Finite Group Databasebeta

← #22619003

Subgroups — #22619003

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989134C211yesmaximal, characteristic
2#17988663C211yesmaximal, characteristic, complemented
3#17988662C211yesmaximal, characteristic, complemented
4#17988660C211yesmaximal, characteristic, complemented
5#17988659C211yesmaximal, characteristic, complemented
6#17988657C211yesmaximal, characteristic, complemented
7C8×C22⋊D73C211yesmaximal, characteristic, complemented
8#17988650C211yesmaximal, characteristic, complemented
9#17988642C211yesmaximal, characteristic, complemented
10#17988639C211yesmaximal, characteristic, complemented
11#17988555C211yesmaximal, characteristic, complemented
12#17988553C211yesmaximal, characteristic, complemented
13#17988552C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924028C2211yescharacteristic
18C2×#11924012C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C22×#10596831C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23C2×C8×D73C2211yescharacteristic
24#14556590C411yescharacteristic
25#14556587C411yescharacteristic
26#14556577C411yescharacteristic
27#14556577C411yescharacteristic
28#14556566C411yescharacteristic
29#14556564C411yescharacteristic
30#14556564C411yescharacteristic
31#14556562C411yescharacteristic
32C4×D292C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34C4×C22⋊D73C2211yescharacteristic
35C42×D73C2211yescharacteristic
36C4⋊#10596831C2211yescharacteristic
37#14556520C2211yescharacteristic
38#14556520C2211yescharacteristic
39C22⋊#10596831C2211yescharacteristic
40C22⋊#10596831C2211yescharacteristic
41#14556503C2211yescharacteristic
42#14556503C2211yescharacteristic
43#14556503C2211yescharacteristic
44#14556503C2211yescharacteristic
45#14556503C2211yescharacteristic
46#14556503C2211yescharacteristic
47#14556503C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556502C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61#11924028—41no—
62#11924028—41no—
63C2×Dic146C2×C411yescharacteristic
64C2×Dic146C2×C411yescharacteristic
65C2×D292C2×C411yescharacteristic
66C2×D292C2×C411yescharacteristic
67C2×D292C2×C411yescharacteristic
68C2×C22⋊D73C2×C411yescharacteristic
69C2×C22⋊D73C2×C411yescharacteristic
70C2×C22⋊D73C2×C411yescharacteristic
71C2×C22⋊D73C2×C411yescharacteristic
72C2×C22⋊D73C2×C411yescharacteristic
73C2×C22⋊D73C2×C411yescharacteristic
74C2×C4×D73C2×C411yescharacteristic
75C2×C4×D73C2×C411yescharacteristic
76C2×C4×D73C2311yescharacteristic
77C2×C4×D73C2311yescharacteristic
78C2×C4×D73C2311yescharacteristic
79#11924012—41no—
80#11924011—41no—
81#11924011—41no—
82C2×#10596831—41no—
83C2×#10596831C2311yescharacteristic
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C8×D73—41no—
88C8×D73—41no—
89C4⋊Dic73C2×C411yescharacteristic
90#11924007C2×C411yescharacteristic
91#11924007C2×C411yescharacteristic
92C22⋊Dic73C2×C411yescharacteristic
93C22⋊Dic73C2×C411yescharacteristic
94#11924005C2×C411yescharacteristic
95#11924005C2×C411yescharacteristic
96#11924005C2×C411yescharacteristic
97#11924005C2×C411yescharacteristic
98C4×Dic73C2×C411yescharacteristic
99C4×Dic73C2×C411yescharacteristic
100C4×Dic73C2311yescharacteristic
101C2×D4×C73C2×C411yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104M16×C73—41no—
105C2×C8×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C4⋊C4×C73C2×C411yescharacteristic
111C22⋊C4×C73C2×C411yescharacteristic
112C22⋊C4×C73C2×C411yescharacteristic
113C42×C73C2311yescharacteristic
114C23×C73C22×C411yescharacteristic
115C23×C73C22×C411yescharacteristic
116C22×D73C22×C411yescharacteristic
117C22×D73C22×C411yescharacteristic
118C22×D73C22×C411yescharacteristic
119D4×C73—41no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C22×C411yescharacteristic
125C2×C4×C73C22×C411yescharacteristic
126C2×C4×C73C22×C411yescharacteristic
127C2×C4×C73C22×C411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—22no—
130C22⋊D73—22no—
131C22⋊D73—41no—
132C22⋊D73—41no—
133C22⋊D73—41no—
134C22⋊D73—41no—
135C2×Dic73C22×C411yescharacteristic
136C2×Dic73C22×C411yescharacteristic
137C2×Dic73C22×C411yescharacteristic
138C2×Dic73C22×C411yescharacteristic
139C2×Dic73C22×C411yescharacteristic
140D292—41no—
141D292—41no—
142D292—41no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—22no—
150C4×D73—41no—
151Dic146—41no—
152Dic146—41no—
153C8×C73—21no—
154C8×C73—21no—
155C8×C73—21no—
156C8×C73—21no—
157#10596831—21no—
158#10596831—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73C23×C411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—21no—
