Finite Group Databasebeta

← #22620621

Subgroups — #22620621

Order 9344.

374 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#17989211C211yesmaximal, characteristic, complemented
2#17989191C211yesmaximal, characteristic, complemented
3#17988993C211yesmaximal, characteristic, complemented
4#17988974C211yesmaximal, characteristic, complemented
5#17988942C211yesmaximal, characteristic, complemented
6#17988839C211yesmaximal, characteristic, complemented
7#17988832C211yesmaximal, characteristic, complemented
8#17988822C211yesmaximal, characteristic, complemented
9#17988815C211yesmaximal, characteristic, complemented
10#17988696C211yesmaximal, characteristic, complemented
11#17988684C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988541C211yesmaximal, characteristic, complemented
15#486×C73C211yesmaximal, characteristic, complemented
16C2×#11924016C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22#14556586—21no—
23#14556583C2211yescharacteristic
24#14556580—21no—
25#14556579C2211yescharacteristic
26#14556576—21no—
27#14556572—21no—
28#14556572—21no—
29#14556571C2211yescharacteristic
30#14556567—21no—
31#14556566C2211yescharacteristic
32#14556563—21no—
33#14556563—21no—
34#14556562C2211yescharacteristic
35#14556562C2211yescharacteristic
36#14556556C2211yescharacteristic
37D4×Dic73C2211yescharacteristic
38D4×Dic73C2211yescharacteristic
39#14556553C2211yescharacteristic
40#14556548C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556524C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556522C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556502C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C4⋊Q8×C73C2211yescharacteristic
53#127×C73C2211yescharacteristic
54#102×C73C2211yescharacteristic
55#102×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C2×D292—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68#11924016—22no—
69#11924016—22no—
70#11924013—22no—
71#11924013—22no—
72#11924011—22no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C8×D73—22no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007D411yescharacteristic
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73—21no—
98C2×D4×C73—21no—
99C2×D4×C73—21no—
100C2×D4×C73C2311yescharacteristic
101C2×D4×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73—21no—
110C22×D73—21no—
111C22×D73C2×D411yescharacteristic
112Q8×C73—81no—
113D4×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—81no—
118D4×C73—81no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—81no—
125C22⋊D73—81no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—81no—
130C2×Dic73—81no—
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—21no—
135D292—21no—
136D292—81no—
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—81no—
140Dic146—21no—
141Dic146—21no—
142C8×C73—21no—
143C8×C73—21no—
144#10596831#4112yes—
145#10596831#4112yes—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73C22×D411yescharacteristic
153C2×D73—21no—
154C2×D73—21no—
155C2×D73—21no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73C2×#4111yescharacteristic
165Dic73—21no—
166Dic73—21no—
167Dic73—21no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—81no—
172C2×C73—81no—
173C2×C73#53211yescharacteristic
174C2×C73#57611yescharacteristic
175C2×C73#57711yescharacteristic
176D73—41no—
177D73—81no—
178#3179—731nomaximal, Sylow
179C73#317911yescharacteristic, complemented, Sylow
180#542—731no—
181#540—731no—
182#501—731no—
183#496—731no—
184#488—731no—
185#486D7311yescharacteristic, complemented
186#469—731no—
187#468—731no—
188#466—731no—
189#465—731no—
190#442—731no—
191#440—731no—
192C4×SD16—731no—
193C4×D8—731no—
194#405—731no—
195C2×SD16—731no—
196C2×SD16—731no—
197C2×D8—731no—
198C2×D8—731no—
199C2×M16—731no—
200C22×C8—731no—
201C4⋊Q8C2×D7311yescharacteristic
202#127C2×D7311yescharacteristic
203#126—1461no—
204#125—731no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208#123—1461no—
209#123—1461no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—731no—
213#121—731no—
214#121—731no—
215#121—1461no—
216#121—1461no—
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—731no—
220C4×D4—731no—
221#117—731no—
222#107—731no—
223#107—731no—
224#106—731no—
225#106—731no—
226#103—731no—
227#103—731no—
228#102—731no—
229#102—731no—
230#102C2×D7311yescharacteristic
231#102C2×D7311yescharacteristic
232#102C2×D7311yescharacteristic
233#102C2×D7311yescharacteristic
234#97—731no—
235#97—731no—
236C4×C8—731no—
237C4×C8C2×D7311yescharacteristic
238C2×Q8—21no—
239C2×Q8—731no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—731no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4—1461no—
246C2×D4C22×D7311yescharacteristic
247C2×D4C22×D7311yescharacteristic
248C22×C4—731no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252SD16—1462no—
253SD16—1462no—
254D8—1462no—
255D8—1462no—
256M16—1462no—
257C2×C8—731no—
258C2×C8—731no—
259C2×C8—1462no—
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4C22×D7311yescharacteristic
272C4⋊C4C22×D7311yescharacteristic
273C22⋊C4—731no—
274C22⋊C4—731no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C42—731no—
285C42—1461no—
286C42C22×D7311yescharacteristic
287C23—21no—
288C23—21no—
289C23—731no—
290C23—1461no—
291Q8—81no—
292Q8—1461no—
293Q8—1461no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—5841no—
301D4—5841no—
302D4—5841no—
303D4—1461no—
304D4—1461no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—5841no—
308C2×C4—5841no—
309C2×C4—5841no—
310C2×C4—731no—
311C2×C4—731no—
312C2×C4—731no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4D4×D7311yescharacteristic
319C2×C4D4×D7311yescharacteristic
320C2×C4C23×D7311yescharacteristic
321C8—21no—
322C8—21no—
323C8—732no—
324C8—732no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2921no—
332C22—2921no—
333C22—2921no—
334C22—1461no—
335C22—1461no—
336C22—1461no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—2921no—
343C4—2921no—
344C4—2921no—
345C4—1461no—
346C4—1461no—
347C4—1461no—
348C4#41×D7311yescharacteristic
349C4#41×D7311yescharacteristic
350C2—81no—
351C2—81no—
352C2—2921no—
353C2—5841no—
354C2#1798913611yescharacteristic
355C2#1798938811yescharacteristic
356C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#486×C73C2
socleC22×C73C22×D4
hypercenter#486D73
hypocenterC73#3179
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #17989211C2semidirect
2. #17989191C2semidirect
3. #17988993C2semidirect
4. #17988974C2semidirect
5. #17988942C2semidirect
6. #17988839C2semidirect
7. #17988832C2semidirect
8. #17988822C2semidirect
9. #17988815C2semidirect
10. #17988696C2semidirect
11. #17988684C2semidirect
12. #17988678C2semidirect
13. #17988667C2semidirect
14. #17988541C2semidirect
15. #486×C73C2semidirect
179. C73#3179semidirect
185. #486D73semidirect