Finite Group Databasebeta

← #22626468

Subgroups — #22626468

Order 9344.

496 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989538C211yesmaximal, characteristic, complemented
2#17989537C211yesmaximal, characteristic
3#17989537C211yesmaximal, characteristic
4#17989537C211yesmaximal, characteristic
5#17989536C211yesmaximal, characteristic, complemented
6#17989536C211yesmaximal, characteristic, complemented
7#17989536C211yesmaximal, characteristic, complemented
8#17989534C211yesmaximal, characteristic
9C4⋊C4×#64408C211yesmaximal, characteristic, complemented
10C4⋊C4×#64408C211yesmaximal, characteristic, complemented
11C4×C4⋊#64408C211yesmaximal, characteristic, complemented
12C22⋊C4×#64408C211yesmaximal, characteristic
13C22⋊C4×#64408C211yesmaximal, characteristic
14#17989523C211yesmaximal, characteristic, complemented
15#126×D73C211yesmaximal, characteristic
16C23×#64408C2211yescharacteristic
17C2×C4⋊#64408C2211yescharacteristic
18C2×C4⋊#64408C2211yescharacteristic
19C2×C4⋊#64408C2211yescharacteristic
20C2×C4⋊#64408C2211yescharacteristic
21C2×C4⋊#64408C2211yescharacteristic
22C2×C22⋊#64408C2211yescharacteristic
23C2×C22⋊#64408C2211yescharacteristic
24C2×C22⋊#64408C2211yescharacteristic
25C2×C4×#64408C2211yescharacteristic
26C2×C4×#64408C2211yescharacteristic
27C2×C4×#64408C2211yescharacteristic
28C2×C4×#64408C2211yescharacteristic
29C2×C4×#64408C2211yescharacteristic
30C2×C4×#64408C2211yescharacteristic
31C2×C4×#64408C2211yescharacteristic
32(C2×#64408)⋊C4C2211yescharacteristic
33(C2×#64408)⋊C4C2211yescharacteristic
34(C2×#64408)⋊C4C2211yescharacteristic
35(C2×#64408)⋊C4C2211yescharacteristic
36(C2×#64408)⋊C4C2211yescharacteristic
37(C2×#64408)⋊C4C2211yescharacteristic
38(C2×#64408)⋊C4C2211yescharacteristic
39(C2×#64408)⋊C4C2211yescharacteristic
40(C2×#64408)⋊C4C2211yescharacteristic
41(C2×#64408)⋊C4C2211yescharacteristic
42(C2×#64408)⋊C4C2211yescharacteristic
43(C2×#64408)⋊C4C2211yescharacteristic
44#14556586C411yescharacteristic, complemented
45#14556586C411yescharacteristic, complemented
46#14556586C411yescharacteristic, complemented
47#14556585C411yescharacteristic, complemented
48#14556584C411yescharacteristic, complemented
49#14556584C411yescharacteristic, complemented
50#14556584C411yescharacteristic, complemented
51C4⋊C4×D73C2211yescharacteristic
52C4⋊C4×D73C2211yescharacteristic
53C4⋊C4×D73C2211yescharacteristic
54C22⋊C4×D73C2211yescharacteristic
55C22⋊C4×D73C2211yescharacteristic
56C22⋊C4×D73C2211yescharacteristic
57C42×D73C2211yescharacteristic
58#126×C73C411yescharacteristic, complemented
59C22×#64408—22no—
60C22×#64408—22no—
61C22×#64408—41no—
62C22×#64408C2311yescharacteristic
63C22×#64408C2311yescharacteristic
64C22×#64408C2311yescharacteristic
65C22×#64408C2311yescharacteristic
66C22×#64408C2311yescharacteristic
67C22×#64408C2311yescharacteristic
68C22×#64408C2311yescharacteristic
69C22×#64408C2311yescharacteristic
70C4⋊#64408—22no—
71C4⋊#64408—22no—
72C4⋊#64408—22no—
