Finite Group Databasebeta

← #21462342

Subgroups — #21462342

Order 7808.

652 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#6923C211yesmaximal, characteristic
2C2×#14519856C211yesmaximal, characteristic, complemented
3#16840713C211yesmaximal, characteristic, complemented
4#16840712C211yesmaximal, characteristic, complemented
5#16840712C211yesmaximal, characteristic, complemented
6#16840711C211yesmaximal, characteristic, complemented
7#16840711C211yesmaximal, characteristic, complemented
8#16840710C211yesmaximal, characteristic
9#16840709C211yesmaximal, characteristic, complemented
10#16840709C211yesmaximal, characteristic, complemented
11C4⋊C4×#6923C211yesmaximal, characteristic, complemented
12C22⋊C4×#6923C211yesmaximal, characteristic, complemented
13C22⋊C4×#6923C211yesmaximal, characteristic, complemented
14C2×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
15#123×D61C211yesmaximal, characteristic
16C23×#6923C2211yescharacteristic
17C23×#6923C2211yescharacteristic
18C23×#6923C2211yescharacteristic
19D4×#6923—24no—
20#14519856—24no—
21C2×C4⋊#6923C2211yescharacteristic
22C2×C4⋊#6923C2211yescharacteristic
23C2×C4⋊#6923C2211yescharacteristic
24C2×C4⋊#6923C2211yescharacteristic
25C2×C4⋊#6923C2211yescharacteristic
26C2×C22⋊#6923C2211yescharacteristic
27C2×C22⋊#6923C2211yescharacteristic
28C2×C22⋊#6923C2211yescharacteristic
29C2×C22⋊#6923C2211yescharacteristic
30C2×C22⋊#6923C2211yescharacteristic
31C2×C4×#6923C2211yescharacteristic
32C2×C4×#6923C2211yescharacteristic
33C2×C4×#6923C2211yescharacteristic
34C2×C4×#6923C2211yescharacteristic
35C2×C4×#6923C2211yescharacteristic
36(C2×#6923)⋊C4C2211yescharacteristic
37(C2×#6923)⋊C4C2211yescharacteristic
38(C2×#6923)⋊C4C2211yescharacteristic
39(C2×#6923)⋊C4C2211yescharacteristic
40(C2×#6923)⋊C4C2211yescharacteristic
41(C2×#6923)⋊C4C2211yescharacteristic
42(C2×#6923)⋊C4C2211yescharacteristic
43(C2×#6923)⋊C4C2211yescharacteristic
44(C2×#6923)⋊C4C2211yescharacteristic
45(C2×#6923)⋊C4C2211yescharacteristic
46C2×D4×D61C2211yescharacteristic
47C22×C4×D61C2211yescharacteristic
48#14519762C411yescharacteristic, complemented
49#14519762C411yescharacteristic, complemented
50#14519761C411yescharacteristic, complemented
51#14519760C411yescharacteristic, complemented
52#14519759C411yescharacteristic, complemented
53#14519759C411yescharacteristic, complemented
54#14519758C411yescharacteristic, complemented
55C4⋊C4×D61C2211yescharacteristic
56C4⋊C4×D61C2211yescharacteristic
57C22⋊C4×D61C2211yescharacteristic
58C22⋊C4×D61C2211yescharacteristic
59C22⋊C4×D61C2211yescharacteristic
60#123×C61C411yescharacteristic, complemented
61C23×D61C2311yescharacteristic
62C23×D61C2311yescharacteristic
63C22×#6923—22no—
64C22×#6923—22no—
65C22×#6923—22no—
66C22×#6923—22no—
67C22×#6923—22no—
68C22×#6923—22no—
69C22×#6923—41no—
70C22×#6923—41no—
71C22×#6923—41no—
72C22×#6923C2311yescharacteristic
73C22×#6923C2311yescharacteristic
74C22×#6923C2311yescharacteristic
75C22×#6923C2311yescharacteristic
76C22×#6923C2311yescharacteristic
77C22×#6923C2311yescharacteristic
78C22×#6923C2311yescharacteristic
79C22×#6923C2311yescharacteristic
80C2×D4×C61C2×C411yescharacteristic
