Finite Group Databasebeta

← #21457479

Subgroups — #21457479

Order 7808.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2#16840431C211yesmaximal, characteristic
3Q8×C22⋊D61C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840008C211yesmaximal, characteristic, complemented
6#16840005C211yesmaximal, characteristic, complemented
7#16839970C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839901C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13Q16×Dic61C211yesmaximal, characteristic, complemented
14#16839838C211yesmaximal, characteristic, complemented
15C2×#137×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18#14519809—24no—
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758201C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25#14519775—21no—
26#14519775C2211yescharacteristic
27#14519773—21no—
28#14519773C2211yescharacteristic
29#14519756—21no—
30#14519756C2211yescharacteristic
31#14519753—21no—
32#14519753C2211yescharacteristic
33#14519751—21no—
34#14519751C2211yescharacteristic
35#14519748—21no—
36#14519748C2211yescharacteristic
37Q8×Dic61C2211yescharacteristic
38Q8×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61C2211yescharacteristic
42#14519711C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519698C2211yescharacteristic
50C22⋊#92418C2211yescharacteristic
51#14519689C2211yescharacteristic
52C8×Dic61C2211yescharacteristic
53C2×#41×C61C2211yescharacteristic
54C22×Q8×C61C2211yescharacteristic
55#137×C61—24no—
56C2×Q16×C61C2211yescharacteristic
57C2×Q16×C61C2211yescharacteristic
58C2×SD16×C61C2211yescharacteristic
59C2×SD16×C61C2211yescharacteristic
60C2×M16×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—41no—
63C2×Q8×C61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61C2311yescharacteristic
67C2×Q8×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×D4×C61—21no—
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⋊D61D411yescharacteristic
79#11758226—22no—
80#11758226—41no—
81Q8×D61—22no—
82Q8×D61—41no—
83C2×D244—21no—
84C2×D244C2311yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61C2311yescharacteristic
88C2×Dic122—21no—
89C2×Dic122C2311yescharacteristic
90Q16×C61—22no—
91Q16×C61D414yescomplemented
92SD16×C61—22no—
93SD16×C61—22no—
94M16×C61—22no—
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61D411yescharacteristic
100#11758202—22no—
101#11758201—22no—
102#11758201—41no—
103#11758200—41no—
104#11758198—21no—
105#11758198—21no—
106#11758198D411yescharacteristic
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61C2311yescharacteristic
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
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×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61—42no—
132Q8×C61C2×D412yes—
133Q8×C61C2×D412yes—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—42no—
137C2×C4×C61—21no—
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—22no—
147C22⋊D61—42no—
148C22⋊D61—81no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157D244—21no—
158D244—21no—
159D244—42no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—42no—
163C4×D61—42no—
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—21no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61C22×D411yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C4×C61—22no—
185C4×C61—22no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61C22×D411yescharacteristic
189C4×C61H(5,𝔽2)11yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61#13712yescomplemented
196#3278—611nomaximal, Sylow
197C2×C61—41no—
198C2×C61—81no—
199C2×C61D4211yescharacteristic
200C2×C61C2×#13711yescharacteristic
201C2×C61#57711yescharacteristic
