C73C22×C411yescharacteristic
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73C22×C411yescharacteristic
191C4⋊C4×C73C22×C411yescharacteristic
192C4⋊C4×C73C22×C411yescharacteristic
193C4⋊C4×C73C22×C411yescharacteristic
194C22⋊C4×C73—21no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73C22×C411yescharacteristic
205C42×C73C2×D411yescharacteristic
206C42×C73#4111yescharacteristic
207C42×C73C2411yescharacteristic
208C23×C73—21no—
209C23×C73C4×D411yescharacteristic
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73—21no—
215Q8×C73—81no—
216Q8×C73#13112yes—
217D4×C73—21no—
218D4×C73—21no—
219D4×C73—42no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
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—41no—
232C2×C4×C73—42no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—81no—
236C2×C4×C73C4×D411yescharacteristic
237C2×C4×C73C4×D411yescharacteristic
238C2×C4×C73C4×D411yescharacteristic
239C2×C4×C73C23×C411yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—41no—
250#10596831—41no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831#13712yes—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73C2×C4×D411yescharacteristic
263C4×C73—21no—
264C4×C73—22no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—21no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73C2×#13111yescharacteristic
275C4×C73#56811yescharacteristic
276C4×C73C2×#13711yescharacteristic
277C4×C73#57511yescharacteristic
278#18013—731nomaximal, Sylow
279C2×C73—41no—
280C2×C73—81no—
281C2×C73#293311yescharacteristic
282C2×C73C4×#13711yescharacteristic
283C2×C73#295711yescharacteristic
284#3107D7311yescharacteristic
285#2971—731no—
286#2962—731no—
287#1592—731no—
288#1590—731no—
289#1588—731no—
290#1587—731no—
291#1584—731no—
292#1583—731no—
293#1579—731no—
294C8×Q16—731no—
295#1573—731no—
296#1497—731no—
297#1477—731no—
298#1453—731no—
299C73#1801311yescharacteristic, complemented, Sylow
300#533C2×D7311yescharacteristic
301C4×#41C2×D7311yescharacteristic
302#485Dic7311yescharacteristic
303#485Dic7311yescharacteristic
304#475Dic7311yescharacteristic
305#474Dic7311yescharacteristic
306#462Dic7311yescharacteristic
307#461Dic7311yescharacteristic
308#452Dic7311yescharacteristic
309#452Dic7311yescharacteristic
310#446—731no—
311#446—731no—
312#446—1461no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C8×Q8—731no—
318C4×Q16C2×D7311yescharacteristic
319C4×Q16C2×D7311yescharacteristic
320C4×SD16C2×D7311yescharacteristic
321C4×SD16C2×D7311yescharacteristic
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#432—731no—
327#432—1461no—
328#431—731no—
329#431C2×D7311yescharacteristic
330#424—1461no—
331C2×C4⋊C8—731no—
332#405—1461no—
333C4×M16—731no—
334C4×M16—1461no—
335#335—731no—
336#335—731no—
337#334—731no—
338#334—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345D4⋊C8—731no—
346D4⋊C8—731no—
347#322—731no—
348#322—731no—
349#322—731no—
350C82—731no—
351C2×#41C2×Dic7311yescharacteristic
352C2×Q16C2×Dic7311yescharacteristic
353C2×Q16C2×Dic7311yescharacteristic
354C2×SD16C2×Dic7311yescharacteristic
355C2×SD16C2×Dic7311yescharacteristic
356C2×M16—731no—
357C2×M16—731no—
358C2×M16—1461no—
359C2×M16—1461no—
360C22×C8—1461no—
361C4⋊Q8C2×Dic7311yescharacteristic
362C4⋊Q8C2×Dic7311yescharacteristic
363#125—21no—
364C22⋊Q8—21no—
365C22⋊Q8C2×Dic7311yescharacteristic
366C22⋊Q8C2×Dic7311yescharacteristic
367C4×Q8—21no—
368C4×Q8C2×Dic7311yescharacteristic
369C4×Q8C22×D7311yescharacteristic
370C4×Q8C22×D7311yescharacteristic
371C4×Q8C22×D7311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C2×Dic7311yescharacteristic
375C4×D4C22×D7311yescharacteristic
376#117—21no—