81C22×C4×C61C2×C411yescharacteristic, complemented
82C2×C22⋊D61C2×C411yescharacteristic
83C2×C22⋊D61C2×C411yescharacteristic
84C22×Dic61C2×C411yescharacteristic, complemented
85D4×D61—22no—
86D4×D61—22no—
87C2×D244C2×C411yescharacteristic
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61C2×C411yescharacteristic, complemented
91C2×C4×D61C2×C411yescharacteristic, complemented
92C2×C4×D61C2311yescharacteristic
93C2×C4×D61C2311yescharacteristic
94C2×C4×D61C2311yescharacteristic
95C2×C4×D61C2311yescharacteristic
96C2×C4×D61C2311yescharacteristic
97C22⋊#6923—22no—
98C22⋊#6923—22no—
99C22⋊#6923—22no—
100C22⋊#6923—41no—
101C22⋊#6923D414yes—
102C4⋊#6923—22no—
103C4⋊#6923—22no—
104C4⋊#6923—22no—
105C4⋊#6923—22no—
106C4⋊#6923—41no—
107C4×#6923—22no—
108C4×#6923—22no—
109C4×#6923—22no—
110C4×#6923—22no—
111C4×#6923—41no—
112C4⋊C4×C61C2×C411yescharacteristic, complemented
113C4⋊C4×C61C2×C411yescharacteristic, complemented
114C22⋊C4×C61C2×C411yescharacteristic, complemented
115C22⋊C4×C61C2×C411yescharacteristic, complemented
116C22⋊C4×C61C2×C411yescharacteristic, complemented
117C22⋊Dic61C2×C411yescharacteristic, complemented
118C22⋊Dic61C2×C411yescharacteristic, complemented
119C22⋊Dic61C2×C411yescharacteristic, complemented
120#11758198C2×C411yescharacteristic, complemented
121#11758198C2×C411yescharacteristic, complemented
122#11758198C2×C411yescharacteristic, complemented
123#11758198C2×C411yescharacteristic, complemented
124#11758198C2×C411yescharacteristic, complemented
125#11758198C2×C411yescharacteristic, complemented
126C4⋊Dic61C2×C411yescharacteristic, complemented
127C4⋊Dic61C2×C411yescharacteristic, complemented
128#11758196C2×C411yescharacteristic, complemented
129#11758196C2×C411yescharacteristic, complemented
130#11758196C2×C411yescharacteristic, complemented
131#11758196C2×C411yescharacteristic, complemented
132C23×C61C22×C411yescharacteristic
133C23×C61C22×C411yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61C22×C411yescharacteristic
145C22×D61C22×C411yescharacteristic
146C22×D61C2×D412yes—
147C22×D61#4112yes—
148C22×D61C2411yescharacteristic
149C2×#6923—21no—
150C2×#6923—21no—
151C2×#6923—21no—
152C2×#6923—21no—
153C2×#6923—21no—
154C2×#6923—21no—
155C2×#6923—21no—
156C2×#6923—21no—
157C2×#6923—21no—
158C2×#6923—21no—
159C2×#6923—21no—
160C2×#6923—21no—
161C2×#6923—21no—
162C2×#6923—21no—
163C2×#6923—21no—
164C2×#6923—21no—
165C2×#6923—21no—
166C2×#6923—21no—
167C2×#6923—21no—
168C2×#6923—21no—
169C2×#6923—44no—
170C2×#6923—44no—
171C2×#6923—44no—
172C2×#6923C2×D412yes—
173C2×#6923C2×D412yes—
174C2×#6923#4112yes—
175C2×#6923#4112yes—
176D4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61C22×C411yescharacteristic
179C2×C4×C61C22×C411yescharacteristic
180C2×C4×C61C22×C411yescharacteristic
181C2×C4×C61C22×C411yescharacteristic
182C2×C4×C61C22×C411yescharacteristic
183C22⋊D61—22no—
184C22⋊D61—22no—
185C2×Dic61—22no—
186C2×Dic61C22×C411yescharacteristic
187C2×Dic61C22×C411yescharacteristic
188C2×Dic61C22×C411yescharacteristic
189C2×Dic61C22×C411yescharacteristic
190C2×Dic61C22×C411yescharacteristic
191D244—22no—
192C4×D61—22no—
193C4×D61—22no—
194C4×D61—21no—
195C4×D61—21no—
