Finite Group Databasebeta

← #22616587

Subgroups — #22616587

Order 9344.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556581C211yesmaximal, characteristic, complemented
2C2×#14556569C211yesmaximal, characteristic
3#17988519C211yesmaximal, characteristic, complemented
4#17988517C211yesmaximal, characteristic, complemented
5#17988517C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic
7#17988509C211yesmaximal, characteristic
8#17988508C211yesmaximal, characteristic, complemented
9#17988492C211yesmaximal, characteristic, complemented
10#17988485C211yesmaximal, characteristic, complemented
11#17988479C211yesmaximal, characteristic
12#17988478C211yesmaximal, characteristic
13#17988461C211yesmaximal, characteristic
14#17988444C211yesmaximal, characteristic
15#389×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18#14556581—24no—
19#14556569—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
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
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C42×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—41no—
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72#11924007—22no—
73#11924007—22no—
74#11924007—22no—
75#11924007—22no—
76#11924007—22no—
77#11924007—22no—
78#11924005—22no—
79#11924005—22no—
80#11924005—41no—
81#11924005—41no—
82#11924005—41no—
83#11924005Q814yescomplemented
84C4×Dic73—22no—
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C4⋊C4×C73—41no—
93C4⋊C4×C73—41no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73D414yes—
96C42×C73—41no—
97C23×C73C2411yescharacteristic
98C22×D73—21no—
99C22×D73—21no—
100C22×D73—21no—
101C22×D73—21no—
102C22×D73—21no—
103C22×D73—21no—
104C22×D73C2×Q812yes—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
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×C73C2×D412yes—
123C2×C4×C73C2×D412yes—
124C2×C4×C73C2×D412yes—
125C2×C4×C73C2×Q812yes—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
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×Dic73C2×Q812yes—
146C2×Dic73#4112yes—
147C4×D73—44no—
148Dic146—44no—
149C22×C73C22×D411yescharacteristic
150C22×C73C22×Q811yescharacteristic
151C22×C73C2×#4111yescharacteristic
152C22×C73H(5,𝔽2)11yescharacteristic
153C22×C73H(5,𝔽2)11yescharacteristic
154C22×C732−1+411yescharacteristic
155C22×C732−1+411yescharacteristic
156C2×D73—22no—
157C2×D73—22no—
158C2×D73—22no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C4×C73—22no—
164C4×C73—22no—
165C4×C73—22no—
166C4×C73—22no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170Dic73—22no—
171Dic73—22no—
172Dic73—41no—
173Dic73—41no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177C2×C73#53711yescharacteristic
178C2×C73#54111yescharacteristic
179C2×C73#54411yescharacteristic
180C2×C73#54611yescharacteristic
181C2×C73D4×Q811yescharacteristic
182C2×C73#55411yescharacteristic
183C2×C73#56211yescharacteristic
184D73—42no—
185#2704—731nomaximal, Sylow
186C73#270411yescharacteristic, complemented, Sylow
187C2×#125—731no—
188C2×C22⋊Q8—731no—
189#398—731no—
190#398—731no—
191#398—731no—
192#396—731no—
193#396—731no—
194#395—731no—
195#391—731no—
196#389—731no—
197#389D7311yescharacteristic, complemented
198#388—731no—
199#388—731no—
200#385—731no—
201#380—731no—
202C22×Q8—731no—
203C23×C4—731no—
204#125—1464no—
205C22⋊Q8—1464no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—731no—
211C2×C4⋊C4—731no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4C2×D7311yescharacteristic
218C2×C4⋊C4C2×D7311yescharacteristic
219C2×C4⋊C4C2×D7311yescharacteristic
220C2×C4⋊C4C2×D7311yescharacteristic
221C2×C22⋊C4—731no—
222C2×C22⋊C4—731no—
223C2×C22⋊C4—731no—
224C2×C22⋊C4—731no—
225C2×C22⋊C4—731no—
226C2×C22⋊C4—731no—
227C2×C42—731no—
228C2×C42C2×D7311yescharacteristic
229#95—731no—
230#95—731no—
231#95—731no—
232#95—731no—
233#95—731no—
234#95—731no—
235#95—731no—
236#95—731no—
237#95C2×D7311yescharacteristic
238#95C2×D7311yescharacteristic
239C24—731no—
240C2×Q8—2921no—
241C2×Q8—1462no—
242C2×Q8—1462no—
243C22×C4—2921no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—1462no—
252C22×C4—1462no—
253C22×C4C22×D7311yescharacteristic
254C22×C4C22×D7311yescharacteristic
255C22×C4C22×D7311yescharacteristic
256C22×C4C22×D7311yescharacteristic
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7311yescharacteristic
259C22×C4C22×D7311yescharacteristic
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—2921no—
264C4⋊C4—2921no—
265C4⋊C4—2921no—
266C4⋊C4—1462no—
267C4⋊C4—1462no—
268C4⋊C4—1462no—
269C4⋊C4—1462no—
270C4⋊C4—1462no—
271C4⋊C4—1462no—
272C4⋊C4—1462no—
273C4⋊C4—1462no—
274C4⋊C4D29214yes—
275C22⋊C4—2921no—
276C22⋊C4—2921no—
277C22⋊C4—2921no—
278C22⋊C4—734no—
279C22⋊C4—1462no—
280C22⋊C4—1462no—
281C42—41no—
282C42—1462no—
283C23—732no—
284C23—1461no—
285C23—1461no—
286C23—1461no—
287C23—1461no—
288C23—1461no—
289C23—1461no—
290C23C23×D7311yescharacteristic
291Q8—2924no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2924no—
310C2×C4—732no—
311C2×C4—732no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4C2×D29212yes—
332C2×C4C2×D29212yes—
333C2×C4C2×D29212yes—
334C2×C4Q8×D7312yes—
335C22—2921no—
336C22—2921no—
337C22—2921no—
338C22—2921no—
339C22—1462no—
340C22—1462no—
341C22—1462no—
342C22C22×D29211yescharacteristic
343C22C2×Q8×D7311yescharacteristic
344C22#41×D7311yescharacteristic
345C22#1455663611yescharacteristic
346C22#1455663611yescharacteristic
347C22#1455663811yescharacteristic
348C22#1455663911yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—2921no—
360C4—2921no—
361C4—1462no—
362C4—1462no—
363C2—2922no—
364C2#1798916811yescharacteristic
365C2#1798919611yescharacteristic
366C2#1798921411yescharacteristic
367C2#1798923211yescharacteristic
368C2Q8×D29211yescharacteristic
369C2#1798929111yescharacteristic
370C2#1798933211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#389×C73C2
hypercenter#389D73
hypocenterC73#2704
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14556581C2semidirect
3. #17988519C2semidirect
4. #17988517C2semidirect
5. #17988517C2semidirect
8. #17988508C2semidirect
9. #17988492C2semidirect
10. #17988485C2semidirect
15. #389×C73C2semidirect
83. #11924005Q8semidirect
186. C73#2704semidirect
197. #389D73semidirect