Finite Group Databasebeta

← #21462439

Subgroups — #21462439

Order 7808.

772 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×#14519856C211yesmaximal, characteristic, complemented
3#16840755C212yesmaximal, complemented
4#16840754C212yesmaximal, complemented
5#16840753C214yesmaximal, complemented
6#16840752C214yesmaximal, complemented
7C2×#41×D61C211yesmaximal, characteristic
8C2×#11758213—21no—
9D61⋊M16—21no—
10D61⋊M16—21no—
11D61⋊M16C2212yes—
12D61⋊M16C2212yescomplemented
13C2×#11758217—21no—
14C2×D61⋊C8C2212yescomplemented
15#14519856—21no—
16#14519856—21no—
17#14519856C2212yes—
18#14519856C2212yescomplemented
19C2×C4⋊#6923C2212yescomplemented
20C2×C22⋊#6923—21no—
21C2×C4×#6923—21no—
22#14519840C2218yescomplemented
23#14519839C2218yescomplemented
24C2×#11758226C411yescharacteristic, complemented
25C2×#11758222—21no—
26C2×#11758222C411yescharacteristic, complemented
27C2×#11758224—21no—
28C2×#11758224C411yescharacteristic, complemented
29#41×D61—21no—
30#41×D61—21no—
31#41×D61—21no—
32#41×D61—21no—
33#41×D61C412yescomplemented
34#41×D61C412yescomplemented
35#41×D61C2212yes—
36#41×D61C2212yes—
37C2×Q8×D61C2211yescharacteristic
38C2×D4×D61—21no—
39C2×D4×D61C2211yescharacteristic
40C22×C4×D61—21no—
41C22×C4×D61C2211yescharacteristic
42C2×#41×C61C411yescharacteristic, complemented
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C22×#6923—22no—
46#41×C61—21no—
47#41×C61—21no—
48#41×C61C2×C412yes—
49#41×C61C2×C412yescomplemented
50C2×Q8×C61C2×C411yescharacteristic, complemented
51C2×D4×C61—21no—
52C2×D4×C61C2×C411yescharacteristic, complemented
53C22×C4×C61—21no—
54C22×C4×C61C2×C411yescharacteristic
55C2×C22⋊D61—21no—
56C2×C22⋊D61—21no—
57C2×C22⋊D61—21no—
58C22×Dic61—21no—
59C22×Dic61D411yescharacteristic
60#11758226—21no—
61#11758226—21no—
62#11758226C2×C412yes—
63#11758226C2×C412yescomplemented
64Q8×D61—21no—
65Q8×D61—21no—
66Q8×D61C2×C412yescomplemented
67Q8×D61C2312yes—
68#11758224—22no—
69#11758224—22no—
70#11758224—22no—
71#11758224—22no—
72#11758224—21no—
73#11758224—21no—
74#11758224C2×C412yes—
75#11758224C2×C412yescomplemented
76D4×D61—22no—
77D4×D61—22no—
78D4×D61—22no—
79D4×D61—22no—
80D4×D61—21no—
81D4×D61—21no—
82D4×D61C2×C412yescomplemented
83D4×D61C2312yes—
84#11758222—21no—
85#11758222—21no—
86#11758222—22no—
87#11758222—22no—
88#11758222—22no—
89#11758222—22no—
90#11758222C2×C412yes—
91#11758222C2×C412yescomplemented
92C2×D244—21no—
93C2×D244C2×C411yescharacteristic, complemented
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61C2×C411yescharacteristic
102C2×C4×D61C2×C411yescharacteristic
103C2×C4×D61C2×C411yescharacteristic
104C2×C4×D61D411yescharacteristic
105C2×C4×D61D411yescharacteristic
106C2×C4×D61D411yescharacteristic
107C2×C4×D61D411yescharacteristic
108C2×C4×D61D411yescharacteristic