181C4×C73H(5,𝔽2)11yescharacteristic
182C4×C73H(5,𝔽2)11yescharacteristic
183Dic73—21no—
184Dic73—21no—
185Dic73—21no—
186Dic73—21no—
187Dic73#13112yes—
188C2×C73—41no—
189C2×C73—41no—
190C2×C73#51811yescharacteristic
191C2×C73C2×#13111yescharacteristic
192C2×C73#56811yescharacteristic
193D73—41no—
194D73—41no—
195D73—41no—
196#2981—731nomaximal, Sylow
197C73#298111yescharacteristic, complemented, Sylow
198#532—731no—
199#436—731no—
200#436—731no—
201#435—731no—
202#435—731no—
203#435—731no—
204#435D7311yescharacteristic, complemented
205C8×D4—731no—
206C8×D4—731no—
207#432—731no—
208#431—731no—
209#408—731no—
210#408—731no—
211#408—731no—
212#408—731no—
213C2×#41—731no—
214C2×#41—731no—
215C2×M16—731no—
216C2×M16—731no—
217C2×M16—731no—
218C2×M16C2×D7311yescharacteristic
219C22×C8—731no—
220C22×C8—731no—
221C22×C8—731no—
222C22×C8C2×D7311yescharacteristic
223C4⋊Q8—731no—
224#127—731no—
225#124—731no—
226#124—731no—
227#121—731no—
228#121—731no—
229#121—731no—
230#121—731no—
231C4×D4—731no—
232C4×D4—731no—
233C4×D4—731no—
234C4×D4C2×D7311yescharacteristic
235C2×C42—731no—
236C4⋊C8—731no—
237C4⋊C8—731no—
238C4⋊C8—731no—
239C4⋊C8C2×D7311yescharacteristic
240C22⋊C8—731no—
241C22⋊C8—731no—
242C22⋊C8—731no—
243C22⋊C8—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246C22⋊C8—731no—
247C22⋊C8—731no—
248C22⋊C8—731no—
249C22⋊C8—731no—
250C22⋊C8C2×D7311yescharacteristic
251C22⋊C8C2×D7311yescharacteristic
252#97—731no—
253#97C2×D7311yescharacteristic
254C4×C8—731no—
255C4×C8—731no—
256#41—2921no—
257#41—2921no—
258#41—2921no—
259#41—2921no—
260C2×Q8—731no—
261C2×Q8—731no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—731no—
267C2×D4—731no—
268C2×D4—731no—
269C2×D4—731no—
270C2×D4—731no—
271C2×D4C4×D7311yescharacteristic
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4C22×D7311yescharacteristic
278C22×C4C22×D7311yescharacteristic
279M16—41no—
280M16—2921no—
281M16—2921no—
282M16—2921no—
283C2×C8—41no—
284C2×C8—2921no—
285C2×C8—2921no—
286C2×C8—2921no—
287C2×C8—731no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8—731no—
291C2×C8C22×D7311yescharacteristic
292C2×C8C22×D7311yescharacteristic
293C2×C8C22×D7311yescharacteristic
294C2×C8C22×D7311yescharacteristic
295C4⋊C4—731no—
296C4⋊C4—731no—
297C4⋊C4—731no—
298C4⋊C4C4×D7311yescharacteristic
299C22⋊C4—731no—
300C22⋊C4—731no—
301C22⋊C4—731no—
302C22⋊C4—731no—
303C22⋊C4—731no—
304C22⋊C4—731no—
305C22⋊C4C4×D7311yescharacteristic
306C22⋊C4C4×D7311yescharacteristic
307C42—731no—
308C42—731no—
309C42—731no—
310C42C22×D7311yescharacteristic
311C23—731no—
312C23—731no—
313C23—731no—
314C23C2×C4×D7311yescharacteristic
315C23C2×C4×D7311yescharacteristic
316Q8—2921no—
317Q8—2921no—
318D4—41no—
319D4—2921no—
320D4—2921no—
321D4—2921no—
322D4—2921no—
323D4—2921no—
324D4—2921no—
325D4—2921no—
326D4—1462no—
327D4—1462no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2921no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—731no—
337C2×C4—731no—
338C2×C4—1462no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4C2×C4×D7311yescharacteristic
346C2×C4C2×C4×D7311yescharacteristic
347C2×C4C2×C4×D7311yescharacteristic
348C2×C4C2×C4×D7311yescharacteristic
349C2×C4C23×D7311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—1461no—
355C8—1461no—
356C8—1461no—
357C8—1461no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—1461no—
365C22—1461no—
366C22—1461no—
367C22—1461no—
368C22—1461no—
369C22—1461no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22C22×C4×D7311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—732no—
379C4—1461no—
380C4—1461no—
381C4—1461no—
382C4—1461no—
383C4#1455663611yescharacteristic
384C4#1455663711yescharacteristic
385C2—41no—
386C2—41no—
387C2—2921no—
388C2—2921no—
389C2—2921no—
390C2#1798905911yescharacteristic
391C2#131×D7311yescharacteristic
392C2#1798935311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D73
commutator, socleC22×C73C23×C4
Fitting#435×C73C2
hypercenter#435D73
hypocenterC73#2981
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #17988663C2semidirect
3. #17988662C2semidirect
4. #17988660C2semidirect
5. #17988659C2semidirect
6. #17988657C2semidirect
7. C8×C22⋊D73C2semidirect
8. #17988650C2semidirect
9. #17988642C2semidirect
10. #17988639C2semidirect
11. #17988555C2semidirect
12. #17988553C2semidirect
13. #17988552C2semidirect
14. #17988552C2semidirect
15. #435×C73C2semidirect
197. C73#2981semidirect
204. #435D73semidirect