Finite Group Databasebeta

← #22619984

Subgroups — #22619984

Order 9344.

434 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989132C211yesmaximal, characteristic, complemented
2#41×Dic73C211yesmaximal, characteristic, complemented
3#17988912C211yesmaximal, characteristic, complemented
4#17988908C211yesmaximal, characteristic, complemented
5#17988880C211yesmaximal, characteristic, complemented
6#17988875C211yesmaximal, characteristic, complemented
7#17988785C211yesmaximal, characteristic, complemented
8#17988780C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10SD16×Dic73C211yesmaximal, characteristic, complemented
11#17988672C211yesmaximal, characteristic, complemented
12D8×Dic73C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988637C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×#11924015C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556587C2211yescharacteristic
21#14556577—21no—
22#14556565C2211yescharacteristic
23#14556563—21no—
24Q8×Dic73C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic
26D4×Dic73—21no—
27D4×Dic73—21no—
28D4×Dic73C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31#14556553C2211yescharacteristic
32#14556551—21no—
33#14556550—21no—
34#14556550C2211yescharacteristic
35C2×C4×Dic73—21no—
36C2×C4×Dic73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73D411yescharacteristic
69C22×Dic73D411yescharacteristic
70C2×C4×D73—21no—
71#11924015—22no—
72#11924013—22no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85#11924005—21no—
86#11924005—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73D411yescharacteristic
91C4×Dic73D411yescharacteristic
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94#41×C73—22no—
95#41×C73—22no—
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73—21no—
98C2×D4×C73—21no—
99C2×D4×C73C2311yescharacteristic
100C2×D4×C73C2311yescharacteristic
101C22×C4×C73—21no—
102C22×C4×C73C2311yescharacteristic
103SD16×C73—22no—
104D8×C73—22no—
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73C2×D411yescharacteristic
112C22×D73—21no—
113Q8×C73—21no—
114Q8×C73#4112yescomplemented
115D4×C73—24no—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—21no—
119D4×C73—42no—
120D4×C73#4112yescomplemented
121C2×C4×C73—24no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—42no—
129C22⋊D73—42no—
130C22⋊D73—42no—
131C2×Dic73—22no—
132C2×Dic73—22no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—42no—
137C2×Dic73—42no—
138C2×Dic73—42no—
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143D292—21no—
144D292—21no—
145C4×D73—42no—
146Dic146—42no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—22no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73C22×D411yescharacteristic
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C4×C73—21no—
165C4×C73—22no—
166C4×C73—41no—
167C4×C73C2×#4111yescharacteristic
168C4×C73C2×#4111yescharacteristic
169Dic73—21no—
170Dic73—21no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174Dic73#13512yes—
175Dic73AGL(1,ℤ/8)12yes—
176C2×C73—41no—
177C2×C73—42no—
178C2×C73—81no—
179C2×C73#52511yescharacteristic
180C2×C73C2×#13511yescharacteristic
181C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
182D73—81no—
183#3106—731nomaximal, Sylow
184C73#310611yescharacteristic, complemented, Sylow
185#532—731no—
186C4×#41—731no—
187#482—731no—
188#482—731no—
189#477—731no—
190#476—731no—
191#460—731no—
192#459—731no—
193#449—731no—
194#449D7311yescharacteristic, complemented
195C4×SD16—731no—
196C4×SD16—731no—
197C4×D8—731no—
198C4×D8—731no—
199#431—731no—
200C2×#41—1461no—
201C2×#41C2×D7311yescharacteristic
202C2×SD16—731no—
203C2×SD16C2×D7311yescharacteristic
204C2×D8—731no—
205C2×D8C2×D7311yescharacteristic
206C4⋊Q8—731no—
207#127—731no—
208#124—1461no—
209#121—731no—
210#121—1461no—
211#121C2×D7311yescharacteristic
212C4×Q8—731no—
213C4×Q8—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—731no—
217C4×D4—731no—
218C4×D4—1461no—
219C4×D4—1461no—
220C4×D4—1461no—
221#117—731no—
222#117—1461no—
223C2×C42—731no—
224C2×C42—1461no—
225#107—731no—
226#107—731no—
227#106—731no—
228#106—731no—
229C4⋊C8—731no—
230C4⋊C8—731no—
231#103—731no—
232#103C2×D7311yescharacteristic
233#102—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237#102—731no—
238#102C2×D7311yescharacteristic
239C22⋊C8—731no—
240C22⋊C8C2×D7311yescharacteristic
241C4×C8—731no—
242C4×C8—731no—
243#41—22no—
244#41—22no—
245#41—2924no—
246C2×Q8—1461no—
247C2×Q8C22×D7311yescharacteristic
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—731no—
251C2×D4—1461no—
252C2×D4—1461no—
253C2×D4—1461no—
254C2×D4C22×D7311yescharacteristic
255C2×D4C22×D7311yescharacteristic
256C22×C4—21no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4C22×D7311yescharacteristic
264SD16—22no—
265SD16—1462no—
266D8—22no—
267D8—1462no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—731no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4C22×D7311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—731no—
287C42—731no—
288C42—731no—
289C42—731no—
290C42—1461no—
291C42—1461no—
292C42—1461no—
293C23—21no—
294C23—21no—
295C23—1461no—
296C23D4×D7311yescharacteristic
297Q8—21no—
298Q8—2922no—
299Q8#1192402712yescomplemented
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—42no—
305D4—2922no—
306D4—2922no—
307D4—2922no—
308D4—1461no—
309D4—1461no—
310D4#1192402712yescomplemented
311C2×C4—24no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—2922no—
317C2×C4—2922no—
318C2×C4—2922no—
319C2×C4—2922no—
320C2×C4—731no—
321C2×C4—731no—
322C2×C4—731no—
323C2×C4—731no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1462no—
328C2×C4—1462no—
329C2×C4D4×D7311yescharacteristic
330C2×C4C23×D7311yescharacteristic
331C8—21no—
332C8—21no—
333C8—1461no—
334C8—1461no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2921no—
345C22—2921no—
346C22—2921no—
347C22C2×D4×D7311yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—2921no—
352C4—2921no—
353C4—2921no—
354C4—732no—
355C4—732no—
356C4—1461no—
357C4—1461no—
358C4C2×#1192402711yescharacteristic
359C4C2×#1192402711yescharacteristic
360C2—41no—
361C2—42no—
362C2—81no—
363C2—5841no—
364C2#1798909311yescharacteristic
365C2#135×D7311yescharacteristic
366C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3106
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17989132C2semidirect
2. #41×Dic73C2semidirect
3. #17988912C2semidirect
4. #17988908C2semidirect
5. #17988880C2semidirect
6. #17988875C2semidirect
7. #17988785C2semidirect
8. #17988780C2semidirect
9. #17988732C2semidirect
10. SD16×Dic73C2semidirect
11. #17988672C2semidirect
12. D8×Dic73C2semidirect
13. #17988667C2semidirect
14. #17988637C2semidirect
15. #449×C73C2semidirect
114. Q8×C73#41semidirect
120. D4×C73#41semidirect
184. C73#3106semidirect
194. #449D73semidirect
299. Q8#11924027semidirect
310. D4#11924027semidirect