Finite Group Databasebeta

← #22613232

Subgroups — #22613232

Order 9344.

432 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73⋊#401C211yesmaximal, characteristic, complemented
2#17988529C211yesmaximal, characteristic, complemented
3#17988526C211yesmaximal, characteristic, complemented
4#17988525C211yesmaximal, characteristic, complemented
5#17988516C211yesmaximal, characteristic
6#17988514C211yesmaximal, characteristic
7#17988513C211yesmaximal, characteristic
8#17988509C211yesmaximal, characteristic
9C4×#11924007C211yesmaximal, characteristic, complemented
10C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
11C4×#11924005C211yesmaximal, characteristic
12C4×#11924005C211yesmaximal, characteristic
13C4×#11924005C211yesmaximal, characteristic
14#17988433C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×C4×D73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×C4×Dic73C2211yescharacteristic
28C2×C4×Dic73C2211yescharacteristic
29C2×C4×Dic73C2211yescharacteristic
30#14556498C2211yescharacteristic
31#14556498C2211yescharacteristic
32#14556498C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C4⋊C4×C73C2211yescharacteristic
46C2×C42×C73C2211yescharacteristic
47C2×C42×C73C2211yescharacteristic
48C2×C42×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C22×Dic73C2311yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C2×C4×D73—22no—
60C2×C4×D73—22no—
61C2×C4×D73—22no—
62C4⋊Dic73—22no—
63C4⋊Dic73—22no—
64#11924007—22no—
65#11924007—22no—
66#11924005—22no—
67#11924005—22no—
68#11924005—22no—
69#11924005—22no—
70#11924005—22no—
71#11924005—22no—
72C4×Dic73—22no—
73C4×Dic73—22no—
74C4×Dic73—22no—
75C22×C4×C73C2311yescharacteristic
76C22×C4×C73C2311yescharacteristic
77C22×C4×C73C2311yescharacteristic
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C22×C4×C73C2311yescharacteristic
82C4⋊C4×C73—22no—
83C4⋊C4×C73—22no—
84C42×C73—22no—
85C42×C73—22no—
86C42×C73—22no—
87C23×C73C2411yescharacteristic
88C22×D73—21no—
89C22×D73—21no—
90C22×D73—21no—
91C22×D73—21no—
92C22×D73—21no—
93C22×D73—21no—
94C22×D73#4112yes—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
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#4112yes—
112C2×C4×C73#4112yes—
113C2×C4×C73#4112yes—
114C2×C4×C73#4112yes—
115C2×C4×C73#4112yes—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
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#4112yes—
137C4×D73—44no—
138C22×C73C2×#4111yescharacteristic
139C22×C73C2×#4111yescharacteristic
140C22×C73C2×#4111yescharacteristic
141C22×C73C2×#4111yescharacteristic
142C22×C73C2×#4111yescharacteristic
143C22×C73C2×#4111yescharacteristic
144C22×C73C2×#4111yescharacteristic
145C2×D73—22no—
146C2×D73—22no—
147C2×D73—22no—
148C2×D73—41no—
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—41no—
152C4×C73—22no—
153C4×C73—22no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73#12614yes—
159Dic73—22no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164Dic73—41no—
165Dic73—41no—
166C2×C73C2×#12611yescharacteristic
167C2×C73#52911yescharacteristic
168C2×C73#52911yescharacteristic
169C2×C73#52911yescharacteristic
170C2×C73#52911yescharacteristic
171C2×C73#52911yescharacteristic
172C2×C73#52911yescharacteristic
173D73—42no—
174#2401—731nomaximal, Sylow
175C73#240111yescharacteristic, complemented, Sylow
176#401—731no—
177#400—731no—
178#400—731no—
