Finite Group Databasebeta

← #22619899

Subgroups — #22619899

Order 9344.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989160C211yesmaximal, characteristic
2#17989068C211yesmaximal, characteristic
3#17988930C211yesmaximal, characteristic, complemented
4#17988929C211yesmaximal, characteristic, complemented
5#17988927C211yesmaximal, characteristic, complemented
6#17988925C211yesmaximal, characteristic, complemented
7#17988924C211yesmaximal, characteristic, complemented
8#17988917C211yesmaximal, characteristic, complemented
9#17988916C211yesmaximal, characteristic, complemented
10#17988628C211yesmaximal, characteristic, complemented
11#17988624C211yesmaximal, characteristic, complemented
12#17988594C211yesmaximal, characteristic, complemented
13#103×D73C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic
15#484×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556590—21no—
21#14556577—21no—
22#14556576—21no—
23#14556573—21no—
24#14556571C2211yescharacteristic
25#14556570C2211yescharacteristic
26#14556567C2211yescharacteristic
27#14556556—21no—
28#14556553—21no—
29C4×C22⋊D73—21no—
30C4×C22⋊D73—21no—
31#14556550C2211yescharacteristic
32#14556549C2211yescharacteristic
33#14556549C2211yescharacteristic
34#14556549C2211yescharacteristic
35C4⋊C4×D73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—22no—
61C2×Dic146—21no—
62C2×Dic146D411yescharacteristic
63C2×Dic146C2311yescharacteristic
64Q8×D73—22no—
65Q8×D73—22no—
66C2×D292D411yescharacteristic
67C2×C22⋊D73D411yescharacteristic
68C2×C22⋊D73D411yescharacteristic
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73C2×C4×D73C2311yescharacteristic
74#11924011—22no—
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C8×D73—22no—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C2×Q8×C73C2311yescharacteristic
98C22×C4×C73—21no—
99C22×C4×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73C2×D411yescharacteristic
109C22×D73C2×D411yescharacteristic
110C22×D73C2×D411yescharacteristic
111Q8×C73—21no—
112Q8×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—81no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—22no—
123C22⋊D73—22no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130D292—22no—
131C4×D73—21no—
132C4×D73—21no—
133C4×D73—42no—
134C4×D73—81no—
135C4×D73—81no—
136C4×D73#4112yes—
137C4×D73#4112yes—
138Dic146—22no—
139Dic146—21no—
140Dic146—21no—
141Dic146—42no—
142C8×C73—21no—
143C8×C73—21no—
144#10596831—21no—
145#10596831—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73C22×D411yescharacteristic
150C2×D73—21no—
151C2×D73—21no—
152C2×D73—21no—
153C2×D73—21no—
154C2×D73—21no—
155C2×D73#12312yes—
156C4×C73—21no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73C2×#4111yescharacteristic
162C4×C73C2×#4111yescharacteristic
163Dic73—21no—
164Dic73—41no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73#12312yes—
169C2×C73—41no—
170C2×C73C2×#12311yescharacteristic
171C2×C73#57711yescharacteristic
172C2×C73#57811yescharacteristic
173D73—22no—
174D73—41no—
175#3097—731nomaximal, Sylow
176C73#309711yescharacteristic, complemented, Sylow
177#536—731no—
178#520—731no—
179#485—731no—
180#485—731no—
181#485—731no—
182#485—731no—
183#484—731no—
184#484D7311yescharacteristic, complemented
185#483—731no—
186#483—731no—
187#428—731no—
188#427—731no—
189#419—731no—
190C2×#103—731no—
191#408—731no—
192C2×#41—731no—
193C22×Q8—731no—
194C2×M16—731no—
195C22×C8—731no—
196C4⋊Q8—1461no—
197#124—1461no—
198#123—1461no—
199#123—1461no—
200C22⋊Q8—731no—
201C22⋊Q8—731no—
202C22⋊Q8—731no—
203C22⋊Q8C2×D7311yescharacteristic
204C4×Q8—1461no—
205C4×D4—1461no—
206C4×D4—1461no—
207C4×D4—1461no—
208#117—731no—
209#117—731no—
210#117—731no—
211#117—731no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4C2×D7311yescharacteristic
215#107—731no—
216#107—731no—
217#107C2×D7311yescharacteristic
218#107C2×D7311yescharacteristic
219#106—731no—
220#106—731no—
221#106—731no—
222#106—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103C2×D7311yescharacteristic
230#103C2×D7311yescharacteristic
231C22⋊C8—731no—
232C22⋊C8—731no—
233C22⋊C8—731no—
234C22⋊C8C2×D7311yescharacteristic
235#41—1462no—
236#41—1462no—
237C2×Q8—731no—
238C2×Q8—731no—
239C2×Q8—1461no—
240C2×Q8—1462no—
241C2×Q8—1462no—
242C2×Q8C22×D7311yescharacteristic
243C2×D4—731no—
244C2×D4—731no—
245C2×D4—731no—
246C22×C4—21no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252C22×C4C22×D7311yescharacteristic
253M16—1462no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—1462no—
257C2×C8C22×D7311yescharacteristic
258C2×C8C22×D7311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—731no—
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4C22×D7311yescharacteristic
270C4⋊C4C22×D7311yescharacteristic
271C4⋊C4C22×D7311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C42—1461no—
281C42—1461no—
282C42—1461no—
283C42—1461no—
284C23—731no—
285C23—731no—
286C23D4×D7311yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—2922no—
290Q8—1462no—
291Q8—1461no—
292Q8—1461no—
293D4—1462no—
294D4—1462no—
295D4—1462no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2922no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—731no—
307C2×C4—732no—
308C2×C4—732no—
309C2×C4—731no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4D4×D7311yescharacteristic
317C2×C4C23×D7311yescharacteristic
318C8—21no—
319C8—21no—
320C8—1461no—
321C8—1461no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—732no—
326C22—1461no—
327C22—1461no—
328C22—1461no—
329C22—1461no—
330C22—1461no—
331C22C2×D4×D7311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2921no—
338C4—2921no—
339C4—2921no—
340C4—2921no—
341C4—732no—
342C4—1461no—
343C4#41×D7311yescharacteristic
344C4#41×D7311yescharacteristic
345C2—41no—
346C2—2921no—
347C2—1462no—
348C2#123×D7311yescharacteristic
349C2#1798939711yescharacteristic
350C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3097
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #17988930C2semidirect
4. #17988929C2semidirect
5. #17988927C2semidirect
6. #17988925C2semidirect
7. #17988924C2semidirect
8. #17988917C2semidirect
9. #17988916C2semidirect
10. #17988628C2semidirect
11. #17988624C2semidirect
12. #17988594C2semidirect
13. #103×D73C2semidirect
15. #484×C73C2semidirect
176. C73#3097semidirect
184. #484D73semidirect