Finite Group Databasebeta

← #22613628

Subgroups — #22613628

Order 9344.

608 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556571C211yesmaximal, characteristic
3C2×#14556569C211yesmaximal, characteristic
4C2×C4⋊C4×D73C211yesmaximal, characteristic
5#17988519C211yesmaximal, characteristic, complemented
6#17988508C211yesmaximal, characteristic, complemented
7#17988507C211yesmaximal, characteristic, complemented
8#17988484C211yesmaximal, characteristic, complemented
9#17988482C211yesmaximal, characteristic, complemented
10#17988461C211yesmaximal, characteristic
11#17988458C211yesmaximal, characteristic
12#17988456C211yesmaximal, characteristic, complemented
13#17988446C211yesmaximal, characteristic
14#17988434C211yesmaximal, characteristic
15#398×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21#14556590—24no—
22#14556571—24no—
23#14556569—24no—
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×C4⋊Dic73C2211yescharacteristic
27C2×C4⋊Dic73C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×#11924007C2211yescharacteristic
33C2×#11924007C2211yescharacteristic
34C2×#11924007C2211yescharacteristic
35C2×#11924007C2211yescharacteristic
36C4⋊C4×D73—24no—
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C2×C4×Dic73C2211yescharacteristic
42C2×C4×Dic73C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47#14556498C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C4⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53#95×C73C2211yescharacteristic
54#95×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C2×Dic146—22no—
57C2×Dic146—22no—
58C2×Dic146—22no—
59C2×Dic146—22no—
60C2×Dic146—41no—
61C2×Dic146—41no—
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C2×C4×D73—22no—
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73Q814yescomplemented
78C4⋊Dic73—22no—
79C4⋊Dic73—22no—
80C4⋊Dic73—22no—
81C4⋊Dic73—22no—
82#11924007—22no—
83#11924007—22no—
84#11924007—22no—
85#11924007—22no—
86#11924007—22no—
87#11924007—41no—
88#11924007—41no—
89#11924007D414yes—
90#11924005—22no—
91#11924005—22no—
92#11924005D414yes—
93#11924005Q814yescomplemented
94C4×Dic73—22no—
95C4×Dic73—22no—
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C4⋊C4×C73—22no—
104C4⋊C4×C73—22no—
105C4⋊C4×C73—22no—
106C4⋊C4×C73—22no—
107C23×C73C2411yescharacteristic
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C22×D73C2×D412yes—
113C22×D73C2×Q812yes—
114C22×D73C2×Q812yes—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
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—21no—
131C2×C4×C73—21no—
132C2×C4×C73C2×D412yes—
133C2×C4×C73C2×D412yes—
134C2×C4×C73C2×Q812yes—
135C2×C4×C73C2×Q812yes—
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×Dic73C2×D412yes—
152C2×Dic73C2×D412yes—
153C2×Dic73C2×D412yes—
154C2×Dic73C2×Q812yes—
155C2×Dic73C2×Q812yes—
156C2×Dic73#4112yes—
157C4×D73—28no—
158C4×D73—44no—
159C4×D73—44no—
160Dic146—44no—
161Dic146—44no—
162C22×C73C22×D411yescharacteristic
163C22×C73C22×D411yescharacteristic
164C22×C73C22×Q811yescharacteristic
165C22×C73C22×Q811yescharacteristic
166C22×C73C2×#4111yescharacteristic
167C22×C73H(5,𝔽2)11yescharacteristic
168C22×C732−1+411yescharacteristic
169C2×D73—22no—
170C2×D73—22no—
171C2×D73—22no—
172C2×D73—22no—
173C2×D73—22no—
174C2×D73—22no—
175C2×D73C4⋊Q814yescomplemented
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73—41no—
183Dic73—22no—
184Dic73—22no—
185Dic73—22no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189Dic73C22⋊Q814yescomplemented
190C2×C73C2×C22⋊Q811yescharacteristic
191C2×C73C2×C4⋊Q811yescharacteristic
192C2×C73#54411yescharacteristic
193C2×C73D4211yescharacteristic