109C2×C4×D61D411yescharacteristic
110C2×C4×D61C2311yescharacteristic
111C2×C4×D61C2311yescharacteristic
112C2×C4×D61C2311yescharacteristic
113C2×Dic122—21no—
114C2×Dic122C2×C411yescharacteristic, complemented
115C22⋊#6923—22no—
116C22⋊#6923—22no—
117#11758217—22no—
118#11758217—22no—
119C2×#92420—22no—
120C4⋊#6923—22no—
121C4⋊#6923C2314yes—
122C4×#6923—22no—
123C4×#6923—22no—
124#11758213—22no—
125#11758213—22no—
126D61⋊C8—22no—
127D61⋊C8C2314yes—
128C23×C61—21no—
129C23×C61C22⋊C411yescharacteristic
130C22×D61—21no—
131C22×D61—22no—
132C22×D61—22no—
133C22×D61—42no—
134C22×D61—44no—
135C22×D61C22⋊C411yescharacteristic
136C22×D61C22⋊C411yescharacteristic
137C22×D61C22⋊C411yescharacteristic
138C22×D61C2×D411yescharacteristic
139C22×D61C2×D411yescharacteristic
140C22×D61C2×D411yescharacteristic
141C2×#6923—24no—
142C2×#6923—44no—
143Q8×C61—21no—
144Q8×C61C22×C412yes—
145D4×C61—22no—
146D4×C61—22no—
147D4×C61—21no—
148D4×C61C22×C412yes—
149C2×C4×C61—21no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61C22⋊C411yescharacteristic
153C2×C4×C61C22⋊C411yescharacteristic
154C2×C4×C61C22⋊C411yescharacteristic
155C2×C4×C61C22×C411yescharacteristic
156C2×C4×C61C22×C411yescharacteristic
157C2×C4×C61C22×C411yescharacteristic
158C22⋊D61—22no—
159C22⋊D61—22no—
160C22⋊D61—22no—
161C22⋊D61—22no—
162C22⋊D61—22no—
163C22⋊D61—22no—
164C2×Dic61—21no—
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61C22⋊C411yescharacteristic
168C2×Dic61C22⋊C411yescharacteristic
169C2×Dic61C22⋊C411yescharacteristic
170C2×Dic61C2×D411yescharacteristic
171C2×Dic61C2×D411yescharacteristic
172C2×Dic61C2×D411yescharacteristic
173D244—22no—
174D244—22no—
175D244—21no—
176D244C22×C412yes—
177C4×D61—22no—
178C4×D61—22no—
179C4×D61—22no—
180C4×D61—22no—
181C4×D61—22no—
182C4×D61—22no—
183C4×D61C22⋊C411yescharacteristic
184C4×D61C22⋊C411yescharacteristic
185C4×D61C22⋊C411yescharacteristic
186C4×D61C22⋊C411yescharacteristic
187C4×D61C22⋊C411yescharacteristic
188C4×D61C22⋊C411yescharacteristic
189C4×D61C22×C411yescharacteristic
190C4×D61C22×C411yescharacteristic
191C4×D61C22×C411yescharacteristic
192C4×D61C2×D411yescharacteristic
193C4×D61C2×D411yescharacteristic
194C4×D61C2×D411yescharacteristic
195C4×D61C2×D411yescharacteristic
196C4×D61C2×D411yescharacteristic
197C4×D61C2×D411yescharacteristic
198C4×D61C2411yescharacteristic
199Dic122—21no—
200Dic122—22no—
201Dic122—22no—
202Dic122C22×C412yes—
203#92420—24no—
204C22×C61—22no—
205C22×C61—41no—
206C22×C61—42no—
207C22×C61C2×C22⋊C411yescharacteristic
208C22×C61C2×C22⋊C411yescharacteristic
209C22×C61C2×C22⋊C411yescharacteristic
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—44no—
218C2×D61—42no—
219C2×D61—44no—
220C2×D61C2×C22⋊C411yescharacteristic
221C2×D61C2×C22⋊C411yescharacteristic
222C2×D61C2×C22⋊C411yescharacteristic