202D61—41no—
203D61—81no—
204C2×#137—611no—
205C2×#137D6111yescharacteristic, complemented
206#550—611no—
207D4×Q8—611no—
208#492—611no—
209#468—611no—
210#468—611no—
211#462—611no—
212#460—611no—
213#452—611no—
214#452—611no—
215#448—611no—
216#448—611no—
217C4×Q16—611no—
218#436—611no—
219C61#327811yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41C2×D6111yescharacteristic
222C22×Q8—611no—
223C22×Q8C2×D6111yescharacteristic
224#137—24no—
225#137—1224no—
226C2×Q16—611no—
227C2×Q16C2×D6111yescharacteristic
228C2×Q16C2×D6111yescharacteristic
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16C2×D6111yescharacteristic
234C2×SD16C2×D6111yescharacteristic
235C2×M16—611no—
236C2×M16C2×D6111yescharacteristic
237C4⋊Q8—611no—
238C4⋊Q8—1221no—
239#127—611no—
240#127—1221no—
241C22⋊Q8—611no—
242C22⋊Q8—611no—
243C22⋊Q8—1221no—
244C22⋊Q8—1221no—
245#121—611no—
246#121—611no—
247#121—1221no—
248#121—1221no—
249C4×Q8—611no—
250C4×Q8—611no—
251C4×D4—611no—
252C4×D4—1221no—
253C4×D4—1221no—
254#107—611no—
255C4⋊C8—611no—
256#103—611no—
257#103—611no—
258#103—611no—
259#103—611no—
260#102—611no—
261#102—611no—
262C22⋊C8—611no—
263C22⋊C8—611no—
264C4×C8—611no—
265#41—22no—
266#41—41no—
267#41—1222no—
268#41—2441no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—611no—
273C2×Q8—1221no—
274C2×Q8—1222no—
275C2×Q8—2441no—
276C2×Q8C22×D6111yescharacteristic
277C2×Q8C22×D6111yescharacteristic
278C2×Q8C22×D6111yescharacteristic
279C2×D4—21no—
280C2×D4—611no—
281C2×D4—611no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4C22×D6111yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4C22×D6111yescharacteristic
294Q16—22no—
295Q16—1222no—
296Q16C22⋊D6114yescomplemented
297SD16—22no—
298SD16—22no—
299SD16—1222no—
300SD16—1222no—
301SD16—2441no—
302SD16—2441no—
303M16—22no—
304M16—1222no—
305C2×C8—611no—
306C2×C8—611no—
307C2×C8C22×D6111yescharacteristic
308C2×C8C22×D6111yescharacteristic
309C4⋊C4—611no—
310C4⋊C4—611no—
311C4⋊C4—611no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C22⋊C4—611no—
319C22⋊C4—611no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C42—611no—
325C42—1221no—
326C42—1221no—
327C23—21no—
328C23—611no—
329C23—1221no—
330C23D4×D6111yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—21no—
335Q8—42no—
336Q8—1221no—
337Q8—1221no—
338Q8—2442no—
339Q8C2×C22⋊D6112yes—
340Q8C2×C22⋊D6112yes—
341D4—21no—
342D4—21no—
343D4—42no—
344D4—1222no—
345D4—1221no—
346D4—1221no—
347D4—4881no—
348D4—4881no—
349D4—4881no—
350D4—2442no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4D4×D6111yescharacteristic
370C2×C4C23×D6111yescharacteristic
371C8—21no—
372C8—1221no—
373C8—1221no—
374C8C2×C22⋊D6112yes—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C2×D4×D6111yescharacteristic
388C4—21no—
389C4—22no—
390C4—22no—
391C4—41no—
392C4—612no—
393C4—1221no—
394C4—1221no—
395C4—2441no—
396C4—2441no—
397C4—2441no—
398C4C22×C22⋊D6111yescharacteristic
399C4#1451982211yescharacteristic
400C2—41no—
401C2—81no—
402C2—4881no—
403C2—2441no—
404C2D4×C22⋊D6111yescharacteristic
405C2#137×D6111yescharacteristic
406C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3278
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
3. Q8×C22⋊D61C2semidirect
4. #16840133C2semidirect
5. #16840008C2semidirect
6. #16840005C2semidirect
7. #16839970C2semidirect
8. #16839960C2semidirect
9. #16839924C2semidirect
10. #16839923C2semidirect
11. #16839901C2semidirect
12. #16839899C2semidirect
13. Q16×Dic61C2semidirect
14. #16839838C2semidirect
15. C2×#137×C61C2semidirect
91. Q16×C61D4semidirect
195. Dic61#137semidirect
205. C2×#137D61semidirect
219. C61#3278semidirect
296. Q16C22⋊D61semidirect