Finite Group Databasebeta

← #22622254

Subgroups — #22622254

Order 9344.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989256C211yesmaximal, characteristic, complemented
2#17989238C211yesmaximal, characteristic, complemented
3#17988932C211yesmaximal, characteristic, complemented
4#17988905C211yesmaximal, characteristic, complemented
5#17988904C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988839C211yesmaximal, characteristic, complemented
9#17988781C211yesmaximal, characteristic, complemented
10#17988735C211yesmaximal, characteristic, complemented
11#17988732C211yesmaximal, characteristic, complemented
12#17988672C211yesmaximal, characteristic, complemented
13#17988663C211yesmaximal, characteristic, complemented
14#17988587C211yesmaximal, characteristic, complemented
15#417×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924028—21no—
18C2×#11924015C2211yescharacteristic
19C2×D584C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22#14556590C2211yescharacteristic
23#14556587—21no—
24#14556587C2211yescharacteristic
25#14556576—21no—
26#14556574—21no—
27#14556569—21no—
28#14556566C2211yescharacteristic
29#14556565—21no—
30#14556565C2211yescharacteristic
31#14556565C2211yescharacteristic
32#14556562—21no—
33#14556562C2211yescharacteristic
34Q8×Dic73C2211yescharacteristic
35#14556553C2211yescharacteristic
36C4×C22⋊D73—21no—
37C4×C22⋊D73C2211yescharacteristic
38C4⋊C4×D73C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924029—22no—
60#11924029—41no—
61#11924028—44no—
62C2×Dic146—21no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73D411yescharacteristic
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77#11924015—22no—
78D584—41no—
79#11924013—41no—
80#11924011—41no—
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C4⋊Dic73—21no—
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007D411yescharacteristic
89C22⋊Dic73—21no—
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005D411yescharacteristic
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98#41×C73—22no—
99#41×C73—41no—
100C2×Q8×C73C2311yescharacteristic
101C2×D4×C73—21no—
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73—21no—
104C22×C4×C73—21no—
105C22×C4×C73C2311yescharacteristic
106M16×C73—41no—
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73—21no—
110C4⋊C4×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73C2×D411yescharacteristic
117Q8×C73—21no—
118Q8×C73#4112yescomplemented
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—42no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—42no—
128C2×C4×C73—42no—
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—22no—
132C22⋊D73—42no—
133C22⋊D73—42no—
134C22⋊D73—81no—
135C22⋊D73—81no—
136C22⋊D73—81no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142D292—21no—
143D292—21no—
144D292—21no—
145D292—21no—
146D292—42no—
147D292—42no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—42no—
151C4×D73—42no—
152C4×D73—42no—
153Dic146—42no—
154C8×C73—21no—
155C8×C73—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C22×D411yescharacteristic
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C4×C73—22no—
175C4×C73—21no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73C2×#4111yescharacteristic
179C4×C73H(5,𝔽2)11yescharacteristic
180Dic73—21no—
181Dic73—21no—
182Dic73—41no—
183Dic73—41no—
184Dic73AGL(1,ℤ/8)12yes—
185C2×C73—41no—
186C2×C73—81no—
187C2×C73#54611yescharacteristic
188C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C73#57711yescharacteristic
190D73—41no—
191D73—81no—
192D73—81no—
193#3332—731nomaximal, Sylow
194C73#333211yescharacteristic, complemented, Sylow
195#550—731no—
196#547—731no—
197#486—731no—
198#481—731no—
199#481—731no—
200#475—731no—
201#469—731no—
202#469—731no—
203#459—731no—
204#449—731no—
205#449—731no—
206C4×SD16—731no—
207#436—731no—
208#417—731no—
209#417D7311yescharacteristic, complemented
210C2×#41—731no—
211C2×#41—1461no—
212C2×#41C2×D7311yescharacteristic
213C2×SD16—731no—
214C2×D8—731no—
215C2×D8—731no—
216C2×M16—731no—
217C2×M16C2×D7311yescharacteristic
218C4⋊Q8—731no—
219#127—731no—
220#127—1461no—
221#123—1461no—
222#123—1461no—
223C22⋊Q8—1461no—
224#121—731no—
225#121—731no—
226#121—731no—
227#121—731no—
228#121—1461no—
229#121—1461no—
230C4×Q8—731no—
231C4×D4—731no—
232C4×D4—731no—
233C4×D4—1461no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4C2×D7311yescharacteristic
236#106—731no—
237#106—731no—
238#106—731no—
239C4⋊C8—731no—
240#103—731no—
241#103C2×D7311yescharacteristic
242#103C2×D7311yescharacteristic
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102C2×D7311yescharacteristic
249#102C2×D7311yescharacteristic
250C22⋊C8—731no—
251C22⋊C8—731no—
252C4×C8—731no—
253#41—22no—
254#41—41no—
255#41—2924no—
256#41—2921no—
257#41—1462no—
258C2×Q8—1461no—
259C2×Q8C22×D7311yescharacteristic
260C2×D4—21no—
261C2×D4—731no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—1461no—
265C2×D4—1461no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4C22×D7311yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4C22×D7311yescharacteristic
279SD16—1462no—
280D8—2921no—
281D8—2921no—
282M16—41no—
283M16—2921no—
284C2×C8—731no—
285C2×C8—731no—
286C2×C8C22×D7311yescharacteristic
287C2×C8C22×D7311yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—731no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4C22×D7311yescharacteristic
296C4⋊C4C22×D7311yescharacteristic
297C22⋊C4—731no—
298C22⋊C4—731no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C42—731no—
305C42—1461no—
306C23—21no—
307C23—731no—
308C23—1461no—
309C23—1461no—
310C23D4×D7311yescharacteristic
311Q8—21no—
312Q8—2922no—
313Q8#1192402812yescomplemented
314D4—21no—
315D4—21no—
316D4—42no—
317D4—2922no—
318D4—2922no—
319D4—2922no—
320D4—2922no—
321D4—5841no—
322D4—5841no—
323D4—5841no—
324D4—1462no—
325D4—1461no—
326D4—1461no—
327D4—1461no—
328D4—1461no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—731no—
340C2×C4—731no—
341C2×C4—731no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4D4×D7311yescharacteristic
347C2×C4C23×D7311yescharacteristic
348C8—21no—
349C8—21no—
350C8—1461no—
351C8—1461no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—1461no—
365C22—1461no—
366C22—1461no—
367C22C2×D4×D7311yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—2921no—
373C4—2921no—
374C4—732no—
375C4—1461no—
376C4—1461no—
377C4C2×#1192402811yescharacteristic
378C4#1455663611yescharacteristic
379C2—41no—
380C2—81no—
381C2—2921no—
382C2—5841no—
383C2—5841no—
384C2#1798922711yescharacteristic
385C2AGL(1,ℤ/8)×D7311yescharacteristic
386C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3332
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989256C2semidirect
2. #17989238C2semidirect
3. #17988932C2semidirect
4. #17988905C2semidirect
5. #17988904C2semidirect
6. #17988870C2semidirect
7. #17988840C2semidirect
8. #17988839C2semidirect
9. #17988781C2semidirect
10. #17988735C2semidirect
11. #17988732C2semidirect
12. #17988672C2semidirect
13. #17988663C2semidirect
14. #17988587C2semidirect
15. #417×C73C2semidirect
118. Q8×C73#41semidirect
194. C73#3332semidirect
209. #417D73semidirect
313. Q8#11924028semidirect