Finite Group Databasebeta

← #22619968

Subgroups — #22619968

Order 9344.

384 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989141C211yesmaximal, characteristic
2C4×Q8×D73C211yesmaximal, characteristic
3#17988924C211yesmaximal, characteristic
4#17988921C211yesmaximal, characteristic
5#17988881C211yesmaximal, characteristic, complemented
6#17988880C211yesmaximal, characteristic, complemented
7#17988796C211yesmaximal, characteristic, complemented
8#17988795C211yesmaximal, characteristic, complemented
9#17988744C211yesmaximal, characteristic
10#17988741C211yesmaximal, characteristic
11C4×Dic292C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924018C211yesmaximal, characteristic, complemented
14#17988638C211yesmaximal, characteristic
15C4×Q16×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556581—21no—
23#14556571C2211yescharacteristic
24#14556569—21no—
25#14556567C2211yescharacteristic
26Q8×Dic73C2211yescharacteristic
27C4×Dic146—21no—
28C4×Dic146—21no—
29C4×Dic146C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31#14556556—21no—
32#14556556C2211yescharacteristic
33#14556548—21no—
34C4⋊C4×D73—21no—
35C4⋊C4×D73C2211yescharacteristic
36C42×D73—21no—
37C42×D73C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×Q8×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—22no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73D411yescharacteristic
68C2×C4×D73D411yescharacteristic
69C2×C4×D73C2311yescharacteristic
70Dic292—22no—
71#11924018—22no—
72#11924018—22no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924005—21no—
88#11924005—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73D411yescharacteristic
94C4×Dic73D411yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98Q16×C73—22no—
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C42×C73—21no—
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C22×D73C2×D411yescharacteristic
109Q8×C73—21no—
110Q8×C73—21no—
111Q8×C73—21no—
112Q8×C73#4112yes—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C4×D73—24no—
128C4×D73—21no—
129C4×D73—21no—
130C4×D73—41no—
131C4×D73—42no—
132C4×D73Q1614yescomplemented
133Dic146—24no—
134Dic146—21no—
135Dic146—21no—
136Dic146—21no—
137Dic146—42no—
138Dic146#4112yes—
139C8×C73—21no—
140C8×C73—21no—
141#10596831—21no—
142#10596831—21no—
143C22×C73C22×D411yescharacteristic
144C2×D73—21no—
145C2×D73—21no—
146C2×D73C2×Q1612yes—
147C4×C73—22no—
148C4×C73—21no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73C2×Q1612yes—
153C4×C73C2×#4111yescharacteristic
154C4×C73C2×#4111yescharacteristic
155Dic73—21no—
156Dic73—22no—
157Dic73—21no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161Dic73C2×Q1612yes—
162C2×C73#52511yescharacteristic
163C2×C73C22×Q1611yescharacteristic
164C2×C73#57511yescharacteristic
165D73—22no—
166#3104—731nomaximal, Sylow
167C73#310411yescharacteristic, complemented, Sylow
168#533—731no—
169C2×C4×Q8—731no—
170#484—731no—
171#484—731no—
172#477—731no—
173#477—731no—
174#462—731no—
175#462—731no—
176#451—731no—
177#451—731no—
178C4×Q16—731no—
179C4×Q16—731no—
180C4×Q16—731no—
181C4×Q16D7311yescharacteristic, complemented
182#431—731no—
183C22×Q8—731no—
184C2×Q16—731no—
185C2×Q16—731no—
186C2×Q16—731no—
187C2×Q16C2×D7311yescharacteristic
188C4⋊Q8—731no—
189C4⋊Q8—731no—
190#125—1461no—
191C22⋊Q8—731no—
192C22⋊Q8—731no—
193C22⋊Q8—1461no—
194C4×Q8—731no—
195C4×Q8—731no—
196C4×Q8—731no—
197C4×Q8—731no—
198C4×Q8—1461no—
199C4×Q8—1461no—
200C4×Q8—1461no—
201C4×Q8C2×D7311yescharacteristic
202C4×Q8C2×D7311yescharacteristic
203#117—1461no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—1461no—
206C2×C42—731no—
207C2×C42—1461no—
208#107—731no—
209#107—731no—
210#107—731no—
211#107C2×D7311yescharacteristic
212C4⋊C8—731no—
213C4⋊C8—731no—
214#103—731no—
215#103—731no—
216#103—731no—
217#103—731no—
218#103—731no—
219#103—731no—
220#103C2×D7311yescharacteristic
221#103C2×D7311yescharacteristic
222C22⋊C8—731no—
223C22⋊C8—731no—
224C4×C8—731no—
225C4×C8C2×D7311yescharacteristic
226C2×Q8—731no—
227C2×Q8—731no—
228C2×Q8—1461no—
229C2×Q8—1461no—
230C2×Q8—1462no—
231C2×Q8—1462no—
232C2×Q8C22×D7311yescharacteristic
233C2×Q8C22×D7311yescharacteristic
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—1461no—
238C22×C4—1461no—
239Q16—22no—
240Q16—1462no—
241Q16—1462no—
242Q16—1462no—
243C2×C8—731no—
244C2×C8—731no—
245C2×C8C22×D7311yescharacteristic
246C2×C8C22×D7311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—731no—
250C4⋊C4—731no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4C22×D7311yescharacteristic
262C4⋊C4C22×D7311yescharacteristic
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C42—21no—
266C42—21no—
267C42—731no—
268C42—731no—
269C42—731no—
270C42—1461no—
271C42—1461no—
272C42—1461no—
273C42—1461no—
274C42C22×D7311yescharacteristic
275C23—731no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—2922no—
280Q8—732no—
281Q8—1464no—
282Q8—1461no—
283Q8—1461no—
284Q8—1461no—
285Q8#1192402812yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2921no—
291C2×C4—2922no—
292C2×C4—731no—
293C2×C4—734no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—1464no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4D4×D7311yescharacteristic
304C2×C4D4×D7311yescharacteristic
305C2×C4C23×D7311yescharacteristic
306C8—21no—
307C8—21no—
308C8—1461no—
309C8—1461no—
310C22—732no—
311C22—1461no—
312C22—1461no—
313C22C2×D4×D7311yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—2921no—
320C4—2921no—
321C4—2921no—
322C4—732no—
323C4—1461no—
324C4—1461no—
325C4—1462no—
326C4Q16×D7312yes—
327C4#41×D7311yescharacteristic
328C4C2×#1192402811yescharacteristic
329C2—1462no—
330C2#1798909611yescharacteristic
331C2C2×Q16×D7311yescharacteristic
332C2#1798938411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×Q16×C73C2
socleC22×C73C22×D4
hypercenterC4×Q16D73
hypocenterC73#3104
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
5. #17988881C2semidirect
6. #17988880C2semidirect
7. #17988796C2semidirect
8. #17988795C2semidirect
11. C4×Dic292C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924018C2semidirect
15. C4×Q16×C73C2semidirect
132. C4×D73Q16semidirect
167. C73#3104semidirect
181. C4×Q16D73semidirect