Finite Group Databasebeta

← #21457534

Subgroups — #21457534

Order 7808.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519798C211yesmaximal, characteristic, complemented
2C2×#14519797C211yesmaximal, characteristic, complemented
3#16840414C211yesmaximal, characteristic, complemented
4#16840411C211yesmaximal, characteristic, complemented
5#16840140C211yesmaximal, characteristic, complemented
6#16840002C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839925C211yesmaximal, characteristic, complemented
12#16839923C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839825C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758224C2211yescharacteristic
19#14519798—24no—
20#14519797—24no—
21C2×Dic244C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C22×#92418C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic
30#14519775C2211yescharacteristic
31#14519775C2211yescharacteristic
32#14519762—21no—
33#14519760—21no—
34#14519759—21no—
35#14519758—21no—
36#14519757C2211yescharacteristic
37#14519756C2211yescharacteristic
38#14519753C2211yescharacteristic
39#14519750—21no—
40#14519749—21no—
41D4×Dic61C2211yescharacteristic
42#14519739C2211yescharacteristic
43C4×C22⋊D61C2211yescharacteristic
44C2×#11758196—21no—
45C4⋊C4×D61—21no—
46#14519710C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519689C2211yescharacteristic
53C8×Dic61C2211yescharacteristic
54C2×#41×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C2×SD16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—41no—
63C2×Q8×C61C2311yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74#11758226—22no—
75#11758226—41no—
76#11758224—22no—
77#11758224—41no—
78#11758222—22no—
79#11758222—41no—
80C2×D244—21no—
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88Q16×C61—41no—
89SD16×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61D411yescharacteristic
98#11758202—22no—
99#11758202—22no—
100#11758201—22no—
101#11758200—22no—
102#11758199D414yescomplemented
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198D411yescharacteristic
107C4⋊Dic61—21no—
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196D411yescharacteristic
116C4×Dic61C2311yescharacteristic
117C2×#92418—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244—41no—
121#11758190—22no—
122C8×D61—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—
131D4×C61—21no—
132D4×C61—42no—
133D4×C61C2×D412yes—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—42no—
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2411yescharacteristic
142C22⋊D61—22no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61C2×D411yescharacteristic
151C2×Dic61C2×D411yescharacteristic
152C2×Dic61C2×D411yescharacteristic
153D244—21no—
154D244—42no—
155D244C2×D412yes—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—21no—
165C8×C61—21no—
166C8×C61—21no—
167#92418—21no—
168#92418C2×D412yes—
169C22×C61—22no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61C22×D411yescharacteristic
176C2×D61—21no—
177C2×D61—22no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61C22×D411yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—21no—
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
192Dic61—41no—
193Dic61#13512yescomplemented
194#3283—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—42no—
197C2×C61D4211yescharacteristic
198C2×C61C2×#13511yescharacteristic
199C2×C61#57811yescharacteristic
200D61—41no—
201D61—42no—
202C2×#135—611no—
203C2×#135—611no—
204#547—611no—
205#547—611no—
206#494—611no—
207#467—611no—
208#467—611no—
209#461—611no—
210#461—611no—
211#452—611no—
212#452—611no—
213#452—611no—
214#452D6111yescharacteristic, complemented
215C4×D8—611no—
216C8×D4—611no—
217C61#328311yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C2×#41—611no—
220C2×#41—611no—
221C2×#41C2×D6111yescharacteristic
222#135—1224no—
223#135—1224no—
224C2×Q16—611no—
225C2×Q16—611no—
226C2×Q16—611no—
227C2×Q16C2×D6111yescharacteristic
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16C2×D6111yescharacteristic
232C2×D8—611no—
233C22×C8—611no—
234C22×C8—611no—
235C4⋊Q8—611no—
236C4⋊Q8—611no—
237#123—1221no—
238#123—1221no—
239#123—1221no—
240#123—1221no—
241C22⋊Q8—611no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8C2×D6111yescharacteristic
245#121—1221no—
246#121—1221no—
247C4×D4—611no—
248C4×D4—611no—
249C4×D4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252#107—611no—
253C4⋊C8—611no—
254#103—611no—
255#103—611no—
256#103—611no—
257#103C2×D6111yescharacteristic
258#102—611no—
259#102C2×D6111yescharacteristic
260C22⋊C8—611no—
261C22⋊C8C2×D6111yescharacteristic
262C4×C8—611no—
263#41—22no—
264#41—41no—
265#41—1222no—
266#41—1222no—
267#41—1222no—
268#41—2441no—
269#41—2441no—
270#41—2441no—
271C2×Q8—611no—
272C2×Q8—611no—
273C2×Q8C22×D6111yescharacteristic
274C2×Q8C22×D6111yescharacteristic
275C2×D4—21no—
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4C22×D6111yescharacteristic
282C22×C4—21no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4C22×D6111yescharacteristic
290Q16—41no—
291Q16—1222no—
292Q16—1222no—
293Q16—2441no—
294SD16—22no—
295SD16—1222no—
296SD16—1222no—
297SD16—1222no—
298D8—614no—
299C2×C8—611no—
300C2×C8—611no—
301C2×C8—1222no—
302C2×C8—1222no—
303C2×C8C22×D6111yescharacteristic
304C2×C8C22×D6111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—611no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4C22×D6111yescharacteristic
316C22⋊C4—21no—
317C22⋊C4—611no—
318C22⋊C4—611no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C42—611no—
325C23—21no—
326C23—611no—
327C23—1221no—
328C23D4×D6111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—1221no—
334Q8—1221no—
335Q8—1221no—
336Q8—1221no—
337D4—21no—
338D4—42no—
339D4—612no—
340D4—1222no—
341D4—1221no—
342D4—2442no—
343D4—2442no—
344D4—2442no—
345D4D4×D6112yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4D4×D6111yescharacteristic
366C2×C4C23×D6111yescharacteristic
367C8—21no—
368C8—21no—
369C8—612no—
370C8—1221no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—1222no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—612no—
389C4—1221no—
390C4—1221no—
391C4—2441no—
392C4—2441no—
393C4—2441no—
394C4C2×D4×D6111yescharacteristic
395C4#1451982211yescharacteristic
396C2—41no—
397C2—42no—
398C2—2441no—
399C2—2442no—
400C2#1684039411yescharacteristic
401C2#135×D6111yescharacteristic
402C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3283
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. C2×#14519797C2semidirect
3. #16840414C2semidirect
4. #16840411C2semidirect
5. #16840140C2semidirect
6. #16840002C2semidirect
7. #16840001C2semidirect
8. #16839966C2semidirect
9. #16839965C2semidirect
10. #16839926C2semidirect
11. #16839925C2semidirect
12. #16839923C2semidirect
13. #16839842C2semidirect
14. #16839825C2semidirect
15. C61×#452C2semidirect
102. #11758199D4semidirect
193. Dic61#135semidirect
214. #452D61semidirect
217. C61#3283semidirect