196C4×D61—21no—
197C4×D61—21no—
198C4×D61—21no—
199C4×D61—21no—
200C4×D61—21no—
201C4×D61—21no—
202C4×D61—21no—
203C4×D61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61C4×D412yes—
210C22×C61C23×C411yescharacteristic
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61C4×D412yes—
225C2×D61C22×D411yescharacteristic
226C2×D61C2×#4111yescharacteristic
227C2×D61C2×#4111yescharacteristic
228C2×D61C2×#4111yescharacteristic
229C2×D61H(5,𝔽2)11yescharacteristic
230C2×D612−1+411yescharacteristic
231#6923—22no—
232#6923—22no—
233#6923—22no—
234#6923—22no—
235#6923—41no—
236#6923—41no—
237#6923—41no—
238#6923—41no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244Dic61—21no—
245Dic61—21no—
246Dic61—21no—
247Dic61—21no—
248Dic61—21no—
249#2359—611nomaximal, Sylow
250C2×C61—22no—
251C2×C61—41no—
252C2×C61C2×C4×D411yescharacteristic
253C2×C61C4×#4111yescharacteristic
254C2×C61#52011yescharacteristic
255D61—22no—
256D61—41no—
257D61#54611yescharacteristic
258D61#54711yescharacteristic
259D61#55111yescharacteristic
260D61#55211yescharacteristic
261C2×#123—611no—
262C2×C4×D4—611no—
263C2×#117—611no—
264#389—611no—
265#388—611no—
266#388—611no—
267#387—611no—
268#387—611no—
269#386—611no—
270#385—611no—
271#385—611no—
272C4×C4⋊C4—611no—
273C4×C22⋊C4—611no—
274C4×C22⋊C4—611no—
275C2×#95—611no—
276C61#235911yescharacteristic, complemented, Sylow
277C22×D4—611no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—611no—
282#123—611no—
283#123—611no—
284#123—611no—
285#123—611no—
286#123—611no—
287#123—611no—
288#123—611no—
289#123#692311yescharacteristic, complemented
290C4×D4—1224no—
291#117—1224no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—611no—
294C2×C4⋊C4—611no—
295C2×C4⋊C4—611no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—611no—
298C2×C4⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C42—611no—
308C2×C42—611no—
309C2×C42—611no—
310C2×C42—611no—
311C2×C42—611no—
312#95—611no—
313#95—611no—
314#95—611no—
315#95—611no—
316#95—611no—
317#95—611no—
318#95—611no—
319#95—611no—
320#95—611no—
321#95—611no—
322C24—611no—
323C24—611no—
324C2×D4—611no—
325C2×D4—611no—
326C2×D4—611no—
327C2×D4—1222no—
328C2×D4—1222no—
329C2×D4C2×#692311yescharacteristic
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4C2×#692311yescharacteristic, complemented
358C4⋊C4—611no—
359C4⋊C4—611no—
360C4⋊C4—611no—
361C4⋊C4—611no—
362C4⋊C4—611no—
363C4⋊C4—611no—
364C4⋊C4—1222no—
365C4⋊C4—1222no—
366C4⋊C4—1222no—
367C4⋊C4—1222no—
368C4⋊C4—2441no—
369C4⋊C4C2×#692311yescharacteristic, complemented
370C4⋊C4C2×#692311yescharacteristic, complemented
371C22⋊C4—614no—
372C22⋊C4—611no—
373C22⋊C4—611no—
374C22⋊C4—611no—
375C22⋊C4—611no—
376C22⋊C4—611no—
377C22⋊C4—611no—
378C22⋊C4—611no—
379C22⋊C4—611no—
380C22⋊C4—611no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—2441no—
385C22⋊C4C2×#692311yescharacteristic, complemented
386C22⋊C4C2×#692311yescharacteristic, complemented
387C22⋊C4C2×#692311yescharacteristic, complemented
388C42—1222no—
389C42—1222no—
390C42—1222no—
391C42—1222no—
392C42—2441no—
393C23—611no—
394C23—612no—
395C23—612no—
396C23—611no—
397C23—611no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23C22×#692311yescharacteristic
