Finite Group Databasebeta

← #22622492

Subgroups — #22622492

Order 9344.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989285C211yesmaximal, characteristic
2#17989276C211yesmaximal, characteristic, complemented
3#17988988C211yesmaximal, characteristic, complemented
4#17988930C211yesmaximal, characteristic, complemented
5#17988917C211yesmaximal, characteristic, complemented
6#17988911C211yesmaximal, characteristic, complemented
7#17988907C211yesmaximal, characteristic, complemented
8#17988897C211yesmaximal, characteristic, complemented
9#17988890C211yesmaximal, characteristic, complemented
10#17988834C211yesmaximal, characteristic, complemented
11#17988833C211yesmaximal, characteristic, complemented
12#17988674C211yesmaximal, characteristic, complemented
13#17988663C211yesmaximal, characteristic, complemented
14#17988626C211yesmaximal, characteristic, complemented
15#428×C73C211yesmaximal, characteristic, complemented
16C2×#11924017C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18#14556586—21no—
19#14556584—21no—
20#14556583—21no—
21#14556582C2211yescharacteristic
22#14556582C2211yescharacteristic
23#14556576—21no—
24#14556573—21no—
25#14556571C2211yescharacteristic
26#14556570C2211yescharacteristic
27#14556566C2211yescharacteristic
28#14556565—21no—
29#14556565C2211yescharacteristic
30#14556556C2211yescharacteristic
31#14556553C2211yescharacteristic
32C4×C22⋊D73—21no—
33C4×C22⋊D73C2211yescharacteristic
34#14556549C2211yescharacteristic
35#14556548—21no—
36C4⋊C4×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#106×C73C2211yescharacteristic
58#106×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C2×D292—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73D411yescharacteristic
64C2×C4×D73—21no—
65C2×C4×D73—21no—
66C2×C4×D73C2311yescharacteristic
67#11924017—22no—
68#11924011—22no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007D411yescharacteristic
82C22⋊Dic73—21no—
83C22⋊Dic73D411yescharacteristic
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005D411yescharacteristic
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C22×C4×C73—21no—
94C22×C4×C73C2311yescharacteristic
95M16×C73—22no—
96C2×C8×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73C2311yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C42×C73—21no—
105C23×C73C2×D411yescharacteristic
106C22×D73—21no—
107C22×D73C2×D411yescharacteristic
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—81no—
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2411yescharacteristic
117C22⋊D73—41no—
118C22⋊D73—42no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125D292—21no—
126D292—21no—
127D292—81no—
128C4×D73—21no—
129C4×D73—21no—
130C4×D73—42no—
131C4×D73—81no—
132Dic146—21no—
133Dic146—21no—
134C8×C73—21no—
135C8×C73#4112yes—
136#10596831—21no—
137#10596831—21no—
138C22×C73—21no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73C22×D411yescharacteristic
142C2×D73—21no—
143C2×D73—21no—
144C2×D73—21no—
145C2×D73—41no—
146C2×D73—41no—
147C2×D73—41no—
148C4×C73—21no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73—41no—
153C4×C73C2×#4111yescharacteristic
154C4×C732−1+411yescharacteristic
155Dic73—21no—
156Dic73—21no—
157Dic73—21no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161C2×C73—41no—
162C2×C73#54711yescharacteristic
163C2×C73#57511yescharacteristic
164C2×C73#57711yescharacteristic
165D73—41no—
166D73—81no—
167#3351—731nomaximal, Sylow
168C73#335111yescharacteristic, complemented, Sylow
169#553—731no—
170#552—731no—
171#499—731no—
172#485—731no—
173#483—731no—
174#482—731no—
175#481—731no—
176#479—731no—
177#478—731no—
178#468—731no—
179#468—731no—
180C4×SD16—731no—
181#436—731no—
182#428—731no—
183#428D7311yescharacteristic, complemented
184C2×SD16—731no—
185C2×M16—731no—
186C2×M16C2×D7311yescharacteristic
187#126—1461no—
188#126—1461no—
189#125—731no—
190#125—731no—
191#125—1461no—
192#123—1461no—
193#123—1461no—
194C22⋊Q8—731no—
195C22⋊Q8—731no—
196#121—731no—
197#121—731no—
198#121—1461no—
199C4×Q8—731no—
200C4×D4—731no—
201C4×D4—731no—
202C4×D4—1461no—
203#117—731no—
204#117—1461no—
205#117C2×D7311yescharacteristic
206C2×C4⋊C4—731no—
207C2×C4⋊C4C2×D7311yescharacteristic
208#107—731no—
209#107—731no—
210#107C2×D7311yescharacteristic
211#107C2×D7311yescharacteristic
212#106—731no—
213#106—731no—
214#106—731no—
215#106C2×D7311yescharacteristic
216#106C2×D7311yescharacteristic
217C4⋊C8—731no—
218#103—731no—
219#103—731no—
220#103—731no—
221#102—731no—
222#102—731no—
223#102—731no—
224C22⋊C8—731no—
225C22⋊C8—731no—
226C4×C8—731no—
227C2×Q8—731no—
228C2×D4—731no—
229C2×D4—731no—
230C2×D4—1461no—
231C2×D4—1461no—
232C22×C4—21no—
233C22×C4—731no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4C22×D7311yescharacteristic
237SD16—1462no—
238M16—22no—
239M16—1462no—
240C2×C8—731no—
241C2×C8—731no—
242C2×C8C22×D7311yescharacteristic
243C2×C8C22×D7311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—731no—
246C4⋊C4—731no—
247C4⋊C4—731no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4C22×D7311yescharacteristic
257C4⋊C4C22×D7311yescharacteristic
258C4⋊C4C22×D7311yescharacteristic
259C4⋊C4C22×D7311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—731no—
262C22⋊C4—731no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C42—21no—
270C42—731no—
271C42—1461no—
272C42—1461no—
273C23—731no—
274C23—1461no—
275C23D4×D7311yescharacteristic
276Q8—1461no—
277Q8—1461no—
278D4—2922no—
279D4—2921no—
280D4—5841no—
281D4—1461no—
282D4—1461no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—2922no—
291C2×C4—5841no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—731no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4D4×D7311yescharacteristic
301C2×C4C23×D7311yescharacteristic
302C8—21no—
303C8—1461no—
304C8—1461no—
305C8#1192402812yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—2921no—
310C22—2921no—
311C22—2921no—
312C22—1461no—
313C22—1461no—
314C22—1461no—
315C22C2×D4×D7311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—2921no—
322C4—2921no—
323C4—2921no—
324C4—1461no—
325C4—1461no—
326C4—1461no—
327C4C2×#1192402811yescharacteristic
328C4#1455663911yescharacteristic
329C2—41no—
330C2—2921no—
331C2—5841no—
332C2#1798923811yescharacteristic
333C2#1798938611yescharacteristic
334C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3351
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #17989276C2semidirect
3. #17988988C2semidirect
4. #17988930C2semidirect
5. #17988917C2semidirect
6. #17988911C2semidirect
7. #17988907C2semidirect
8. #17988897C2semidirect
9. #17988890C2semidirect
10. #17988834C2semidirect
11. #17988833C2semidirect
12. #17988674C2semidirect
13. #17988663C2semidirect
14. #17988626C2semidirect
15. #428×C73C2semidirect
168. C73#3351semidirect
183. #428D73semidirect