Finite Group Databasebeta

← #22622519

Subgroups — #22622519

Order 9344.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989301C211yesmaximal, characteristic, complemented
2#17989238C211yesmaximal, characteristic, complemented
3#17988984C211yesmaximal, characteristic, complemented
4#17988913C211yesmaximal, characteristic, complemented
5#17988912C211yesmaximal, characteristic, complemented
6#17988904C211yesmaximal, characteristic, complemented
7#17988876C211yesmaximal, characteristic, complemented
8#17988865C211yesmaximal, characteristic, complemented
9#17988839C211yesmaximal, characteristic, complemented
10#17988838C211yesmaximal, characteristic, complemented
11#17988667C211yesmaximal, characteristic, complemented
12#17988662C211yesmaximal, characteristic, complemented
13#17988627C211yesmaximal, characteristic, complemented
14#17988626C211yesmaximal, characteristic, complemented
15#481×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924013C2211yescharacteristic
18C2×#11924012C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556578—21no—
23#14556577—21no—
24#14556576—21no—
25#14556574—21no—
26#14556569—21no—
27#14556566C2211yescharacteristic
28#14556565C2211yescharacteristic
29#14556563—21no—
30#14556562C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556550C2211yescharacteristic
35#14556549C2211yescharacteristic
36#14556547—21no—
37C4⋊C4×D73C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556522C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#121×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54#106×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73D411yescharacteristic
67C22×Dic73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924013—22no—
72#11924012—22no—
73#11924011—22no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007D411yescharacteristic
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73D411yescharacteristic
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×D4×C73—21no—
96C2×D4×C73C2311yescharacteristic
97C22×C4×C73—21no—
98C22×C4×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C23×C73—21no—
107C23×C73C2×D411yescharacteristic
108C22×D73—21no—
109C22×D73C2×D411yescharacteristic
110D4×C73—21no—
111D4×C73—21no—
112D4×C73—81no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—42no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—22no—
122C22⋊D73—42no—
123C22⋊D73—81no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—42no—
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131D292—21no—
132D292—21no—
133D292—42no—
134C4×D73—21no—
135C4×D73—21no—
136C4×D73—42no—
137C4×D73—42no—
138Dic146—42no—
139Dic146—81no—
140C8×C73—21no—
141C8×C73—21no—
142#10596831—21no—
143#10596831#4112yescomplemented
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73C22×D411yescharacteristic
151C2×D73—21no—
152C2×D73—21no—
153C2×D73—21no—
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C4×C73—21no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73C2×#4111yescharacteristic
162C4×C732−1+411yescharacteristic
163Dic73—21no—
164Dic73—21no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73AGL(1,ℤ/8)12yes—
169C2×C73—41no—
170C2×C73—81no—
171C2×C73#54711yescharacteristic
172C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C73#57711yescharacteristic
174D73—41no—
175D73—81no—
176#3354—731nomaximal, Sylow
177C73#335411yescharacteristic, complemented, Sylow
178#555—731no—
179#547—731no—
180#498—731no—
181#482—731no—
182#482—731no—
183#481—731no—
184#481D7311yescharacteristic, complemented
185#476—731no—
186#474—731no—
187#469—731no—
188#469—731no—
189C4×D8—731no—
190#436—731no—
191#428—731no—
192#428—731no—
193C2×#41—1461no—
194C2×D8—731no—
195C2×M16—731no—
196C2×M16—731no—
197C4⋊Q8—731no—
198C4⋊Q8—731no—
199#124—1461no—
200#124—1461no—
201#123—1461no—
202#123—1461no—
203C22⋊Q8—1461no—
204#121—731no—
205#121—731no—
206#121—731no—
207#121—1461no—
208#121C2×D7311yescharacteristic
209C4×D4—731no—
210C4×D4—731no—
211C4×D4—731no—
212#117—731no—
213#117—731no—
214#117—1461no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4C2×D7311yescharacteristic
217#107—731no—
218#107—731no—
219#107—731no—
220#106—731no—
221#106—731no—
222#106—731no—
223#106—731no—
224#106C2×D7311yescharacteristic
225#106C2×D7311yescharacteristic
226C4⋊C8—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102C2×D7311yescharacteristic
232#102C2×D7311yescharacteristic
233C22⋊C8—731no—
234C22⋊C8C2×D7311yescharacteristic
235C4×C8—731no—
236#41—2924no—
237C2×Q8—1461no—
238C2×Q8—1461no—
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—731no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4C22×D7311yescharacteristic
246C22×C4—21no—
247C22×C4—731no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4C22×D7311yescharacteristic
252D8—1462no—
253M16—1462no—
254M16—1462no—
255C2×C8—731no—
256C2×C8—731no—
257C2×C8C22×D7311yescharacteristic
258C2×C8C22×D7311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4C22×D7311yescharacteristic
268C4⋊C4C22×D7311yescharacteristic
269C4⋊C4C22×D7311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C42—731no—
281C42—1461no—
282C42—1461no—
283C23—21no—
284C23—731no—
285C23—1461no—
286C23D4×D7311yescharacteristic
287Q8—2922no—
288Q8—5841no—
289D4—21no—
290D4—21no—
291D4—81no—
292D4—2922no—
293D4—2922no—
294D4—5841no—
295D4—1462no—
296D4—1461no—
297D4—1461no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—2922no—
305C2×C4—2922no—
306C2×C4—2922no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4D4×D7311yescharacteristic
316C2×C4C23×D7311yescharacteristic
317C8—21no—
318C8—21no—
319C8—732no—
320C8—1461no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—2921no—
328C22—2921no—
329C22—2921no—
330C22—1461no—
331C22—1461no—
332C22—1461no—
333C22C2×D4×D7311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2921no—
339C4—2921no—
340C4—2921no—
341C4—732no—
342C4—1461no—
343C4—1461no—
344C4#41×D7311yescharacteristic
345C4#1455663811yescharacteristic
346C2—41no—
347C2—81no—
348C2—2921no—
349C2—5841no—
350C2#1798923511yescharacteristic
351C2AGL(1,ℤ/8)×D7311yescharacteristic
352C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#481×C73C2
socleC22×C73C22×D4
hypercenter#481D73
hypocenterC73#3354
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #17989301C2semidirect
2. #17989238C2semidirect
3. #17988984C2semidirect
4. #17988913C2semidirect
5. #17988912C2semidirect
6. #17988904C2semidirect
7. #17988876C2semidirect
8. #17988865C2semidirect
9. #17988839C2semidirect
10. #17988838C2semidirect
11. #17988667C2semidirect
12. #17988662C2semidirect
13. #17988627C2semidirect
14. #17988626C2semidirect
15. #481×C73C2semidirect
143. #10596831#41semidirect
177. C73#3354semidirect
184. #481D73semidirect