Finite Group Databasebeta

← #22612608

Subgroups — #22612608

Order 9344.

556 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556569C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic, complemented
3C2×#14556549C211yesmaximal, characteristic
4#17988491C211yesmaximal, characteristic, complemented
5#17988482C211yesmaximal, characteristic, complemented
6#17988482C211yesmaximal, characteristic, complemented
7#17988478C211yesmaximal, characteristic
8#17988477C211yesmaximal, characteristic
9#17988477C211yesmaximal, characteristic
10#17988476C211yesmaximal, characteristic
11#17988474C211yesmaximal, characteristic, complemented
12#17988473C211yesmaximal, characteristic, complemented
13#17988446C211yesmaximal, characteristic
14C4×#11924007C211yesmaximal, characteristic, complemented
15#389×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18#14556569C418yescomplemented
19#14556556—24no—
20#14556549—24no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38C2×C4×Dic73C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C42×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53#95×C73C2211yescharacteristic
54C23×D73C2311yescharacteristic
55C2×Dic146—22no—
56C2×Dic146—22no—
57C2×Dic146C2×C414yes—
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73C2×C414yes—
68C4⋊Dic73—22no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—41no—
73#11924007C2×C414yes—
74#11924007C2×C414yes—
75#11924005—22no—
76#11924005—22no—
77#11924005—41no—
78#11924005—41no—
79#11924005C2×C414yes—
80#11924005C2×C414yes—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C4×Dic73—41no—
85C4×Dic73D414yes—
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C4⋊C4×C73—22no—
94C4⋊C4×C73—22no—
95C4⋊C4×C73—41no—
96C4⋊C4×C73C2×C414yes—
97C42×C73—41no—
98C23×C73C2411yescharacteristic
99C22×D73—21no—
100C22×D73—21no—
101C22×D73—21no—
102C22×D73—21no—
103C22×D73—21no—
104C22×D73—21no—
105C22×D73C22×C412yes—
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×C73—21no—
123C2×C4×C73C22×C412yes—
124C2×C4×C73C22×C412yes—
125C2×C4×C73C22×C412yes—
126C2×C4×C73C2×D412yes—
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×Dic73C22×C412yes—
143C2×Dic73C22×C412yes—
144C2×Dic73C22×C412yes—
145C2×Dic73C2×D412yes—
146C2×Dic73C2×D412yes—
147C2×Dic73#4112yes—
148C4×D73—28no—
149Dic146—28no—
150C22×C73C23×C411yescharacteristic
151C22×C73C22×D411yescharacteristic
152C22×C73C2×#4111yescharacteristic
153C22×C73H(5,𝔽2)11yescharacteristic
154C22×C732−1+411yescharacteristic
155C22×C732−1+411yescharacteristic
156C22×C732−1+411yescharacteristic
157C2×D73—22no—
158C2×D73—22no—
159C2×D73—22no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C4×C73—22no—
165C4×C73—22no—
166C4×C73—22no—
167C4×C73—22no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—41no—
171Dic73—22no—
172Dic73—22no—
173Dic73—22no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73C4×D414yes—
178C2×C73C2×C4×D411yescharacteristic
179C2×C73#51911yescharacteristic
180C2×C73#52011yescharacteristic
181C2×C73#53611yescharacteristic
182C2×C73#53711yescharacteristic
183C2×C73#54111yescharacteristic
184C2×C73#54211yescharacteristic
185D73—42no—
186#2323—731nomaximal, Sylow
187C73#232311yescharacteristic, complemented, Sylow
188C2×C22⋊Q8—731no—
189C2×C4×Q8—731no—
190C2×#117—731no—
191#391—731no—
192#389—731no—
193#389—731no—
194#389D7311yescharacteristic, complemented
