Finite Group Databasebeta

← #22622201

Subgroups — #22622201

Order 9344.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989277C211yesmaximal, characteristic, complemented
2#17989246C211yesmaximal, characteristic
3#17988942C211yesmaximal, characteristic, complemented
4#17988923C211yesmaximal, characteristic, complemented
5#17988912C211yesmaximal, characteristic, complemented
6#17988895C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988810C211yesmaximal, characteristic, complemented
10#17988751C211yesmaximal, characteristic, complemented
11#17988745C211yesmaximal, characteristic, complemented
12C4×Dic292C211yesmaximal, characteristic, complemented
13#17988597C211yesmaximal, characteristic, complemented
14#17988589C211yesmaximal, characteristic, complemented
15#436×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21#14556584—21no—
22#14556583C2211yescharacteristic
23#14556581—21no—
24#14556579C2211yescharacteristic
25#14556577—21no—
26#14556572—21no—
27#14556570C2211yescharacteristic
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic
30#14556569—21no—
31#14556565C2211yescharacteristic
32#14556563—21no—
33C4×Dic146C2211yescharacteristic
34C4×Dic146C2211yescharacteristic
35#14556551—21no—
36#14556550C2211yescharacteristic
37#14556547—21no—
38C2×C4⋊Dic73C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—41no—
61C2×Dic146—22no—
62C2×Dic146—21no—
63C2×Dic146—41no—
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73Dic292—22no—
74Dic292—41no—
75#11924017—41no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C2×D4×C73D411yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101M16×C73—41no—
102M16×C73—41no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114D4×C73—41no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—42no—
125C22⋊D73—42no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—42no—
134C2×Dic73—42no—
135D292—21no—
136D292—21no—
137C4×D73—42no—
138Dic146—21no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—42no—
144Dic146#4112yes—
145C8×C73—21no—
146C8×C73—21no—
147C8×C73—21no—
148C8×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73C22×D411yescharacteristic
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73C2×#4111yescharacteristic
164C4×C73H(5,𝔽2)11yescharacteristic
165Dic73—22no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—41no—
173C2×C73—41no—
174C2×C73#54611yescharacteristic
175C2×C73#57511yescharacteristic
176C2×C73#57811yescharacteristic
177D73—81no—
178#3327—731nomaximal, Sylow
179C73#332711yescharacteristic, complemented, Sylow
180#552—731no—
181#548—731no—
182#488—731no—
183#484—731no—
184#482—731no—
185#479—731no—
186#470—731no—
187#468—731no—
188#464—731no—
189#452—731no—
190#451—731no—
191C4×Q16—731no—
192#436D7311yescharacteristic, complemented
193#419—731no—
194#417—731no—
195C2×#41—731no—
196C22×Q8—731no—
197C2×Q16—731no—
198C2×Q16—731no—
199C2×SD16—731no—
200C2×M16C2×D7311yescharacteristic
201C2×M16C2×D7311yescharacteristic
202#126—1461no—
203#125—731no—
204#125—1461no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—731no—
213#121—1461no—
214C4×Q8—731no—
215C4×Q8—731no—
216C4×D4—1461no—
217C4×D4C2×D7311yescharacteristic
218#117—731no—
219#117—1461no—
220C2×C4⋊C4—731no—
221#107—731no—
222#107—731no—
223#106—731no—
224C4⋊C8C2×D7311yescharacteristic
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235C22⋊C8C2×D7311yescharacteristic
236C22⋊C8C2×D7311yescharacteristic
237C4×C8C2×D7311yescharacteristic
238#41—2921no—
239#41—1462no—
240C2×Q8—2921no—
241C2×Q8—731no—
242C2×Q8—731no—
243C2×Q8—731no—
244C2×Q8—1462no—
245C2×Q8—1461no—
246C2×D4—731no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4D29211yescharacteristic
250C22×C4—1461no—
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4C22×D7311yescharacteristic
254C22×C4C22×D7311yescharacteristic
255Q16—2921no—
256Q16—1462no—
257SD16—2921no—
258M16—41no—
259M16—41no—
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C2×C8C22×D7311yescharacteristic
263C2×C8C22×D7311yescharacteristic
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4D29211yescharacteristic
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4D29211yescharacteristic
285C22⋊C4D29211yescharacteristic
286C42—1461no—
287C42—1461no—
288C42—1461no—
289C42C22×D7311yescharacteristic
290C23—1461no—
291C23C2×D29211yescharacteristic
292C23C2×D29211yescharacteristic
293Q8—2922no—
294Q8—732no—
295Q8—1461no—
296Q8—1461no—
297Q8—1461no—
298Q8—1461no—
299Q8—1461no—
300D4—41no—
301D4—2922no—
302D4—2922no—
303D4—1461no—
304D4—1461no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2922no—
310C2×C4—2922no—
311C2×C4—2922no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4C2×D29211yescharacteristic
320C2×C4C2×D29211yescharacteristic
321C2×C4C2×D29211yescharacteristic
322C2×C4C2×D29211yescharacteristic
323C2×C4C23×D7311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22C22×D29211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—2921no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4—1462no—
349C4#41×D7311yescharacteristic
350C4#1455663611yescharacteristic
351C2—41no—
352C2—41no—
353C2—5841no—
354C2#1798923211yescharacteristic
355C2#1798938711yescharacteristic
356C2#1798940411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#436×C73C2
socleC22×C73C22×D4
hypercenter#436D73
hypocenterC73#3327
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #17989277C2semidirect
3. #17988942C2semidirect
4. #17988923C2semidirect
5. #17988912C2semidirect
6. #17988895C2semidirect
7. #17988845C2semidirect
8. #17988833C2semidirect
9. #17988810C2semidirect
10. #17988751C2semidirect
11. #17988745C2semidirect
12. C4×Dic292C2semidirect
13. #17988597C2semidirect
14. #17988589C2semidirect
15. #436×C73C2semidirect
179. C73#3327semidirect
192. #436D73semidirect