Finite Group Databasebeta

← #22614940

Subgroups — #22614940

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×#14556569C211yesmaximal, characteristic
2C2×#14556567C211yesmaximal, characteristic
3#17988521C211yesmaximal, characteristic, complemented
4#17988518C211yesmaximal, characteristic, complemented
5#17988508C211yesmaximal, characteristic, complemented
6#17988506C211yesmaximal, characteristic, complemented
7#17988491C211yesmaximal, characteristic, complemented
8#17988485C211yesmaximal, characteristic, complemented
9#17988484C211yesmaximal, characteristic, complemented
10#17988461C211yesmaximal, characteristic
11#17988461C211yesmaximal, characteristic
12#17988446C211yesmaximal, characteristic
13C4×#11924005C211yesmaximal, characteristic
14#95×D73C211yesmaximal, characteristic
15#391×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556569—24no—
21#14556567—24no—
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×#11924007C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C22×Q8×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C42×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×Dic146—22no—
55C2×Dic146—22no—
56C2×Dic146—41no—
57C22×Dic73C2311yescharacteristic
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—41no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73Q814yescomplemented
73C4⋊Dic73—22no—
74C4⋊Dic73—22no—
75C4⋊Dic73—41no—
76#11924007—22no—
77#11924007—22no—
78#11924007—22no—
79#11924007—22no—
80#11924007—22no—
81#11924007—41no—
82#11924007—41no—
83#11924007—41no—
84#11924005—22no—
85#11924005—22no—
86#11924005D414yes—
87#11924005Q814yescomplemented
88C4×Dic73—41no—
89C2×Q8×C73—22no—
90C2×Q8×C73—22no—
91C2×Q8×C73—41no—
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—22no—
100C42×C73—41no—
101C23×C73C2411yescharacteristic
102C22×D73—21no—
103C22×D73—21no—
104C22×D73—21no—
105C22×D73—21no—
106C22×D73C2×D412yes—
107C22×D73C2×Q812yes—
108C22×D73C2×Q812yes—
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—21no—
126C2×C4×C73—21no—
127C2×C4×C73C2×D412yes—
128C2×C4×C73C2×Q812yes—
129C2×C4×C73C2×Q812yes—
130C2×C4×C73#4112yes—
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×Dic73C2×D412yes—
149C2×Dic73C2×Q812yes—
150C2×Dic73C2×Q812yes—
151C2×Dic73#4112yes—
152C4×D73—44no—
153C4×D73—44no—
154C4×D73—44no—
155Dic146—44no—
156C22×C73C22×D411yescharacteristic
157C22×C73C22×Q811yescharacteristic
158C22×C73C22×Q811yescharacteristic
159C22×C73C2×#4111yescharacteristic
160C22×C73C2×#4111yescharacteristic
161C22×C73H(5,𝔽2)11yescharacteristic
162C22×C73H(5,𝔽2)11yescharacteristic
163C2×D73—22no—
164C2×D73—22no—
165C2×D73—22no—
166C2×D73—22no—
167C2×D73—22no—
168C2×D73—22no—
169C2×D73C4⋊Q814yes—
170C4×C73—22no—
171C4×C73—22no—
172C4×C73—22no—
173C4×C73—22no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73—41no—
177Dic73—22no—
178Dic73—22no—
179Dic73—22no—
180Dic73—22no—
181Dic73—41no—
182Dic73—41no—
183Dic73—41no—
184C2×C73C2×C4⋊Q811yescharacteristic
185C2×C73#53311yescharacteristic
186C2×C73#54311yescharacteristic
187C2×C73#54611yescharacteristic
188C2×C73#54611yescharacteristic
189C2×C73#55411yescharacteristic
190C2×C73#55411yescharacteristic
191D73—24no—
192#2549—731nomaximal, Sylow
193C73#254911yescharacteristic, complemented, Sylow
194C2×C22⋊Q8—731no—
195C2×C22⋊Q8—731no—
196#398—731no—
197#398—731no—
198#395—731no—
199#395—731no—
200#391—731no—
201#391D7311yescharacteristic, complemented
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×C4—731no—
214C22⋊Q8—1464no—
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⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4C2×D7311yescharacteristic
228C2×C22⋊C4—731no—
229C2×C22⋊C4—731no—
230C2×C22⋊C4—731no—
231C2×C22⋊C4—731no—
232C2×C42—731no—
233C2×C42C2×D7311yescharacteristic
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#95C2×D7311yescharacteristic
243#95C2×D7311yescharacteristic
244#95C2×D7311yescharacteristic
245#95C2×D7311yescharacteristic
246C24—731no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—2921no—
251C2×Q8—1462no—
252C2×Q8—1462no—
253C22×C4—2921no—
254C22×C4—2921no—
255C22×C4—2921no—
256C22×C4—2921no—
257C22×C4—734no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—1462no—
266C22×C4—1462no—
267C22×C4—1462no—
268C22×C4—1462no—
269C22×C4C22×D7311yescharacteristic
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274C22×C4C22×D7311yescharacteristic
275C22×C4C22×D7311yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—2921no—
278C4⋊C4—2921no—
279C4⋊C4—2921no—
280C4⋊C4—2921no—
281C4⋊C4—1462no—
282C4⋊C4—1462no—
283C4⋊C4—1462no—
284C4⋊C4—1462no—
285C4⋊C4—1462no—
286C4⋊C4—1462no—
287C4⋊C4—1462no—
288C22⋊C4—734no—
289C22⋊C4—734no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C42—41no—
293C42—2921no—
294C23—732no—
295C23—732no—
296C23—732no—
297C23—1461no—
298C23—1461no—
299C23—1461no—
300C23—1461no—
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—21no—
320C2×C4—21no—
321C2×C4—2924no—
322C2×C4—2924no—
323C2×C4—2924no—
324C2×C4—732no—
325C2×C4—732no—
326C2×C4—732no—
327C2×C4—732no—
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×C4D4×D7312yes—
346C2×C4Q8×D7312yes—
347C2×C4Q8×D7312yes—
348C2×C4#1192402812yes—
349C22—734no—
350C22—1462no—
351C22—1462no—
352C22—1462no—
353C22—1462no—
354C22—1462no—
355C22—1462no—
356C22C2×D4×D7311yescharacteristic
357C22C2×Q8×D7311yescharacteristic
358C22C2×Q8×D7311yescharacteristic
359C22#41×D7311yescharacteristic
360C22C2×#1192402811yescharacteristic
361C22#1455663611yescharacteristic
362C22#1455663711yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—2921no—
371C4—2921no—
372C4—2921no—
373C4—1462no—
374C4—1462no—
375C4—1462no—
376C4—1462no—
377C2—1464no—
378C2C4⋊Q8×D7311yescharacteristic
379C2#1798914111yescharacteristic
380C2#1798921211yescharacteristic
381C2#1798922711yescharacteristic
382C2#1798923011yescharacteristic
383C2#1798929111yescharacteristic
384C2#1798929711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#391×C73C2
hypercenter#391D73
hypocenterC73#2549
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #17988521C2semidirect
4. #17988518C2semidirect
5. #17988508C2semidirect
6. #17988506C2semidirect
7. #17988491C2semidirect
8. #17988485C2semidirect
9. #17988484C2semidirect
15. #391×C73C2semidirect
72. C2×C4×D73Q8semidirect
87. #11924005Q8semidirect
193. C73#2549semidirect
201. #391D73semidirect