Finite Group Databasebeta

← #21456928

Subgroups — #21456928

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840383C211yesmaximal, characteristic, complemented
2#16840154C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840121C211yesmaximal, characteristic, complemented
5#16840112C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839969C211yesmaximal, characteristic, complemented
9#16839964C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839918C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic
13#16839901C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#536C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24#14519777C2211yescharacteristic
25#14519772—21no—
26#14519765C2211yescharacteristic
27#14519763—21no—
28#14519759—21no—
29#14519756C2211yescharacteristic
30#14519755—21no—
31#14519751C2211yescharacteristic
32C4×Dic122C2211yescharacteristic
33C4×D244C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35C4⋊#92418C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519701C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C22×Q8×C61C2211yescharacteristic
50C4⋊Q8×C61C2211yescharacteristic
51C4⋊Q8×C61C2211yescharacteristic
52#124×C61C2211yescharacteristic
53#124×C61C2211yescharacteristic
54#123×C61—21no—
55#123×C61—21no—
56C22⋊Q8×C61—21no—
57C22⋊Q8×C61—21no—
58#117×C61C2211yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C2×D4×C61—21no—
68C2×D4×C61C2311yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C2311yescharacteristic
72C2×C22⋊D61—21no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61D411yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61C2311yescharacteristic
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92#11758202—41no—
93#11758202—41no—
94#11758202—41no—
95#11758201—41no—
96#11758201—41no—
97#11758201—41no—
98#11758200—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—42no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—42no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—81no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144D244—21no—
145D244—21no—
146C4×D61—81no—
147Dic122—21no—
148Dic122—21no—
149Dic122—81no—
150#92418—21no—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61H(5,𝔽2)11yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3225—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—81no—
180C2×C61#53511yescharacteristic
181C2×C61#57711yescharacteristic
182C2×C61#57811yescharacteristic
183D61—81no—
184#542—611no—
185#536D6111yescharacteristic, complemented
186#497—611no—
187#495—611no—
188#489—611no—
189#487—611no—
190#464—611no—
191#463—611no—
192#462—611no—
193#461—611no—
194#452—611no—
195#451—611no—
196#449—611no—
197#448—611no—
198#433—611no—
199C61#322511yescharacteristic, complemented, Sylow
200C2×#41C2×D6111yescharacteristic
201C22×Q8C2×D6111yescharacteristic
202C2×Q16—611no—
203C2×Q16—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C4⋊Q8—611no—
211C4⋊Q8C2×D6111yescharacteristic
212C4⋊Q8C2×D6111yescharacteristic
213#126—1221no—
214#124—611no—
215#124—1221no—
216#124C2×D6111yescharacteristic
217#124C2×D6111yescharacteristic
218#123—21no—
219#123—21no—
220#123—1221no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—611no—
224C22⋊Q8—1221no—
225#121—611no—
226C4×Q8—611no—
227C4×D4—611no—
228#117C2×D6111yescharacteristic
229C4⋊C8—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#102—611no—
238#102—611no—
239C22⋊C8—611no—
240C22⋊C8—611no—
241#97—611no—
242C4×C8—611no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—611no—
249C2×Q8—1221no—
250C2×Q8C22×D6111yescharacteristic
251C2×Q8C22×D6111yescharacteristic
252C2×Q8C22×D6111yescharacteristic
253C2×D4—21no—
254C2×D4—611no—
255C2×D4—1221no—
256C2×D4C22×D6111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261Q16—2441no—
262Q16—2441no—
263Q16—2441no—
264SD16—2441no—
265SD16—2441no—
266SD16—2441no—
267SD16—2441no—
268D8—2441no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—611no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4C22⋊D6111yescharacteristic
283C4⋊C4C22⋊D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4C22⋊D6111yescharacteristic
294C22⋊C4C22⋊D6111yescharacteristic
295C42—1221no—
296C42C22×D6111yescharacteristic
297C42C22×D6111yescharacteristic
298C23—21no—
299C23—1221no—
300C23C2×C22⋊D6111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—1221no—
309Q8—1221no—
310Q8—4881no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4C2×C22⋊D6111yescharacteristic
329C2×C4C2×C22⋊D6111yescharacteristic
330C2×C4C2×C22⋊D6111yescharacteristic
331C2×C4C2×C22⋊D6111yescharacteristic
332C2×C4C2×C22⋊D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—1221no—
335C8—1221no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C22×C22⋊D6111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4#1451982211yescharacteristic
360C4#1451982211yescharacteristic
361C2—41no—
362C2—81no—
363C2—4881no—
364C2#1684032911yescharacteristic
365C2#1684057011yescharacteristic
366C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840154C2semidirect
3. #16840144C2semidirect
4. #16840121C2semidirect
5. #16840112C2semidirect
6. #16839981C2semidirect
7. #16839974C2semidirect
8. #16839969C2semidirect
9. #16839964C2semidirect
10. #16839924C2semidirect
11. #16839918C2semidirect
13. #16839901C2semidirect
14. #16839823C2semidirect
15. C61×#536C2semidirect
185. #536D61semidirect
199. C61#3225semidirect