Finite Group Databasebeta

← #22616953

Subgroups — #22616953

Order 9344.

528 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556571C211yesmaximal, characteristic, complemented
2C2×#14556568C211yesmaximal, characteristic, complemented
3#17988522C211yesmaximal, characteristic, complemented
4#17988520C211yesmaximal, characteristic, complemented
5#17988518C211yesmaximal, characteristic, complemented
6#17988510C211yesmaximal, characteristic, complemented
7#17988509C211yesmaximal, characteristic, complemented
8#17988491C211yesmaximal, characteristic, complemented
9#17988487C211yesmaximal, characteristic
10#17988486C211yesmaximal, characteristic, complemented
11#17988464C211yesmaximal, characteristic
12#17988463C211yesmaximal, characteristic
13#17988462C211yesmaximal, characteristic, complemented
14#17988461C211yesmaximal, characteristic, complemented
15#399×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556571—24no—
21#14556568—24no—
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×Dic146—41no—
55C2×Dic146—41no—
56C2×Dic146D414yescomplemented
57C2×C22⋊D73—41no—
58C2×C22⋊D73—41no—
59C2×C22⋊D73Q814yescomplemented
60C22×Dic73—22no—
61C22×Dic73—41no—
62C22×Dic73—41no—
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C2×C4×D73—22no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C4⋊Dic73—22no—
74C4⋊Dic73—22no—
75C4⋊Dic73—22no—
76C4⋊Dic73—41no—
77#11924007—22no—
78#11924007—22no—
79#11924007—41no—
80#11924007—41no—
81#11924007—41no—
82C22⋊Dic73—22no—
83C22⋊Dic73—41no—
84#11924005—22no—
85#11924005—22no—
86#11924005—22no—
87#11924005—41no—
88#11924005—41no—
89C4×Dic73—41no—
90C24×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C4⋊C4×C73—22no—
98C4⋊C4×C73—22no—
99C4⋊C4×C73—41no—
100C22⋊C4×C73—22no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—41no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73C2×Q812yes—
110C23×C73C2411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73C2×Q812yes—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
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×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73C2×D412yes—
135C2×C4×C73#4112yes—
136C22⋊D73—44no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—44no—
156C2×Dic73C2×D412yes—
157C2×Dic73C2×D412yes—
158C2×Dic73C2×Q812yes—
159C4×D73—44no—
160Dic146—44no—
161C22×C73—22no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73C22×D411yescharacteristic
169C22×C73C22×Q811yescharacteristic
170C22×C73C2×#4111yescharacteristic
171C22×C73H(5,𝔽2)11yescharacteristic
172C22×C73H(5,𝔽2)11yescharacteristic
173C22×C73H(5,𝔽2)11yescharacteristic
174C22×C732−1+411yescharacteristic
175C2×D73—22no—
176C2×D73—22no—
177C2×D73—22no—
178C2×D73—41no—
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—41no—
182C4×C73—22no—
183C4×C73—22no—
184C4×C73—41no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73—41no—
188Dic73—22no—
189Dic73—22no—
190Dic73—22no—
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194Dic73—41no—
195C2×C73—42no—
196C2×C73#53411yescharacteristic
197C2×C73#53911yescharacteristic
198C2×C73#54311yescharacteristic
199C2×C73D4×Q811yescharacteristic
200C2×C73#55011yescharacteristic
201C2×C73#55411yescharacteristic
202C2×C73#56211yescharacteristic
203D73—42no—
204#2732—731nomaximal, Sylow
205C73#273211yescharacteristic, complemented, Sylow
206C2×C22⋊Q8—731no—
207C2×C22⋊Q8—731no—
208#399—731no—
209#399D7311yescharacteristic, complemented
210#398—731no—
211#398—731no—
212#396—731no—
213#396—731no—
214#391—731no—
215#390—731no—
216#389—731no—
217#386—731no—
218#386—731no—
219#385—731no—
220#385—731no—
221C22×Q8—731no—
222C22×D4—731no—
223C23×C4—731no—
224C23×C4—731no—
225C22⋊Q8—1464no—
226C22⋊Q8—1464no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4C2×D7311yescharacteristic
237C2×C4⋊C4C2×D7311yescharacteristic
238C2×C4⋊C4C2×D7311yescharacteristic
239C2×C22⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4—731no—
246C2×C22⋊C4C2×D7311yescharacteristic
247C2×C22⋊C4C2×D7311yescharacteristic
248C2×C22⋊C4C2×D7311yescharacteristic
249C2×C42—731no—
250#95—731no—
251#95—731no—
252#95—731no—
253#95—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95C2×D7311yescharacteristic
258C24—731no—
259C24C22×D7311yescharacteristic
260C2×Q8—2921no—
261C2×Q8—2921no—
262C2×Q8—734no—
263C2×D4—2921no—
264C2×D4—2921no—
265C2×D4—734no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—1462no—
278C22×C4—1462no—
279C22×C4C22×D7311yescharacteristic
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—2921no—
289C4⋊C4—2921no—
290C4⋊C4—2921no—
291C4⋊C4—2921no—
292C4⋊C4—1462no—
293C4⋊C4—1462no—
294C4⋊C4—1462no—
295C4⋊C4—1462no—
296C4⋊C4—1462no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—41no—
300C22⋊C4—2921no—
301C22⋊C4—2921no—
302C22⋊C4—2921no—
303C22⋊C4—1462no—
304C22⋊C4—1462no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C42—2921no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—732no—
315C23—1461no—
316C23—1461no—
317C23—1461no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23Q8×D7312yes—
322C23C23×D7311yescharacteristic
323Q8—2924no—
324D4—2924no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2924no—
342C2×C4—2924no—
343C2×C4—732no—
344C2×C4—732no—
345C2×C4—732no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4D4×D7312yes—
365C2×C4#1192402712yes—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—2921no—
374C22—2921no—
375C22—2921no—
376C22—2921no—
377C22—1462no—
378C22—1462no—
379C22—1462no—
380C22C2×D4×D7311yescharacteristic
381C22C2×Q8×D7311yescharacteristic
382C22C2×#1192402711yescharacteristic
383C22#1455663611yescharacteristic
384C22#1455663711yescharacteristic
385C22#1455663711yescharacteristic
386C22#1455663811yescharacteristic
387C4—22no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—2921no—
394C4—2921no—
395C4—2921no—
396C4—2921no—
397C4—1462no—
398C4—1462no—
399C4—1462no—
400C2—42no—
401C2—2922no—
402C2#1798914811yescharacteristic
403C2#1798918111yescharacteristic
404C2#1798921211yescharacteristic
405C2#1798925011yescharacteristic
406C2#1798925711yescharacteristic
407C2#1798929511yescharacteristic
408C2#1798933411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2732
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556571C2semidirect
2. C2×#14556568C2semidirect
3. #17988522C2semidirect
4. #17988520C2semidirect
5. #17988518C2semidirect
6. #17988510C2semidirect
7. #17988509C2semidirect
8. #17988491C2semidirect
10. #17988486C2semidirect
13. #17988462C2semidirect
14. #17988461C2semidirect
15. #399×C73C2semidirect
56. C2×Dic146D4semidirect
59. C2×C22⋊D73Q8semidirect
205. C73#2732semidirect
209. #399D73semidirect