Finite Group Databasebeta

← #22621010

Subgroups — #22621010

Order 9344.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989197C211yesmaximal, characteristic, complemented
2#17989161C211yesmaximal, characteristic
3#17988980C211yesmaximal, characteristic, complemented
4#17988965C211yesmaximal, characteristic, complemented
5#17988954C211yesmaximal, characteristic, complemented
6#17988943C211yesmaximal, characteristic, complemented
7#17988812C211yesmaximal, characteristic, complemented
8#17988811C211yesmaximal, characteristic, complemented
9#17988796C211yesmaximal, characteristic, complemented
10#17988795C211yesmaximal, characteristic, complemented
11#17988751C211yesmaximal, characteristic
12#17988747C211yesmaximal, characteristic
13#17988743C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#451×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20C2×#11924018C2211yescharacteristic
21C2×#11924017C2211yescharacteristic
22C2×#11924015C2211yescharacteristic
23#14556589C2211yescharacteristic
24#14556589C2211yescharacteristic
25#14556589C2211yescharacteristic
26#14556584—21no—
27#14556584—21no—
28#14556582—21no—
29#14556582C2211yescharacteristic
30#14556581—21no—
31#14556580C2211yescharacteristic
32#14556580C2211yescharacteristic
33#14556574—21no—
34#14556574—21no—
35#14556570C2211yescharacteristic
36#14556567—21no—
37#14556567—21no—
38Q8×Dic73C2211yescharacteristic
39#14556556C2211yescharacteristic
40#14556550C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×Q16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C4×D73—21no—
66Dic292—41no—
67#11924018—41no—
68#11924018—41no—
69#11924018—41no—
70#11924017—41no—
71#11924015—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73D411yescharacteristic
77C4⋊Dic73D411yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73D411yescharacteristic
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98C4×Dic73C2311yescharacteristic
99C2×Q8×C73—21no—
100C2×Q8×C73—41no—
101C2×Q8×C73—41no—
102C2×Q8×C73C2311yescharacteristic
103C2×Q8×C73C2311yescharacteristic
104C2×Q8×C73C2311yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73C2311yescharacteristic
107Q16×C73—41no—
108Q16×C73—41no—
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—21no—
122Q8×C73—42no—
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—42no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—42no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142C4×D73—42no—
143Dic146—21no—
144Dic146—21no—
145Dic146—21no—
146Dic146—21no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73C22×D411yescharacteristic
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C4×C73—21no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73H(5,𝔽2)11yescharacteristic
164C4×C73H(5,𝔽2)11yescharacteristic
165Dic73—21no—
166Dic73—21no—
167Dic73—21no—
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—41no—
173C2×C73#53511yescharacteristic
174C2×C73#57811yescharacteristic
175C2×C73#57811yescharacteristic
176D73—81no—
177#3223—731nomaximal, Sylow
178C73#322311yescharacteristic, complemented, Sylow
179#541—731no—
180#536—731no—
181#497—731no—
182#494—731no—
183#491—731no—
184#488—731no—
185#464—731no—
186#464—731no—
187#462—731no—
188#462—731no—
189#452—731no—
190#452—731no—
191#451—731no—
192#451D7311yescharacteristic, complemented
193#433—731no—
194C2×#41—731no—
195C22×Q8C2×D7311yescharacteristic
196C2×Q16—731no—
197C2×Q16—731no—
198C2×Q16—731no—
199C2×Q16—731no—
200C2×Q16C2×D7311yescharacteristic
201C2×Q16C2×D7311yescharacteristic
202C2×SD16—731no—
203C2×SD16—731no—
204C4⋊Q8—731no—
205C4⋊Q8—731no—
206C4⋊Q8—731no—
207#126—1461no—
208#126—1461no—
209#125—731no—
210#125—1461no—
211#125—1461no—
212#124—731no—
213#124—731no—
214#123—1461no—
215#123—1461no—
216C22⋊Q8—731no—
217C22⋊Q8—1461no—
218C22⋊Q8—1461no—
219C22⋊Q8C2×D7311yescharacteristic
220C4×Q8—731no—
221C4×Q8—731no—
222#117—731no—
223C4⋊C8—731no—
224C4⋊C8—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103C2×D7311yescharacteristic
230#103C2×D7311yescharacteristic
231#102—731no—
232#102—731no—
233C22⋊C8—731no—
234C22⋊C8C2×D7311yescharacteristic
235#97—731no—
236C4×C8—731no—
237#41—2921no—
238#41—2921no—
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—731no—
243C2×Q8—731no—
244C2×Q8C22×D7311yescharacteristic
245C2×Q8C22×D7311yescharacteristic
246C2×Q8C22×D7311yescharacteristic
247C2×D4—731no—
248C2×D4—1461no—
249C22×C4—21no—
250C22×C4—1461no—
251C22×C4C22×D7311yescharacteristic
252Q16—41no—
253Q16—41no—
254Q16—2921no—
255Q16—2921no—
256Q16—2921no—
257Q16—2921no—
258SD16—2921no—
259SD16—2921no—
260C2×C8—731no—
261C2×C8—731no—
262C2×C8C22×D7311yescharacteristic
263C2×C8C22×D7311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4C22×D7311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—731no—
282C22⋊C4—731no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C42—731no—
289C42—731no—
290C42—1461no—
291C42—1461no—
292C23—1461no—
293C23D4×D7311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—1461no—
302Q8—1461no—
303Q8—1461no—
304Q8—1461no—
305D4—2922no—
306D4—1461no—
307D4—1461no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—2922no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4D4×D7311yescharacteristic
324C2×C4C23×D7311yescharacteristic
325C8—21no—
326C8—21no—
327C8—1461no—
328C8—1461no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22C2×D4×D7311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2921no—
342C4—2921no—
343C4—2921no—
344C4—1461no—
345C4—1461no—
346C4—1461no—
347C4—1461no—
348C4#1455663611yescharacteristic
349C4#1455663611yescharacteristic
350C2—41no—
351C2—5841no—
352C2#1798915211yescharacteristic
353C2#1798940011yescharacteristic
354C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3223
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #17989197C2semidirect
3. #17988980C2semidirect
4. #17988965C2semidirect
5. #17988954C2semidirect
6. #17988943C2semidirect
7. #17988812C2semidirect
8. #17988811C2semidirect
9. #17988796C2semidirect
10. #17988795C2semidirect
13. #17988743C2semidirect
14. #17988645C2semidirect
15. #451×C73C2semidirect
178. C73#3223semidirect
192. #451D73semidirect