Finite Group Databasebeta

← #22620815

Subgroups — #22620815

Order 9344.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989165C211yesmaximal, characteristic
2#17989158C211yesmaximal, characteristic, complemented
3#17988929C211yesmaximal, characteristic, complemented
4#17988923C211yesmaximal, characteristic, complemented
5#17988918C211yesmaximal, characteristic, complemented
6#17988912C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988828C211yesmaximal, characteristic, complemented
10#17988816C211yesmaximal, characteristic, complemented
11#17988751C211yesmaximal, characteristic, complemented
12#17988751C211yesmaximal, characteristic, complemented
13#17988745C211yesmaximal, characteristic, complemented
14#17988728C211yesmaximal, characteristic, complemented
15#408×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924017C2211yescharacteristic
22#14556589—21no—
23#14556578—21no—
24#14556572—21no—
25#14556572—21no—
26#14556570C2211yescharacteristic
27#14556570C2211yescharacteristic
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556570C2211yescharacteristic
32#14556567—21no—
33#14556565C2211yescharacteristic
34#14556565C2211yescharacteristic
35#14556563—21no—
36#14556563—21no—
37#14556562—21no—
38#14556550C2211yescharacteristic
39C2×C4⋊Dic73C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556525C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556523C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556516C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22×C8×C73C2211yescharacteristic
55C22⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146—21no—
62C2×Dic146—41no—
63C2×Dic146—41no—
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C2×C4×D73—21no—
74Dic292—41no—
75Dic292—41no—
76#11924017—41no—
77#11924017—41no—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93C22⋊Dic73—21no—
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96#11924005—21no—
97#11924005—21no—
98C4×Dic73—21no—
99#41×C73—41no—
100#41×C73—41no—
101C2×Q8×C73D411yescharacteristic
102C2×D4×C73D411yescharacteristic
103C2×D4×C73D411yescharacteristic
104C2×D4×C73D411yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108M16×C73—41no—
109C2×C8×C73—41no—
110C2×C8×C73C2311yescharacteristic
111C2×C8×C73C2311yescharacteristic
112C2×C8×C73C2311yescharacteristic
113C2×C8×C73C2311yescharacteristic
114C23×C73C2×D411yescharacteristic
115C23×C73C2×D411yescharacteristic
116C23×C73C2×D411yescharacteristic
117C22×D73—21no—
118Q8×C73—41no—
119D4×C73—41no—
120D4×C73—41no—
121D4×C73—41no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—42no—
133C22⋊D73—81no—
134C22⋊D73—81no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—42no—
143C2×Dic73—81no—
144D292—21no—
145D292—21no—
146C4×D73—42no—
147Dic146—21no—
148Dic146—21no—
149Dic146—21no—
150Dic146—21no—
151Dic146—21no—
152Dic146—21no—
153Dic146—42no—
154C8×C73—21no—
155C8×C73—21no—
156C8×C73—21no—
157C8×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73C22×D411yescharacteristic
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73H(5,𝔽2)11yescharacteristic
175C4×C73H(5,𝔽2)11yescharacteristic
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—41no—
184C2×C73—41no—
185C2×C73—41no—
186C2×C73#53411yescharacteristic
187C2×C73#57711yescharacteristic
188C2×C73#57811yescharacteristic
189D73—81no—
190#3201—731nomaximal, Sylow
191C73#320111yescharacteristic, complemented, Sylow
192#537—731no—
193#536—731no—
194#485—731no—
195#484—731no—
196#483—731no—
197#482—731no—
198#470—731no—
199#468—731no—
200#467—731no—
201#465—731no—
202#452—731no—
203#452—731no—
204#451—731no—
205#448—731no—
206#408D7311yescharacteristic, complemented
207C2×#41—731no—
208C2×#41C2×D7311yescharacteristic
209C22×Q8—731no—
210C2×Q16—731no—
211C2×Q16—731no—
212C2×SD16—731no—
213C2×SD16—731no—
214C2×M16C2×D7311yescharacteristic
215C22×C8C2×D7311yescharacteristic
216C4⋊Q8—1461no—
217#124—1461no—
218#123—1461no—
219#123—1461no—
220C22⋊Q8—731no—
221C22⋊Q8—731no—
222C22⋊Q8—731no—
223C22⋊Q8—731no—
224C22⋊Q8—731no—
225C22⋊Q8—731no—
226C22⋊Q8—1461no—
227#121—731no—
228#121—731no—
229#121—1461no—
230#121—1461no—
231#121—1461no—
232#117—731no—
233C2×C4⋊C4—731no—
234#107—731no—
235#107—731no—
236#106—731no—
237#106—731no—
238#103—731no—
239#103—731no—
240#103—731no—
241#103—731no—
242#103—731no—
243#103—731no—
244#102—731no—
245#102—731no—
246C22⋊C8C2×D7311yescharacteristic
247C22⋊C8C2×D7311yescharacteristic
248C22⋊C8C2×D7311yescharacteristic
249C22⋊C8C2×D7311yescharacteristic
250#41—41no—
251#41—41no—
252#41—2921no—
253#41—2921no—
254C2×Q8—2921no—
255C2×Q8—2921no—
256C2×Q8—731no—
257C2×Q8—731no—
258C2×Q8—731no—
259C2×Q8—1461no—
260C2×Q8D29211yescharacteristic
261C2×D4—731no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4D29211yescharacteristic
266C2×D4D29211yescharacteristic
267C2×D4D29211yescharacteristic
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274Q16—2921no—
275Q16—2921no—
276SD16—2921no—
277SD16—2921no—
278M16—41no—
279C2×C8—41no—
280C2×C8C22×D7311yescharacteristic
281C2×C8C22×D7311yescharacteristic
282C2×C8C22×D7311yescharacteristic
283C2×C8C22×D7311yescharacteristic
284C4⋊C4—731no—
285C4⋊C4—731no—
286C4⋊C4—731no—
287C4⋊C4—731no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C4⋊C4—1461no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C42—1461no—
305C23—1461no—
306C23C2×D29211yescharacteristic
307C23C2×D29211yescharacteristic
308C23C2×D29211yescharacteristic
309Q8—41no—
310Q8—2922no—
311Q8—1461no—
312Q8—1461no—
313Q8—1461no—
314Q8—1461no—
315Q8—1461no—
316Q8—1461no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—2922no—
321D4—5841no—
322D4—5841no—
323D4—1461no—
324D4—1461no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—5841no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4C2×D29211yescharacteristic
342C2×C4C2×D29211yescharacteristic
343C2×C4C2×D29211yescharacteristic
344C2×C4C23×D7311yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22C22×D29211yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—2921no—
366C4—2921no—
367C4—2921no—
368C4—2921no—
369C4—2921no—
370C4—2921no—
371C4—2921no—
372C4#1455663611yescharacteristic
373C4#1455663611yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—5841no—
378C2#1798914911yescharacteristic
379C2#1798939911yescharacteristic
380C2#1798940411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#408×C73C2
socleC22×C73C22×D4
hypercenter#408D73
hypocenterC73#3201
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #17989158C2semidirect
3. #17988929C2semidirect
4. #17988923C2semidirect
5. #17988918C2semidirect
6. #17988912C2semidirect
7. #17988845C2semidirect
8. #17988833C2semidirect
9. #17988828C2semidirect
10. #17988816C2semidirect
11. #17988751C2semidirect
12. #17988751C2semidirect
13. #17988745C2semidirect
14. #17988728C2semidirect
15. #408×C73C2semidirect
191. C73#3201semidirect
206. #408D73semidirect