Finite Group Databasebeta

← #22621908

Subgroups — #22621908

Order 9344.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989285C211yesmaximal, characteristic, complemented
2#17989236C211yesmaximal, characteristic, complemented
3#17988954C211yesmaximal, characteristic, complemented
4#17988927C211yesmaximal, characteristic, complemented
5#17988917C211yesmaximal, characteristic, complemented
6#17988885C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988819C211yesmaximal, characteristic, complemented
9#17988791C211yesmaximal, characteristic, complemented
10#17988733C211yesmaximal, characteristic, complemented
11#17988732C211yesmaximal, characteristic, complemented
12#17988696C211yesmaximal, characteristic, complemented
13#17988656C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#417×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×C8×D73C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556586—21no—
23#14556582C2211yescharacteristic
24#14556576—21no—
25#14556574—21no—
26#14556572—21no—
27#14556570C2211yescharacteristic
28#14556567C2211yescharacteristic
29#14556566C2211yescharacteristic
30#14556565—21no—
31#14556565C2211yescharacteristic
32#14556563—21no—
33D4×Dic73C2211yescharacteristic
34#14556553C2211yescharacteristic
35C4×C22⋊D73—21no—
36C4×C22⋊D73C2211yescharacteristic
37#14556549C2211yescharacteristic
38C2×#11924007—21no—
39#14556525C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146C2311yescharacteristic
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73D411yescharacteristic
67C22×Dic73—21no—
68C22×Dic73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924017—41no—
72#11924015—41no—
73#11924013—22no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C8×D73—41no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007D411yescharacteristic
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73D411yescharacteristic
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73C2311yescharacteristic
105M16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117D4×C73—21no—
118D4×C73—42no—
119D4×C73#4112yes—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—42no—
126C2×C4×C73—81no—
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—41no—
130C22⋊D73—42no—
131C22⋊D73—42no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—42no—
136C2×Dic73—42no—
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142D292—81no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—81no—
146Dic146—21no—
147Dic146—21no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—22no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73H(5,𝔽2)11yescharacteristic
171Dic73—21no—
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177C2×C73—41no—
178C2×C73—42no—
179C2×C73#54611yescharacteristic
180C2×C73#57511yescharacteristic
181C2×C73#57711yescharacteristic
182D73—41no—
183D73—81no—
184#3307—731nomaximal, Sylow
185C73#330711yescharacteristic, complemented, Sylow
186#553—731no—
187#547—731no—
188#491—731no—
189#485—731no—
190#483—731no—
191#478—731no—
192#468—731no—
193#465—731no—
194#461—731no—
195#449—731no—
196#449—731no—
197#442—731no—
198#435—731no—
199#417D7311yescharacteristic, complemented
200#416—731no—
201C2×#41—731no—
202C2×#41C2×D7311yescharacteristic
203C2×SD16—731no—
204C2×SD16—731no—
205C2×D8—731no—
206C2×M16C2×D7311yescharacteristic
207C22×C8—731no—
208C4⋊Q8—731no—
209#126—1461no—
210#125—731no—
211#123—1461no—
212#123—1461no—
213#123—1461no—
214C22⋊Q8—731no—
215C22⋊Q8—731no—
216#121—731no—
217#121—731no—
218#121—1461no—
219#121—1461no—
220C4×D4—731no—
221C4×D4—731no—
222C4×D4—731no—
223C4×D4—1461no—
224#117—731no—
225C2×C4⋊C4—1461no—
226C2×C4⋊C4C2×D7311yescharacteristic
227#107—731no—
228#106—731no—
229#106—731no—
230C4⋊C8—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103C2×D7311yescharacteristic
236#103C2×D7311yescharacteristic
237#102—731no—
238#102—731no—
239#102C2×D7311yescharacteristic
240#102C2×D7311yescharacteristic
241C22⋊C8—731no—
242C22⋊C8—731no—
243#97—731no—
244#41—22no—
245#41—41no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—21no—
251C2×D4—731no—
252C2×D4—731no—
253C2×D4—1461no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4C22×D7311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—731no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4C22×D7311yescharacteristic
264SD16—2921no—
265SD16—2921no—
266D8—1462no—
267M16—41no—
268C2×C8—2921no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8C22×D7311yescharacteristic
272C2×C8C22×D7311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4C22×D7311yescharacteristic
284C4⋊C4C22×D7311yescharacteristic
285C22⋊C4—731no—
286C22⋊C4—731no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C42—731no—
295C42—1461no—
296C23—21no—
297C23—731no—
298C23—1461no—
299C23D4×D7311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—1461no—
303Q8—1461no—
304D4—21no—
305D4—42no—
306D4—2922no—
307D4—2922no—
308D4—2921no—
309D4—5841no—
310D4—1461no—
311D4—1461no—
312D4#1192402812yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—2922no—
321C2×C4—2922no—
322C2×C4—5841no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4D4×D7311yescharacteristic
332C2×C4C23×D7311yescharacteristic
333C8—21no—
334C8—21no—
335C8—1461no—
336C8—1461no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—2921no—
344C22—2921no—
345C22—2921no—
346C22—1461no—
347C22—1461no—
348C22—1461no—
349C22C2×D4×D7311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—2921no—
355C4—2921no—
356C4—2921no—
357C4—1461no—
358C4—1461no—
359C4—1461no—
360C4C2×#1192402811yescharacteristic
361C4#1455663611yescharacteristic
362C2—41no—
363C2—42no—
364C2—2921no—
365C2—5841no—
366C2#1798922711yescharacteristic
367C2#1798938611yescharacteristic
368C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3307
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989285C2semidirect
2. #17989236C2semidirect
3. #17988954C2semidirect
4. #17988927C2semidirect
5. #17988917C2semidirect
6. #17988885C2semidirect
7. #17988833C2semidirect
8. #17988819C2semidirect
9. #17988791C2semidirect
10. #17988733C2semidirect
11. #17988732C2semidirect
12. #17988696C2semidirect
13. #17988656C2semidirect
14. #17988580C2semidirect
15. #417×C73C2semidirect
185. C73#3307semidirect
199. #417D73semidirect