Finite Group Databasebeta

← #22620524

Subgroups — #22620524

Order 9344.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989134C211yesmaximal, characteristic, complemented
2#17989119C211yesmaximal, characteristic, complemented
3#17988995C211yesmaximal, characteristic, complemented
4#17988975C211yesmaximal, characteristic, complemented
5#17988950C211yesmaximal, characteristic, complemented
6#17988945C211yesmaximal, characteristic, complemented
7#17988839C211yesmaximal, characteristic, complemented
8#17988837C211yesmaximal, characteristic, complemented
9#17988834C211yesmaximal, characteristic, complemented
10#17988832C211yesmaximal, characteristic, complemented
11C4×#11924017C211yesmaximal, characteristic, complemented
12C4×#11924016C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14C4×#11924011C211yesmaximal, characteristic, complemented
15C4×D8×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924017C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22#14556590C2211yescharacteristic
23#14556587C2211yescharacteristic
24#14556584—21no—
25#14556582C2211yescharacteristic
26#14556578C2211yescharacteristic
27#14556577—21no—
28#14556573—21no—
29#14556571C2211yescharacteristic
30#14556566C2211yescharacteristic
31#14556564—21no—
32#14556562C2211yescharacteristic
33#14556562C2211yescharacteristic
34C4×Dic146C2211yescharacteristic
35C4×D292C2211yescharacteristic
36C4×C22⋊D73—21no—
37C4×C22⋊D73—21no—
38#14556550—21no—
39C42×D73C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556501C2211yescharacteristic
50#14556501C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×D8×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146C2311yescharacteristic
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73D411yescharacteristic
70C2×C4×D73D411yescharacteristic
71C2×C4×D73C2311yescharacteristic
72#11924017—22no—
73#11924016—22no—
74#11924013—22no—
75#11924011—22no—
76#11924011—22no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93C4×Dic73—21no—
94C4×Dic73D411yescharacteristic
95C4×Dic73D411yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100C22×C4×C73—21no—
101D8×C73—22no—
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C42×C73C2311yescharacteristic
109C23×C73—21no—
110C23×C73—21no—
111C22×D73—21no—
112C22×D73C2×D411yescharacteristic
113D4×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—42no—
120C2×C4×C73—42no—
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—42no—
125C22⋊D73—42no—
126C22⋊D73—42no—
127C22⋊D73—42no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—21no—
135D292—21no—
136D292—42no—
137C4×D73—22no—
138C4×D73—21no—
139C4×D73—21no—
140C4×D73—41no—
141C4×D73—42no—
142Dic146—21no—
143Dic146—21no—
144Dic146—42no—
145C8×C73—21no—
146C8×C73#4112yescomplemented
147#10596831—21no—
148#10596831#4112yescomplemented
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—21no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73AGL(1,ℤ/8)12yes—
166C4×C73C2×#4111yescharacteristic
167C4×C73C2×#4111yescharacteristic
168Dic73—21no—
169Dic73—21no—
170Dic73—21no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—81no—
175C2×C73—81no—
176C2×C73#53211yescharacteristic
177C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C73#57511yescharacteristic
179D73—41no—
180D73—81no—
181#3171—731nomaximal, Sylow
182C73#317111yescharacteristic, complemented, Sylow
183#532—731no—
184#529—731no—
185#501—731no—
186#496—731no—
187#490—731no—
188#489—731no—
189#469—731no—
190#469—731no—
191#468—731no—
192#468—731no—
193C4×SD16—731no—
194C4×SD16—731no—
195C4×D8—731no—
196C4×D8D7311yescharacteristic, complemented
197C4×M16—731no—
198C2×#41—1461no—
199C2×SD16—731no—
200C2×SD16—731no—
201C2×D8—731no—
202C2×D8C2×D7311yescharacteristic
203C2×M16—731no—
204C2×M16—731no—
205C4⋊Q8—731no—
206#127—731no—
207#126—1461no—
208#125—731no—
209#124—731no—
210#124—1461no—
211#123—1461no—
212C22⋊Q8—731no—
213#121—731no—
214#121—731no—
215#121—731no—
216#121—1461no—
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—1461no—
220C4×D4—1461no—
221C4×D4C2×D7311yescharacteristic
222C4×D4C2×D7311yescharacteristic
223#117—1461no—
224C2×C42—731no—
225#107—731no—
226#107C2×D7311yescharacteristic
227#106—731no—
228#106—731no—
229#103—731no—
230#103—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102C2×D7311yescharacteristic
236#102C2×D7311yescharacteristic
237#97—731no—
238#97—731no—
239C4×C8—731no—
240C4×C8C2×D7311yescharacteristic
241#41—2924no—
242C2×Q8—731no—
243C2×Q8—1461no—
244C2×D4—731no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4—1461no—
250C2×D4C22×D7311yescharacteristic
251C2×D4C22×D7311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—1461no—
258SD16—1462no—
259SD16—1462no—
260D8—22no—
261D8—1462no—
262M16—1462no—
263M16—1462no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4C22×D7311yescharacteristic
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—731no—
287C42—731no—
288C42—731no—
289C42—1461no—
290C42C22×D7311yescharacteristic
291C23—21no—
292C23—21no—
293C23—731no—
294C23—1461no—
295Q8—2922no—
296Q8—1461no—
297Q8—1461no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—2922no—
303D4—2922no—
304D4—2922no—
305D4—2922no—
306D4—2922no—
307D4—1461no—
308D4—1461no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2921no—
314C2×C4—2922no—
315C2×C4—731no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1462no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4D4×D7311yescharacteristic
325C2×C4D4×D7311yescharacteristic
326C2×C4C23×D7311yescharacteristic
327C8—21no—
328C8—732no—
329C8—1461no—
330C8#1192402812yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2921no—
338C22—2921no—
339C22—2921no—
340C22—1461no—
341C22—1461no—
342C22—1461no—
343C22C2×D4×D7311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—1461no—
351C4—1461no—
352C4—1461no—
353C4#1455661512yes—
354C4#41×D7311yescharacteristic
355C4C2×#1192402811yescharacteristic
356C2—81no—
357C2—81no—
358C2—2921no—
359C2—5841no—
360C2#1798913411yescharacteristic
361C2C2×#1455661511yescharacteristic
362C2#1798938411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×D8×C73C2
socleC22×C73C22×D4
hypercenterC4×D8D73
hypocenterC73#3171
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #17989134C2semidirect
2. #17989119C2semidirect
3. #17988995C2semidirect
4. #17988975C2semidirect
5. #17988950C2semidirect
6. #17988945C2semidirect
7. #17988839C2semidirect
8. #17988837C2semidirect
9. #17988834C2semidirect
10. #17988832C2semidirect
11. C4×#11924017C2semidirect
12. C4×#11924016C2semidirect
13. C4×#11924013C2semidirect
14. C4×#11924011C2semidirect
15. C4×D8×C73C2semidirect
146. C8×C73#41semidirect
148. #10596831#41semidirect
182. C73#3171semidirect
196. C4×D8D73semidirect
330. C8#11924028semidirect