Finite Group Databasebeta

← #22620197

Subgroups — #22620197

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#17989209C211yesmaximal, characteristic, complemented
2#17989066C211yesmaximal, characteristic, complemented
3#17988921C211yesmaximal, characteristic, complemented
4#17988902C211yesmaximal, characteristic, complemented
5#17988881C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988812C211yesmaximal, characteristic, complemented
8#17988804C211yesmaximal, characteristic, complemented
9#17988746C211yesmaximal, characteristic, complemented
10#17988733C211yesmaximal, characteristic
11#17988689C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988649C211yesmaximal, characteristic, complemented
15#440×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556585—21no—
22#14556580C2211yescharacteristic
23#14556579—21no—
24#14556576—21no—
25#14556569—21no—
26#14556567C2211yescharacteristic
27#14556566C2211yescharacteristic
28C4×Dic146C2211yescharacteristic
29#14556556C2211yescharacteristic
30C4×D292C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32C4×C22⋊D73—21no—
33#14556551—21no—
34#14556548C2211yescharacteristic
35#14556547—21no—
36C2×#11924007—21no—
37C4⋊C4×D73C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—22no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924018—22no—
72#11924017—22no—
73#11924013—22no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005D411yescharacteristic
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99SD16×C73—22no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73—21no—
110C22×D73C2×D411yescharacteristic
111Q8×C73—21no—
112Q8×C73—21no—
113D4×C73—21no—
114D4×C73#4112yes—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—81no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—24no—
123C2×Dic73—24no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—81no—
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131D292—21no—
132D292—21no—
133D292—81no—
134C4×D73—21no—
135C4×D73—21no—
136C4×D73—81no—
137C4×D73—81no—
138Dic146—21no—
139Dic146—81no—
140Dic146#4112yes—
141C8×C73—21no—
142C8×C73—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—22no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73C22×D411yescharacteristic
149C2×D73—21no—
150C2×D73—21no—
151C2×D73—21no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73C2×#4111yescharacteristic
161C4×C73C2×#4111yescharacteristic
162Dic73—22no—
163Dic73—21no—
164Dic73—21no—
165Dic73—21no—
166Dic73—41no—
167Dic73—41no—
168C2×C73—42no—
169C2×C73#52511yescharacteristic
170C2×C73#57611yescharacteristic
171C2×C73#57811yescharacteristic
172D73—41no—
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#452—731no—
185#449—731no—
186#440—731no—
187#440D7311yescharacteristic, complemented
188C4×Q16—731no—
189C4×D8—731no—
190#433—731no—
191C2×#41—731no—
192C2×Q16—731no—
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—731no—
202C22⋊Q8—1461no—
203#121—731no—
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8C2×D7311yescharacteristic
207C4×D4—731no—
208C4×D4—731no—
209C4×D4—1461no—
210C4×D4—1461no—
211C4×D4C2×D7311yescharacteristic
212#117—731no—
213#117—1461no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—1461no—
216#107—731no—
217#107—731no—
218#107—731no—
219#107C2×D7311yescharacteristic
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⋊C8—731no—
232#97C2×D7311yescharacteristic
233C4×C8—731no—
234#41—1462no—
235#41—1462no—
236C2×Q8—731no—
237C2×Q8—1461no—
238C2×Q8C22×D7311yescharacteristic
239C2×D4—731no—
240C2×D4—1461no—
241C2×D4—1461no—
242C2×D4C22×D7311yescharacteristic
243C22×C4—21no—
244C22×C4—731no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4—1461no—
249Q16—1462no—
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—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4C22×D7311yescharacteristic
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—21no—
279C42—731no—
280C42—1461no—
281C42—1461no—
282C42C22×D7311yescharacteristic
283C23—21no—
284C23—731no—
285C23—1461no—
286Q8—21no—
287Q8—21no—
288Q8—5841no—
289Q8—732no—
290Q8—1461no—
291D4—21no—
292D4—5841no—
293D4—1464no—
294D4—1461no—
295D4—1461no—
296D4#1192402812yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—5841no—
302C2×C4—5841no—
303C2×C4—5841no—
304C2×C4—731no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1464no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4D4×D7311yescharacteristic
314C2×C4D4×D7311yescharacteristic
315C2×C4C23×D7311yescharacteristic
316C8—21no—
317C8—21no—
318C8—1461no—
319C8—1461no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—2921no—
324C22—2921no—
325C22—2921no—
326C22—1461no—
327C22—1461no—
328C22—1461no—
329C22C2×D4×D7311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2921no—
336C4—2921no—
337C4—1461no—
338C4—1461no—
339C4—1461no—
340C4—1462no—
341C4#41×D7311yescharacteristic
342C4C2×#1192402811yescharacteristic
343C2—42no—
344C2—2921no—
345C2—5841no—
346C2#1798909611yescharacteristic
347C2#1798939111yescharacteristic
348C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#440×C73C2
socleC22×C73C22×D4
hypercenter#440D73
hypocenterC73#3124
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #17989209C2semidirect
2. #17989066C2semidirect
3. #17988921C2semidirect
4. #17988902C2semidirect
5. #17988881C2semidirect
6. #17988865C2semidirect
7. #17988812C2semidirect
8. #17988804C2semidirect
9. #17988746C2semidirect
11. #17988689C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924013C2semidirect
14. #17988649C2semidirect
15. #440×C73C2semidirect
175. C73#3124semidirect
187. #440D73semidirect