73C4⋊#64408—22no—
74C4⋊#64408—41no—
75C22⋊#64408—22no—
76C22⋊#64408—22no—
77C22⋊#64408—41no—
78C4×#64408—22no—
79C4×#64408—22no—
80C4×#64408—22no—
81C4×#64408—22no—
82C4×#64408—41no—
83C4×#64408—41no—
84C4×#64408—41no—
85C23×D73C2311yescharacteristic
86C2×C4×D73C2311yescharacteristic
87C2×C4×D73C2311yescharacteristic
88C2×C4×D73C2311yescharacteristic
89C2×C4×D73C2311yescharacteristic
90C2×C4×D73C2311yescharacteristic
91C2×C4×D73C2311yescharacteristic
92C4⋊Dic73C2×C411yescharacteristic, complemented
93C4⋊Dic73C2×C411yescharacteristic, complemented
94C4⋊Dic73C2×C411yescharacteristic, complemented
95#11924007C2×C411yescharacteristic, complemented
96#11924007C2×C411yescharacteristic, complemented
97#11924007C2×C411yescharacteristic, complemented
98#11924007C2×C411yescharacteristic, complemented
99#11924007C2×C411yescharacteristic, complemented
100#11924007C2×C411yescharacteristic, complemented
101C22⋊Dic73C2×C411yescharacteristic
102C22⋊Dic73C2×C411yescharacteristic
103C22⋊Dic73C2×C411yescharacteristic
104#11924005C2×C411yescharacteristic
105#11924005C2×C411yescharacteristic
106#11924005C2×C411yescharacteristic
107#11924005C2×C411yescharacteristic
108#11924005C2×C411yescharacteristic
109#11924005C2×C411yescharacteristic
110C4×Dic73C2×C411yescharacteristic, complemented
111C4×Dic73C2×C411yescharacteristic, complemented
112C4×Dic73C2×C411yescharacteristic, complemented
113C4⋊C4×C73C2×C411yescharacteristic, complemented
114C4⋊C4×C73C2×C411yescharacteristic, complemented
115C4⋊C4×C73C2×C411yescharacteristic, complemented
116C22⋊C4×C73C2×C411yescharacteristic
117C22⋊C4×C73C2×C411yescharacteristic
118C22⋊C4×C73C2×C411yescharacteristic
119C42×C73C2×C411yescharacteristic, complemented
120C23×C73C22×C411yescharacteristic
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—21no—
127C22×D73C22×C411yescharacteristic
128C22×D73C2411yescharacteristic
129C2×#64408—21no—
130C2×#64408—21no—
131C2×#64408—21no—
132C2×#64408—21no—
133C2×#64408—21no—
134C2×#64408—21no—
135C2×#64408—21no—
136C2×#64408—21no—
137C2×#64408—21no—
138C2×#64408—21no—
139C2×#64408—21no—
140C2×#64408—21no—
141C2×#64408—21no—
142C2×#64408—21no—
143C2×#64408—21no—
144C2×#64408—21no—
145C2×#64408—21no—
146C2×#64408—21no—
147C2×#64408—21no—
148C2×#64408—21no—
149C2×#64408—44no—
150C2×#64408#4112yes—
151C2×#64408#4112yes—
152C2×#64408#4112yes—
153C2×#64408#4112yes—
154C2×C4×C73C22×C411yescharacteristic
155C2×C4×C73C22×C411yescharacteristic
156C2×C4×C73C22×C411yescharacteristic
157C2×C4×C73C22×C411yescharacteristic
158C2×C4×C73C22×C411yescharacteristic
159C2×C4×C73C22×C411yescharacteristic
160C2×Dic73C22×C411yescharacteristic
161C2×Dic73C22×C411yescharacteristic
162C2×Dic73C22×C411yescharacteristic
163C2×Dic73C22×C411yescharacteristic
164C2×Dic73C22×C411yescharacteristic
165C2×Dic73C22×C411yescharacteristic
166C4×D73—21no—
167C4×D73—21no—
168C4×D73—21no—
169C4×D73—21no—
170C4×D73—21no—
171C4×D73—21no—
172C4×D73—21no—
173C4×D73—21no—
174C4×D73—21no—
