Finite Group Databasebeta

← #21457404

Subgroups — #21457404

Order 7808.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2#16840431C211yesmaximal, characteristic, complemented
3#16840419C211yesmaximal, characteristic, complemented
4#16840150C211yesmaximal, characteristic, complemented
5#16840012C211yesmaximal, characteristic, complemented
6#16839991C211yesmaximal, characteristic, complemented
7#16839982C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839907C211yesmaximal, characteristic, complemented
11#16839906C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839869C211yesmaximal, characteristic, complemented
14#16839833C211yesmaximal, characteristic, complemented
15C2×#135×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18#14519809—24no—
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25#14519773—21no—
26#14519773C2211yescharacteristic
27#14519764—21no—
28#14519764C2211yescharacteristic
29#14519756—21no—
30#14519756C2211yescharacteristic
31#14519751—21no—
32#14519751C2211yescharacteristic
33#14519748—21no—
34#14519748—21no—
35#14519748C2211yescharacteristic
36#14519748C2211yescharacteristic
37Q8×Dic61C2211yescharacteristic
38Q8×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50C22⋊#92418C2211yescharacteristic
51#14519689C2211yescharacteristic
52#14519687C2211yescharacteristic
53C2×#41×C61C2211yescharacteristic
54C2×#41×C61C2211yescharacteristic
55#135×C61—24no—
56C2×Q16×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C2×SD16×C61C2211yescharacteristic
59C2×D8×C61C2211yescharacteristic
60C22×C8×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—22no—
63#41×C61—41no—
64#41×C61—41no—
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C2×C22⋊D61D411yescharacteristic
80#11758226—22no—
81#11758226—41no—
82Q8×D61—22no—
83Q8×D61—41no—
84C2×D244—21no—
85C2×D244C2311yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61C2311yescharacteristic
89C2×Dic122—21no—
90C2×Dic122C2311yescharacteristic
91Q16×C61D414yescomplemented
92SD16×C61—22no—
93SD16×C61—22no—
94D8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61D411yescharacteristic
104#11758202—22no—
105#11758201—22no—
106#11758200—41no—
107#11758199—41no—
108#11758198—21no—
109#11758198D411yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61C2311yescharacteristic
113C4⋊Dic61C2311yescharacteristic
114#11758196—21no—
115#11758196D411yescharacteristic
116C4×Dic61—21no—
117C4×Dic61—21no—
118C4×Dic61C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190—22no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61C2×D411yescharacteristic
126C22×D61—21no—
127C22×D61C2×D411yescharacteristic
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61C2×D412yes—
131Q8×C61C2×D412yes—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—42no—
137D4×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2411yescharacteristic
146C22⋊D61—41no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C22⋊D61—81no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157C2×Dic61C2×D411yescharacteristic
158D244—21no—
159D244—21no—
160D244—42no—
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—42no—
164C4×D61—42no—
165Dic122—21no—
166Dic122—21no—
167Dic122—42no—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C4×C61—22no—
189C4×C61—22no—
190C4×C61—21no—
191C4×C61C22×D411yescharacteristic
192C4×C61H(5,𝔽2)11yescharacteristic
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199#3271—611nomaximal, Sylow
200C2×C61—41no—
201C2×C61—81no—
202C2×C61—81no—
203C2×C61D4211yescharacteristic
204C2×C61#57511yescharacteristic
205C2×C61#57711yescharacteristic
206D61—41no—
207D61—81no—
208C2×#137—611no—
209C2×#135D6111yescharacteristic, complemented
