Finite Group Databasebeta

← #22614939

Subgroups — #22614939

Order 9344.

544 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556568C211yesmaximal, characteristic
2#17988518C211yesmaximal, characteristic, complemented
3#17988517C211yesmaximal, characteristic, complemented
4#17988507C211yesmaximal, characteristic, complemented
5#17988506C211yesmaximal, characteristic, complemented
6#17988494C211yesmaximal, characteristic, complemented
7#17988492C211yesmaximal, characteristic, complemented
8#17988482C211yesmaximal, characteristic, complemented
9#17988482C211yesmaximal, characteristic, complemented
10#17988460C211yesmaximal, characteristic
11#17988459C211yesmaximal, characteristic
12#17988445C211yesmaximal, characteristic
13C22⋊C4×Dic73C211yesmaximal, characteristic
14C2×#14556498C211yesmaximal, characteristic
15C2×C22⋊Q8×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19#14556568—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C4×Dic73C2211yescharacteristic
32C2×C4×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×Q8×C73C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C22⋊Q8×C73—24no—
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146—41no—
56C22×Dic73—22no—
57C22×Dic73—22no—
58C22×Dic73—41no—
59C22×Dic73—41no—
60C22×Dic73—41no—
61C22×Dic73Q814yescomplemented
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C4⋊Dic73—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—22no—
74#11924007—22no—
75#11924007—41no—
76#11924007—41no—
77#11924007—41no—
78#11924007—41no—
79C22⋊Dic73—22no—
80C22⋊Dic73Q814yescomplemented
81C4×Dic73—41no—
82C4×Dic73—41no—
83C24×C73C2311yescharacteristic
84C2×Q8×C73—22no—
85C2×Q8×C73—22no—
86C2×Q8×C73—41no—
87C22×C4×C73—22no—
88C22×C4×C73—22no—
89C22×C4×C73—41no—
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—
98C4⋊C4×C73—22no—
99C22⋊C4×C73—22no—
100C22⋊C4×C73D414yes—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73C2×D412yes—
106C23×C73C2×Q812yes—
107C23×C73C2×Q812yes—
108C23×C73C2411yescharacteristic
109Q8×C73—44no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
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—44no—
126C2×C4×C73C2×D412yes—
127C2×C4×C73C2×D412yes—
128C2×C4×C73#4112yes—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
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—44no—
149C2×Dic73—44no—
150C2×Dic73C2×Q812yes—
151C2×Dic73C2×Q812yes—
152C2×Dic73C2×Q812yes—
153C2×Dic73C2×Q812yes—
154C2×Dic73#4112yes—
155Dic146—44no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73—22no—
161C22×C73—22no—
162C22×C73C4⋊Q814yes—
163C22×C73C22×D411yescharacteristic
164C22×C73C22×Q811yescharacteristic
165C22×C73C22×Q811yescharacteristic
166C22×C73C2×#4111yescharacteristic
167C22×C73C2×#4111yescharacteristic
168C22×C73H(5,𝔽2)11yescharacteristic
169C22×C73H(5,𝔽2)11yescharacteristic
170C4×C73—22no—
171C4×C73—22no—
172C4×C73—22no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176Dic73—22no—
177Dic73—22no—
178Dic73—22no—
179Dic73—22no—
180Dic73—22no—
181Dic73—41no—
182Dic73—41no—
183Dic73—41no—
184C2×C73—24no—
185C2×C73C2×C4⋊Q811yescharacteristic
186C2×C73#53311yescharacteristic
187C2×C73#54311yescharacteristic
188C2×C73#54611yescharacteristic
189C2×C73#54611yescharacteristic
190C2×C73#55411yescharacteristic
191C2×C73#55411yescharacteristic
