Finite Group Databasebeta

← #22622264

Subgroups — #22622264

Order 9344.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989295C211yesmaximal, characteristic, complemented
2#17989255C211yesmaximal, characteristic
3#17988932C211yesmaximal, characteristic, complemented
4#17988902C211yesmaximal, characteristic, complemented
5#17988898C211yesmaximal, characteristic, complemented
6#17988881C211yesmaximal, characteristic, complemented
7#17988836C211yesmaximal, characteristic, complemented
8#17988785C211yesmaximal, characteristic, complemented
9#17988747C211yesmaximal, characteristic, complemented
10#17988746C211yesmaximal, characteristic, complemented
11#17988679C211yesmaximal, characteristic, complemented
12#17988663C211yesmaximal, characteristic, complemented
13#17988589C211yesmaximal, characteristic, complemented
14#17988585C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556587—21no—
23#14556587C2211yescharacteristic
24#14556581—21no—
25#14556571—21no—
26#14556568—21no—
27#14556567C2211yescharacteristic
28#14556566C2211yescharacteristic
29#14556564—21no—
30#14556563—21no—
31Q8×Dic73C2211yescharacteristic
32#14556556C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556551—21no—
35#14556551—21no—
36C2×C4⋊Dic73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556516C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—41no—
61#11924027—22no—
62#11924027—41no—
63C2×Dic146—21no—
64C2×Dic146C2311yescharacteristic
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73D411yescharacteristic
72C22×Dic73—21no—
73C22×Dic73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77#11924018—22no—
78#11924015—41no—
79#11924011—41no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73—21no—
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90#11924007D411yescharacteristic
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98C2×Q8×C73C2311yescharacteristic
99C2×D4×C73—21no—
100C2×D4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102SD16×C73—41no—
103M16×C73—41no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73—21no—
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73C2×D411yescharacteristic
115Q8×C73—21no—
116Q8×C73—21no—
117D4×C73—21no—
118D4×C73—21no—
119D4×C73—81no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—22no—
128C22⋊D73—42no—
129C22⋊D73—42no—
130C22⋊D73—42no—
131C22⋊D73—81no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—42no—
136C2×Dic73—81no—
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142D292—81no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—42no—
146C4×D73—81no—
147Dic146—21no—
148Dic146—81no—
149Dic146#4112yes—
150C8×C73—21no—
151C8×C73—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73C22×D411yescharacteristic
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C4×C73—21no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73C2×#4111yescharacteristic
172C4×C73H(5,𝔽2)11yescharacteristic
173Dic73—22no—
174Dic73—21no—
175Dic73—21no—
176Dic73—41no—
177Dic73—41no—
178Dic73#13712yes—
179C2×C73—41no—
180C2×C73—81no—
181C2×C73#54611yescharacteristic
182C2×C73C2×#13711yescharacteristic
183C2×C73#57611yescharacteristic
184D73—41no—
185D73—81no—
186#3333—731nomaximal, Sylow
187C73#333311yescharacteristic, complemented, Sylow
188#554—731no—
189#550—731no—
190#486—731no—
191#480—731no—
192#480—731no—
193#477—731no—
194#468—731no—
195#468D7311yescharacteristic, complemented
196#460—731no—
197#452—731no—
198#452—731no—
199C4×Q16—731no—
200#436—731no—
201#417—731no—
202#417—731no—
203C2×#41—731no—
204C2×#41—731no—
205C2×Q16—731no—
206C2×SD16—731no—
207C2×SD16C2×D7311yescharacteristic
208C2×M16—731no—
209C2×M16C2×D7311yescharacteristic
210C4⋊Q8—731no—
211#127—731no—
212#127—1461no—
213#125—1461no—
214C22⋊Q8—731no—
215C22⋊Q8—1461no—
216C22⋊Q8—1461no—
217C22⋊Q8C2×D7311yescharacteristic
218#121—731no—
219#121—1461no—
220#121—1461no—
221#121C2×D7311yescharacteristic
222C4×Q8—731no—
223C4×Q8—731no—
224C4×D4—731no—
225C4×D4—1461no—
226C4×D4—1461no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229#107—731no—
230#107—731no—
231#107C2×D7311yescharacteristic
232C4⋊C8—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#103C2×D7311yescharacteristic
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242#102C2×D7311yescharacteristic
243C22⋊C8—731no—
244C22⋊C8—731no—
245C4×C8—731no—
246#41—2921no—
247#41—2921no—
248#41—1462no—
249#41—1462no—
250C2×Q8—731no—
251C2×Q8—1461no—
252C2×Q8C22×D7311yescharacteristic
253C2×D4—21no—
254C2×D4—731no—
255C2×D4—731no—
256C2×D4—1461no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4C22×D7311yescharacteristic
262C22×C4—731no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4C22×D7311yescharacteristic
268Q16—1462no—
269SD16—41no—
270SD16—2921no—
271M16—41no—
272M16—2921no—
273C2×C8—731no—
274C2×C8—731no—
275C2×C8C22×D7311yescharacteristic
276C2×C8C22×D7311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—731no—
279C4⋊C4—731no—
280C4⋊C4—731no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4C22×D7311yescharacteristic
288C4⋊C4C22×D7311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—731no—
292C22⋊C4—731no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C42—731no—
296C42—1461no—
297C42—1461no—
298C23—21no—
299C23—731no—
300C23—1461no—
301C23D4×D7311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—5841no—
305Q8—732no—
306Q8—1461no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—2922no—
311D4—2922no—
312D4—2922no—
313D4—5841no—
314D4—5841no—
315D4—1462no—
316D4—1461no—
317D4—1461no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2922no—
324C2×C4—2922no—
325C2×C4—5841no—
326C2×C4—5841no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4D4×D7311yescharacteristic
336C2×C4C23×D7311yescharacteristic
337C8—21no—
338C8—21no—
339C8—1461no—
340C8—1461no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—2921no—
348C22—2921no—
349C22—2921no—
350C22—1461no—
351C22—1461no—
352C22—1461no—
353C22C2×D4×D7311yescharacteristic
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—2921no—
359C4—2921no—
360C4—732no—
361C4—1461no—
362C4—1461no—
363C4—1462no—
364C4#41×D7311yescharacteristic
365C4#1455663611yescharacteristic
366C2—41no—
367C2—81no—
368C2—2921no—
369C2—5841no—
370C2#1798922611yescharacteristic
371C2#137×D7311yescharacteristic
372C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3333
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. #17989295C2semidirect
3. #17988932C2semidirect
4. #17988902C2semidirect
5. #17988898C2semidirect
6. #17988881C2semidirect
7. #17988836C2semidirect
8. #17988785C2semidirect
9. #17988747C2semidirect
10. #17988746C2semidirect
11. #17988679C2semidirect
12. #17988663C2semidirect
13. #17988589C2semidirect
14. #17988585C2semidirect
15. #468×C73C2semidirect
187. C73#3333semidirect
195. #468D73semidirect