210#550—611no—
211#548—611no—
212#496—611no—
213#469—611no—
214#465—611no—
215#464—611no—
216#460—611no—
217#452—611no—
218#449—611no—
219#449—611no—
220#448—611no—
221#441—611no—
222#435—611no—
223C61#327111yescharacteristic, complemented, Sylow
224C2×#41—611no—
225C2×#41C2×D6111yescharacteristic
226C2×#41C2×D6111yescharacteristic
227C22×Q8—611no—
228#137—1224no—
229#135—24no—
230C2×Q16—611no—
231C2×Q16C2×D6111yescharacteristic
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16C2×D6111yescharacteristic
236C2×SD16C2×D6111yescharacteristic
237C2×D8—611no—
238C2×D8C2×D6111yescharacteristic
239C2×M16—611no—
240C22×C8C2×D6111yescharacteristic
241#127—611no—
242#127—1221no—
243#124—611no—
244#124—1221no—
245C22⋊Q8—611no—
246C22⋊Q8—1221no—
247#121—611no—
248#121—611no—
249#121—611no—
250#121—1221no—
251#121—1221no—
252#121—1221no—
253C4×Q8—611no—
254C4×Q8—611no—
255C4×D4—611no—
256C4×D4—1221no—
257C4×D4—1221no—
258#106—611no—
259C4⋊C8—611no—
260#103—611no—
261#103—611no—
262#103—611no—
263#102—611no—
264#102—611no—
265#102—611no—
266C22⋊C8—611no—
267C22⋊C8—611no—
268#97—611no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—1222no—
274#41—2441no—
275C2×Q8—611no—
276C2×Q8—1221no—
277C2×Q8—1222no—
278C2×Q8—2441no—
279C2×Q8C22×D6111yescharacteristic
280C2×Q8C22×D6111yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—611no—
284C2×D4—611no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4C22×D6111yescharacteristic
292C2×D4C22×D6111yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4C22×D6111yescharacteristic
299Q16—1222no—
300Q16C22⋊D6114yescomplemented
301SD16—22no—
302SD16—22no—
303SD16—1222no—
304SD16—1222no—
305SD16—2441no—
306D8—22no—
307D8—2441no—
308M16—1222no—
309C2×C8—22no—
310C2×C8—611no—
311C2×C8—611no—
312C2×C8C22×D6111yescharacteristic
313C2×C8C22×D6111yescharacteristic
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—611no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C22⋊C4—611no—
321C22⋊C4—611no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C42—611no—
329C42—1221no—
330C42—1221no—
331C23—21no—
332C23—21no—
333C23—611no—
334C23—1221no—
335C23D4×D6111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—1221no—
339Q8—1221no—
340Q8—2442no—
341Q8C2×C22⋊D6112yes—
342Q8C2×C22⋊D6112yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—42no—
348D4—42no—
349D4—1221no—
350D4—1221no—
351D4—4881no—
352D4—4881no—
353D4—4881no—
354D4—2442no—
355D4—2441no—
356D4—2442no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4D4×D6111yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—1221no—
378C8—1221no—
379C8C2×C22⋊D6112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—1221no—
390C22—1221no—
391C22—1221no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—22no—
398C4—22no—
399C4—1221no—
400C4—1221no—
401C4—1221no—
402C4—2441no—
403C4—2441no—
404C4—2441no—
405C4C22×C22⋊D6111yescharacteristic
406C4#1451982211yescharacteristic
407C2—41no—
408C2—81no—
409C2—81no—
410C2—4881no—
411C2—2441no—
412C2D4×C22⋊D6111yescharacteristic
413C2#1684055911yescharacteristic
414C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#135×C61C2
socleC22×C61C22×D4
hypercenterC2×#135D61
hypocenterC61#3271
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. #16840431C2semidirect
3. #16840419C2semidirect
4. #16840150C2semidirect
5. #16840012C2semidirect
6. #16839991C2semidirect
7. #16839982C2semidirect
8. #16839960C2semidirect
9. #16839924C2semidirect
10. #16839907C2semidirect
11. #16839906C2semidirect
12. #16839899C2semidirect
13. #16839869C2semidirect
14. #16839833C2semidirect
15. C2×#135×C61C2semidirect
91. Q16×C61D4semidirect
209. C2×#135D61semidirect
223. C61#3271semidirect
300. Q16C22⋊D61semidirect