192#2549—731nomaximal, Sylow
193C73#254911yescharacteristic, complemented, Sylow
194C2×C22⋊Q8—731no—
195C2×C22⋊Q8D7311yescharacteristic
196#398—731no—
197#398—731no—
198#395—731no—
199#395—731no—
200#391—731no—
201#391—731no—
202#389—731no—
203#389—731no—
204#385—731no—
205#385—731no—
206#380—731no—
207C4×C22⋊C4—731no—
208C2×#95—731no—
209C22×Q8—731no—
210C22×Q8C2×D7311yescharacteristic
211C23×C4—731no—
212C23×C4—731no—
213C23×C4C2×D7311yescharacteristic
214C22⋊Q8—24no—
215C22⋊Q8—1464no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4C2×D7311yescharacteristic
226C2×C4⋊C4C2×D7311yescharacteristic
227C2×C4⋊C4C2×D7311yescharacteristic
228C2×C22⋊C4—731no—
229C2×C22⋊C4—731no—
230C2×C22⋊C4C2×D7311yescharacteristic
231C2×C22⋊C4C2×D7311yescharacteristic
232C2×C42—731no—
233C2×C42—731no—
234#95—731no—
235#95—731no—
236#95—731no—
237#95—731no—
238#95—731no—
239#95—731no—
240#95—731no—
241#95—731no—
242#95—731no—
243#95—731no—
244#95—731no—
245#95—731no—
246C24C22×D7311yescharacteristic
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—2921no—
251C2×Q8—1462no—
252C2×Q8—1462no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—2921no—
257C22×C4—2921no—
258C22×C4—2921no—
259C22×C4—734no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—1462no—
269C22×C4—1462no—
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274C22×C4C22×D7311yescharacteristic
275C22×C4C22×D7311yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—2921no—
280C4⋊C4—2921no—
281C4⋊C4—2921no—
282C4⋊C4—2921no—
283C4⋊C4—1462no—
284C4⋊C4—1462no—
285C4⋊C4—1462no—
286C4⋊C4—1462no—
287C4⋊C4—1462no—
288C22⋊C4—22no—
289C22⋊C4—734no—
290C22⋊C4—1462no—
291C22⋊C4C22⋊D7314yes—
292C42—2921no—
293C42—2921no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23C2×C22⋊D7312yes—
299C23Q8×D7312yes—
300C23Q8×D7312yes—
301C23C23×D7311yescharacteristic
302Q8—44no—
303Q8—2924no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—2924no—
321C2×C4—2924no—
322C2×C4—732no—
323C2×C4—732no—
324C2×C4—732no—
325C2×C4—732no—
326C2×C4—732no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4C2×C22⋊D7312yes—
347C2×C4C2×C22⋊D7312yes—
348C2×C4#1192402712yes—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22#1455658914yes—
356C22C22×C22⋊D7311yescharacteristic
357C22C2×Q8×D7311yescharacteristic
358C22C2×Q8×D7311yescharacteristic
359C22#41×D7311yescharacteristic
360C22C2×#1192402711yescharacteristic
361C22#1455663611yescharacteristic
362C22#1455663711yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2921no—
370C4—2921no—
371C4—2921no—
372C4—1462no—
373C4—1462no—
374C4—1462no—
375C4—1462no—
376C4—1462no—
377C2—24no—
378C2C2×#1455658911yescharacteristic
379C2#1798913911yescharacteristic
380C2#1798921211yescharacteristic
381C2#1798922511yescharacteristic
382C2#1798923111yescharacteristic
383C2#1798929111yescharacteristic
384C2#1798929511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C22⋊Q8×C73C2
hypercenterC2×C22⋊Q8D73
hypocenterC73#2549
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988518C2semidirect
3. #17988517C2semidirect
4. #17988507C2semidirect
5. #17988506C2semidirect
6. #17988494C2semidirect
7. #17988492C2semidirect
8. #17988482C2semidirect
9. #17988482C2semidirect
61. C22×Dic73Q8semidirect
80. C22⋊Dic73Q8semidirect
193. C73#2549semidirect