Finite Group Databasebeta

← #22621676

Subgroups — #22621676

Order 9344.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11924018C211yesmaximal, characteristic, complemented
2C2×Q16×D73C211yesmaximal, characteristic, complemented
3Q8×C22⋊D73C211yesmaximal, characteristic
4#17989250C211yesmaximal, characteristic
5#17988965C211yesmaximal, characteristic, complemented
6#17988827C211yesmaximal, characteristic, complemented
7#17988826C211yesmaximal, characteristic, complemented
8#17988796C211yesmaximal, characteristic, complemented
9#17988795C211yesmaximal, characteristic, complemented
10#17988745C211yesmaximal, characteristic, complemented
11#17988744C211yesmaximal, characteristic, complemented
12#17988741C211yesmaximal, characteristic, complemented
13#17988679C211yesmaximal, characteristic, complemented
14#17988650C211yesmaximal, characteristic
15#451×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C2×Q8×D73C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×Dic292C2211yescharacteristic
21C2×#11924018—24no—
22C2×#11924018C2211yescharacteristic
23C2×#11924018C2211yescharacteristic
24C2×#11924018C2211yescharacteristic
25C2×#11924018C2211yescharacteristic
26C2×#11924018C2211yescharacteristic
27Q16×D73—24no—
28C22×#10596831C2211yescharacteristic
29C2×C8×D73C2211yescharacteristic
30#14556590—21no—
31#14556589—21no—
32#14556589C2211yescharacteristic
33#14556589C2211yescharacteristic
34#14556571C2211yescharacteristic
35#14556570—21no—
36#14556570C2211yescharacteristic
37#14556569—21no—
38#14556568—21no—
39#14556567—21no—
40#14556567C2211yescharacteristic
41Q8×Dic73C2211yescharacteristic
42#14556556C2211yescharacteristic
43C4×C22⋊D73—21no—
44C4×C22⋊D73C2211yescharacteristic
45#14556551—21no—
46#14556524C2211yescharacteristic
47#14556520C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556516C2211yescharacteristic
50#14556515C2211yescharacteristic
51#14556514C2211yescharacteristic
52#14556503C2211yescharacteristic
53C8×Dic73C2211yescharacteristic
54C22×Q8×C73C2211yescharacteristic
55C2×Q16×C73C2211yescharacteristic
56C2×Q16×C73C2211yescharacteristic
57C22⋊Q8×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59#103×C73C2211yescharacteristic
60C22⋊C8×C73C2211yescharacteristic
61C2×Dic146—22no—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—21no—
65C2×Dic146—41no—
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C2×Dic146C2311yescharacteristic
69Q8×D73—22no—
70Q8×D73—22no—
71Q8×D73—41no—
72Q8×D73—41no—
73C2×C22⋊D73D411yescharacteristic
74C22×Dic73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73C2311yescharacteristic
78Dic292—22no—
79Dic292—41no—
80#11924018—22no—
81#11924018—22no—
82#11924018—22no—
83#11924018—22no—
84#11924018D414yescomplemented
85C2×#10596831—22no—
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C8×D73—22no—
89C4⋊Dic73—21no—
90C4⋊Dic73—21no—
91C4⋊Dic73C2311yescharacteristic
92#11924007—21no—
93#11924007—21no—
94#11924007—21no—
95#11924007—21no—
96#11924007—21no—
97#11924007—21no—
98#11924007—21no—
99#11924007D411yescharacteristic
100C22⋊Dic73—21no—
101C22⋊Dic73D411yescharacteristic
102#11924005—21no—
103#11924005—21no—
104#11924005D411yescharacteristic
105C4×Dic73—21no—
106C4×Dic73—21no—
107C4×Dic73C2311yescharacteristic
108C2×Q8×C73—21no—
109C2×Q8×C73—22no—
110C2×Q8×C73—41no—
111C2×Q8×C73C2311yescharacteristic
112C2×Q8×C73C2311yescharacteristic
113C2×Q8×C73C2311yescharacteristic
114C22×C4×C73—21no—
115C22×C4×C73C2311yescharacteristic
116Q16×C73—22no—
117Q16×C73—41no—
118C2×C8×C73C2311yescharacteristic
119C2×C8×C73C2311yescharacteristic
120C4⋊C4×C73—21no—
121C4⋊C4×C73C2311yescharacteristic
122C22⋊C4×C73—21no—
123C23×C73C2×D411yescharacteristic
124C22×D73C2×D411yescharacteristic
125Q8×C73—21no—
126Q8×C73—21no—
127Q8×C73—21no—
128Q8×C73—21no—
129Q8×C73—21no—
130Q8×C73—42no—
131Q8×C73C2×D412yes—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—42no—
139C2×C4×C73C2×D411yescharacteristic
140C2×C4×C73C2411yescharacteristic
141C22⋊D73Q1614yescomplemented
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—42no—
147C2×Dic73C2×D411yescharacteristic
148C2×Dic73C2×D411yescharacteristic
149C2×Dic73C2×D411yescharacteristic
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—42no—
153C4×D73—42no—
154Dic146—21no—
155Dic146—21no—
156Dic146—21no—
157Dic146—21no—
158Dic146—21no—
159Dic146—42no—
160Dic146—42no—
161Dic146—42no—
162Dic146C2×D412yes—
163C8×C73—21no—
164C8×C73—21no—
165#10596831—21no—
166#10596831C2×D412yes—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73C2×Q1612yescomplemented
