Finite Group Databasebeta

← #22620194

Subgroups — #22620194

Order 9344.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989210C211yesmaximal, characteristic, complemented
2#17989070C211yesmaximal, characteristic, complemented
3#17988920C211yesmaximal, characteristic, complemented
4#17988901C211yesmaximal, characteristic, complemented
5#17988880C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988811C211yesmaximal, characteristic, complemented
8#17988804C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic
10#17988690C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12Q16×Dic73C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#452×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924013C2211yescharacteristic
18#14556590C2211yescharacteristic
19#14556586—21no—
20#14556580C2211yescharacteristic
21#14556577—21no—
22#14556573—21no—
23#14556571—21no—
24#14556565C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic
26Q8×Dic73C2211yescharacteristic
27Q8×Dic73C2211yescharacteristic
28D4×Dic73—21no—
29D4×Dic73—21no—
30D4×Dic73C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556550—21no—
34#14556550C2211yescharacteristic
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×D292C2311yescharacteristic
61C2×C22⋊D73—21no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66#11924015—22no—
67#11924013—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73D411yescharacteristic
75C4⋊Dic73D411yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73D411yescharacteristic
83C22⋊Dic73D411yescharacteristic
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C4×Dic73C2311yescharacteristic
93#41×C73—22no—
94#41×C73—22no—
95C2×Q8×C73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100C22×C4×C73C2311yescharacteristic
101Q16×C73—22no—
102SD16×C73—22no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73—21no—
114Q8×C73#4112yes—
115D4×C73—24no—
116D4×C73—21no—
117D4×C73#4112yes—
118C2×C4×C73—24no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—81no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—81no—
131C2×Dic73—81no—
132C2×Dic73—81no—
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—21no—
138D292—21no—
139C4×D73—81no—
140Dic146—81no—
141C8×C73—21no—
142C8×C73—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—21no—
146C22×C73—22no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C4×C73—21no—
156C4×C73—22no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73C2×#4111yescharacteristic
160C4×C73C2×#4111yescharacteristic
161Dic73—21no—
162Dic73—21no—
163Dic73—21no—
164Dic73—21no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168C2×C73—41no—
169C2×C73—42no—
170C2×C73#52511yescharacteristic
171C2×C73#57611yescharacteristic
172C2×C73#57811yescharacteristic
173D73—81no—
174#3124—731nomaximal, Sylow
175C73#312411yescharacteristic, complemented, Sylow
176#542—731no—
177#520—731no—
178#484—731no—
179#480—731no—
180#477—731no—
181#474—731no—
182#464—731no—
183#463—731no—
184#452D7311yescharacteristic, complemented
185#449—731no—
186#440—731no—
187#440—731no—
188C4×Q16—731no—
189C4×D8—731no—
190#433—731no—
191C2×#41C2×D7311yescharacteristic
192C2×Q16C2×D7311yescharacteristic
193C2×SD16—731no—
194C2×SD16C2×D7311yescharacteristic
195C2×D8—731no—
196C4⋊Q8—731no—
197#126—1461no—
198#124—731no—
199#124—1461no—
200#123—1461no—
201C22⋊Q8—1461no—
202C22⋊Q8C2×D7311yescharacteristic
203#121—731no—
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8—731no—
207C4×D4—731no—
208C4×D4—731no—
209C4×D4—731no—
210C4×D4—1461no—
211C4×D4—1461no—
212#117—731no—
213#117—1461no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—1461no—
216#107—731no—
217#107—731no—
218#107—731no—
219#107—731no—
220C4⋊C8—731no—
221C4⋊C8—731no—
222#103—731no—
223#103—731no—
224#103—731no—
225#103C2×D7311yescharacteristic
226#102—731no—
227#102—731no—
228#102—731no—
229#102C2×D7311yescharacteristic
230C22⋊C8—731no—
231C22⋊C8C2×D7311yescharacteristic
232#97—731no—
233C4×C8—731no—
234#41—22no—
235#41—22no—
236C2×Q8—1461no—
237C2×Q8C22×D7311yescharacteristic
238C2×Q8C22×D7311yescharacteristic
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4C22×D7311yescharacteristic
243C22×C4—21no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4C22×D7311yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—1462no—
252D8—1462no—
253C2×C8—731no—
254C2×C8—731no—
255C2×C8C22×D7311yescharacteristic
256C2×C8C22×D7311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—731no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4C22×D7311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—731no—
271C22⋊C4—731no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C42—731no—
279C42—731no—
280C42—1461no—
281C42—1461no—
282C42—1461no—
283C23—21no—
284C23—1461no—
285C23D4×D7311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—5841no—
290Q8#1192402712yes—
291D4—24no—
292D4—21no—
293D4—5841no—
294D4—1461no—
295D4—1461no—
296D4#1192402712yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—5841no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—5841no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4D4×D7311yescharacteristic
315C2×C4C23×D7311yescharacteristic
316C8—21no—
317C8—21no—
318C8—1461no—
319C8—1461no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—2921no—
327C22—2921no—
328C22—2921no—
329C22C2×D4×D7311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—2921no—
335C4—2921no—
336C4—2921no—
337C4—1461no—
338C4—1461no—
339C4—1461no—
340C4—1461no—
341C4C2×#1192402711yescharacteristic
342C4C2×#1192402711yescharacteristic
343C2—41no—
344C2—42no—
345C2—5841no—
346C2#1798909311yescharacteristic
347C2#1798938911yescharacteristic
348C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#452×C73C2
socleC22×C73C22×D4
hypercenter#452D73
hypocenterC73#3124
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #17989210C2semidirect
2. #17989070C2semidirect
3. #17988920C2semidirect
4. #17988901C2semidirect
5. #17988880C2semidirect
6. #17988865C2semidirect
7. #17988811C2semidirect
8. #17988804C2semidirect
10. #17988690C2semidirect
11. #17988688C2semidirect
12. Q16×Dic73C2semidirect
13. #17988667C2semidirect
14. #17988645C2semidirect
15. #452×C73C2semidirect
175. C73#3124semidirect
184. #452D73semidirect