Finite Group Databasebeta

← #21457476

Subgroups — #21457476

Order 7808.

476 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×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519808C211yesmaximal, characteristic, complemented
3#16840423C211yesmaximal, characteristic, complemented
4#16840422C211yesmaximal, characteristic, complemented
5#16840147C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16839987C211yesmaximal, characteristic, complemented
9#16839986C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11#16839910C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic, complemented
13#16839854C211yesmaximal, characteristic, complemented
14#16839837C211yesmaximal, characteristic, complemented
15C61×#451C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519809—24no—
20#14519808—24no—
21C2×#11758202C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×D488C2211yescharacteristic
28C2×#11758194C2211yescharacteristic
29C2×#11758189C2211yescharacteristic
30#14519766—21no—
31#14519766C2211yescharacteristic
32#14519766C2211yescharacteristic
33#14519763—21no—
34#14519755—21no—
35#14519753—21no—
36#14519753C2211yescharacteristic
37#14519752C2211yescharacteristic
38#14519751—21no—
39#14519751C2211yescharacteristic
40#14519750—21no—
41Q8×Dic61C2211yescharacteristic
42#14519742C2211yescharacteristic
43#14519739—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61C2211yescharacteristic
46#14519710C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519697C2211yescharacteristic
52#14519689C2211yescharacteristic
53C8×Dic61C2211yescharacteristic
54C22×Q8×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C2×Q16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61C2×Q8×C61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72#11758226—22no—
73#11758226—41no—
74Q8×D61—22no—
75Q8×D61—41no—
76#11758222—22no—
77#11758222—41no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61C2311yescharacteristic
86C2×Dic122—21no—
87C2×Dic122C2311yescharacteristic
88Q16×C61—22no—
89Q16×C61—41no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊Dic61D411yescharacteristic
96#11758202—22no—
97#11758202D414yescomplemented
98#11758201—22no—
99#11758201—22no—
100#11758201—22no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198D411yescharacteristic
109C4⋊Dic61—21no—
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112#11758196—21no—
113#11758196D411yescharacteristic
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117#11758194—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120D488—41no—
121#11758190—22no—
122#11758189—22no—
123C23×C61C2×D411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61—21no—
132Q8×C61—42no—
133Q8×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—21no—
140C2×C4×C61—42no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2411yescharacteristic
143C22⋊D61—41no—
144C22⋊D61—42no—
145C22⋊D61—42no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151D244—21no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—42no—
156D244—42no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162Dic122—21no—
163Dic122—42no—
164Dic122C2×D412yes—
165C8×C61—21no—
166C8×C61—21no—
167#92418—21no—
168#92418C2×D412yes—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61C22×D411yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—21no—
183C4×C61—22no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61C22×D411yescharacteristic
188C4×C61H(5,𝔽2)11yescharacteristic
189Dic61—22no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194#3277—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61D4211yescharacteristic
197C2×C61#57511yescharacteristic
198C2×C61#57811yescharacteristic
199D61—41no—
200D61—81no—
201D61—81no—
202C2×#137—611no—
203C2×#137—611no—
204#548—611no—
205#548—611no—
206#495—611no—
207#468—611no—
208#468—611no—
209#464—611no—
210#464—611no—
211#451—611no—
212#451D6111yescharacteristic, complemented
213#449—611no—
214#449—611no—
215C4×Q16—611no—
216#436—611no—
217C61#327711yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C2×#41—611no—
220C22×Q8—611no—
221C22×Q8C2×D6111yescharacteristic
222#137—1224no—
223#137—1224no—
224C2×Q16—611no—
225C2×Q16—611no—
226C2×Q16C2×D6111yescharacteristic
227C2×Q16C2×D6111yescharacteristic
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×D8—611no—
233C2×M16—611no—
234C2×M16—611no—
235#124—611no—
236#124—611no—
237#124—1221no—
238#124—1221no—
239C22⋊Q8—611no—
240C22⋊Q8—1221no—
241C22⋊Q8—1221no—
242C22⋊Q8C2×D6111yescharacteristic
243#121—611no—
244#121—611no—
245#121—1221no—
246#121—1221no—
247C4×Q8—611no—
248C4×Q8—611no—
249C4×D4—611no—
250C4×D4—1221no—
251C4×D4—1221no—
252#107—611no—
253C4⋊C8—611no—
254#103—611no—
255#103—611no—
256#103C2×D6111yescharacteristic
257#103C2×D6111yescharacteristic
258#102—611no—
259#102—611no—
260C22⋊C8—611no—
261C22⋊C8C2×D6111yescharacteristic
262C4×C8—611no—
263#41—1222no—
264#41—1222no—
265#41—2441no—
266#41—2441no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—611no—
271C2×Q8—1221no—
272C2×Q8—1222no—
273C2×Q8—2441no—
274C2×Q8C22×D6111yescharacteristic
275C2×Q8C22×D6111yescharacteristic
276C2×Q8C22×D6111yescharacteristic
277C2×D4—611no—
278C2×D4—611no—
279C2×D4—611no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C22×C4—21no—
285C22×C4—611no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4C22×D6111yescharacteristic
290Q16—22no—
291Q16—41no—
292Q16—614no—
293Q16—1222no—
294SD16—1222no—
295SD16—1222no—
296SD16—1222no—
297SD16—1222no—
298D8—2441no—
299M16—1222no—
300M16—1222no—
301C2×C8—611no—
302C2×C8—611no—
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⋊C4C22×D6111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—611no—
314C22⋊C4—611no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C42—611no—
323C42—1221no—
324C42—1221no—
325C23—611no—
326C23—1221no—
327C23—1221no—
328C23D4×D6111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—612no—
336Q8—1221no—
337Q8—2442no—
338Q8D4×D6112yes—
339D4—1221no—
340D4—1221no—
341D4—1221no—
342D4—1221no—
343D4—2442no—
344D4—2442no—
345D4—2441no—
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
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—1221no—
375C22—1221no—
376C22—1221no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—1222no—
393C4—2441no—
394C4C2×D4×D6111yescharacteristic
395C4#1451982211yescharacteristic
396C2—41no—
397C2—4881no—
398C2—4881no—
399C2—2441no—
400C2#1684039411yescharacteristic
401C2#1684056111yescharacteristic
402C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3277
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519808C2semidirect
3. #16840423C2semidirect
4. #16840422C2semidirect
5. #16840147C2semidirect
6. #16840011C2semidirect
7. #16840010C2semidirect
8. #16839987C2semidirect
9. #16839986C2semidirect
10. #16839916C2semidirect
11. #16839910C2semidirect
12. #16839909C2semidirect
13. #16839854C2semidirect
14. #16839837C2semidirect
15. C61×#451C2semidirect
97. #11758202D4semidirect
212. #451D61semidirect
217. C61#3277semidirect