Finite Group Databasebeta

← #22621313

Subgroups — #22621313

Order 9344.

386 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989139C211yesmaximal, characteristic, complemented
2#17989132C211yesmaximal, characteristic
3#17988881C211yesmaximal, characteristic, complemented
4#17988880C211yesmaximal, characteristic, complemented
5#17988866C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988831C211yesmaximal, characteristic, complemented
10#17988791C211yesmaximal, characteristic, complemented
11#17988790C211yesmaximal, characteristic, complemented
12#17988786C211yesmaximal, characteristic, complemented
13#17988785C211yesmaximal, characteristic, complemented
14#17988610C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×#11924017C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924012C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556590C2211yescharacteristic
23#14556589C2211yescharacteristic
24#14556587C2211yescharacteristic
25#14556581—21no—
26#14556577—21no—
27#14556570C2211yescharacteristic
28#14556568—21no—
29#14556565C2211yescharacteristic
30#14556563—21no—
31Q8×Dic73C2211yescharacteristic
32#14556556—21no—
33#14556556C2211yescharacteristic
34D4×Dic73C2211yescharacteristic
35#14556553C2211yescharacteristic
36#14556551—21no—
37#14556547—21no—
38C2×C4×Dic73C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556515C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556512C2211yescharacteristic
51#14556511C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C22×Dic73—21no—
68C22×Dic73D411yescharacteristic
69C22×Dic73D411yescharacteristic
70C2×C4×D73—21no—
71#11924017—41no—
72#11924016—41no—
73#11924015—41no—
74#11924012—41no—
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73D411yescharacteristic
93C4×Dic73D411yescharacteristic
94C4×Dic73C2311yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100SD16×C73—41no—
101M16×C73—41no—
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C22⋊C4×C73—21no—
109C23×C73—21no—
110C23×C73C2×D411yescharacteristic
111C22×D73—21no—
112Q8×C73—21no—
113Q8×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—42no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—42no—
125C22⋊D73—42no—
126C22⋊D73—42no—
127C2×Dic73—22no—
128C2×Dic73—22no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—42no—
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—21no—
138D292—21no—
139C4×D73—42no—
140Dic146—21no—
141Dic146—21no—
142Dic146—42no—
143Dic146—42no—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73C22×D411yescharacteristic
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C4×C73—21no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73H(5,𝔽2)11yescharacteristic
163C4×C732−1+411yescharacteristic
164Dic73—21no—
165Dic73—21no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73AGL(1,ℤ/8)12yes—
170Dic73#13712yes—
171C2×C73—41no—
172C2×C73—81no—
173C2×C73#53711yescharacteristic
174C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C73C2×#13711yescharacteristic
176D73—81no—
177#3254—731nomaximal, Sylow
178C73#325411yescharacteristic, complemented, Sylow
179#533—731no—
180#532—731no—
181#477—731no—
182#477—731no—
183#474—731no—
184#474—731no—
185#468—731no—
186#468—731no—
187#468—731no—
188#468D7311yescharacteristic, complemented
189#461—731no—
190#461—731no—
191#460—731no—
192#460—731no—
193#423—731no—
194C2×#41—1461no—
195C2×SD16—731no—
196C2×SD16—731no—
197C2×SD16—731no—
198C2×SD16C2×D7311yescharacteristic
199C2×M16—731no—
200C2×M16C2×D7311yescharacteristic
201C4⋊Q8—731no—
202C4⋊Q8—731no—
203C4⋊Q8—731no—
204#127—731no—
205#125—1461no—
206#124—1461no—
207C22⋊Q8—731no—
208C22⋊Q8—1461no—
209C22⋊Q8C2×D7311yescharacteristic
210#121—731no—
211#121—1461no—
212#121C2×D7311yescharacteristic
213C4×Q8—731no—
214C4×Q8—731no—
215C4×Q8—1461no—
216C4×D4—731no—
217C4×D4—731no—
218C4×D4—1461no—
219#117—1461no—
220C2×C42—731no—
221#107—731no—
222#107—731no—
223#107—731no—
224#107C2×D7311yescharacteristic
225C4⋊C8—731no—
226C4⋊C8—731no—
227C4⋊C8—731no—
228C4⋊C8—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103C2×D7311yescharacteristic
233#102—731no—
234#102—731no—
235#102—731no—
236#102C2×D7311yescharacteristic
237#41—2924no—
238C2×Q8—731no—
239C2×Q8—1461no—
240C2×Q8—1461no—
241C2×Q8C22×D7311yescharacteristic
242C2×D4—21no—
243C2×D4—731no—
244C2×D4—1461no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4C22×D7311yescharacteristic
248C22×C4—731no—
249C22×C4—731no—
250C22×C4—1461no—
251C22×C4—1461no—
252C22×C4C22×D7311yescharacteristic
253SD16—41no—
254SD16—2921no—
255SD16—2921no—
256SD16—2921no—
257M16—41no—
258M16—2921no—
259C2×C8—731no—
260C2×C8—731no—
261C2×C8C22×D7311yescharacteristic
262C2×C8C22×D7311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4C22×D7311yescharacteristic
274C4⋊C4C22×D7311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C42—731no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—1461no—
286C42—1461no—
287C23—21no—
288C23—1461no—
289C23D4×D7311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2922no—
293Q8—2922no—
294Q8—1461no—
295Q8—1461no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—2922no—
300D4—2922no—
301D4—2922no—
302D4—1461no—
303D4—1461no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2922no—
310C2×C4—2922no—
311C2×C4—731no—
312C2×C4—731no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1462no—
319C2×C4—1462no—
320C2×C4D4×D7311yescharacteristic
321C2×C4C23×D7311yescharacteristic
322C8—21no—
323C8—21no—
324C8—1461no—
325C8—1461no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22C2×D4×D7311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2921no—
341C4—2921no—
342C4—2921no—
343C4—732no—
344C4—732no—
345C4—1461no—
346C4—1461no—
347C4#1455663611yescharacteristic
348C4#1455663811yescharacteristic
349C2—41no—
350C2—81no—
351C2—5841no—
352C2#1798916411yescharacteristic
353C2AGL(1,ℤ/8)×D7311yescharacteristic
354C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3254
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #17989139C2semidirect
3. #17988881C2semidirect
4. #17988880C2semidirect
5. #17988866C2semidirect
6. #17988865C2semidirect
7. #17988835C2semidirect
8. #17988833C2semidirect
9. #17988831C2semidirect
10. #17988791C2semidirect
11. #17988790C2semidirect
12. #17988786C2semidirect
13. #17988785C2semidirect
14. #17988610C2semidirect
15. #468×C73C2semidirect
178. C73#3254semidirect
188. #468D73semidirect