Finite Group Databasebeta

← #22622046

Subgroups — #22622046

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989295C211yesmaximal, characteristic, complemented
2#17989248C211yesmaximal, characteristic
3#17988948C211yesmaximal, characteristic, complemented
4#17988916C211yesmaximal, characteristic, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988842C211yesmaximal, characteristic, complemented
8#17988818C211yesmaximal, characteristic, complemented
9#17988811C211yesmaximal, characteristic, complemented
10#17988748C211yesmaximal, characteristic, complemented
11#17988694C211yesmaximal, characteristic, complemented
12#17988655C211yesmaximal, characteristic, complemented
13#17988587C211yesmaximal, characteristic, complemented
14C2×#14556515C211yesmaximal, characteristic, complemented
15#451×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556581—21no—
22#14556580—21no—
23#14556580C2211yescharacteristic
24#14556571—21no—
25#14556568—21no—
26#14556567—21no—
27#14556567C2211yescharacteristic
28#14556567C2211yescharacteristic
29#14556565—21no—
30#14556565C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32Q8×Dic73C2211yescharacteristic
33C4×C22⋊D73—21no—
34C4×C22⋊D73C2211yescharacteristic
35#14556551—21no—
36C2×C4⋊Dic73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic
54C2×Q16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924029—22no—
60#11924029—41no—
61C2×Dic146—21no—
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73D411yescharacteristic
66C22×Dic73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73C2311yescharacteristic
70#11924015—41no—
71#11924011—41no—
72C2×#10596831—41no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007D411yescharacteristic
86C22⋊Dic73D411yescharacteristic
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73—21no—
97C2×Q8×C73—22no—
98C2×Q8×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×Q8×C73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73C2311yescharacteristic
104Q16×C73—22no—
105Q16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C23×C73C2×D411yescharacteristic
112C22×D73—21no—
113C22×D73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—21no—
119Q8×C73—42no—
120Q8×C73#4112yes—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—42no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—22no—
131C22⋊D73—42no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—81no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139D292—21no—
140D292—21no—
141D292—42no—
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—42no—
145C4×D73—81no—
146Dic146—81no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73#13712yes—
154C22×C73C22×D411yescharacteristic
155C2×D73—21no—
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C4×C73—22no—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73C2×#4111yescharacteristic
167C4×C73H(5,𝔽2)11yescharacteristic
168Dic73—21no—
169Dic73—21no—
170Dic73—21no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—22no—
175C2×C73#54611yescharacteristic
176C2×C73C2×#13711yescharacteristic
177C2×C73#57711yescharacteristic
178D73—41no—
179D73—81no—
180#3316—731nomaximal, Sylow
181C73#331611yescharacteristic, complemented, Sylow
182#554—731no—
183#548—731no—
184#489—731no—
185#483—731no—
186#481—731no—
187#475—731no—
188#470—731no—
189#465—731no—
190#464—731no—
191#452—731no—
192#451D7311yescharacteristic, complemented
193#441—731no—
194#435—731no—
195#417—731no—
196C2×#103—731no—
197C2×#41—731no—
198C22×Q8C2×D7311yescharacteristic
199C2×Q16C2×D7311yescharacteristic
200C2×Q16C2×D7311yescharacteristic
201C2×SD16—731no—
202C2×M16—731no—
203C22×C8—731no—
204C4⋊Q8—731no—
205#125—1461no—
206#124—731no—
207#124—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—731no—
210C22⋊Q8—1461no—
211C22⋊Q8—1461no—
212C22⋊Q8—1461no—
213C22⋊Q8C2×D7311yescharacteristic
214#121—731no—
215#121—1461no—
216C4×Q8—731no—
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—1461no—
220C4×D4—1461no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223#106—731no—
224#106—731no—
225#106—731no—
226C4⋊C8—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103C2×D7311yescharacteristic
233#103C2×D7311yescharacteristic
234#102—731no—
235#102—731no—
236#102—731no—
237C22⋊C8—731no—
238C22⋊C8C2×D7311yescharacteristic
239#97—731no—
240#41—2921no—
241#41—1462no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—1461no—
246C2×Q8C22×D7311yescharacteristic
247C2×Q8C22×D7311yescharacteristic
248C2×Q8C22×D7311yescharacteristic
249C2×D4—731no—
250C2×D4—731no—
251C2×D4—1461no—
252C2×D4—1461no—
253C22×C4—21no—
254C22×C4—731no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4C22×D7311yescharacteristic
259Q16—22no—
260Q16—41no—
261SD16—2921no—
262M16—2921no—
263C2×C8—2921no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—731no—
272C4⋊C4—731no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4C22×D7311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—731no—
283C22⋊C4—731no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C42—731no—
290C42—1461no—
291C42—1461no—
292C23—731no—
293C23—1461no—
294C23D4×D7311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—5841no—
302Q8#1192402712yes—
303D4—2922no—
304D4—2922no—
305D4—1462no—
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—5841no—
317C2×C4—5841no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—731no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4D4×D7311yescharacteristic
327C2×C4C23×D7311yescharacteristic
328C8—21no—
329C8—21no—
330C8—1461no—
331C8—1461no—
332C22—21no—
333C22—21no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22—1461no—
338C22—1461no—
339C22—1461no—
340C22#1455662312yes—
341C22C2×D4×D7311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—1461no—
351C4—1461no—
352C4—1461no—
353C4C2×#1192402711yescharacteristic
354C4#1455663611yescharacteristic
355C2—22no—
356C2—2921no—
357C2—5841no—
358C2#1798922411yescharacteristic
359C2C2×#1455662311yescharacteristic
360C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3316
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. #17989295C2semidirect
3. #17988948C2semidirect
4. #17988916C2semidirect
5. #17988906C2semidirect
6. #17988870C2semidirect
7. #17988842C2semidirect
8. #17988818C2semidirect
9. #17988811C2semidirect
10. #17988748C2semidirect
11. #17988694C2semidirect
12. #17988655C2semidirect
13. #17988587C2semidirect
14. C2×#14556515C2semidirect
15. #451×C73C2semidirect
181. C73#3316semidirect
192. #451D73semidirect