Finite Group Databasebeta

← #21457329

Subgroups — #21457329

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519806C211yesmaximal, characteristic, complemented
2Q8×C22⋊D61C211yesmaximal, characteristic, complemented
3#16840406C211yesmaximal, characteristic
4#16840153C211yesmaximal, characteristic, complemented
5#16840005C211yesmaximal, characteristic, complemented
6#16840003C211yesmaximal, characteristic, complemented
7#16839982C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839921C211yesmaximal, characteristic, complemented
10#16839918C211yesmaximal, characteristic, complemented
11#16839913C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839863C211yesmaximal, characteristic, complemented
14#16839833C211yesmaximal, characteristic, complemented
15C22×SD16×C61C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic, complemented
18#14519806—24no—
19C2×Dic244C2211yescharacteristic, complemented
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758202C2211yescharacteristic, complemented
22C2×#11758200C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758189C2211yescharacteristic, complemented
25#14519775—21no—
26#14519775C2211yescharacteristic, complemented
27#14519764C2211yescharacteristic
28#14519758—21no—
29#14519756—21no—
30#14519756C2211yescharacteristic
31#14519756C2211yescharacteristic
32#14519753—21no—
33#14519753C2211yescharacteristic, complemented
34#14519749—21no—
35#14519748C2211yescharacteristic
36#14519746—21no—
37Q8×Dic61C2211yescharacteristic, complemented
38D4×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61C2211yescharacteristic
41C2×C22⋊Dic61—21no—
42#14519711C2211yescharacteristic, complemented
43#14519706C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519701C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50C22⋊#92418C2211yescharacteristic
51#14519689C2211yescharacteristic, complemented
52#14519687C2211yescharacteristic, complemented
53C22×Q8×C61C2211yescharacteristic
54C22×D4×C61C2211yescharacteristic
55C2×SD16×C61—24no—
56C2×SD16×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C2×SD16×C61C2211yescharacteristic
59C2×SD16×C61C2211yescharacteristic
60C22×C8×C61C2211yescharacteristic
61C24×C61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—22no—
64C2×Q8×C61—41no—
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C2×D4×C61—22no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61C2311yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79Q8×D61—22no—
80Q8×D61—41no—
81#11758224—22no—
82#11758224—41no—
83C2×C4×D61—21no—
84C2×C4×D61C2311yescharacteristic
85C2×Dic122—21no—
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88SD16×C61—22no—
89SD16×C61—22no—
90SD16×C61—22no—
91SD16×C61D414yescomplemented
92C2×C8×C61—22no—
93C2×C8×C61C2311yescharacteristic
94C2×C8×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758202—22no—
103#11758202—41no—
104#11758200—22no—
105#11758200—41no—
106#11758198—21no—
107#11758198D411yescharacteristic
108C4⋊Dic61—21no—
109C4⋊Dic61C2311yescharacteristic
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196D411yescharacteristic
117C4×Dic61—21no—
118C4×Dic61C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121Dic244—22no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—42no—
126C23×C61—42no—
127C23×C61—81no—
128C23×C61C2×D411yescharacteristic
129C22×D61C2×D411yescharacteristic
130Q8×C61—21no—
131Q8×C61—21no—
132Q8×C61—21no—
133Q8×C61—42no—
134Q8×C61C2×D412yes—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—21no—
138D4×C61—42no—
139D4×C61C2×D412yes—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—42no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C22⋊D61—22no—
148C22⋊D61—42no—
149C22⋊D61—81no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—42no—
155C2×Dic61—81no—
156C2×Dic61C2×D411yescharacteristic
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—42no—
162Dic122—21no—
163Dic122—21no—
164Dic122—21no—
165Dic122—21no—
166Dic122—42no—
167C8×C61—21no—
168C8×C61C2×D412yes—
169#92418—21no—
170#92418—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—22no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—84no—
180C22×C61#13712yescomplemented
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C4×C61—22no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61C22×D411yescharacteristic
189C4×C61H(5,𝔽2)11yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194Dic61—41no—
195Dic61—41no—
196Dic61—41no—
197#3266—611nomaximal, Sylow
