Finite Group Databasebeta

← #22619987

Subgroups — #22619987

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#17989134C211yesmaximal, characteristic, complemented
2C4×#11924027C211yesmaximal, characteristic, complemented
3#17988914C211yesmaximal, characteristic, complemented
4#17988910C211yesmaximal, characteristic, complemented
5#17988881C211yesmaximal, characteristic, complemented
6#17988875C211yesmaximal, characteristic, complemented
7#17988786C211yesmaximal, characteristic, complemented
8#17988780C211yesmaximal, characteristic, complemented
9#17988733C211yesmaximal, characteristic, complemented
10#17988729C211yesmaximal, characteristic, complemented
11C4×#11924017C211yesmaximal, characteristic, complemented
12C4×#11924016C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988638C211yesmaximal, characteristic, complemented
15C4×D8×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924027C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556577—21no—
24#14556566C2211yescharacteristic
25#14556564—21no—
26#14556562C2211yescharacteristic
27C4×Dic146C2211yescharacteristic
28#14556556C2211yescharacteristic
29C4×D292C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31C4×C22⋊D73—21no—
32C4×C22⋊D73—21no—
33#14556551—21no—
34#14556549C2211yescharacteristic
35#14556547—21no—
36C2×C4×Dic73—21no—
37C42×D73C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×D8×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59#11924028—44no—
60#11924027—22no—
61#11924027—22no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×D292—21no—
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73D411yescharacteristic
74C2×C4×D73D411yescharacteristic
75C2×C4×D73C2311yescharacteristic
76#11924017—22no—
77#11924016—22no—
78#11924013—22no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73D411yescharacteristic
95C4×Dic73D411yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100C22×C4×C73—21no—
101D8×C73—22no—
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C42×C73C2311yescharacteristic
109C23×C73—21no—
110C23×C73—21no—
111C22×D73—21no—
112C22×D73C2×D411yescharacteristic
113D4×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73#4112yescomplemented
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—42no—
120C2×C4×C73—42no—
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—24no—
125C22⋊D73—42no—
126C22⋊D73—42no—
127C22⋊D73—42no—
128C2×Dic73—24no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—42no—
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136D292—21no—
137D292—21no—
138D292—42no—
139C4×D73—22no—
140C4×D73—21no—
141C4×D73—21no—
142C4×D73—22no—
143C4×D73—42no—
144Dic146—21no—
145Dic146—42no—
146Dic146#4112yescomplemented
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C4×C73—21no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73AGL(1,ℤ/8)12yes—
168C4×C73C2×#4111yescharacteristic
169C4×C73C2×#4111yescharacteristic
170Dic73—22no—
171Dic73—21no—
172Dic73—21no—
173Dic73—41no—
174Dic73—41no—
175Dic73#13512yes—
176C2×C73—42no—
177C2×C73—81no—
178C2×C73#52511yescharacteristic
179C2×C73C2×#13511yescharacteristic
180C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
181D73—41no—
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#449—731no—
195C4×SD16—731no—
196C4×SD16—731no—
197C4×D8—731no—
198C4×D8D7311yescharacteristic, complemented
199#431—731no—
200C2×#41—731no—
201C2×#41—1461no—
202C2×SD16—731no—
203C2×SD16—731no—
204C2×D8—731no—
205C2×D8C2×D7311yescharacteristic
206C4⋊Q8—731no—
207#127—731no—
208#124—1461no—
209#121—731no—
210#121—731no—
211#121—1461no—
212C4×Q8—731no—
213C4×Q8—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—1461no—
217C4×D4—1461no—
218C4×D4—1461no—
219C4×D4C2×D7311yescharacteristic
220C4×D4C2×D7311yescharacteristic
221#117—731no—
222#117—1461no—
223C2×C42—731no—
224C2×C42—1461no—
225#107—731no—
226#107C2×D7311yescharacteristic
227#106—731no—
228#106—731no—
229C4⋊C8—731no—
230C4⋊C8—731no—
231#103—731no—
232#103—731no—
233#102—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237#102C2×D7311yescharacteristic
238#102C2×D7311yescharacteristic
239C22⋊C8—731no—
240C22⋊C8—731no—
241C4×C8—731no—
242C4×C8C2×D7311yescharacteristic
243#41—2924no—
244#41—1462no—
245#41—1462no—
246C2×Q8—731no—
247C2×Q8—1461no—
248C2×D4—731no—
249C2×D4—1461no—
250C2×D4—1461no—
251C2×D4—1461no—
252C2×D4—1461no—
253C2×D4—1461no—
254C2×D4C22×D7311yescharacteristic
255C2×D4C22×D7311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264SD16—1462no—
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—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—731no—
287C42—731no—
288C42—731no—
289C42—1461no—
290C42—1461no—
291C42—1461no—
292C42C22×D7311yescharacteristic
293C23—21no—
294C23—21no—
295C23—731no—
296C23—1461no—
297Q8—2922no—
298Q8—732no—
299Q8—1461no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2922no—
304D4—2922no—
305D4—2922no—
306D4—2922no—
307D4—1464no—
308D4—1461no—
309D4—1461no—
310D4#1192402812yescomplemented
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—2922no—
316C2×C4—2922no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—1462no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1464no—
324C2×C4—1461no—
325C2×C4—1462no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4D4×D7311yescharacteristic
329C2×C4D4×D7311yescharacteristic
330C2×C4C23×D7311yescharacteristic
331C8—21no—
332C8—21no—
333C8—1461no—
334C8—1461no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2921no—
342C22—2921no—
343C22—2921no—
344C22—1461no—
345C22—1461no—
346C22—1461no—
347C22C2×D4×D7311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—2921no—
352C4—2921no—
353C4—732no—
354C4—1461no—
355C4—1462no—
356C4—1461no—
357C4#1455661512yes—
358C4#41×D7311yescharacteristic
359C4C2×#1192402811yescharacteristic
360C2—42no—
361C2—81no—
362C2—2921no—
363C2—5841no—
364C2#1798909611yescharacteristic
365C2#135×D7311yescharacteristic
366C2C2×#1455661511yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×D8×C73C2
socleC22×C73C22×D4
hypercenterC4×D8D73
hypocenterC73#3106
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #17989134C2semidirect
2. C4×#11924027C2semidirect
3. #17988914C2semidirect
4. #17988910C2semidirect
5. #17988881C2semidirect
6. #17988875C2semidirect
7. #17988786C2semidirect
8. #17988780C2semidirect
9. #17988733C2semidirect
10. #17988729C2semidirect
11. C4×#11924017C2semidirect
12. C4×#11924016C2semidirect
13. C4×#11924013C2semidirect
14. #17988638C2semidirect
15. C4×D8×C73C2semidirect
116. D4×C73#41semidirect
146. Dic146#41semidirect
184. C73#3106semidirect
198. C4×D8D73semidirect
310. D4#11924028semidirect