Finite Group Databasebeta

← #22620824

Subgroups — #22620824

Order 9344.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989161C211yesmaximal, characteristic
2#17989160C211yesmaximal, characteristic
3#17988929C211yesmaximal, characteristic, complemented
4#17988927C211yesmaximal, characteristic, complemented
5#17988926C211yesmaximal, characteristic, complemented
6#17988925C211yesmaximal, characteristic, complemented
7#17988844C211yesmaximal, characteristic, complemented
8#17988842C211yesmaximal, characteristic, complemented
9#17988827C211yesmaximal, characteristic, complemented
10#17988825C211yesmaximal, characteristic, complemented
11#17988743C211yesmaximal, characteristic, complemented
12#17988741C211yesmaximal, characteristic, complemented
13#17988741C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic
15#451×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22#14556590—21no—
23#14556589—21no—
24#14556580—21no—
25#14556577—21no—
26#14556576—21no—
27#14556574—21no—
28#14556574—21no—
29#14556573—21no—
30#14556571C2211yescharacteristic
31#14556570C2211yescharacteristic
32#14556567C2211yescharacteristic
33#14556567C2211yescharacteristic
34#14556567C2211yescharacteristic
35#14556567C2211yescharacteristic
36#14556567C2211yescharacteristic
37#14556550C2211yescharacteristic
38#14556549C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556515C2211yescharacteristic
48#14556515C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×Q16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146—21no—
62C2×Dic146D411yescharacteristic
63C2×Dic146C2311yescharacteristic
64Q8×D73—41no—
65Q8×D73—41no—
66C2×D292D411yescharacteristic
67C2×C22⋊D73D411yescharacteristic
68C2×C22⋊D73D411yescharacteristic
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71C2×C4×D73C2311yescharacteristic
72#11924018—41no—
73#11924018—41no—
74#11924011—41no—
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C8×D73—41no—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C2×Q8×C73—21no—
100C2×Q8×C73—41no—
101C2×Q8×C73—41no—
102C2×Q8×C73C2311yescharacteristic
103C2×Q8×C73C2311yescharacteristic
104C2×Q8×C73C2311yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73C2311yescharacteristic
107Q16×C73—41no—
108Q16×C73—41no—
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73C2×D411yescharacteristic
116C22×D73C2×D411yescharacteristic
117Q8×C73—21no—
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—21no—
122Q8×C73—21no—
123Q8×C73—42no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—42no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—41no—
134C22⋊D73—41no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141D292—41no—
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—42no—
147Dic146—21no—
148Dic146—21no—
149Dic146—41no—
150Dic146—42no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73H(5,𝔽2)11yescharacteristic
171C4×C73H(5,𝔽2)11yescharacteristic
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73#53411yescharacteristic
180C2×C73#57811yescharacteristic
181C2×C73#57811yescharacteristic
182D73—41no—
183D73—41no—
184#3202—731nomaximal, Sylow
185C73#320211yescharacteristic, complemented, Sylow
186#536—731no—
187#536—731no—
188#485—731no—
189#485—731no—
190#485—731no—
191#485—731no—
192#470—731no—
193#470—731no—
194#467—731no—
195#467—731no—
196#451—731no—
197#451—731no—
198#451—731no—
199#451D7311yescharacteristic, complemented
200#408—731no—
201C2×#41—731no—
202C22×Q8—731no—
203C22×Q8C2×D7311yescharacteristic
204C2×Q16—731no—
205C2×Q16—731no—
206C2×Q16C2×D7311yescharacteristic
207C2×Q16C2×D7311yescharacteristic
208C2×M16—731no—
209C22×C8—731no—
210C4⋊Q8—1461no—
211C4⋊Q8—1461no—
212#124—1461no—
213#124—1461no—
214#123—1461no—
215#123—1461no—
216#123—1461no—
217#123—1461no—
218C22⋊Q8—731no—
219C22⋊Q8—731no—
220C22⋊Q8—731no—
221C22⋊Q8—731no—
222C22⋊Q8—731no—
223C22⋊Q8—731no—
224C22⋊Q8—731no—
225C22⋊Q8C2×D7311yescharacteristic
226#117—731no—
227#117—731no—
228#107—731no—
229#107—731no—
230#106—731no—
231#106—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#103C2×D7311yescharacteristic
239#103C2×D7311yescharacteristic
240C22⋊C8—731no—
241C22⋊C8—731no—
242C22⋊C8—731no—
243C22⋊C8C2×D7311yescharacteristic
244#41—2921no—
245#41—2921no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—2921no—
250C2×Q8—2921no—
251C2×Q8—731no—
252C2×Q8—731no—
253C2×Q8—1461no—
254C2×Q8C22×D7311yescharacteristic
255C2×Q8C22×D7311yescharacteristic
256C2×Q8C22×D7311yescharacteristic
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—731no—
260C22×C4—21no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—1461no—
264C22×C4C22×D7311yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—2921no—
268Q16—2921no—
269M16—2921no—
270C2×C8—2921no—
271C2×C8—731no—
272C2×C8—731no—
273C2×C8C22×D7311yescharacteristic
274C2×C8C22×D7311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—731no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4C22×D7311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C42—1461no—
298C42—1461no—
299C23—731no—
300C23—731no—
301C23D4×D7311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—2921no—
310Q8—2922no—
311Q8—1461no—
312Q8—1461no—
313D4—2921no—
314D4—2921no—
315D4—2921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—2922no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4D4×D7311yescharacteristic
335C2×C4C23×D7311yescharacteristic
336C8—21no—
337C8—21no—
338C8—1461no—
339C8—1461no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1461no—
344C22—1461no—
345C22—1461no—
346C22—1461no—
347C22—1461no—
348C22—1461no—
349C22C2×D4×D7311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2921no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4#1455663611yescharacteristic
362C4#1455663611yescharacteristic
363C2—41no—
364C2—2921no—
365C2—2921no—
366C2#1798914711yescharacteristic
367C2#1798940011yescharacteristic
368C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3202
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #17988929C2semidirect
4. #17988927C2semidirect
5. #17988926C2semidirect
6. #17988925C2semidirect
7. #17988844C2semidirect
8. #17988842C2semidirect
9. #17988827C2semidirect
10. #17988825C2semidirect
11. #17988743C2semidirect
12. #17988741C2semidirect
13. #17988741C2semidirect
15. #451×C73C2semidirect
185. C73#3202semidirect
199. #451D73semidirect