409C23C22×#692311yescharacteristic
410D4—22no—
411D4—1222no—
412D4—1222no—
413D4—1222no—
414C2×C4—22no—
415C2×C4—612no—
416C2×C4—612no—
417C2×C4—612no—
418C2×C4—612no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—611no—
423C2×C4—611no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1222no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—1221no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—2444no—
458C2×C4—2444no—
459C2×C4—2444no—
460C2×C4C22×#692311yescharacteristic
461C2×C4C22×#692311yescharacteristic
462C2×C4C22×#692311yescharacteristic
463C2×C4C22×#692311yescharacteristic
464C2×C4C22×#692311yescharacteristic
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—611no—
471C22—611no—
472C22—611no—
473C22—611no—
474C22—611no—
475C22—611no—
476C22—612no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—1222no—
481C22—1221no—
482C22—1221no—
483C22—1221no—
484C22—1221no—
485C22—1221no—
486C22—2441no—
487C22—2441no—
488C22—2441no—
489C22—2441no—
490C22D4×#692312yes—
491C22C23×#692311yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—1222no—
498C4—1222no—
499C4—1222no—
500C4—1222no—
501C4—1221no—
502C4—1221no—
503C4—1221no—
504C4—1221no—
505C4—1221no—
506C4—2441no—
507C4—2441no—
508C4—2441no—
509C4—2441no—
510C2—22no—
511C2—41no—
512C2—611no—
513C2—611no—
514C2—611no—
515C2—611no—
516C2—1222no—
517C2—2441no—
518C2C2×D4×#692311yescharacteristic
519C2#41×#692311yescharacteristic
520C2#1684083111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#6923
commutator, socleC22×C61C23×C4
Fitting#123×C61C4
hypercenter#123#6923
hypocenterC61#2359
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C2×#14519856C2semidirect
3. #16840713C2semidirect
4. #16840712C2semidirect
5. #16840712C2semidirect
6. #16840711C2semidirect
7. #16840711C2semidirect
9. #16840709C2semidirect
10. #16840709C2semidirect
11. C4⋊C4×#6923C2semidirect
12. C22⋊C4×#6923C2semidirect
13. C22⋊C4×#6923C2semidirect
14. C2×(C2×#6923)⋊C4C2semidirect
48. #14519762C4semidirect
49. #14519762C4semidirect
50. #14519761C4semidirect
51. #14519760C4semidirect
52. #14519759C4semidirect
53. #14519759C4semidirect
54. #14519758C4semidirect
60. #123×C61C4semidirect
81. C22×C4×C61C2×C4semidirect
84. C22×Dic61C2×C4semidirect
90. C2×C4×D61C2×C4semidirect
91. C2×C4×D61C2×C4semidirect
112. C4⋊C4×C61C2×C4semidirect
113. C4⋊C4×C61C2×C4semidirect
114. C22⋊C4×C61C2×C4semidirect
115. C22⋊C4×C61C2×C4semidirect
116. C22⋊C4×C61C2×C4semidirect
117. C22⋊Dic61C2×C4semidirect
118. C22⋊Dic61C2×C4semidirect
119. C22⋊Dic61C2×C4semidirect
120. #11758198C2×C4semidirect
121. #11758198C2×C4semidirect
122. #11758198C2×C4semidirect
123. #11758198C2×C4semidirect
124. #11758198C2×C4semidirect
125. #11758198C2×C4semidirect
126. C4⋊Dic61C2×C4semidirect
127. C4⋊Dic61C2×C4semidirect
128. #11758196C2×C4semidirect
129. #11758196C2×C4semidirect
130. #11758196C2×C4semidirect
131. #11758196C2×C4semidirect
276. C61#2359semidirect
289. #123#6923semidirect
357. C22×C4C2×#6923semidirect
369. C4⋊C4C2×#6923semidirect
370. C4⋊C4C2×#6923semidirect
385. C22⋊C4C2×#6923semidirect
386. C22⋊C4C2×#6923semidirect
387. C22⋊C4C2×#6923semidirect