170C22×C73C22×D411yescharacteristic
171C2×D73—21no—
172C2×D73—21no—
173C2×D73C2×Q1612yescomplemented
174C4×C73—21no—
175C4×C73—22no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73C22×D411yescharacteristic
180C4×C73H(5,𝔽2)11yescharacteristic
181Dic73—22no—
182Dic73—21no—
183Dic73—21no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187Dic73C2×Q1612yescomplemented
188C2×C73—22no—
189C2×C73D4211yescharacteristic
190C2×C73C22×Q1611yescharacteristic
191C2×C73#57811yescharacteristic
192D73—22no—
193D4×Q16—731nomaximal, Sylow
194C73D4×Q1611yescharacteristic, complemented, Sylow
195C22×Q16—731no—
196C22×Q16—731no—
197D4×Q8—731no—
198D4×Q8—731no—
199#494—731no—
200#467—731no—
201#467—731no—
202#462—731no—
203#462—731no—
204#451—731no—
205#451—731no—
206#451—731no—
207#451D7311yescharacteristic, complemented
208C4×Q16—731no—
209C8×D4—731no—
210C22×Q8—731no—
211C22×Q8—731no—
212C22×Q8—731no—
213C22×Q8C2×D7311yescharacteristic
214C2×Q16—731no—
215C2×Q16—731no—
216C2×Q16—731no—
217C2×Q16—731no—
218C2×Q16—731no—
219C2×Q16—731no—
220C2×Q16—731no—
221C2×Q16—1464no—
222C2×Q16—1464no—
223C2×Q16C2×D7311yescharacteristic
224C2×Q16C2×D7311yescharacteristic
225C22×C8—731no—
226C22×C8—731no—
227C4⋊Q8—731no—
228C4⋊Q8—731no—
229C4⋊Q8—1461no—
230C4⋊Q8—1461no—
231C22⋊Q8—731no—
232C22⋊Q8—731no—
233C22⋊Q8—731no—
234C22⋊Q8—1461no—
235C22⋊Q8—1461no—
236C22⋊Q8—1461no—
237C22⋊Q8—1461no—
238C22⋊Q8C2×D7311yescharacteristic
239C4×Q8—731no—
240C4×Q8—731no—
241C4×D4—731no—
242C4×D4—1461no—
243C4×D4—1461no—
244#107—731no—
245C4⋊C8—731no—
246#103—731no—
247#103—731no—
248#103—731no—
249#103—731no—
250#103C2×D7311yescharacteristic
251#103C2×D7311yescharacteristic
252C22⋊C8—731no—
253C22⋊C8C2×D7311yescharacteristic
254C4×C8—731no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—2921no—
259C2×Q8—2921no—
260C2×Q8—2921no—
261C2×Q8—731no—
262C2×Q8—731no—
263C2×Q8—731no—
264C2×Q8—1462no—
265C2×Q8—1461no—
266C2×Q8—1461no—
267C2×Q8—1462no—
268C2×Q8—1462no—
269C2×Q8—1461no—
270C2×Q8C22×D7311yescharacteristic
271C2×Q8C22×D7311yescharacteristic
272C2×Q8C22×D7311yescharacteristic
273C2×D4—731no—
274C22×C4—21no—
275C22×C4—731no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4—1461no—
279C22×C4C22×D7311yescharacteristic
280Q16—22no—
281Q16—41no—
282Q16—2921no—
283Q16—734no—
284Q16—1462no—
285Q16—1462no—
286Q16—1462no—
287Q16—1462no—
288Q16—1462no—
289C2×C8—731no—
290C2×C8—731no—
291C2×C8—1462no—
292C2×C8—1462no—
293C2×C8C22×D7311yescharacteristic
294C2×C8C22×D7311yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—731no—
297C4⋊C4—731no—
298C4⋊C4—1461no—
299C4⋊C4—1461no—
300C4⋊C4—1461no—
301C4⋊C4—1461no—
302C4⋊C4—1461no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4C22×D7311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—731no—
310C22⋊C4—731no—
311C22⋊C4—1461no—
312C22⋊C4—1461no—
313C22⋊C4—1461no—
314C42—731no—
315C42—1461no—
316C42—1461no—
317C23—731no—
318C23D4×D7311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—2922no—
326Q8—2922no—
327Q8—2922no—
328Q8—732no—
329Q8—1461no—
330Q8—1461no—
331Q8—1461no—
332Q8—1461no—
333Q8—1461no—
334Q8D4×D7312yes—
335D4—734no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—2922no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—731no—
347C2×C4—731no—
348C2×C4—731no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4D4×D7311yescharacteristic
356C2×C4C23×D7311yescharacteristic
357C8—21no—
358C8—21no—
359C8—732no—
360C8—1461no—
361C22—21no—
362C22—21no—
363C22—732no—
364C22—1461no—
365C22—1461no—
366C22Q16×D7312yescomplemented
367C22C2×D4×D7311yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—2921no—
374C4—2921no—
375C4—2921no—
376C4—732no—
377C4—1461no—
378C4—1462no—
379C4—1461no—
380C4C2×D4×D7311yescharacteristic
381C4#1455663611yescharacteristic
382C2—22no—
383C2—1462no—
384C2#1798921911yescharacteristic
385C2C2×Q16×D7311yescharacteristic
386C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73D4×Q16
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C22×#11924018C2semidirect
2. C2×Q16×D73C2semidirect
5. #17988965C2semidirect
6. #17988827C2semidirect
7. #17988826C2semidirect
8. #17988796C2semidirect
9. #17988795C2semidirect
10. #17988745C2semidirect
11. #17988744C2semidirect
12. #17988741C2semidirect
13. #17988679C2semidirect
15. #451×C73C2semidirect
84. #11924018D4semidirect
141. C22⋊D73Q16semidirect
169. C22×C73C2×Q16semidirect
173. C2×D73C2×Q16semidirect
187. Dic73C2×Q16semidirect
194. C73D4×Q16semidirect
207. #451D73semidirect
366. C22Q16×D73semidirect