195#388—731no—
196#388—731no—
197#388—731no—
198#388—731no—
199#387—731no—
200#387—731no—
201#380—731no—
202C4×C4⋊C4—731no—
203C22×Q8—731no—
204C23×C4—731no—
205C22⋊Q8—738no—
206C4×Q8—1464no—
207#117—1464no—
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⋊C4C2×D7311yescharacteristic
216C2×C4⋊C4C2×D7311yescharacteristic
217C2×C4⋊C4C2×D7311yescharacteristic
218C2×C4⋊C4C2×D7311yescharacteristic
219C2×C22⋊C4—731no—
220C2×C22⋊C4—731no—
221C2×C22⋊C4—731no—
222C2×C22⋊C4—731no—
223C2×C22⋊C4—731no—
224C2×C22⋊C4—731no—
225C2×C42—731no—
226C2×C42—731no—
227C2×C42—731no—
228C2×C42—731no—
229C2×C42—731no—
230C2×C42C2×D7311yescharacteristic
231#95—731no—
232#95—731no—
233#95—731no—
234#95—731no—
235#95—731no—
236#95—731no—
237#95—731no—
238#95—731no—
239#95C2×D7311yescharacteristic
240#95C2×D7311yescharacteristic
241C24—731no—
242C2×Q8—734no—
243C2×Q8—1462no—
244C2×Q8—1462no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—734no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—1462no—
254C22×C4—1462no—
255C22×C4C22×D7311yescharacteristic
256C22×C4C22×D7311yescharacteristic
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7311yescharacteristic
259C22×C4C22×D7311yescharacteristic
260C22×C4C22×D7311yescharacteristic
261C22×C4C22×D7311yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—2921no—
266C4⋊C4—734no—
267C4⋊C4—734no—
268C4⋊C4—1462no—
269C4⋊C4—1462no—
270C4⋊C4—1462no—
271C4⋊C4—1462no—
272C4⋊C4C4×D7314yes—
273C22⋊C4—2921no—
274C22⋊C4—2921no—
275C22⋊C4—734no—
276C22⋊C4—734no—
277C22⋊C4—1462no—
278C22⋊C4—1462no—
279C42—41no—
280C42—2921no—
281C42—734no—
282C42—1462no—
283C42—1462no—
284C42—1462no—
285C23—732no—
286C23—1461no—
287C23—1461no—
288C23—1461no—
289C23—1461no—
290C23—1461no—
291C23—1461no—
292C23C23×D7311yescharacteristic
293Q8—1468no—
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—21no—
310C2×C4—21no—
311C2×C4—732no—
312C2×C4—732no—
313C2×C4—732no—
314C2×C4—732no—
315C2×C4—732no—
316C2×C4—732no—
317C2×C4—1468no—
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×C4—1461no—
332C2×C4—1461no—
333C2×C4C2×C4×D7312yes—
334C2×C4C2×C4×D7312yes—
335C2×C4C2×C4×D7312yes—
336C2×C4D4×D7312yes—
337C22—2921no—
338C22—2921no—
339C22—2921no—
340C22—2921no—
341C22—1462no—
342C22—1462no—
343C22—1462no—
344C22C22×C4×D7311yescharacteristic
345C22C2×D4×D7311yescharacteristic
346C22#41×D7311yescharacteristic
347C22#1455663611yescharacteristic
348C22#1455663811yescharacteristic
349C22#1455663911yescharacteristic
350C22#1455663911yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—2921no—
359C4—2921no—
360C4—2921no—
361C4—734no—
362C4—1462no—
363C4—1462no—
364C4—1462no—
365C2—2922no—
366C2C4×D4×D7311yescharacteristic
367C2#1798906311yescharacteristic
368C2#1798906811yescharacteristic
369C2#1798916211yescharacteristic
370C2#1798916411yescharacteristic
371C2#1798919611yescharacteristic
372C2#1798920711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutatorC22×C73C23×C4
Fitting#389×C73C2
socleC23×C73C24
hypercenter#389D73
hypocenterC73#2323
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#14556556C2semidirect
4. #17988491C2semidirect
5. #17988482C2semidirect
6. #17988482C2semidirect
11. #17988474C2semidirect
12. #17988473C2semidirect
14. C4×#11924007C2semidirect
15. #389×C73C2semidirect
18. #14556569C4semidirect
187. C73#2323semidirect
194. #389D73semidirect