Finite Group Databasebeta

← #22621833

Subgroups — #22621833

Order 9344.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989283C211yesmaximal, characteristic, complemented
2#17988941C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988903C211yesmaximal, characteristic, complemented
5#17988894C211yesmaximal, characteristic, complemented
6#17988821C211yesmaximal, characteristic, complemented
7#17988818C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10#17988726C211yesmaximal, characteristic, complemented
11C4×#11924015C211yesmaximal, characteristic, complemented
12D4×#10596831C211yesmaximal, characteristic, complemented
13#17988583C211yesmaximal, characteristic, complemented
14C2×#14556515C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21#14556586—21no—
22#14556583C2211yescharacteristic
23#14556573—21no—
24#14556565C2211yescharacteristic
25#14556565C2211yescharacteristic
26#14556563—21no—
27C4×D292C2211yescharacteristic
28#14556551—21no—
29#14556550C2211yescharacteristic
30C2×C4⋊Dic73C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556515C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C22×Q8×C73C2211yescharacteristic
50#124×C73—21no—
51#124×C73C2211yescharacteristic
52C22⋊Q8×C73—21no—
53C22⋊Q8×C73C2211yescharacteristic
54#121×C73—21no—
55#121×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×D4×C73—21no—
58C4×D4×C73C2211yescharacteristic
59C2×D292C2311yescharacteristic
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C22×Dic73—21no—
63C2×C4×D73—21no—
64#11924015—22no—
65#11924015—41no—
66#11924013—41no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C4⋊Dic73—21no—
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80#11924005—21no—
81#11924005—21no—
82#11924005—21no—
83C4×Dic73—21no—
84#41×C73—22no—
85#41×C73—41no—
86C2×Q8×C73—21no—
87C2×Q8×C73—22no—
88C2×Q8×C73—41no—
89C2×Q8×C73C2311yescharacteristic
90C2×Q8×C73C2311yescharacteristic
91C2×D4×C73—21no—
92C2×D4×C73—21no—
93C2×D4×C73D411yescharacteristic
94C2×D4×C73C2311yescharacteristic
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73D411yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—42no—
119Q8×C73#4112yes—
120D4×C73—22no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—42no—
124D4×C73—42no—
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—42no—
133C2×C4×C73—42no—
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2411yescharacteristic
139C22⋊D73—42no—
140C22⋊D73—81no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—81no—
145D292—21no—
146D292—21no—
147C4×D73—81no—
148#10596831—21no—
149#10596831—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73#13512yes—
161C22×C73C22×D411yescharacteristic
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—22no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73C2×#4111yescharacteristic
173C4×C73H(5,𝔽2)11yescharacteristic
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177C2×C73—22no—
178C2×C73—41no—
179C2×C73—81no—
180C2×C73#54611yescharacteristic
181C2×C73C2×#13511yescharacteristic
182C2×C73#57711yescharacteristic
183D73—81no—
184#3301—731nomaximal, Sylow
185C73#330111yescharacteristic, complemented, Sylow
186#553—731no—
187#548D7311yescharacteristic, complemented
188#488—731no—
189#485—731no—
190#481—731no—
191#479—731no—
192#466—731no—
193#465—731no—
194#463—731no—
195#449—731no—
196#448—731no—
197C4×SD16—731no—
198C8×D4—731no—
199#416—731no—
200C2×#103—731no—
201C2×#41C2×D7311yescharacteristic
202C22×Q8C2×D7311yescharacteristic
203C2×SD16—731no—
204C2×SD16—731no—
205C2×D8—731no—
206C22×C8—731no—
207C22×C8—731no—
208#126—1461no—
209#125—731no—
210#124—21no—
211#124C2×D7311yescharacteristic
212#123—1461no—
213C22⋊Q8—21no—
214C22⋊Q8C2×D7311yescharacteristic
215#121—21no—
216#121—731no—
217#121—731no—
218#121—1461no—
219#121C2×D7311yescharacteristic
220C4×Q8C2×D7311yescharacteristic
221C4×D4—21no—
222C4×D4—731no—
223C4×D4—1461no—
224C4×D4C2×D7311yescharacteristic
225#117—731no—
226C2×C4⋊C4—731no—
227#107—731no—
228#106—731no—
229#106—731no—
230C4⋊C8—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241C22⋊C8—731no—
242C22⋊C8—731no—
243C4×C8—731no—
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D7311yescharacteristic
250C2×Q8C22×D7311yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—731no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4C22⋊D7311yescharacteristic
257C2×D4C22×D7311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4C22×D7311yescharacteristic
263C22×C4C22×D7311yescharacteristic
264SD16—2921no—
265SD16—1462no—
266D8—2921no—
267C2×C8—2921no—
268C2×C8—2921no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8—731no—
272C2×C8—731no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4C22⋊D7311yescharacteristic
282C4⋊C4C22×D7311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4C22⋊D7311yescharacteristic
292C22⋊C4C22⋊D7311yescharacteristic
293C42—21no—
294C42—1461no—
295C42C22×D7311yescharacteristic
296C23—21no—
297C23—1461no—
298C23C2×C22⋊D7311yescharacteristic
299C23C2×C22⋊D7311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1192402712yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—2922no—
311D4—5841no—
312D4—1461no—
313D4—1461no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—5841no—
324C2×C4—5841no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4C2×C22⋊D7311yescharacteristic
329C2×C4C2×C22⋊D7311yescharacteristic
330C2×C4C2×C22⋊D7311yescharacteristic
331C2×C4C2×C22⋊D7311yescharacteristic
332C2×C4C23×D7311yescharacteristic
333C8—1461no—
334C8—1461no—
335C8—1461no—
336C8—1461no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—2921no—
346C22—2921no—
347C22—2921no—
348C22#1455661112yes—
349C22C22×C22⋊D7311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—2921no—
358C4—2921no—
359C4—2921no—
360C4C2×#1192402711yescharacteristic
361C4#1455663611yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—5841no—
366C2#1798923111yescharacteristic
367C2C2×#1455661111yescharacteristic
368C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#548×C73C2
socleC22×C73C22×D4
hypercenter#548D73
hypocenterC73#3301
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #17989283C2semidirect
2. #17988941C2semidirect
3. #17988925C2semidirect
4. #17988903C2semidirect
5. #17988894C2semidirect
6. #17988821C2semidirect
7. #17988818C2semidirect
8. #17988799C2semidirect
9. #17988732C2semidirect
10. #17988726C2semidirect
11. C4×#11924015C2semidirect
12. D4×#10596831C2semidirect
13. #17988583C2semidirect
14. C2×#14556515C2semidirect
15. #548×C73C2semidirect
185. C73#3301semidirect
187. #548D73semidirect