Finite Group Databasebeta

← #22622027

Subgroups — #22622027

Order 9344.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989277C211yesmaximal, characteristic, complemented
2#17988955C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988920C211yesmaximal, characteristic, complemented
5#17988887C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988826C211yesmaximal, characteristic, complemented
8#17988794C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988749C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14#17988583C211yesmaximal, characteristic, complemented
15#547×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21#14556584—21no—
22#14556583C2211yescharacteristic
23#14556581—21no—
24#14556572—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic
27C4×Dic146C2211yescharacteristic
28#14556550C2211yescharacteristic
29#14556547—21no—
30C2×C4⋊Dic73C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556515C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556514C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556512C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C2×#41×C73C2211yescharacteristic
50C4⋊Q8×C73C2211yescharacteristic
51#123×C73—21no—
52#123×C73—21no—
53C22⋊Q8×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73—21no—
56C4×D4×C73C2211yescharacteristic
57C4×D4×C73C2211yescharacteristic
58C2×C4⋊C4×C73—21no—
59C2×Dic146C2311yescharacteristic
60C22×Dic73—21no—
61#11924018—41no—
62#11924018—41no—
63#11924016—22no—
64#11924012—41no—
65C2×#10596831—41no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84#41×C73—22no—
85#41×C73—22no—
86#41×C73—41no—
87#41×C73—41no—
88C2×Q8×C73C2311yescharacteristic
89C2×Q8×C73C2311yescharacteristic
90C2×D4×C73—21no—
91C2×D4×C73—21no—
92C2×D4×C73D411yescharacteristic
93C2×D4×C73C2311yescharacteristic
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73D411yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118D4×C73—21no—
119D4×C73—41no—
120D4×C73—42no—
121D4×C73—42no—
122D4×C73#4112yes—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73—42no—
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2411yescharacteristic
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—42no—
143Dic146—21no—
144Dic146—21no—
145#10596831—21no—
146#10596831—21no—
147#10596831—21no—
148#10596831—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—22no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73C2×#4111yescharacteristic
167C4×C73H(5,𝔽2)11yescharacteristic
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—41no—
173C2×C73—41no—
174C2×C73—42no—
175C2×C73#54611yescharacteristic
176C2×C73#57511yescharacteristic
177C2×C73#57811yescharacteristic
178#3315—731nomaximal, Sylow
179C73#331511yescharacteristic, complemented, Sylow
180#552—731no—
181#547D7311yescharacteristic
182#491—731no—
183#485—731no—
184#484—731no—
185#478—731no—
186#470—731no—
187#467—731no—
188#462—731no—
189#452—731no—
190#452—731no—
191#440—731no—
192#435—731no—
193#417—731no—
194#416—731no—
195C2×#41C2×D7311yescharacteristic
196C2×#41C2×D7311yescharacteristic
197C2×Q16—731no—
198C2×Q16—731no—
199C2×SD16—731no—
200C2×M16—731no—
201C22×C8—731no—
202C4⋊Q8C2×D7311yescharacteristic
203#126—1461no—
204#125—731no—
205#125—1461no—
206#123—21no—
207#123—21no—
208#123—1461no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8C2×D7311yescharacteristic
212C22⋊Q8C2×D7311yescharacteristic
213#121—21no—
214C4×Q8—731no—
215C4×D4C2×D7311yescharacteristic
216C4×D4C2×D7311yescharacteristic
217#117—731no—
218#117—1461no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—731no—
221#107—731no—
222#107—731no—
223#106—731no—
224C4⋊C8—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235C22⋊C8—731no—
236C22⋊C8—731no—
237#97—731no—
238#41—22no—
239#41—22no—
240#41—41no—
241#41—41no—
242C2×Q8—731no—
243C2×Q8C22×D7311yescharacteristic
244C2×Q8C22×D7311yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C22⋊D7311yescharacteristic
248C2×D4C22×D7311yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—1461no—
253C22×C4C22×D7311yescharacteristic
254C22×C4C22×D7311yescharacteristic
255Q16—2921no—
256Q16—2921no—
257SD16—1462no—
258M16—2921no—
259C2×C8—2921no—
260C2×C8—731no—
261C2×C8—731no—
262C2×C8—731no—
263C2×C8—731no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
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
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4C22⋊D7311yescharacteristic
286C22⋊C4C22⋊D7311yescharacteristic
287C42—1461no—
288C42—1461no—
289C42C22×D7311yescharacteristic
290C23—21no—
291C23C2×C22⋊D7311yescharacteristic
292C23C2×C22⋊D7311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—1461no—
298Q8—1461no—
299D4—21no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4#1192402712yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—2922no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4C2×C22⋊D7311yescharacteristic
320C2×C4C2×C22⋊D7311yescharacteristic
321C2×C4C2×C22⋊D7311yescharacteristic
322C2×C4C2×C22⋊D7311yescharacteristic
323C2×C4C23×D7311yescharacteristic
324C8—1461no—
325C8—1461no—
326C8—1461no—
327C8—1461no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D7311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4C2×#1192402711yescharacteristic
350C4#1455663611yescharacteristic
351C2—41no—
352C2—41no—
353C2—42no—
354C2#1798923111yescharacteristic
355C2#1798938511yescharacteristic
356C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#547×C73C2
socleC22×C73C22×D4
hypercenter#547D73
hypocenterC73#3315
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #17989277C2semidirect
2. #17988955C2semidirect
3. #17988925C2semidirect
4. #17988920C2semidirect
5. #17988887C2semidirect
6. #17988843C2semidirect
7. #17988826C2semidirect
8. #17988794C2semidirect
9. #17988749C2semidirect
10. #17988749C2semidirect
11. #17988687C2semidirect
12. #17988659C2semidirect
13. #17988588C2semidirect
14. #17988583C2semidirect
179. C73#3315semidirect