377#117—21no—
378#117C2×Dic7311yescharacteristic
379C2×C42—21no—
380C2×C42C22×D7311yescharacteristic
381#107C2×Dic7311yescharacteristic
382#107C2×Dic7311yescharacteristic
383#106C2×Dic7311yescharacteristic
384#106C2×Dic7311yescharacteristic
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C2×Dic7311yescharacteristic
398C4⋊C8C2×Dic7311yescharacteristic
399#103C2×Dic7311yescharacteristic
400#103C2×Dic7311yescharacteristic
401#103C2×Dic7311yescharacteristic
402#103C2×Dic7311yescharacteristic
403#103C2×Dic7311yescharacteristic
404#103C2×Dic7311yescharacteristic
405#102C2×Dic7311yescharacteristic
406#102C2×Dic7311yescharacteristic
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C2×Dic7311yescharacteristic
412C22⋊C8C2×Dic7311yescharacteristic
413#97—731no—
414#97—731no—
415#97—1461no—
416#97—1461no—
417#97—1461no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428#41—22no—
429#41—41no—
430C2×Q8—21no—
431C2×Q8C22×Dic7311yescharacteristic
432C2×Q8C22×Dic7311yescharacteristic
433C2×Q8C22×Dic7311yescharacteristic
434C2×D4—21no—
435C2×D4C22×Dic7311yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4C22×Dic7311yescharacteristic
440C22×C4D4×D7311yescharacteristic
441C22×C4#1192402711yescharacteristic
442Q16—22no—
443Q16—22no—
444SD16—41no—
445SD16—41no—
446M16—2922no—
447M16—2922no—
448M16—2921no—
449M16—1462no—
450C2×C8—2922no—
451C2×C8—731no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8C22×Dic7311yescharacteristic
462C2×C8C22×Dic7311yescharacteristic
463C2×C8C22×Dic7311yescharacteristic
464C2×C8C22×Dic7311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4C22×Dic7311yescharacteristic
475C4⋊C4C22×Dic7311yescharacteristic
476C4⋊C4C22×Dic7311yescharacteristic
477C4⋊C4C22×Dic7311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42C22×Dic7311yescharacteristic
489C42D4×D7311yescharacteristic
490C42#1192402711yescharacteristic
491C42C23×D7311yescharacteristic
492C23—21no—
493C23D4×Dic7311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—81no—
500Q8#1455659812yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4D4×Dic7311yescharacteristic
521C2×C4D4×Dic7311yescharacteristic
522C2×C4D4×Dic7311yescharacteristic
523C2×C4C23×Dic7311yescharacteristic
524C2×C4C2×D4×D7311yescharacteristic
525C2×C4C2×#1192402711yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—2921no—
531C8—2921no—
532C8—2921no—
533C8—2921no—
534C8—2921no—
535C8—2921no—
536C8—732no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×D4×Dic7311yescharacteristic
547C4—21no—
548C4—22no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4C2×#1455659811yescharacteristic
559C4#1798935411yescharacteristic
560C4#137×D7311yescharacteristic
561C4#1798938611yescharacteristic
562C2—41no—
563C2—81no—
564C2#2261865811yescharacteristic
565C2#137×Dic7311yescharacteristic
566C2#2261884811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#3107C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C2×C4
cosocleC42×C73C24
hypercenter#3107D73
hypocenterC73#18013
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
2. #22618880C2semidirect
3. #22608834C2semidirect
4. #22608822C2semidirect
5. #22608810C2semidirect
6. #22608803C2semidirect
7. #22608782C2semidirect
8. #22608775C2semidirect
9. #22608750C2semidirect
10. Q16×#10596831C2semidirect
11. #22608716C2semidirect
12. #22608404C2semidirect
14. #22608226C2semidirect
299. C73#18013semidirect

Maximal subgroups

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

subgroupindex
#226189512
#226188802
#226088342
#226088222
#226088102
#226088032
#226087822
#226087752
#226087502
Q16×#105968312
#226087162
#226084042
#226083182
#226082262
C73×#31072
#1801373