175C4×D73—21no—
176C4×D73—21no—
177C4×D73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73C23×C411yescharacteristic
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—21no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
189C2×D73C2×#4111yescharacteristic
190C2×D73C2×#4111yescharacteristic
191C2×D73C2×#4111yescharacteristic
192C2×D73C2×#4111yescharacteristic
193C2×D73H(5,𝔽2)11yescharacteristic
194C2×D732−1+411yescharacteristic
195#64408—22no—
196#64408—22no—
197#64408—22no—
198#64408—22no—
199#64408—41no—
200#64408—41no—
201#64408—41no—
202#64408—41no—
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—21no—
207C4×C73—21no—
208C4×C73—21no—
209Dic73—21no—
210Dic73—21no—
211Dic73—21no—
212Dic73—21no—
213Dic73—21no—
214Dic73—21no—
215C2×C73—41no—
216C2×C73C4×#4111yescharacteristic
217C2×C73C4×#4111yescharacteristic
218C2×C73#52011yescharacteristic
219D73—41no—
220D73#55111yescharacteristic
221D73#55211yescharacteristic
222D73#55311yescharacteristic
223D73#55611yescharacteristic
224#2373—731nomaximal, Sylow
225C73#237311yescharacteristic, complemented, Sylow
226C2×#126—731no—
227#389—731no—
228#388—731no—
229#388—731no—
230#388—731no—
231#387—731no—
232#387—731no—
233#387—731no—
234#385—731no—
235C4×C4⋊C4—731no—
236C4×C4⋊C4—731no—
237C4×C4⋊C4—731no—
238C4×C22⋊C4—731no—
239C4×C22⋊C4—731no—
240#376—731no—
241C23×C4—731no—
242#126—731no—
243#126—731no—
244#126—731no—
245#126—731no—
246#126—731no—
247#126—731no—
248#126—731no—
249#126#6440811yescharacteristic, complemented
250C2×C4⋊C4—731no—
251C2×C4⋊C4—731no—
252C2×C4⋊C4—731no—
253C2×C4⋊C4—731no—
254C2×C4⋊C4—731no—
255C2×C4⋊C4—731no—
256C2×C4⋊C4—731no—
257C2×C4⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4—731no—
260C2×C22⋊C4—731no—
261C2×C22⋊C4—731no—
262C2×C22⋊C4—731no—
263C2×C22⋊C4—731no—
264C2×C42—731no—
265C2×C42—731no—
266C2×C42—731no—
267C2×C42—731no—
268C2×C42—731no—
269C2×C42—731no—
270C2×C42—731no—
271C2×C42—731no—
272#95—731no—
273#95—731no—
274#95—731no—
275#95—731no—
276#95—731no—
277#95—731no—
278#95—731no—
279#95—731no—
280#95—731no—
281#95—731no—
282#95—731no—
283#95—731no—
284C24—731no—
285C22×C4—2921no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—731no—
300C22×C4—1462no—
301C22×C4—1462no—
302C4⋊C4—2921no—
303C4⋊C4—731no—
304C4⋊C4—731no—
305C4⋊C4—731no—
306C4⋊C4—731no—
307C4⋊C4—731no—
308C4⋊C4—731no—
309C4⋊C4—731no—
310C4⋊C4—731no—
311C4⋊C4—731no—
312C4⋊C4—1462no—
313C4⋊C4—1462no—
314C4⋊C4—1462no—
315C4⋊C4—1462no—
316C4⋊C4C2×#6440811yescharacteristic, complemented
317C4⋊C4C2×#6440811yescharacteristic, complemented
318C4⋊C4C2×#6440811yescharacteristic, complemented
319C22⋊C4—2921no—
320C22⋊C4—731no—
321C22⋊C4—731no—
322C22⋊C4—731no—
323C22⋊C4—731no—
324C22⋊C4—731no—
325C22⋊C4—731no—
326C22⋊C4—731no—
327C22⋊C4—731no—
328C22⋊C4—731no—
329C22⋊C4—1462no—
330C22⋊C4—1462no—
331C22⋊C4C2×#6440811yescharacteristic
332C22⋊C4C2×#6440811yescharacteristic
333C22⋊C4C2×#6440811yescharacteristic
334C42—2921no—
