Finite Group Databasebeta

← #21459587

Subgroups — #21459587

Order 7808.

1492 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519825C211yesmaximal, characteristic, complemented
2C2×#14519824C211yesmaximal, characteristic, complemented
3#16840431C211yesmaximal, characteristic, complemented
4#16840430C213yesmaximal, complemented
5Q8×C22⋊D61C211yesmaximal, characteristic, complemented
6#16840425C213yesmaximal, complemented
7#16840424C211yesmaximal, characteristic, complemented
8#16840421C213yesmaximal, complemented
9#16840420C213yesmaximal, complemented
10#16840342C213yesmaximal, complemented
11#16840341C213yesmaximal, complemented
12#16840311C213yesmaximal, complemented
13#16840309C213yesmaximal, complemented
14C4×Q8×D61C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic, complemented
16#14519825—28no—
17#14519824—28no—
18C2×#11758226C2213yes—
19C2×#11758226C2211yescharacteristic
20C2×#11758222C2213yes—
21C2×#11758222C2213yes—
22C2×#11758222C2213yes—
23C2×#11758224C2213yes—
24C2×#11758224C2213yes—
25C22×Dic122C2213yes—
26C2×Q8×D61C2211yescharacteristic
27C2×Q8×D61C2213yes—
28C2×Q8×D61C2211yescharacteristic
29#14519776C2213yes—
30#14519775C2213yes—
31#14519773C2213yes—
32#14519773C2213yes—
33#14519765C2213yes—
34#14519763C2213yes—
35#14519763C2213yes—
36#14519757C2213yes—
37#14519756C2213yes—
38#14519755C2216yes—
39#14519754C2216yes—
40#14519753C2213yes—
41#14519752C2213yes—
42#14519752C2213yes—
43#14519751C2213yes—
44#14519750C2211yescharacteristic
45#14519750C2213yes—
46#14519750C2216yes—
47#14519750C2216yes—
48#14519749C2216yes—
49#14519748C2213yes—
50#14519748C2213yes—
51Q8×Dic61C2211yescharacteristic
52C4×Dic122C2213yes—
53#14519742C2213yes—
54C4×D244C2213yes—
55C4×C22⋊D61C2213yes—
56C4×C22⋊D61C2213yes—
57#14519737C2216yes—
58#14519737C2216yes—
59C4⋊C4×D61C2213yes—
60C42×D61C2213yes—
61C2×#41×C61C2211yescharacteristic
62C22×Q8×C61C2211yescharacteristic
63#124×C61C2213yes—
64C22⋊Q8×C61C2213yes—
65#121×C61C2213yes—
66C4×Q8×C61C2211yescharacteristic
67C4×D4×C61C2213yes—
68#41×C61—24no—
69C2×Q8×C61—24no—
70C2×Q8×C61C2313yes—
71C2×Q8×C61C2311yescharacteristic
72C2×D4×C61C2313yes—
73C2×D4×C61C2313yes—
74C22×C4×C61C2313yes—
75C22×C4×C61C2313yes—
76C2×C22⋊D61C2313yes—
77C2×C22⋊D61C2313yes—
78C2×C22⋊D61C2311yescharacteristic
79C2×C22⋊D61C2313yes—
80C2×C22⋊D61C2313yes—
81C2×C22⋊D61C2311yescharacteristic
82C2×C22⋊D61C2316yes—
83C22×Dic61C2316yes—
84#11758226—24no—
85#11758226—212no—
86Q8×D61—24no—
87Q8×D61—212no—
88Q8×D61D418yescomplemented
89#11758224—212no—
90#11758224—212no—
91#11758222—212no—
92#11758222—212no—
93#11758222—212no—
94C2×D244C2311yescharacteristic
95C2×D244C2313yes—
96C2×D244C2313yes—
97C2×D244C2313yes—
98C2×C4×D61C2313yes—
99C2×C4×D61C2316yes—
100C2×C4×D61C2313yes—
101C2×C4×D61C2311yescharacteristic
102C2×C4×D61C2313yes—
103C2×C4×D61C2313yes—
104C2×Dic122—212no—
105C2×Dic122C2313yes—
106C2×Dic122C2313yes—
107C2×Dic122C2313yes—
108C2×Dic122C2313yes—
109C4⋊C4×C61C2313yes—
110C4⋊C4×C61C2313yes—
111C22⋊C4×C61C2311yescharacteristic
112C22⋊C4×C61C2313yes—
113C22⋊C4×C61C2316yes—
114C42×C61C2313yes—
115C22⋊Dic61C2313yes—
