Finite Group Databasebeta

← #22621868

Subgroups — #22621868

Order 9344.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989305C211yesmaximal, characteristic, complemented
2#17989255C211yesmaximal, characteristic
3#17988932C211yesmaximal, characteristic, complemented
4#17988914C211yesmaximal, characteristic, complemented
5#17988871C211yesmaximal, characteristic, complemented
6#17988817C211yesmaximal, characteristic, complemented
7#17988814C211yesmaximal, characteristic, complemented
8#17988786C211yesmaximal, characteristic, complemented
9#17988751C211yesmaximal, characteristic, complemented
10#17988750C211yesmaximal, characteristic, complemented
11#17988681C211yesmaximal, characteristic, complemented
12#17988650C211yesmaximal, characteristic, complemented
13#17988581C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C22×#10596831C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23#14556590C2211yescharacteristic
24#14556587—21no—
25#14556587C2211yescharacteristic
26#14556585—21no—
27#14556584—21no—
28#14556577—21no—
29#14556571C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556566C2211yescharacteristic
32#14556564—21no—
33#14556563—21no—
34C4×Dic146—21no—
35#14556556C2211yescharacteristic
36#14556556C2211yescharacteristic
37C4×C22⋊D73C2211yescharacteristic
38#14556551—21no—
39#14556549C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—41no—
61#11924027—22no—
62#11924027—41no—
63C2×Dic146—21no—
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×D292—21no—
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73D411yescharacteristic
73C22×Dic73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76Dic292—22no—
77#11924017—41no—
78#11924016—41no—
79C2×#10596831—41no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C8×D73—41no—
83C4⋊Dic73—21no—
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007D411yescharacteristic
90C22⋊Dic73—21no—
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005D411yescharacteristic
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73C2×D411yescharacteristic
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—81no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2411yescharacteristic
125C22⋊D73—22no—
126C22⋊D73—42no—
127C22⋊D73—42no—
128C22⋊D73—42no—
129C22⋊D73—81no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—42no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—21no—
138D292—21no—
139D292—81no—
140C4×D73—21no—
141C4×D73—21no—
142C4×D73—42no—
143Dic146—21no—
144Dic146—21no—
145Dic146—21no—
146Dic146—42no—
147Dic146#4112yes—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73H(5,𝔽2)11yescharacteristic
171Dic73—22no—
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73#13512yes—
177C2×C73—41no—
178C2×C73—81no—
179C2×C73#54611yescharacteristic
180C2×C73C2×#13511yescharacteristic
181C2×C73#57711yescharacteristic
182D73—41no—
183D73—81no—
184#3304—731nomaximal, Sylow
185C73#330411yescharacteristic, complemented, Sylow
186#556—731no—
187#550—731no—
188#486—731no—
189#482—731no—
190#482D7311yescharacteristic, complemented
191#475—731no—
192#465—731no—
193#465—731no—
194#460—731no—
195#452—731no—
196#452—731no—
197C4×Q16—731no—
198C8×D4—731no—
199#416—731no—
200#416—731no—
201C2×#41—731no—
202C2×#41—731no—
203C2×Q16—731no—
204C2×SD16—731no—
205C2×SD16—731no—
206C22×C8—731no—
207C22×C8—731no—
208C4⋊Q8—731no—
209#127—731no—
210#127—1461no—
211#126—1461no—
212#126—1461no—
213#124—1461no—
214C22⋊Q8—731no—
215C22⋊Q8—731no—
216#121—731no—
217#121—1461no—
218#121—1461no—
219#121C2×D7311yescharacteristic
220C4×Q8—731no—
221C4×Q8—731no—
222C4×Q8—1461no—
223C4×D4—731no—
224C4×D4—1461no—
225#117—731no—
226#117C2×D7311yescharacteristic
227#107C2×D7311yescharacteristic
228#106—731no—
229#106C2×D7311yescharacteristic
230C4⋊C8—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#102—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102C2×D7311yescharacteristic
240#102C2×D7311yescharacteristic
241C22⋊C8—731no—
242C22⋊C8C2×D7311yescharacteristic
243C4×C8—731no—
244#41—2921no—
245#41—2921no—
246#41—1462no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8—731no—
250C2×Q8—1461no—
251C2×D4—21no—
252C2×D4—731no—
253C2×D4—731no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4—1461no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4C22×D7311yescharacteristic
260C22×C4—731no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4C22×D7311yescharacteristic
264Q16—1462no—
265SD16—2921no—
266SD16—2921no—
267C2×C8—2921no—
268C2×C8—2921no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8C22×D7311yescharacteristic
272C2×C8C22×D7311yescharacteristic
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4C22×D7311yescharacteristic
281C4⋊C4C22×D7311yescharacteristic
282C4⋊C4C22×D7311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—731no—
286C22⋊C4—731no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C42—21no—
292C42—731no—
293C42—1461no—
294C42—1461no—
295C42—1461no—
296C23—21no—
297C23—731no—
298C23—1461no—
299C23D4×D7311yescharacteristic
300Q8—2922no—
301Q8—732no—
302Q8—1461no—
303Q8—1461no—
304Q8—1461no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—2922no—
309D4—2922no—
310D4—2922no—
311D4—5841no—
312D4—5841no—
313D4—1462no—
314D4—1461no—
315D4—1461no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
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×C4D4×D7311yescharacteristic
332C2×C4C23×D7311yescharacteristic
333C8—21no—
334C8—21no—
335C8—1461no—
336C8—1461no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—2921no—
344C22—2921no—
345C22—2921no—
346C22—1461no—
347C22—1461no—
348C22—1461no—
349C22C2×D4×D7311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—2921no—
355C4—2921no—
356C4—732no—
357C4—1461no—
358C4—1461no—
359C4—1462no—
360C4#41×D7311yescharacteristic
361C4#1455663711yescharacteristic
362C2—41no—
363C2—81no—
364C2—2921no—
365C2—5841no—
366C2#1798922911yescharacteristic
367C2#135×D7311yescharacteristic
368C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3304
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17989305C2semidirect
3. #17988932C2semidirect
4. #17988914C2semidirect
5. #17988871C2semidirect
6. #17988817C2semidirect
7. #17988814C2semidirect
8. #17988786C2semidirect
9. #17988751C2semidirect
10. #17988750C2semidirect
11. #17988681C2semidirect
12. #17988650C2semidirect
13. #17988581C2semidirect
14. #17988580C2semidirect
15. #482×C73C2semidirect
185. C73#3304semidirect
190. #482D73semidirect