Finite Group Databasebeta

← #22613413

Subgroups — #22613413

Order 9344.

560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556576C211yesmaximal, characteristic
2C2×C4×D292C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic, complemented
4#17988517C211yesmaximal, characteristic, complemented
5#17988516C211yesmaximal, characteristic, complemented
6#17988516C211yesmaximal, characteristic, complemented
7#17988471C211yesmaximal, characteristic, complemented
8#17988465C211yesmaximal, characteristic
9#17988458C211yesmaximal, characteristic, complemented
10#17988458C211yesmaximal, characteristic, complemented
11#17988449C211yesmaximal, characteristic, complemented
12#17988449C211yesmaximal, characteristic, complemented
13#17988446C211yesmaximal, characteristic, complemented
14#95×D73C211yesmaximal, characteristic, complemented
15#387×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21#14556576—24no—
22C4×D292—24no—
23C2×C4⋊Dic73C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C42×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C23×D73C2311yescharacteristic
55C2×D292—22no—
56C2×D292—22no—
57C2×D292D414yes—
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C2×C4×D73—22no—
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73—22no—
68C2×C4×D73—22no—
69C2×C4×D73—22no—
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C4⋊Dic73—22no—
77#11924007—22no—
78#11924007—22no—
79#11924007—41no—
80#11924007—41no—
81#11924005—22no—
82#11924005—22no—
83#11924005—22no—
84#11924005—22no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88#11924005—41no—
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C4⋊C4×C73—22no—
97C4⋊C4×C73—22no—
98C42×C73—22no—
99C23×C73C2411yescharacteristic
100C22×D73—21no—
101C22×D73—21no—
102C22×D73—21no—
103C22×D73—21no—
104C22×D73—21no—
105C22×D73—21no—
106C22×D73—21no—
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73C2×D412yes—
111C22×D73C2×D412yes—
112C22×D73#4112yes—
113C22×D73#4112yes—
114C2×C4×C73—21no—
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×C73—21no—
133C2×C4×C73C2×D412yes—
134C2×C4×C73#4112yes—
135C2×Dic73—21no—
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#4112yes—
153D292—28no—
154C4×D73—44no—
155C4×D73—44no—
156C4×D73—44no—
157C4×D73—44no—
158C22×C73C22×D411yescharacteristic
159C22×C73C2×#4111yescharacteristic
160C22×C73C2×#4111yescharacteristic
161C22×C73C2×#4111yescharacteristic
162C22×C73C2×#4111yescharacteristic
163C22×C73H(5,𝔽2)11yescharacteristic
164C22×C732−1+411yescharacteristic
165C2×D73—22no—
166C2×D73—22no—
167C2×D73—22no—
168C2×D73—22no—
169C2×D73—22no—
170C2×D73—22no—
171C2×D73—22no—
172C2×D73—22no—
173C2×D73—22no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—41no—
178C2×D73#12314yes—
179C4×C73—22no—
180C4×C73—22no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73—41no—
184C4×C73—41no—
185C4×C73—41no—
186Dic73—22no—
187Dic73—41no—
188Dic73—41no—
189Dic73—41no—
190Dic73—41no—
191Dic73—41no—
192C2×C73C2×#12311yescharacteristic
193C2×C73#52911yescharacteristic
194C2×C73#53911yescharacteristic
195C2×C73#54611yescharacteristic
196C2×C73#54711yescharacteristic
197C2×C73#55111yescharacteristic
198C2×C73#55211yescharacteristic
199D73—24no—
200D73—42no—
201#2419—731nomaximal, Sylow
202C73#241911yescharacteristic, complemented, Sylow
203C2×#123—731no—
204C2×C4×D4—731no—
205#400—731no—
206#398—731no—