116C22⋊Dic61C2313yes—
117#11758198C2313yes—
118#11758198C2316yes—
119#11758198C2313yes—
120#11758198C2313yes—
121#11758198C2311yescharacteristic
122C4⋊Dic61C2313yes—
123C4⋊Dic61C2313yes—
124#11758196C2316yes—
125#11758196C2313yes—
126#11758196C2316yes—
127#11758196C2311yescharacteristic
128C4×Dic61C2313yes—
129C4×Dic61C2313yes—
130C4×Dic61C2313yes—
131C23×C61C2411yescharacteristic
132C23×C61C2413yes—
133C22×D61C2413yes—
134C22×D61C2411yescharacteristic
135C22×D61C2411yescharacteristic
136Q8×C61—26no—
137Q8×C61C2×D414yes—
138D4×C61—26no—
139D4×C61—43no—
140C2×C4×C61—26no—
141C2×C4×C61—26no—
142C2×C4×C61C2411yescharacteristic
143C2×C4×C61C2413yes—
144C2×C4×C61C2413yes—
145C2×C4×C61C2411yescharacteristic
146C2×C4×C61C2413yes—
147C22⋊D61—22no—
148C22⋊D61—26no—
149C22⋊D61—26no—
150C22⋊D61—26no—
151C22⋊D61—26no—
152C22⋊D61—22no—
153C22⋊D61—46no—
154C2×Dic61—212no—
155C2×Dic61C2413yes—
156C2×Dic61C2413yes—
157C2×Dic61C2411yescharacteristic
158C2×Dic61C2413yes—
159C2×Dic61C2411yescharacteristic
160D244—22no—
161D244—26no—
162D244—26no—
163D244—43no—
164C4×D61—26no—
165C4×D61—26no—
166C4×D61—212no—
167C4×D61—22no—
168C4×D61—43no—
169C4×D61C2×D4112yes—
170Dic122—26no—
171Dic122—26no—
172Dic122—26no—
173Dic122C2×D4112yes—
174C22×C61—23no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—23no—
178C22×C61—23no—
179C22×C61—21no—
180C22×C61C2511yescharacteristic
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—23no—
184C2×D61—21no—
185C2×D61—23no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—23no—
189C2×D61C22×D412yes—
190C4×C61—21no—
191C4×C61—23no—
192C4×C61—21no—
193C4×C61—23no—
194C4×C61C22×D416yes—
195Dic61—21no—
196Dic61—23no—
197Dic61—23no—
198Dic61C22×D416yes—
199Dic612−1+412yescomplemented
200#3497—611nomaximal, Sylow
201C2×C61—43no—
202C2×C61—41no—
203C2×C61C23×D411yescharacteristic
204C2×C61C2×2−1+411yescharacteristic
205C2×C61#58511yescharacteristic
206D61—22no—
207D61—43no—
208D61—41no—
209C2×2−1+4—611no—
210C2×2−1+4—611no—
211#550—611no—
212#550—613no—
213D4×Q8—611no—
214D4×Q8—613no—
215#548—613no—
216#548—611no—
217#548—613no—
218#548D6111yescharacteristic, complemented
219#537—613no—
220#537—613no—
221#532—613no—
222#532—613no—
223C2×C4×Q8—611no—
224C61#349711yescharacteristic, complemented, Sylow
2252−1+4—1228no—
2262−1+4—1228no—
227C2×#41—613no—
228C2×#41—611no—
229C2×#41—613no—
230C2×#41—613no—
231C2×#41—613no—
232C2×#41—613no—
233C2×#41—613no—
234C2×#41C2×D6111yescharacteristic
235C22×Q8—611no—
236C22×Q8—613no—
237C22×Q8—611no—
238C22×Q8—613no—
239C22×Q8C2×D6111yescharacteristic
240C4⋊Q8—613no—
241C4⋊Q8—613no—
242#127—613no—
243#127—613no—
244#124—613no—
245#124—613no—
246#124—613no—
247#124C2×D6113yes—
248C22⋊Q8—613no—
249C22⋊Q8—613no—
250C22⋊Q8—616no—
251C22⋊Q8—613no—
252C22⋊Q8—616no—
253C22⋊Q8C2×D6113yes—
254#121—613no—
255#121—613no—
256#121—616no—
257#121—613no—
258#121—613no—
259#121—613no—
260#121—613no—
261#121—611no—
262#121—616no—
263#121—616no—
264#121C2×D6113yes—
265C4×Q8—611no—
266C4×Q8—613no—
267C4×Q8—613no—
268C4×Q8C2×D6111yescharacteristic
269C4×D4—613no—
270C4×D4—613no—
271C4×D4—616no—
272C4×D4—616no—
