Finite Group Databasebeta

← #22619886

Subgroups — #22619886

Order 9344.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989153C211yesmaximal, characteristic
2#17989067C211yesmaximal, characteristic, complemented
3#17988914C211yesmaximal, characteristic, complemented
4#17988911C211yesmaximal, characteristic, complemented
5#17988909C211yesmaximal, characteristic, complemented
6#17988907C211yesmaximal, characteristic, complemented
7#17988903C211yesmaximal, characteristic, complemented
8#17988901C211yesmaximal, characteristic, complemented
9#17988899C211yesmaximal, characteristic, complemented
10#17988626C211yesmaximal, characteristic, complemented
11#17988624C211yesmaximal, characteristic, complemented
12#17988590C211yesmaximal, characteristic, complemented
13#102×D73C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556587—21no—
21#14556577—21no—
22#14556566C2211yescharacteristic
23#14556565C2211yescharacteristic
24#14556562C2211yescharacteristic
25#14556561—21no—
26#14556559—21no—
27C4×Dic146—21no—
28C4×D292—21no—
29#14556551—21no—
30#14556551—21no—
31#14556549C2211yescharacteristic
32#14556549C2211yescharacteristic
33#14556549C2211yescharacteristic, complemented
34C2×C4⋊Dic73C2211yescharacteristic, complemented
35C4⋊C4×D73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic, complemented
37#14556525C2211yescharacteristic, complemented
38#14556525C2211yescharacteristic, complemented
39#14556524C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic, complemented
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—22no—
61#11924028—22no—
62C2×Dic146D411yescharacteristic
63C2×D292—21no—
64C2×D292D411yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73D411yescharacteristic
70C2×C22⋊D73D411yescharacteristic
71D4×D73—22no—
72D4×D73—22no—
73C22×Dic73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77C2×C4×D73C2311yescharacteristic
78#11924011—22no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C8×D73—22no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111C22×D73—42no—
112C22×D73—81no—
113C22×D73—81no—
114C22×D73C2×D411yescharacteristic
115C22×D73C2×D411yescharacteristic
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—81no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—22no—
127C22⋊D73—22no—
128C22⋊D73—42no—
129C22⋊D73—81no—
130C22⋊D73—81no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—81no—
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—22no—
138D292—21no—
139D292—21no—
140D292—81no—
141C4×D73—21no—
142C4×D73—21no—
143C4×D73—81no—
144C4×D73—81no—
145C4×D73#4112yes—
146C4×D73#4112yes—
147Dic146—22no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—84no—
168C2×D73#12312yes—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73C2×#4111yescharacteristic
174C4×C73C2×#4111yescharacteristic
175Dic73—21no—
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179Dic73#12312yes—
180C2×C73—41no—
181C2×C73—81no—
182C2×C73C2×#12311yescharacteristic
183C2×C73#57611yescharacteristic
184C2×C73#57711yescharacteristic
185D73—22no—
186D73—41no—
187D73—81no—
188#3096—731nomaximal, Sylow
189C73#309611yescharacteristic, complemented, Sylow
190#535—731no—
191#520—731no—
192#482—731no—
193#482—731no—
194#482—731no—
195#482D7311yescharacteristic, complemented
196#481—731no—
197#481—731no—
198#480—731no—
199#480—731no—
200#428—731no—
201#427—731no—
202#418—731no—
203C2×#102—731no—
204#408—731no—
205C2×#41—731no—
206C22×D4—731no—
207C2×M16—731no—
208C22×C8—731no—
209#127—1461no—
210#124—1461no—
211#121—731no—
212#121—731no—
213#121—731no—
214#121C2×D7311yescharacteristic
215#120—1461no—
216#120—1461no—
217C4×Q8—1461no—
218C4×D4—1461no—
219C4×D4—1461no—
220C4×D4—1461no—
221#117—731no—
222#117—731no—
223#117—731no—
224#117C2×D7311yescharacteristic, complemented
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228#107—731no—
229#107—731no—
230#107—731no—
231#107C2×D7311yescharacteristic, complemented
232#106—731no—
233#106—731no—
234#106—731no—
235#106C2×D7311yescharacteristic, complemented
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242#102C2×D7311yescharacteristic
243#102C2×D7311yescharacteristic
244C22⋊C8—731no—
245C22⋊C8—731no—
246C22⋊C8—731no—
247C22⋊C8C2×D7311yescharacteristic, complemented
248C24—1461no—
249#41—1462no—
250#41—1462no—
251C2×Q8—731no—
252C2×D4—21no—
253C2×D4—731no—
254C2×D4—731no—
255C2×D4—731no—
256C2×D4—731no—
257C2×D4—1461no—
258C2×D4—1462no—
259C2×D4—1462no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4C22×D7311yescharacteristic
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4C22×D7311yescharacteristic
270M16—1462no—
271C2×C8—731no—
272C2×C8—731no—
273C2×C8—1462no—
274C2×C8C22×D7311yescharacteristic
275C2×C8C22×D7311yescharacteristic
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—731no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4C22×D7311yescharacteristic
283C4⋊C4C22×D7311yescharacteristic
284C4⋊C4C22×D7311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C42—21no—
294C42—1461no—
295C42—1461no—
296C42—1461no—
297C23—21no—
298C23—2922no—
299C23—5841no—
300C23—5841no—
301C23—731no—
302C23—731no—
303C23—1461no—
304C23D4×D7311yescharacteristic
305Q8—1462no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—2922no—
310D4—5841no—
311D4—5841no—
312D4—5841no—
313D4—1462no—
314D4—1462no—
315D4—1462no—
316D4—1461no—
317D4—1461no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—5841no—
324C2×C4—5841no—
325C2×C4—5841no—
326C2×C4—731no—
327C2×C4—732no—
328C2×C4—732no—
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—5844no—
351C22—732no—
352C22—1461no—
353C22—1461no—
354C22—1461no—
355C22—1461no—
356C22—1461no—
357C22C2×D4×D7311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—2921no—
363C4—2921no—
364C4—2921no—
365C4—732no—
366C4—1461no—
367C4#41×D7311yescharacteristic
368C4#41×D7311yescharacteristic
369C2—41no—
370C2—81no—
371C2—2921no—
372C2—5841no—
373C2—1462no—
374C2#123×D7311yescharacteristic
375C2#1798938911yescharacteristic
376C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3096
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #17989067C2semidirect
3. #17988914C2semidirect
4. #17988911C2semidirect
5. #17988909C2semidirect
6. #17988907C2semidirect
7. #17988903C2semidirect
8. #17988901C2semidirect
9. #17988899C2semidirect
10. #17988626C2semidirect
11. #17988624C2semidirect
12. #17988590C2semidirect
13. #102×D73C2semidirect
14. #17988552C2semidirect
15. #482×C73C2semidirect
33. #14556549C22semidirect
34. C2×C4⋊Dic73C22semidirect
36. C4⋊C4×D73C22semidirect
37. #14556525C22semidirect
38. #14556525C22semidirect
39. #14556524C22semidirect
40. #14556522C22semidirect
41. #14556522C22semidirect
42. #14556522C22semidirect
49. C22⋊#10596831C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
53. #117×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
58. C22⋊C8×C73C22semidirect
189. C73#3096semidirect
195. #482D73semidirect
224. #117C2×D73semidirect
231. #107C2×D73semidirect
235. #106C2×D73semidirect
247. C22⋊C8C2×D73semidirect