179#400—731no—
180#397—731no—
181#397—731no—
182#397—731no—
183#396—731no—
184C4×C4⋊C4—731no—
185C4×C4⋊C4—731no—
186C4×C4⋊C4D7311yescharacteristic, complemented
187C4×C22⋊C4—731no—
188C4×C22⋊C4—731no—
189C4×C22⋊C4—731no—
190#376—731no—
191C23×C4—731no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—731no—
194C2×C4⋊C4—731no—
195C2×C4⋊C4—731no—
196C2×C4⋊C4C2×D7311yescharacteristic
197C2×C4⋊C4C2×D7311yescharacteristic
198C2×C22⋊C4—731no—
199C2×C22⋊C4—731no—
200C2×C22⋊C4—731no—
201C2×C22⋊C4—731no—
202C2×C22⋊C4—731no—
203C2×C22⋊C4—731no—
204C2×C42—731no—
205C2×C42—731no—
206C2×C42—731no—
207C2×C42C2×D7311yescharacteristic
208C2×C42C2×D7311yescharacteristic
209C2×C42C2×D7311yescharacteristic
210#95—731no—
211#95—731no—
212#95—731no—
213#95—731no—
214#95—731no—
215#95—731no—
216#95—731no—
217#95—731no—
218#95—731no—
219#95—731no—
220#95—731no—
221#95—731no—
222#95—731no—
223#95—731no—
224#95C2×D7311yescharacteristic
225#95C2×D7311yescharacteristic
226C24—731no—
227C22×C4—731no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—731no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—1462no—
235C22×C4—1462no—
236C22×C4—1462no—
237C22×C4C22×D7311yescharacteristic
238C22×C4C22×D7311yescharacteristic
239C22×C4C22×D7311yescharacteristic
240C22×C4C22×D7311yescharacteristic
241C22×C4C22×D7311yescharacteristic
242C22×C4C22×D7311yescharacteristic
243C22×C4C22×D7311yescharacteristic
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—1462no—
247C4⋊C4—1462no—
248C4⋊C4—1462no—
249C4⋊C4—1462no—
250C22⋊C4—1462no—
251C22⋊C4—1462no—
252C22⋊C4—1462no—
253C22⋊C4—1462no—
254C22⋊C4—1462no—
255C22⋊C4—1462no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—1462no—
260C42—1462no—
261C42—1462no—
262C23—732no—
263C23—1461no—
264C23—1461no—
265C23—1461no—
266C23—1461no—
267C23—1461no—
268C23—1461no—
269C23C23×D7311yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—2924no—
287C2×C4—732no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4#1192402712yes—
309C2×C4#1192402812yes—
310C2×C4#1192402812yes—
311C2×C4#1192402812yes—
312C2×C4#1192402912yes—
313C22—2921no—
314C22—2921no—
315C22—2921no—
316C22—2921no—
317C22—1462no—
318C22—1462no—
319C22—1462no—
320C22#41×D7311yescharacteristic
321C22#41×D7311yescharacteristic
322C22C2×#1192402711yescharacteristic
323C22C2×#1192402811yescharacteristic
324C22C2×#1192402811yescharacteristic
325C22C2×#1192402811yescharacteristic
326C22C2×#1192402911yescharacteristic
327C4—22no—
328C4—22no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—2921no—
334C4—2921no—
335C4—2921no—
336C4—2921no—
337C4—2921no—
338C4—2921no—
339C4—1462no—
340C4#1455658614yes—
341C2—2922no—
342C2C2×#1455658611yescharacteristic
343C2#1798911511yescharacteristic
344C2#1798911711yescharacteristic
345C2#1798911911yescharacteristic
346C2#1798912111yescharacteristic
347C2#1798912411yescharacteristic
348C2#1798912411yescharacteristic
subgroupG/H
centerC22×C4C22×D73
commutator, socleC23×C73C24
FrattiniC23C23×D73
FittingC4×C4⋊C4×C73C2
hypercenterC4×C4⋊C4D73
hypocenterC73#2401
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C73⋊#401C2semidirect
2. #17988529C2semidirect
3. #17988526C2semidirect
4. #17988525C2semidirect
9. C4×#11924007C2semidirect
10. C4×C4⋊Dic73C2semidirect
14. #17988433C2semidirect
15. C4×C4⋊C4×C73C2semidirect
175. C73#2401semidirect
186. C4×C4⋊C4D73semidirect