Finite Group Databasebeta

← #22621288

Subgroups — #22621288

Order 9344.

392 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#17989132C211yesmaximal, characteristic, complemented
2#17989123C211yesmaximal, characteristic, complemented
3#17988890C211yesmaximal, characteristic, complemented
4#17988889C211yesmaximal, characteristic, complemented
5#17988870C211yesmaximal, characteristic, complemented
6#17988866C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988838C211yesmaximal, characteristic, complemented
9#17988835C211yesmaximal, characteristic, complemented
10#17988805C211yesmaximal, characteristic, complemented
11#17988804C211yesmaximal, characteristic, complemented
12#17988785C211yesmaximal, characteristic, complemented
13#17988781C211yesmaximal, characteristic, complemented
14#17988610C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×#11924015C2211yescharacteristic
18C2×D584C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924012C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556586—21no—
24#14556582C2211yescharacteristic
25#14556580C2211yescharacteristic
26#14556577—21no—
27#14556575—21no—
28#14556565C2211yescharacteristic
29#14556565C2211yescharacteristic
30#14556563—21no—
31Q8×Dic73C2211yescharacteristic
32D4×Dic73C2211yescharacteristic
33#14556553C2211yescharacteristic
34#14556553C2211yescharacteristic
35#14556551—21no—
36#14556551—21no—
37#14556549—21no—
38C2×C4×Dic73C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556511C2211yescharacteristic
51#14556511C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C22×Dic73—21no—
68C22×Dic73D411yescharacteristic
69C22×Dic73D411yescharacteristic
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72#11924015—41no—
73D584—41no—
74#11924013—41no—
75#11924012—41no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84C22⋊Dic73—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73D411yescharacteristic
93C4×Dic73D411yescharacteristic
94C4×Dic73C2311yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100SD16×C73—41no—
101M16×C73—41no—
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C22⋊C4×C73—21no—
109C23×C73—21no—
110C23×C73C2×D411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113Q8×C73—21no—
114Q8×C73—21no—
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—42no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2411yescharacteristic
125C22⋊D73—42no—
126C22⋊D73—42no—
127C22⋊D73—42no—
128C22⋊D73—42no—
129C2×Dic73—22no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—41no—
133C2×Dic73—42no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138D292—21no—
139D292—21no—
140D292—21no—
141D292—21no—
142C4×D73—42no—
143C4×D73—42no—
144Dic146—42no—
145C8×C73—21no—
146C8×C73—21no—
147#10596831—21no—
148#10596831—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C4×C73—21no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73H(5,𝔽2)11yescharacteristic
167C4×C732−1+411yescharacteristic
168Dic73—21no—
169Dic73—21no—
170Dic73—21no—
171Dic73—41no—
172Dic73—41no—
173Dic73AGL(1,ℤ/8)12yes—
174C2×C73—41no—
175C2×C73—81no—
176C2×C73#53711yescharacteristic
177C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C73#57511yescharacteristic
179D73—81no—
180D73—81no—
181#3251—731nomaximal, Sylow
182C73#325111yescharacteristic, complemented, Sylow
183#532—731no—
184#529—731no—
185#478—731no—
186#478—731no—
187#475—731no—
188#474—731no—
189#469—731no—
190#469—731no—
191#468—731no—
192#468D7311yescharacteristic, complemented
193#463—731no—
194#463—731no—
195#460—731no—
196#459—731no—
197#423—731no—
198C2×#41—1461no—
199C2×SD16—731no—
200C2×SD16C2×D7311yescharacteristic
201C2×D8—731no—
202C2×D8—731no—
203C2×M16—731no—
204C2×M16C2×D7311yescharacteristic
205C4⋊Q8—731no—
206#127—731no—
207#126—1461no—
208#125—731no—
209#124—731no—
210#124—1461no—
211#123—1461no—
212C22⋊Q8C2×D7311yescharacteristic
213#121—731no—
214#121—731no—
215#121—1461no—
216#121C2×D7311yescharacteristic
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—731no—
220C4×D4—731no—
221C4×D4—1461no—
222C4×D4—1461no—
223#117—1461no—
224C2×C42—731no—
225#107—731no—
226#107C2×D7311yescharacteristic
227#106—731no—
228#106—731no—
229C4⋊C8—731no—
230C4⋊C8—731no—
231C4⋊C8—731no—
232C4⋊C8—731no—
233#103—731no—
234#103C2×D7311yescharacteristic
235#102—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102C2×D7311yescharacteristic
241#41—2924no—
242C2×Q8—1461no—
243C2×Q8C22×D7311yescharacteristic
244C2×D4—21no—
245C2×D4—731no—
246C2×D4—731no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4—1461no—
250C2×D4—1461no—
251C2×D4C22×D7311yescharacteristic
252C22×C4—731no—
253C22×C4—731no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4C22×D7311yescharacteristic
258SD16—41no—
259SD16—2921no—
260D8—2921no—
261D8—2921no—
262M16—41no—
263M16—2921no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—731no—
270C4⋊C4—731no—
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—731no—
290C42—1461no—
291C23—21no—
292C23—1461no—
293C23—1461no—
294C23D4×D7311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—2922no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—2922no—
302D4—2922no—
303D4—2922no—
304D4—2922no—
305D4—1461no—
306D4—1461no—
307D4—1461no—
308D4—1461no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—2922no—
315C2×C4—2922no—
316C2×C4—2922no—
317C2×C4—2921no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—731no—
321C2×C4—731no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1462no—
325C2×C4D4×D7311yescharacteristic
326C2×C4C23×D7311yescharacteristic
327C8—21no—
328C8—21no—
329C8—1461no—
330C8—1461no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2921no—
338C22—2921no—
339C22—2921no—
340C22—2921no—
341C22—2921no—
342C22—2921no—
343C22C2×D4×D7311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2921no—
349C4—2921no—
350C4—732no—
351C4—1461no—
352C4—1461no—
353C4—1461no—
354C4#1455663611yescharacteristic
355C4#1455663811yescharacteristic
356C2—41no—
357C2—81no—
358C2—5841no—
359C2—5841no—
360C2#1798916411yescharacteristic
361C2AGL(1,ℤ/8)×D7311yescharacteristic
362C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3251
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #17989132C2semidirect
2. #17989123C2semidirect
3. #17988890C2semidirect
4. #17988889C2semidirect
5. #17988870C2semidirect
6. #17988866C2semidirect
7. #17988840C2semidirect
8. #17988838C2semidirect
9. #17988835C2semidirect
10. #17988805C2semidirect
11. #17988804C2semidirect
12. #17988785C2semidirect
13. #17988781C2semidirect
14. #17988610C2semidirect
15. #468×C73C2semidirect
182. C73#3251semidirect
192. #468D73semidirect