194C2×C73#54711yescharacteristic
195C2×C73D4×Q811yescharacteristic
196C2×C73#55411yescharacteristic
197D73—24no—
198#2440—731nomaximal, Sylow
199C73#244011yescharacteristic, complemented, Sylow
200C2×C4⋊Q8—731no—
201C2×C22⋊Q8—731no—
202C2×C22⋊Q8—731no—
203C22×C4⋊C4—731no—
204#398—731no—
205#398D7311yescharacteristic, complemented
206#395—731no—
207#395—731no—
208#389—731no—
209#389—731no—
210#385—731no—
211#385—731no—
212#384—731no—
213#380—731no—
214C4×C22⋊C4—731no—
215C22×Q8—731no—
216C22×Q8—731no—
217C23×C4—731no—
218C23×C4—731no—
219C23×C4—731no—
220C4⋊Q8—1464no—
221C22⋊Q8—1464no—
222C22⋊Q8—1464no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—1464no—
236C2×C4⋊C4C2×D7311yescharacteristic
237C2×C4⋊C4C2×D7311yescharacteristic
238C2×C4⋊C4C2×D7311yescharacteristic
239C2×C4⋊C4C2×D7311yescharacteristic
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C42—731no—
245C2×C42—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95—731no—
250#95—731no—
251#95C2×D7311yescharacteristic
252#95C2×D7311yescharacteristic
253#95C2×D7311yescharacteristic
254C24—731no—
255C2×Q8—2921no—
256C2×Q8—2921no—
257C2×Q8—1462no—
258C2×Q8—1462no—
259C2×Q8—1462no—
260C2×Q8—1462no—
261C22×C4—2921no—
262C22×C4—2921no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—734no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—1462no—
272C22×C4—1462no—
273C22×C4—1462no—
274C22×C4—1462no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4C22×D7311yescharacteristic
278C22×C4C22×D7311yescharacteristic
279C22×C4C22×D7311yescharacteristic
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283C22×C4C22×D7311yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—2921no—
289C4⋊C4—2921no—
290C4⋊C4—734no—
291C4⋊C4—1462no—
292C4⋊C4—1462no—
293C4⋊C4—1462no—
294C4⋊C4—1462no—
295C4⋊C4—1462no—
296C4⋊C4—1462no—
297C4⋊C4—1462no—
298C4⋊C4—1462no—
299C4⋊C4—1462no—
300C22⋊C4—734no—
301C22⋊C4—734no—
302C22⋊C4—1462no—
303C22⋊C4—1462no—
304C42—1462no—
305C42—1462no—
306C23—732no—
307C23—732no—
308C23—732no—
309C23—1461no—
310C23—1461no—
311C23—1461no—
312C23—1461no—
313C23C23×D7311yescharacteristic
314Q8—2924no—
315Q8—2924no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—2924no—
334C2×C4—2924no—
335C2×C4—732no—
336C2×C4—732no—
337C2×C4—732no—
338C2×C4—732no—
339C2×C4—732no—
340C2×C4—732no—
341C2×C4—1468no—
342C2×C4—1461no—
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×C4D4×D7312yes—
358C2×C4D4×D7312yes—
359C2×C4Q8×D7312yes—
360C2×C4Q8×D7312yes—
361C22—734no—
362C22—1462no—
363C22—1462no—
364C22—1462no—
365C22—1462no—
366C22—1462no—
367C22—1462no—
368C22C2×D4×D7311yescharacteristic
369C22C2×D4×D7311yescharacteristic
370C22C2×Q8×D7311yescharacteristic
371C22C2×Q8×D7311yescharacteristic
372C22#41×D7311yescharacteristic
373C22#1455663711yescharacteristic
374C22#1455663811yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2921no—
383C4—2921no—
384C4—2921no—
385C4—734no—
386C4—1462no—
387C4—1462no—
388C4—1462no—
389C2—1464no—
390C2C22⋊Q8×D7311yescharacteristic
391C2C4⋊Q8×D7311yescharacteristic
392C2#1798921711yescharacteristic
393C2#1798922111yescharacteristic
394C2#1798923511yescharacteristic
395C2#1798925011yescharacteristic
396C2#1798929311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2440
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
5. #17988519C2semidirect
6. #17988508C2semidirect
7. #17988507C2semidirect
8. #17988484C2semidirect
9. #17988482C2semidirect
12. #17988456C2semidirect
15. #398×C73C2semidirect
77. C2×C4×D73Q8semidirect
93. #11924005Q8semidirect
175. C2×D73C4⋊Q8semidirect
189. Dic73C22⋊Q8semidirect
199. C73#2440semidirect
205. #398D73semidirect