198C2×C61—22no—
199C2×C61—42no—
200C2×C61—81no—
201C2×C61D4211yescharacteristic
202C2×C61C2×#13711yescharacteristic
203C2×C61#57711yescharacteristic
204D61—41no—
205C2×#137—611no—
206C22×SD16D6111yescharacteristic, complemented
207D4×Q8—611no—
208#546—611no—
209#497—611no—
210#468—611no—
211#467—611no—
212#464—611no—
213#461—611no—
214#452—611no—
215#451—611no—
216#450—611no—
217#448—611no—
218#440—611no—
219#435—611no—
220C61#326611yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—611no—
223C22×Q8C2×D6111yescharacteristic
224C22×D4C2×D6111yescharacteristic
225#137—1224no—
226C2×Q16—611no—
227C2×Q16—611no—
228C2×Q16—611no—
229C2×SD16—24no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16C2×D6111yescharacteristic
233C2×SD16C2×D6111yescharacteristic
234C2×SD16C2×D6111yescharacteristic
235C2×SD16C2×D6111yescharacteristic
236C2×M16—611no—
237C22×C8C2×D6111yescharacteristic
238C4⋊Q8—611no—
239C4⋊Q8—1221no—
240#124—611no—
241#123—1221no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8—611no—
245C22⋊Q8—1221no—
246C22⋊Q8—1221no—
247#121—611no—
248#121—1221no—
249#120—1221no—
250C4×Q8—611no—
251C4×D4—611no—
252C4×D4—611no—
253C4×D4—1221no—
254C2×C22⋊C4—1221no—
255#107—611no—
256C4⋊C8—611no—
257#103—611no—
258#103—611no—
259#103—611no—
260#103—611no—
261#102—611no—
262#102—611no—
263C22⋊C8—611no—
264C22⋊C8—611no—
265#97—611no—
266C24—21no—
267#41—1222no—
268#41—2441no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—611no—
273C2×Q8—611no—
274C2×Q8—1221no—
275C2×Q8—1222no—
276C2×Q8—2441no—
277C2×Q8C22×D6111yescharacteristic
278C2×Q8C22×D6111yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—611no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4C22×D6111yescharacteristic
286C2×D4C22×D6111yescharacteristic
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4C22×D6111yescharacteristic
293Q16—1222no—
294Q16—1222no—
295Q16—2441no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—1222no—
300SD16—2441no—
301SD16C22⋊D6114yescomplemented
302M16—1222no—
303C2×C8—22no—
304C2×C8—611no—
305C2×C8—611no—
306C2×C8C22×D6111yescharacteristic
307C2×C8C22×D6111yescharacteristic
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—611no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C22⋊C4—611no—
318C22⋊C4—611no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C42—611no—
327C42—1221no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—611no—
334C23D4×D6111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—1221no—
340Q8—1221no—
341Q8—1221no—
342Q8—1221no—
343Q8—2442no—
344Q8C2×C22⋊D6112yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—1222no—
350D4—4881no—
351D4—2442no—
352D4C2×C22⋊D6112yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—4881no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4D4×D6111yescharacteristic
371C2×C4C23×D6111yescharacteristic
372C8—21no—
373C8—1221no—
374C8—1221no—
375C8C2×C22⋊D6112yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—1221no—
386C22—1221no—
387C22—1221no—
388C22#1451980612yescomplemented
389C22C2×D4×D6111yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—2441no—
397C4—2441no—
398C4—2441no—
399C4—2441no—
400C4C22×C22⋊D6111yescharacteristic
401C4#1451982211yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—2441no—
406C2D4×C22⋊D6111yescharacteristic
407C2C2×#1451980611yescharacteristic
408C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×SD16×C61C2
socleC22×C61C22×D4
hypercenterC22×SD16D61
hypocenterC61#3266
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. Q8×C22⋊D61C2semidirect
4. #16840153C2semidirect
5. #16840005C2semidirect
6. #16840003C2semidirect
7. #16839982C2semidirect
8. #16839965C2semidirect
9. #16839921C2semidirect
10. #16839918C2semidirect
11. #16839913C2semidirect
12. #16839899C2semidirect
13. #16839863C2semidirect
14. #16839833C2semidirect
15. C22×SD16×C61C2semidirect
17. C2×Q8×D61C22semidirect
19. C2×Dic244C22semidirect
20. C2×#11758202C22semidirect
21. C2×#11758202C22semidirect
24. C2×#11758189C22semidirect
26. #14519775C22semidirect
33. #14519753C22semidirect
37. Q8×Dic61C22semidirect
42. #14519711C22semidirect
43. #14519706C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
46. #14519701C22semidirect
47. #14519701C22semidirect
51. #14519689C22semidirect
52. #14519687C22semidirect
91. SD16×C61D4semidirect
180. C22×C61#137semidirect
206. C22×SD16D61semidirect
220. C61#3266semidirect
301. SD16C22⋊D61semidirect
388. C22#14519806semidirect