Finite Group Databasebeta

← #22613749

Subgroups — #22613749

Order 9344.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556568C211yesmaximal, characteristic, complemented
2#17988526C211yesmaximal, characteristic, complemented
3#17988520C211yesmaximal, characteristic, complemented
4#17988510C211yesmaximal, characteristic, complemented
5#17988499C211yesmaximal, characteristic, complemented
6#17988493C211yesmaximal, characteristic, complemented
7#17988471C211yesmaximal, characteristic, complemented
8#17988467C211yesmaximal, characteristic
9#17988467C211yesmaximal, characteristic
10#17988462C211yesmaximal, characteristic, complemented
11#17988460C211yesmaximal, characteristic, complemented
12#17988460C211yesmaximal, characteristic, complemented
13#17988447C211yesmaximal, characteristic, complemented
14C2×#14556498C211yesmaximal, characteristic, complemented
15C2×C4×D4×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19#14556568—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C22×D4×C73C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C23×C4×C73C2211yescharacteristic
48C4×D4×C73—24no—
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146—41no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58C22×Dic73—22no—
59C22×Dic73—41no—
60C22×Dic73—41no—
61C22×Dic73—41no—
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C4⋊Dic73—22no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73#11924007—22no—
74#11924007—22no—
75#11924007—22no—
76#11924007—41no—
77C22⋊Dic73—22no—
78C22⋊Dic73—22no—
79C22⋊Dic73—22no—
80C22⋊Dic73—41no—
81C22⋊Dic73—41no—
82C22⋊Dic73—41no—
83C24×C73C2311yescharacteristic
84C24×C73C2311yescharacteristic
85C2×D4×C73—22no—
86C2×D4×C73—22no—
87C2×D4×C73Q814yescomplemented
88C22×C4×C73—22no—
89C22×C4×C73—22no—
90C22×C4×C73—22no—
91C22×C4×C73—22no—
92C22×C4×C73—41no—
93C22×C4×C73—41no—
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—22no—
100C22⋊C4×C73—22no—
101C22⋊C4×C73D414yes—
102C42×C73—22no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73C2×D412yes—
114C23×C73C2×Q812yes—
115C23×C73C2×Q812yes—
116C23×C73#4112yes—
117C23×C73C2411yescharacteristic
118D4×C73—28no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—44no—
131C2×C4×C73—44no—
132C2×C4×C73C2×D412yes—
133C2×C4×C73C2×D412yes—
134C2×C4×C73C2×Q812yes—
135C2×C4×C73#4112yes—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—44no—
160C2×Dic73—44no—
161C2×Dic73#4112yes—
162Dic146—44no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—22no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73—22no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73C22⋊Q814yes—
177C22×C73C22×D411yescharacteristic
178C22×C73C22×Q811yescharacteristic
179C22×C73C2×#4111yescharacteristic
180C22×C73C2×#4111yescharacteristic
181C22×C73C2×#4111yescharacteristic
182C22×C73H(5,𝔽2)11yescharacteristic
183C22×C73H(5,𝔽2)11yescharacteristic
184C4×C73—22no—
185C4×C73—22no—
186C4×C73—22no—
187C4×C73—22no—
188C4×C73—41no—
189Dic73—22no—
190Dic73—41no—
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194Dic73—41no—
195Dic73—41no—
196Dic73—41no—
197C2×C73—24no—
198C2×C73—42no—
199C2×C73C2×C22⋊Q811yescharacteristic
200C2×C73#52911yescharacteristic
201C2×C73#53811yescharacteristic
202C2×C73#54611yescharacteristic
203C2×C73#54611yescharacteristic
204C2×C73#55411yescharacteristic
205C2×C73#55411yescharacteristic
206#2450—731nomaximal, Sylow
207C73#245011yescharacteristic, complemented, Sylow
208C2×C22⋊Q8—731no—
209C2×C4×D4D7311yescharacteristic
210#400—731no—
211#398—731no—
212#396—731no—
213#393—731no—
214#391—731no—
215#387—731no—
216#386—731no—
217#386—731no—
218#385—731no—
219#385—731no—
220#385—731no—
221#380—731no—
222C2×#95—731no—
223C22×Q8—731no—
224C22×D4C2×D7311yescharacteristic
225C23×C4—731no—
226C23×C4—731no—
227C23×C4C2×D7311yescharacteristic
228C23×C4C2×D7311yescharacteristic
229C22⋊Q8—1464no—
230C4×D4—24no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4—731no—
238C2×C4⋊C4C2×D7311yescharacteristic
239C2×C22⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4C2×D7311yescharacteristic
246C2×C22⋊C4C2×D7311yescharacteristic
247C2×C42C2×D7311yescharacteristic
248#95—731no—
249#95—731no—
250#95—731no—
251#95—731no—
252#95—731no—
253#95—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95—731no—
258#95—731no—
259#95—731no—
260C24C22×D7311yescharacteristic
261C24C22×D7311yescharacteristic
262C2×Q8—2921no—
263C2×Q8—1462no—
264C2×Q8—1462no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4Dic14614yescomplemented
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—2921no—
275C22×C4—2921no—
276C22×C4—2921no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4—1462no—
286C22×C4—1462no—
287C22×C4—1462no—
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290C22×C4C22×D7311yescharacteristic
291C22×C4C22×D7311yescharacteristic
292C22×C4C22×D7311yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—2921no—
295C4⋊C4—2921no—
296C4⋊C4—2921no—
297C4⋊C4—1462no—
298C4⋊C4—1462no—
299C4⋊C4—1462no—
300C4⋊C4—1462no—
301C22⋊C4—22no—
302C22⋊C4—2921no—
303C22⋊C4—2921no—
304C22⋊C4—2921no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C22⋊C4C22⋊D7314yes—
309C42—22no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×C22⋊D7312yes—
321C23C2×Dic14612yes—
322C23C2×Dic14612yes—
323C23#1192402812yes—
324C23C23×D7311yescharacteristic
325Q8—2924no—
326D4—28no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—2924no—
341C2×C4—2924no—
342C2×C4—732no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4C2×C22⋊D7312yes—
367C2×C4C2×C22⋊D7312yes—
368C2×C4C2×Dic14612yes—
369C2×C4#1192402712yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22#1455657014yes—
384C22C22×C22⋊D7311yescharacteristic
385C22C22×Dic14611yescharacteristic
386C22#41×D7311yescharacteristic
387C22C2×#1192402711yescharacteristic
388C22C2×#1192402811yescharacteristic
389C22#1455663611yescharacteristic
390C22#1455663711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—2921no—
397C4—2921no—
398C4—2921no—
399C4—2921no—
400C4—2921no—
401C4—2921no—
402C4—2921no—
403C4—1462no—
404C2—24no—
405C2—42no—
406C2C2×#1455657011yescharacteristic
407C2#1798911711yescharacteristic
408C2#1798917011yescharacteristic
409C2#1798922511yescharacteristic
410C2#1798923111yescharacteristic
411C2#1798929411yescharacteristic
412C2#1798929611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C4×D4×C73C2
hypercenterC2×C4×D4D73
hypocenterC73#2450
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14556568C2semidirect
2. #17988526C2semidirect
3. #17988520C2semidirect
4. #17988510C2semidirect
5. #17988499C2semidirect
6. #17988493C2semidirect
7. #17988471C2semidirect
10. #17988462C2semidirect
11. #17988460C2semidirect
12. #17988460C2semidirect
13. #17988447C2semidirect
14. C2×#14556498C2semidirect
87. C2×D4×C73Q8semidirect
207. C73#2450semidirect
267. C2×D4Dic146semidirect