223C2×D61C22×D411yescharacteristic
224#6923—44no—
225C4×C61—22no—
226C4×C61C2×C22⋊C411yescharacteristic
227C4×C61C2×C22⋊C411yescharacteristic
228C4×C61C2×C22⋊C411yescharacteristic
229C4×C61C23×C411yescharacteristic
230Dic61—22no—
231Dic61C2×C22⋊C411yescharacteristic
232Dic61C2×C22⋊C411yescharacteristic
233Dic61C2×C22⋊C411yescharacteristic
234Dic61C22×D411yescharacteristic
235#2896—611nomaximal, Sylow
236C2×C61—21no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—42no—
240C2×C61C22×C22⋊C411yescharacteristic
241D61—21no—
242D61—21no—
243D61—21no—
244D61—42no—
245D61#57512yes—
246C22×#41—611no—
247C22×M16—611no—
248C2×#117—611no—
249#419—612no—
250#418—612no—
251#417—614no—
252#416—614no—
253C61#289611yescharacteristic, complemented, Sylow
254C2×#41—612no—
255C2×#41—612no—
256C2×#41—612no—
257C2×#41—612no—
258C2×#41—611no—
259C2×#41—611no—
260C2×#41—611no—
261C2×#41—1221no—
262C2×#41—1221no—
263C2×#41—1221no—
264C2×#41—1221no—
265C2×#41—1221no—
266C2×#41—1221no—
267C2×#41#692311yescharacteristic, complemented
268C22×Q8—611no—
269C22×D4—611no—
270C22×D4—1221no—
271C23×C4—611no—
272C23×C4—1221no—
273C2×M16—612no—
274C2×M16—612no—
275C2×M16—1221no—
276C2×M16—1221no—
277C2×M16—1221no—
278C2×M16—1221no—
279C22×C8—612no—
280#117—612no—
281#117—612no—
282#117—1221no—
283#117—1221no—
284C2×C4⋊C4—612no—
285C2×C22⋊C4—1221no—
286C2×C42—1221no—
287#103—618no—
288#102—618no—
289C24—611no—
290C24—1221no—
291#41—21no—
292#41—21no—
293#41—612no—
294#41—612no—
295#41—612no—
296#41—612no—
297#41—612no—
298#41—612no—
299#41—1222no—
300#41—1222no—
301#41—1222no—
302#41—1222no—
303#41—1222no—
304#41—1222no—
305#41—1222no—
306#41—1222no—
307#41—1221no—
308#41—1221no—
309#41—1221no—
310#41—1221no—
311#41—1221no—
312#41—1221no—
313#41C2×#692312yes—
314#41C2×#692312yescomplemented
315C2×Q8—612no—
316C2×Q8—612no—
317C2×Q8—611no—
318C2×Q8—1221no—
319C2×Q8—1221no—
320C2×Q8—1221no—
321C2×Q8C2×#692311yescharacteristic, complemented
322C2×D4—21no—
323C2×D4—612no—
324C2×D4—612no—
325C2×D4—611no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—1222no—
333C2×D4—1222no—
334C2×D4—1221no—
335C2×D4—1221no—
336C2×D4C2×#692311yescharacteristic, complemented
337C22×C4—21no—
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—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1222no—
360C22×C4C2×#692311yescharacteristic
361M16—1222no—
362M16—1222no—
363M16—1222no—
364M16—1222no—
365C2×C8—614no—
366C2×C8—1222no—
367C2×C8—1222no—
368C4⋊C4—614no—
369C4⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C42—1222no—
373C42—1222no—
374C23—21no—
375C23—611no—
376C23—611no—
377C23—611no—
378C23—611no—
379C23—611no—
380C23—611no—
381C23—1222no—
382C23—1222no—
383C23—1221no—
384C23—2442no—
385C23—2444no—
386C23C22⋊#692311yescharacteristic
387Q8—21no—
388Q8—612no—
389Q8—1222no—
