Finite Group Databasebeta

← #21457459

Subgroups — #21457459

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 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#16840411C211yesmaximal, characteristic
4#16840140C211yesmaximal, characteristic, complemented
5#16840020C211yesmaximal, characteristic, complemented
6#16840017C211yesmaximal, characteristic, complemented
7#16839970C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839921C211yesmaximal, characteristic, complemented
11#16839918C211yesmaximal, characteristic, complemented
12#16839916C211yesmaximal, characteristic, complemented
13SD16×Dic61C211yesmaximal, characteristic, complemented
14#16839838C211yesmaximal, characteristic, complemented
15C2×#137×C61C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18#14519806—24no—
19C2×Dic244C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25#14519775—21no—
26#14519775C2211yescharacteristic
27#14519775C2211yescharacteristic
28#14519760—21no—
29#14519758—21no—
30#14519756—21no—
31#14519756C2211yescharacteristic
32#14519756C2211yescharacteristic
33#14519753—21no—
34#14519753C2211yescharacteristic
35#14519753C2211yescharacteristic
36#14519749—21no—
37Q8×Dic61C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61C2211yescharacteristic
41C2×#11758196—21no—
42#14519709C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519701C2211yescharacteristic
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⋊D61D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78Q8×D61—22no—
79Q8×D61—41no—
80#11758224—22no—
81#11758224—41no—
82C2×C4×D61—21no—
83C2×C4×D61C2311yescharacteristic
84C2×Dic122—21no—
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87Q16×C61—22no—
88Q16×C61—22no—
89SD16×C61—22no—
90SD16×C61D414yescomplemented
91M16×C61—22no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61D411yescharacteristic
98#11758202—22no—
99#11758202—41no—
100#11758202—41no—
101#11758200—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198D411yescharacteristic
105C4⋊Dic61—21no—
106C4⋊Dic61C2311yescharacteristic
107C4⋊Dic61C2311yescharacteristic
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
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×C61C2×D411yescharacteristic
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61—42no—
132Q8×C61C2×D412yes—
133D4×C61—21no—
134D4×C61—42no—
135D4×C61C2×D412yes—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—22no—
146C22⋊D61—42no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61C2×D411yescharacteristic
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—42no—
159Dic122—21no—
160Dic122—21no—
161Dic122—21no—
162Dic122—21no—
163Dic122—42no—
164C8×C61—21no—
165C8×C61C2×D412yes—
166#92418—21no—
167#92418—21no—
168C22×C61—22no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61C22×D411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C4×C61—22no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61C22×D411yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61#13712yescomplemented
191#3276—611nomaximal, Sylow
192C2×C61—41no—
193C2×C61—42no—
194C2×C61D4211yescharacteristic
195C2×C61C2×#13711yescharacteristic
196C2×C61#57811yescharacteristic
197D61—41no—
198C2×#137—611no—
199C2×#137D6111yescharacteristic, complemented
200D4×Q8—611no—
201#547—611no—
202#494—611no—
203#470—611no—
204#470—611no—
205#462—611no—
206#461—611no—
207#452—611no—
208#452—611no—
209#451—611no—
210#451—611no—
211C4×SD16—611no—
212#436—611no—
213C61#327611yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41C2×D6111yescharacteristic
216C22×Q8—611no—
217C22×Q8C2×D6111yescharacteristic
218#137—24no—
219#137—1224no—
220C2×Q16—611no—
221C2×Q16—611no—
222C2×Q16—611no—
223C2×Q16—611no—
224C2×Q16C2×D6111yescharacteristic
225C2×Q16C2×D6111yescharacteristic
226C2×SD16—611no—
227C2×SD16C2×D6111yescharacteristic
228C2×SD16C2×D6111yescharacteristic
229C2×M16—611no—
230C2×M16C2×D6111yescharacteristic
231C4⋊Q8—611no—
232C4⋊Q8—611no—
233C4⋊Q8—1221no—
234#123—1221no—
235#123—1221no—
236C22⋊Q8—611no—
237C22⋊Q8—611no—
238C22⋊Q8—611no—
239C22⋊Q8—611no—
240C22⋊Q8—1221no—
241C22⋊Q8—1221no—
242#121—1221no—
243C4×Q8—611no—
244C4×D4—611no—
245C4×D4—611no—
246C4×D4—1221no—
247C2×C4⋊C4—1221no—
248#106—611no—
249C4⋊C8—611no—
250#103—611no—
251#103—611no—
252#103—611no—
253#103—611no—
254#103—611no—
255#102—611no—
256C22⋊C8—611no—
257C22⋊C8—611no—
258C4×C8—611no—
259#41—22no—
260#41—41no—
261#41—1222no—
262#41—2441no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—611no—
267C2×Q8—611no—
268C2×Q8—1221no—
269C2×Q8—1222no—
270C2×Q8—2441no—
271C2×Q8C22×D6111yescharacteristic
272C2×Q8C22×D6111yescharacteristic
273C2×Q8C22×D6111yescharacteristic
274C2×D4—21no—
275C2×D4—611no—
276C2×D4—1221no—
277C2×D4C22×D6111yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—1222no—
288Q16—1222no—
289Q16—2441no—
290Q16—2441no—
291SD16—22no—
292SD16—1222no—
293SD16C22⋊D6114yescomplemented
294M16—22no—
295M16—1222no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C4⋊C4—611no—
301C4⋊C4—611no—
302C4⋊C4—611no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C22⋊C4—611no—
313C22⋊C4—611no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C42—611no—
320C42—1221no—
321C23—21no—
322C23—611no—
323C23D4×D6111yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—1221no—
331Q8—1221no—
332Q8—1221no—
333Q8—1221no—
334Q8—2442no—
335Q8C2×C22⋊D6112yes—
336D4—21no—
337D4—42no—
338D4—1222no—
339D4—2442no—
340D4C2×C22⋊D6112yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—1221no—
364C8—1221no—
365C8C2×C22⋊D6112yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—612no—
381C4—1221no—
382C4—1221no—
383C4—2441no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4C22×C22⋊D6111yescharacteristic
388C4#1451982211yescharacteristic
389C2—41no—
390C2—42no—
391C2—2441no—
392C2D4×C22⋊D6111yescharacteristic
393C2#137×D6111yescharacteristic
394C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3276
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×#14519806C2semidirect
2. Q8×C22⋊D61C2semidirect
4. #16840140C2semidirect
5. #16840020C2semidirect
6. #16840017C2semidirect
7. #16839970C2semidirect
8. #16839965C2semidirect
9. #16839924C2semidirect
10. #16839921C2semidirect
11. #16839918C2semidirect
12. #16839916C2semidirect
13. SD16×Dic61C2semidirect
14. #16839838C2semidirect
15. C2×#137×C61C2semidirect
90. SD16×C61D4semidirect
190. Dic61#137semidirect
199. C2×#137D61semidirect
213. C61#3276semidirect
293. SD16C22⋊D61semidirect