207#397—731no—
208#397—731no—
209#387—731no—
210#387D7311yescharacteristic, complemented
211#386—731no—
212#385—731no—
213#385—731no—
214#381—731no—
215#381—731no—
216#380—731no—
217C2×#95—731no—
218C22×D4—731no—
219C23×C4—731no—
220C23×C4—731no—
221C23×C4—731no—
222C23×C4—731no—
223#123—1464no—
224C4×D4—1464no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4C2×D7311yescharacteristic
231C2×C4⋊C4C2×D7311yescharacteristic
232C2×C22⋊C4—731no—
233C2×C22⋊C4—731no—
234C2×C22⋊C4—731no—
235C2×C22⋊C4—731no—
236C2×C22⋊C4—731no—
237C2×C22⋊C4—731no—
238C2×C22⋊C4—731no—
239C2×C22⋊C4—731no—
240C2×C42C2×D7311yescharacteristic
241#95—731no—
242#95—731no—
243#95—731no—
244#95—731no—
245#95—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
254#95C2×D7311yescharacteristic
255C24—731no—
256C24—731no—
257C2×D4—734no—
258C2×D4—1462no—
259C2×D4—1462no—
260C22×C4—2921no—
261C22×C4—2921no—
262C22×C4—2921no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—1462no—
270C22×C4—1462no—
271C22×C4—1462no—
272C22×C4—1462no—
273C22×C4—1462no—
274C22×C4—1462no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4—1462no—
278C22×C4C22×D7311yescharacteristic
279C22×C4C22×D7311yescharacteristic
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—2921no—
288C4⋊C4—2921no—
289C4⋊C4—1462no—
290C4⋊C4—1462no—
291C4⋊C4—1462no—
292C22⋊C4—2921no—
293C22⋊C4—1462no—
294C22⋊C4—1462no—
295C22⋊C4—1462no—
296C22⋊C4—1462no—
297C22⋊C4—1462no—
298C22⋊C4—1462no—
299C22⋊C4—1462no—
300C42—22no—
301C23—732no—
302C23—732no—
303C23—732no—
304C23—732no—
305C23—1461no—
306C23—1461no—
307C23—1461no—
308C23—1461no—
309C23—1461no—
310C23—1461no—
311C23—1461no—
312C23—1461no—
313C23—1461no—
314C23—1461no—
315C23C23×D7311yescharacteristic
316D4—1468no—
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—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—2924no—
337C2×C4—2924no—
338C2×C4—2924no—
339C2×C4—2924no—
340C2×C4—732no—
341C2×C4—1461no—
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×C4—1461no—
358C2×C4D4×D7312yes—
359C2×C4#1192402812yes—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—734no—
365C22—1462no—
366C22—1462no—
367C22—1462no—
368C22—1462no—
369C22—1462no—
370C22—1462no—
371C22—1462no—
372C22—1462no—
373C22—1462no—
374C22C2×D4×D7311yescharacteristic
375C22#41×D7311yescharacteristic
376C22#41×D7311yescharacteristic
377C22#41×D7311yescharacteristic
378C22C2×#1192402811yescharacteristic
379C22#1455663711yescharacteristic
380C22#1455663911yescharacteristic
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—2921no—
389C4—2921no—
390C4—2921no—
391C4—2921no—
392C4—2921no—
393C4—1462no—
394C2—2922no—
395C2—1464no—
396C2#123×D7311yescharacteristic
397C2#1798911511yescharacteristic
398C2#1798918511yescharacteristic
399C2#1798923311yescharacteristic
400C2#1798923911yescharacteristic
401C2#1798926211yescharacteristic
402C2#1798927811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#387×C73C2
hypercenter#387D73
hypocenterC73#2419
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. #17988527C2semidirect
4. #17988517C2semidirect
5. #17988516C2semidirect
6. #17988516C2semidirect
7. #17988471C2semidirect
9. #17988458C2semidirect
10. #17988458C2semidirect
11. #17988449C2semidirect
12. #17988449C2semidirect
13. #17988446C2semidirect
14. #95×D73C2semidirect
15. #387×C73C2semidirect
202. C73#2419semidirect
210. #387D73semidirect