390Q8—1222no—
391Q8—1221no—
392Q8C22×#692312yes—
393D4—22no—
394D4—22no—
395D4—21no—
396D4—612no—
397D4—1222no—
398D4—1222no—
399D4—1222no—
400D4—1222no—
401D4—1222no—
402D4—1222no—
403D4—1222no—
404D4—1222no—
405D4—1221no—
406D4C22×#692312yes—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—611no—
411C2×C4—611no—
412C2×C4—611no—
413C2×C4—611no—
414C2×C4—611no—
415C2×C4—611no—
416C2×C4—611no—
417C2×C4—611no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—611no—
423C2×C4—611no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—1222no—
436C2×C4—1222no—
437C2×C4—1222no—
438C2×C4—1221no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1224no—
442C2×C4—2444no—
443C2×C4C22⋊#692311yescharacteristic
444C2×C4C22⋊#692311yescharacteristic
445C2×C4C22⋊#692311yescharacteristic
446C2×C4C22×#692311yescharacteristic
447C2×C4C22×#692311yescharacteristic
448C2×C4C22×#692311yescharacteristic
449C8—1224no—
450C22—22no—
451C22—41no—
452C22—42no—
453C22—611no—
454C22—611no—
455C22—611no—
456C22—611no—
457C22—1222no—
458C22—1222no—
459C22—1222no—
460C22—1222no—
461C22—2441no—
462C22—2441no—
463C22—2441no—
464C22—2442no—
465C22—2444no—
466C22—2444no—
467C22C2×C22⋊#692311yescharacteristic
468C22C2×C22⋊#692311yescharacteristic
469C22C2×C22⋊#692311yescharacteristic
470C4—22no—
471C4—611no—
472C4—611no—
473C4—611no—
474C4—611no—
475C4—1222no—
476C4—2444no—
477C4C2×C22⋊#692311yescharacteristic
478C4C2×C22⋊#692311yescharacteristic
479C4C2×C22⋊#692311yescharacteristic
480C4C23×#692311yescharacteristic
481C2—21no—
482C2—21no—
483C2—21no—
484C2—42no—
485C2—612no—
486C2—1221no—
487C2—1221no—
488C2—1221no—
489C2—2442no—
490C2C22×C22⋊#692311yescharacteristic
subgroupG/H
centerC4C2×C22⋊#6923
commutatorC4×C61C23×C4
FrattiniC4C23×#6923
FittingC2×#41×C61C4
socleC2×C61C22×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#2896
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊M16C2semidirect
2. C2×#14519856C2semidirect
3. #16840755C2semidirect
4. #16840754C2semidirect
5. #16840753C2semidirect
6. #16840752C2semidirect
12. D61⋊M16C22semidirect
14. C2×D61⋊C8C22semidirect
18. #14519856C22semidirect
19. C2×C4⋊#6923C22semidirect
22. #14519840C22semidirect
23. #14519839C22semidirect
24. C2×#11758226C4semidirect
26. C2×#11758222C4semidirect
28. C2×#11758224C4semidirect
33. #41×D61C4semidirect
34. #41×D61C4semidirect
42. C2×#41×C61C4semidirect
49. #41×C61C2×C4semidirect
50. C2×Q8×C61C2×C4semidirect
52. C2×D4×C61C2×C4semidirect
63. #11758226C2×C4semidirect
66. Q8×D61C2×C4semidirect
75. #11758224C2×C4semidirect
82. D4×D61C2×C4semidirect
91. #11758222C2×C4semidirect
93. C2×D244C2×C4semidirect
114. C2×Dic122C2×C4semidirect
253. C61#2896semidirect
267. C2×#41#6923semidirect
314. #41C2×#6923semidirect
321. C2×Q8C2×#6923semidirect
336. C2×D4C2×#6923semidirect