273C4×D4—613no—
274C4×D4C2×D6113yes—
275C2×C4⋊C4—613no—
276C2×C42—613no—
277#41—24no—
278#41—12212no—
279#41—12212no—
280#41—12212no—
281#41—12212no—
282#41—12212no—
283#41—12212no—
284#41—1224no—
285C2×Q8—24no—
286C2×Q8—618no—
287C2×Q8—613no—
288C2×Q8—613no—
289C2×Q8—613no—
290C2×Q8—613no—
291C2×Q8—12212no—
292C2×Q8—12212no—
293C2×Q8—1224no—
294C2×Q8C22×D6113yes—
295C2×Q8C22×D6111yescharacteristic
296C2×D4—611no—
297C2×D4—613no—
298C2×D4—611no—
299C2×D4—613no—
300C2×D4—613no—
301C2×D4—613no—
302C2×D4—616no—
303C2×D4—611no—
304C2×D4—613no—
305C2×D4—613no—
306C2×D4—613no—
307C2×D4C22×D6113yes—
308C2×D4C22×D6113yes—
309C22×C4—613no—
310C22×C4—616no—
311C22×C4—611no—
312C22×C4—616no—
313C22×C4—613no—
314C22×C4—613no—
315C22×C4—613no—
316C22×C4C22×D6113yes—
317C22×C4C22×D6113yes—
318C4⋊C4—616no—
319C4⋊C4—613no—
320C4⋊C4—611no—
321C4⋊C4—613no—
322C4⋊C4—616no—
323C4⋊C4—613no—
324C4⋊C4C22×D6113yes—
325C4⋊C4C22×D6113yes—
326C22⋊C4—613no—
327C22⋊C4—613no—
328C22⋊C4—613no—
329C22⋊C4—611no—
330C22⋊C4—613no—
331C22⋊C4—613no—
332C22⋊C4—616no—
333C22⋊C4C22×D6113yes—
334C22⋊C4C22×D6116yes—
335C22⋊C4C22×D6111yescharacteristic
336C42—613no—
337C42—613no—
338C42—613no—
339C42C22×D6113yes—
340C23—611no—
341C23—611no—
342C23—613no—
343C23C23×D6111yescharacteristic
344C23C23×D6113yes—
345Q8—26no—
346Q8—6112no—
347Q8—1226no—
348Q8—1226no—
349Q8—1226no—
350Q8D4×D6114yes—
351D4—26no—
352D4—43no—
353D4—1222no—
354D4—1226no—
355D4—1222no—
356D4—1226no—
357D4—1226no—
358D4—1226no—
359D4—1222no—
360D4—1226no—
361D4—1226no—
362D4—2443no—
363D4—2446no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—611no—
367C2×C4—613no—
368C2×C4—6112no—
369C2×C4—613no—
370C2×C4—613no—
371C2×C4—611no—
372C2×C4—1222no—
373C2×C4—12212no—
374C2×C4—12212no—
375C2×C4—1226no—
376C2×C4—1226no—
377C2×C4—2443no—
378C2×C4C23×D6111yescharacteristic
379C2×C4C23×D6113yes—
380C2×C4C23×D6111yescharacteristic
381C2×C4C23×D6113yes—
382C2×C4C23×D6113yes—
383C22—21no—
384C22—23no—
385C22—21no—
386C22—23no—
387C22—21no—
388C22—23no—
389C22—612no—
390C22—1221no—
391C22—1221no—
392C22—1223no—
393C22—1221no—
394C22—1221no—
395C22—1223no—
396C22—1221no—
397C22—1223no—
398C22C24×D6111yescharacteristic
399C4—21no—
400C4—23no—
401C4—21no—
402C4—23no—
403C4—616no—
404C4—612no—
405C4—1221no—
406C4—1223no—
407C4—1223no—
408C4C2×D4×D6116yes—
409C2—41no—
410C2—43no—
411C2—1222no—
412C2—2443no—
413C2—2441no—
414C2C22×D4×D6111yescharacteristic
415C22−1+4×D6111yescharacteristic
416C2#1684059811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#548C2
hypercenter#548D61
hypocenterC61#3497
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14519825C2semidirect
2. C2×#14519824C2semidirect
3. #16840431C2semidirect
4. #16840430C2semidirect
5. Q8×C22⋊D61C2semidirect
6. #16840425C2semidirect
7. #16840424C2semidirect
8. #16840421C2semidirect
9. #16840420C2semidirect
10. #16840342C2semidirect
11. #16840341C2semidirect
12. #16840311C2semidirect
13. #16840309C2semidirect
14. C4×Q8×D61C2semidirect
15. C61×#548C2semidirect
88. Q8×D61D4semidirect
199. Dic612−1+4semidirect
218. #548D61semidirect
224. C61#3497semidirect