Finite Group Databasebeta

← #22621939

Subgroups — #22621939

Order 9344.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989283C211yesmaximal, characteristic, complemented
2#17989258C211yesmaximal, characteristic, complemented
3#17988952C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988901C211yesmaximal, characteristic, complemented
6#17988895C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988823C211yesmaximal, characteristic, complemented
9#17988783C211yesmaximal, characteristic, complemented
10#17988734C211yesmaximal, characteristic, complemented
11#17988734C211yesmaximal, characteristic, complemented
12#17988689C211yesmaximal, characteristic, complemented
13#17988589C211yesmaximal, characteristic, complemented
14#17988584C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924028C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×D584C2211yescharacteristic
20C2×D584C2211yescharacteristic
21#14556588C2211yescharacteristic
22#14556587—21no—
23#14556586—21no—
24#14556583C2211yescharacteristic
25#14556573—21no—
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic
28#14556565C2211yescharacteristic
29#14556565C2211yescharacteristic
30#14556564—21no—
31#14556564—21no—
32#14556563—21no—
33C4×Dic146C2211yescharacteristic
34C4×D292C2211yescharacteristic
35#14556553—21no—
36#14556551—21no—
37#14556550C2211yescharacteristic
38C2×C4⋊Dic73C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—22no—
61#11924028—41no—
62#11924028—41no—
63C2×Dic146C2311yescharacteristic
64C2×D292—21no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C22×Dic73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79#11924017—22no—
80D584—41no—
81D584—41no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90C22⋊Dic73—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C2×D4×C73D411yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101M16×C73—41no—
102C2×C8×C73—41no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116D4×C73—41no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—42no—
127C22⋊D73—42no—
128C22⋊D73—42no—
129C22⋊D73—81no—
130C22⋊D73—81no—
131C22⋊D73—81no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—81no—
138D292—21no—
139D292—21no—
140D292—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—42no—
145D292—81no—
146C4×D73—42no—
147C4×D73—42no—
148C4×D73—81no—
149Dic146—21no—
150Dic146#4112yes—
151C8×C73—21no—
152C8×C73—21no—
153C8×C73—21no—
154C8×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73C22×D411yescharacteristic
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73C2×#4111yescharacteristic
176C4×C73H(5,𝔽2)11yescharacteristic
177Dic73—22no—
178Dic73—41no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182C2×C73—41no—
183C2×C73—41no—
184C2×C73#54611yescharacteristic
185C2×C73#57511yescharacteristic
186C2×C73#57611yescharacteristic
187D73—81no—
188D73—81no—
189D73—81no—
190#3309—731nomaximal, Sylow
191C73#330911yescharacteristic, complemented, Sylow
192#553—731no—
193#550—731no—
194#490—731no—
195#482—731no—
196#480—731no—
197#479—731no—
198#469—731no—
199#466—731no—
200#459—731no—
201#449—731no—
202#449—731no—
203#440—731no—
204#435D7311yescharacteristic, complemented
205#417—731no—
206#416—731no—
207C2×#41—731no—
208C2×#41—731no—
209C2×SD16—731no—
210C2×D8—731no—
211C2×D8—731no—
212C2×M16C2×D7311yescharacteristic
213C22×C8C2×D7311yescharacteristic
214#127—731no—
215#127—1461no—
216#126—1461no—
217#125—731no—
218#123—1461no—
219#121—731no—
220#121—731no—
221#121—731no—
222#121—731no—
223#121—1461no—
224#121—1461no—
225#121—1461no—
226C4×Q8—731no—
227C4×D4—731no—
228C4×D4—1461no—
229C4×D4—1461no—
230C4×D4C2×D7311yescharacteristic
231#117—731no—
232C2×C4⋊C4—731no—
233#107—731no—
234#107—731no—
235#106—731no—
236C4⋊C8C2×D7311yescharacteristic
237#103—731no—
238#103—731no—
239#103—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247C22⋊C8C2×D7311yescharacteristic
248C22⋊C8C2×D7311yescharacteristic
249#97C2×D7311yescharacteristic
250#41—2921no—
251#41—2921no—
252#41—1462no—
253#41—1462no—
254C2×Q8—731no—
255C2×D4—731no—
256C2×D4—731no—
257C2×D4—731no—
258C2×D4—1461no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4—1461no—
266C2×D4D29211yescharacteristic
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273SD16—1462no—
274D8—2921no—
275D8—2921no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D7311yescharacteristic
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C2×C8C22×D7311yescharacteristic
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—731no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C4⋊C4D29211yescharacteristic
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4D29211yescharacteristic
298C22⋊C4D29211yescharacteristic
299C42—1461no—
300C42—1461no—
301C42C22×D7311yescharacteristic
302C23—1461no—
303C23—1461no—
304C23—1461no—
305C23C2×D29211yescharacteristic
306C23C2×D29211yescharacteristic
307Q8—732no—
308Q8—1461no—
309D4—41no—
310D4—2922no—
311D4—2922no—
312D4—2922no—
313D4—2922no—
314D4—5841no—
315D4—5841no—
316D4—5841no—
317D4—5841no—
318D4—1461no—
319D4—1461no—
320D4—1461no—
321D4—1461no—
322D4—1461no—
323D4—1461no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2922no—
329C2×C4—2922no—
330C2×C4—5841no—
331C2×C4—5841no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4C2×D29211yescharacteristic
338C2×C4C2×D29211yescharacteristic
339C2×C4C2×D29211yescharacteristic
340C2×C4C2×D29211yescharacteristic
341C2×C4C23×D7311yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2921no—
353C22—2921no—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22C22×D29211yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—2921no—
367C4—2921no—
368C4—2921no—
369C4—2921no—
370C4—1462no—
371C4#41×D7311yescharacteristic
372C4#1455663611yescharacteristic
373C2—41no—
374C2—41no—
375C2—5841no—
376C2—5841no—
377C2—5841no—
378C2#1798923211yescharacteristic
379C2#1798938711yescharacteristic
380C2#1798939211yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3309
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17989283C2semidirect
2. #17989258C2semidirect
3. #17988952C2semidirect
4. #17988912C2semidirect
5. #17988901C2semidirect
6. #17988895C2semidirect
7. #17988840C2semidirect
8. #17988823C2semidirect
9. #17988783C2semidirect
10. #17988734C2semidirect
11. #17988734C2semidirect
12. #17988689C2semidirect
13. #17988589C2semidirect
14. #17988584C2semidirect
15. #435×C73C2semidirect
191. C73#3309semidirect
204. #435D73semidirect