Finite Group Databasebeta

← #22619923

Subgroups — #22619923

Order 9344.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989166C211yesmaximal, characteristic
2#17989067C211yesmaximal, characteristic, complemented
3#17988930C211yesmaximal, characteristic, complemented
4#17988928C211yesmaximal, characteristic, complemented
5#17988919C211yesmaximal, characteristic, complemented
6#17988918C211yesmaximal, characteristic, complemented
7#17988910C211yesmaximal, characteristic, complemented
8#17988904C211yesmaximal, characteristic, complemented
9#17988903C211yesmaximal, characteristic, complemented
10#17988628C211yesmaximal, characteristic, complemented
11#106×D73C211yesmaximal, characteristic, complemented
12#17988585C211yesmaximal, characteristic, complemented
13#17988580C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556571C2211yescharacteristic
21#14556570C2211yescharacteristic
22#14556568—21no—
23#14556564—21no—
24#14556563—21no—
25#14556562—21no—
26#14556562C2211yescharacteristic
27C4×Dic146—21no—
28C4×D292—21no—
29#14556551—21no—
30#14556551—21no—
31#14556549C2211yescharacteristic
32#14556549C2211yescharacteristic
33C2×C4⋊Dic73C2211yescharacteristic
34C4⋊C4×D73C2211yescharacteristic
35C4⋊C4×D73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37#14556524C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
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—22no—
61#11924027—22no—
62#11924027—22no—
63C2×Dic146D411yescharacteristic
64C2×Dic146C2311yescharacteristic
65C2×D292D411yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73D411yescharacteristic
69C2×C22⋊D73D411yescharacteristic
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76C2×C4×D73C2311yescharacteristic
77#11924011—22no—
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C8×D73—22no—
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73C2×D411yescharacteristic
111C22×D73C2×D411yescharacteristic
112D4×C73—21no—
113D4×C73—21no—
114D4×C73—81no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—22no—
123C22⋊D73—22no—
124C22⋊D73—42no—
125C22⋊D73—81no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—42no—
131C2×Dic73—81no—
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—22no—
135C4×D73—21no—
136C4×D73—21no—
137C4×D73—81no—
138C4×D73—81no—
139C4×D73—81no—
140C4×D73#4112yes—
141C4×D73#4112yes—
142Dic146—22no—
143Dic146—21no—
144Dic146—21no—
145C8×C73—21no—
146C8×C73—21no—
147#10596831—21no—
148#10596831—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—21no—
161C2×D73#12312yes—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73C2×#4111yescharacteristic
167C4×C73C2×#4111yescharacteristic
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173Dic73#12312yes—
174C2×C73—41no—
175C2×C73—81no—
176C2×C73C2×#12311yescharacteristic
177C2×C73#57711yescharacteristic
178C2×C73#57711yescharacteristic
179D73—22no—
180D73—41no—
181#3099—731nomaximal, Sylow
182C73#309911yescharacteristic, complemented, Sylow
183#537—731no—
184#520—731no—
185#485—731no—
186#485—731no—
187#483—731no—
188#483—731no—
189#482—731no—
190#482D7311yescharacteristic, complemented
191#481—731no—
192#481—731no—
193#428—731no—
194C2×#106—731no—
195#417—731no—
196#416—731no—
197#408—731no—
198C2×#41—731no—
199C2×#41—731no—
200C2×M16—731no—
201C22×C8—731no—
202C22⋊Q8—731no—
203C22⋊Q8—731no—
204C22⋊Q8—1461no—
205#121—731no—
206#121—1461no—
207#121—1461no—
208#121—1461no—
209#121C2×D7311yescharacteristic
210C4×Q8—1461no—
211C4×D4—1461no—
212C4×D4—1461no—
213C4×D4—1461no—
214#117—731no—
215#117—731no—
216#117C2×D7311yescharacteristic
217C2×C4⋊C4—731no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221#107—731no—
222#107C2×D7311yescharacteristic
223#106—731no—
224#106—731no—
225#106—731no—
226#106—731no—
227#106—731no—
228#106C2×D7311yescharacteristic
229#103—731no—
230#103—731no—
231#103—731no—
232#103—731no—
233#102—731no—
234#102—731no—
235#102C2×D7311yescharacteristic
236#102C2×D7311yescharacteristic
237C22⋊C8—731no—
238C22⋊C8—731no—
239C22⋊C8—731no—
240C22⋊C8C2×D7311yescharacteristic
241#41—1462no—
242#41—1462no—
243#41—1462no—
244#41—1462no—
245C2×Q8—731no—
246C2×Q8—731no—
247C2×D4—21no—
248C2×D4—731no—
249C2×D4—731no—
250C2×D4—731no—
251C2×D4—1461no—
252C2×D4—1461no—
253C2×D4C22×D7311yescharacteristic
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4C22×D7311yescharacteristic
262M16—1462no—
263C2×C8—731no—
264C2×C8—731no—
265C2×C8—1462no—
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C4⋊C4C22×D7311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C42—21no—
288C42—1461no—
289C42—1461no—
290C23—21no—
291C23—731no—
292C23—731no—
293C23D4×D7311yescharacteristic
294Q8—1462no—
295Q8—1461no—
296Q8—1461no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—2922no—
301D4—5841no—
302D4—1462no—
303D4—1462no—
304D4—1462no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2922no—
311C2×C4—5841no—
312C2×C4—5841no—
313C2×C4—5841no—
314C2×C4—5841no—
315C2×C4—731no—
316C2×C4—732no—
317C2×C4—732no—
318C2×C4—731no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4D4×D7311yescharacteristic
326C2×C4C23×D7311yescharacteristic
327C8—21no—
328C8—21no—
329C8—1461no—
330C8—1461no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—732no—
338C22—1461no—
339C22—1461no—
340C22—1461no—
341C22—1461no—
342C22—1461no—
343C22C2×D4×D7311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2921no—
349C4—2921no—
350C4—2921no—
351C4—2921no—
352C4—732no—
353C4—1461no—
354C4#41×D7311yescharacteristic
355C4#41×D7311yescharacteristic
356C2—41no—
357C2—81no—
358C2—2921no—
359C2—1462no—
360C2#123×D7311yescharacteristic
361C2#1798939411yescharacteristic
362C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3099
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
2. #17989067C2semidirect
3. #17988930C2semidirect
4. #17988928C2semidirect
5. #17988919C2semidirect
6. #17988918C2semidirect
7. #17988910C2semidirect
8. #17988904C2semidirect
9. #17988903C2semidirect
10. #17988628C2semidirect
11. #106×D73C2semidirect
12. #17988585C2semidirect
13. #17988580C2semidirect
14. #17988552C2semidirect
15. #482×C73C2semidirect
182. C73#3099semidirect
190. #482D73semidirect