335C42—2921no—
336C42—2921no—
337C42—731no—
338C42—731no—
339C42—731no—
340C42—1462no—
341C42—1462no—
342C42—1462no—
343C42—1462no—
344C42C2×#6440811yescharacteristic, complemented
345C23—731no—
346C23—731no—
347C23—1461no—
348C23—1461no—
349C23—1461no—
350C23—1461no—
351C23—1461no—
352C23—1461no—
353C23C22×#6440811yescharacteristic
354C2×C4—2924no—
355C2×C4—732no—
356C2×C4—732no—
357C2×C4—732no—
358C2×C4—732no—
359C2×C4—731no—
360C2×C4—731no—
361C2×C4—731no—
362C2×C4—731no—
363C2×C4—731no—
364C2×C4—731no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4—1461no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4—1461no—
375C2×C4—1461no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1461no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4—1461no—
395C2×C4—1461no—
396C2×C4—1461no—
397C2×C4C22×#6440811yescharacteristic
398C2×C4C22×#6440811yescharacteristic
399C2×C4C22×#6440811yescharacteristic
400C2×C4C22×#6440811yescharacteristic
401C2×C4C22×#6440811yescharacteristic
402C2×C4C22×#6440811yescharacteristic
403C22—21no—
404C22—21no—
405C22—21no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—2921no—
410C22—731no—
411C22—731no—
412C22—731no—
413C22—731no—
414C22—731no—
415C22—731no—
416C22—1461no—
417C22—1461no—
418C22—1461no—
419C22C23×#6440811yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—2921no—
427C4—2921no—
428C4—2921no—
429C4—2921no—
430C4—1462no—
431C4—1462no—
432C4—1462no—
433C4—1462no—
434C4—1461no—
435C4—1461no—
436C4—1461no—
437C4—1461no—
438C4—1461no—
439C4—1461no—
440C2—41no—
441C2—2921no—
442C2—731no—
443C2—731no—
444C2—731no—
445C2—731no—
446C2#41×#6440811yescharacteristic
447C2#41×#6440811yescharacteristic
448C2#1798965611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#64408
commutator, socleC22×C73C23×C4
Fitting#126×C73C4
hypercenter#126#64408
hypocenterC73#2373
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #17989538C2semidirect
5. #17989536C2semidirect
6. #17989536C2semidirect
7. #17989536C2semidirect
9. C4⋊C4×#64408C2semidirect
10. C4⋊C4×#64408C2semidirect
11. C4×C4⋊#64408C2semidirect
14. #17989523C2semidirect
44. #14556586C4semidirect
45. #14556586C4semidirect
46. #14556586C4semidirect
47. #14556585C4semidirect
48. #14556584C4semidirect
49. #14556584C4semidirect
50. #14556584C4semidirect
58. #126×C73C4semidirect
92. C4⋊Dic73C2×C4semidirect
93. C4⋊Dic73C2×C4semidirect
94. C4⋊Dic73C2×C4semidirect
95. #11924007C2×C4semidirect
96. #11924007C2×C4semidirect
97. #11924007C2×C4semidirect
98. #11924007C2×C4semidirect
99. #11924007C2×C4semidirect
100. #11924007C2×C4semidirect
110. C4×Dic73C2×C4semidirect
111. C4×Dic73C2×C4semidirect
112. C4×Dic73C2×C4semidirect
113. C4⋊C4×C73C2×C4semidirect
114. C4⋊C4×C73C2×C4semidirect
115. C4⋊C4×C73C2×C4semidirect
119. C42×C73C2×C4semidirect
225. C73#2373semidirect
249. #126#64408semidirect
316. C4⋊C4C2×#64408semidirect
317. C4⋊C4C2×#64408semidirect
318. C4⋊C4C2×#64408semidirect
344. C42C2×#64408semidirect