Finite Group Databasebeta

← #22620939

Subgroups — #22620939

Order 9344.

390 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989139C211yesmaximal, characteristic, complemented
2#17989133C211yesmaximal, characteristic
3#17988980C211yesmaximal, characteristic, complemented
4#17988978C211yesmaximal, characteristic, complemented
5#17988948C211yesmaximal, characteristic, complemented
6#17988945C211yesmaximal, characteristic, complemented
7#17988796C211yesmaximal, characteristic, complemented
8#17988795C211yesmaximal, characteristic, complemented
9#17988786C211yesmaximal, characteristic, complemented
10#17988785C211yesmaximal, characteristic, complemented
11#17988751C211yesmaximal, characteristic, complemented
12#17988749C211yesmaximal, characteristic, complemented
13#17988747C211yesmaximal, characteristic, complemented
14#17988641C211yesmaximal, characteristic, complemented
15#452×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924016C2211yescharacteristic
22C2×#11924015C2211yescharacteristic
23#14556590C2211yescharacteristic
24#14556589C2211yescharacteristic
25#14556589C2211yescharacteristic
26#14556587C2211yescharacteristic
27#14556581—21no—
28#14556580C2211yescharacteristic
29#14556578C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556568—21no—
32#14556563—21no—
33#14556563—21no—
34Q8×Dic73C2211yescharacteristic
35#14556556—21no—
36#14556556C2211yescharacteristic
37C4×C22⋊D73—21no—
38C4×C22⋊D73—21no—
39#14556547—21no—
40C2×C4×Dic73C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C22×Dic73D411yescharacteristic
69C22×Dic73D411yescharacteristic
70C2×C4×D73—21no—
71Dic292—41no—
72#11924018—41no—
73#11924018—41no—
74#11924017—41no—
75#11924016—41no—
76#11924015—41no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
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—
91#11924005—21no—
92#11924005—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73D411yescharacteristic
96C4×Dic73D411yescharacteristic
97C4×Dic73C2311yescharacteristic
98C4×Dic73C2311yescharacteristic
99#41×C73—41no—
100#41×C73—41no—
101C2×Q8×C73C2311yescharacteristic
102C2×Q8×C73C2311yescharacteristic
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73C2311yescharacteristic
107Q16×C73—41no—
108SD16×C73—41no—
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73C2×D411yescharacteristic
116C22×D73—21no—
117Q8×C73—21no—
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121D4×C73—21no—
122D4×C73—21no—
123D4×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—42no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—42no—
133C22⋊D73—42no—
134C22⋊D73—42no—
135C2×Dic73—22no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—41no—
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143C2×Dic73C2×D411yescharacteristic
144D292—21no—
145D292—21no—
146C4×D73—42no—
147Dic146—21no—
148Dic146—21no—
149Dic146—21no—
150Dic146—21no—
151Dic146—42no—
152C8×C73—21no—
153C8×C73—21no—
154#10596831—21no—
155#10596831—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73C22×D411yescharacteristic
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73H(5,𝔽2)11yescharacteristic
171C4×C73H(5,𝔽2)11yescharacteristic
172Dic73—21no—
173Dic73—21no—
174Dic73—21no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178Dic73#13712yes—
179C2×C73—41no—
180C2×C73—81no—
181C2×C73#53511yescharacteristic
182C2×C73C2×#13711yescharacteristic
183C2×C73#57511yescharacteristic
184D73—81no—
185#3216—731nomaximal, Sylow
186C73#321611yescharacteristic, complemented, Sylow
187#533—731no—
188#532—731no—
189#497—731no—
190#497—731no—
191#489—731no—
192#489—731no—
193#462—731no—
194#462—731no—
195#460—731no—
196#460—731no—
197#452—731no—
198#452—731no—
199#452—731no—
200#452D7311yescharacteristic, complemented
201#432—731no—
202C2×#41—731no—
203C2×#41C2×D7311yescharacteristic
204C2×Q16—731no—
205C2×Q16—731no—
206C2×Q16—731no—
207C2×Q16C2×D7311yescharacteristic
208C2×SD16—731no—
209C2×SD16—731no—
210C2×SD16—731no—
211C2×SD16C2×D7311yescharacteristic
212C4⋊Q8—731no—
213C4⋊Q8—731no—
214C4⋊Q8—731no—
215#127—731no—
216#125—1461no—
217#124—731no—
218#124—731no—
219C22⋊Q8—731no—
220C22⋊Q8—1461no—
221C22⋊Q8C2×D7311yescharacteristic
222#121—1461no—
223#121—1461no—
224C4×Q8—731no—
225C4×Q8—731no—
226C4×Q8—1461no—
227C4×D4—1461no—
228C4×D4—1461no—
229#117—1461no—
230C2×C42—731no—
231C4⋊C8—731no—
232C4⋊C8—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#103C2×D7311yescharacteristic
237#102—731no—
238#102—731no—
239#102—731no—
240#102C2×D7311yescharacteristic
241C22⋊C8—731no—
242C22⋊C8C2×D7311yescharacteristic
243#97—731no—
244#97—731no—
245#41—41no—
246#41—41no—
247#41—2921no—
248#41—2921no—
249C2×Q8—731no—
250C2×Q8—731no—
251C2×Q8—1461no—
252C2×Q8C22×D7311yescharacteristic
253C2×Q8C22×D7311yescharacteristic
254C2×D4—21no—
255C2×D4—731no—
256C2×D4—1461no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4C22×D7311yescharacteristic
260C22×C4—21no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—1461no—
264C22×C4C22×D7311yescharacteristic
265Q16—41no—
266Q16—2921no—
267Q16—2921no—
268Q16—2921no—
269SD16—41no—
270SD16—2921no—
271SD16—2921no—
272SD16—2921no—
273C2×C8—731no—
274C2×C8—731no—
275C2×C8C22×D7311yescharacteristic
276C2×C8C22×D7311yescharacteristic
277C4⋊C4—21no—
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⋊C4—1461no—
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C42—731no—
295C42—731no—
296C42—731no—
297C42—731no—
298C42—1461no—
299C42—1461no—
300C23—21no—
301C23—1461no—
302C23D4×D7311yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—2922no—
308Q8—1461no—
309Q8—1461no—
310Q8—1461no—
311Q8—1461no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—2922no—
316D4—2922no—
317D4—2922no—
318D4—1461no—
319D4—1461no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—2922no—
327C2×C4—2921no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—731no—
331C2×C4—731no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1462no—
336C2×C4D4×D7311yescharacteristic
337C2×C4C23×D7311yescharacteristic
338C8—21no—
339C8—21no—
340C8—1461no—
341C8—1461no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—2921no—
349C22—2921no—
350C22—2921no—
351C22C2×D4×D7311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—732no—
360C4—1461no—
361C4—1461no—
362C4—1461no—
363C4#1455663611yescharacteristic
364C4#1455663611yescharacteristic
365C2—41no—
366C2—81no—
367C2—5841no—
368C2#1798915211yescharacteristic
369C2#137×D7311yescharacteristic
370C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#452×C73C2
socleC22×C73C22×D4
hypercenter#452D73
hypocenterC73#3216
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #17989139C2semidirect
3. #17988980C2semidirect
4. #17988978C2semidirect
5. #17988948C2semidirect
6. #17988945C2semidirect
7. #17988796C2semidirect
8. #17988795C2semidirect
9. #17988786C2semidirect
10. #17988785C2semidirect
11. #17988751C2semidirect
12. #17988749C2semidirect
13. #17988747C2semidirect
14. #17988641C2semidirect
15. #452×C73C2semidirect
186. C73#3216semidirect
200. #452D73semidirect