Finite Group Databasebeta

← #22621789

Subgroups — #22621789

Order 9344.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D73C211yesmaximal, characteristic, complemented
2#17989237C211yesmaximal, characteristic
3#17988936C211yesmaximal, characteristic, complemented
4#17988918C211yesmaximal, characteristic, complemented
5#17988916C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988814C211yesmaximal, characteristic, complemented
8#17988813C211yesmaximal, characteristic, complemented
9#17988790C211yesmaximal, characteristic, complemented
10#17988724C211yesmaximal, characteristic, complemented
11SD16×Dic73C211yesmaximal, characteristic, complemented
12#17988650C211yesmaximal, characteristic, complemented
13C2×#14556515C211yesmaximal, characteristic, complemented
14#103×D73C211yesmaximal, characteristic, complemented
15#448×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×Q8×D73C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20C2×C8×D73C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556589—21no—
23#14556589C2211yescharacteristic
24#14556573—21no—
25#14556572—21no—
26#14556570—21no—
27#14556570C2211yescharacteristic
28#14556568—21no—
29#14556567—21no—
30#14556567C2211yescharacteristic
31#14556562C2211yescharacteristic
32Q8×Dic73C2211yescharacteristic
33D4×Dic73C2211yescharacteristic
34C4×C22⋊D73—21no—
35C4×C22⋊D73C2211yescharacteristic
36C2×C4⋊Dic73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556515C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—41no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73D411yescharacteristic
67C22×Dic73—21no—
68C22×Dic73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73C2311yescharacteristic
72#11924016—41no—
73C2×#10596831—41no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C8×D73—41no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007D411yescharacteristic
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73D411yescharacteristic
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73—21no—
98C2×Q8×C73—22no—
99C2×Q8×C73—41no—
100C2×Q8×C73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73—21no—
103C2×D4×C73C2311yescharacteristic
104C22×C4×C73—21no—
105C22×C4×C73C2311yescharacteristic
106SD16×C73—22no—
107SD16×C73—41no—
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C22×D73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—42no—
119Q8×C73#4112yescomplemented
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—42no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—42no—
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—42no—
132C22⋊D73SD1614yescomplemented
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—42no—
138C2×Dic73—42no—
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—42no—
145C4×D73—42no—
146Dic146—21no—
147Dic146—21no—
148Dic146—42no—
149Dic146—42no—
150C8×C73—21no—
151C8×C73—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73C2×SD1612yes—
160C22×C73C22×D411yescharacteristic
161C2×D73—21no—
162C2×D73—21no—
163C2×D73C2×SD1612yes—
164C4×C73—22no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73C2×#4111yescharacteristic
169C4×C73H(5,𝔽2)11yescharacteristic
170Dic73—21no—
171Dic73—21no—
172Dic73—41no—
173Dic73—41no—
174Dic73—41no—
175Dic73—41no—
176Dic73C2×SD1612yes—
177C2×C73—22no—
178C2×C73—81no—
179C2×C73#54611yescharacteristic
180C2×C73C22×SD1611yescharacteristic
181C2×C73#57811yescharacteristic
182D73—22no—
183#3298—731nomaximal, Sylow
184C73#329811yescharacteristic, complemented, Sylow
185D4×Q8—731no—
186#547—731no—
187#487—731no—
188#483—731no—
189#483—731no—
190#475—731no—
191#465—731no—
192#465—731no—
193#461—731no—
194#448—731no—
195#448D7311yescharacteristic, complemented
196C4×SD16—731no—
197C8×D4—731no—
198C2×#103—731no—
199C2×#103—731no—
200C2×#41—1461no—
201C22×Q8—731no—
202C22×Q8C2×D7311yescharacteristic
203C2×SD16—731no—
204C2×SD16C2×D7311yescharacteristic
205C2×SD16C2×D7311yescharacteristic
206C22×C8—731no—
207C22×C8—731no—
208C4⋊Q8—731no—
209C4⋊Q8—731no—
210C4⋊Q8—1461no—
211#123—1461no—
212#123—1461no—
213C22⋊Q8—731no—
214C22⋊Q8—731no—
215C22⋊Q8—1461no—
216C22⋊Q8—1461no—
217C22⋊Q8—1461no—
218#121—731no—
219#121C2×D7311yescharacteristic
220C4×Q8—731no—
221C4×D4—731no—
222C4×D4—731no—
223C4×D4—1461no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226#106—731no—
227#106—731no—
228#106—731no—
229C4⋊C8—731no—
230#103—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103C2×D7311yescharacteristic
238#103C2×D7311yescharacteristic
239#102—731no—
240C22⋊C8—731no—
241C22⋊C8C2×D7311yescharacteristic
242C4×C8—731no—
243#41—2924no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—2921no—
248C2×Q8—731no—
249C2×Q8—1461no—
250C2×Q8—1461no—
251C2×Q8—1462no—
252C2×Q8C22×D7311yescharacteristic
253C2×Q8C22×D7311yescharacteristic
254C2×D4—21no—
255C2×D4—731no—
256C2×D4—1461no—
257C2×D4C22×D7311yescharacteristic
258C22×C4—21no—
259C22×C4—731no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4C22×D7311yescharacteristic
265SD16—22no—
266SD16—41no—
267SD16—2921no—
268C2×C8—2921no—
269C2×C8—2921no—
270C2×C8—731no—
271C2×C8—731no—
272C2×C8C22×D7311yescharacteristic
273C2×C8C22×D7311yescharacteristic
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4C22×D7311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—731no—
289C22⋊C4—731no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C42—731no—
295C42—1461no—
296C23—21no—
297C23—731no—
298C23D4×D7311yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—2922no—
304Q8—2922no—
305Q8—1461no—
306Q8—1461no—
307Q8#1192402712yescomplemented
308D4—21no—
309D4—21no—
310D4—42no—
311D4—2922no—
312D4—734no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—2922no—
320C2×C4—2922no—
321C2×C4—2922no—
322C2×C4—2922no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—732no—
344C22—1461no—
345C22—1461no—
346C22SD16×D7312yes—
347C22C2×D4×D7311yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—2921no—
353C4—2921no—
354C4—2921no—
355C4—2921no—
356C4—732no—
357C4—1461no—
358C4—1461no—
359C4C2×#1192402711yescharacteristic
360C4#1455663611yescharacteristic
361C2—22no—
362C2—81no—
363C2—1462no—
364C2#1798922411yescharacteristic
365C2C2×SD16×D7311yescharacteristic
366C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#448×C73C2
socleC22×C73C22×D4
hypercenter#448D73
hypocenterC73#3298
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D73C2semidirect
3. #17988936C2semidirect
4. #17988918C2semidirect
5. #17988916C2semidirect
6. #17988870C2semidirect
7. #17988814C2semidirect
8. #17988813C2semidirect
9. #17988790C2semidirect
10. #17988724C2semidirect
11. SD16×Dic73C2semidirect
12. #17988650C2semidirect
13. C2×#14556515C2semidirect
14. #103×D73C2semidirect
15. #448×C73C2semidirect
119. Q8×C73#41semidirect
132. C22⋊D73SD16semidirect
184. C73#3298semidirect
195. #448D73semidirect
307. Q8#11924027semidirect