Finite Group Databasebeta

← #28393260

Subgroups — #28393260

Order 14464.

668 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
1C2×#16813594C211yesmaximal, characteristic
2C2×#16813582C211yesmaximal, characteristic, complemented
3C2×#16813578C211yesmaximal, characteristic, complemented
4#20298498C211yesmaximal, characteristic, complemented
5#20298498C211yesmaximal, characteristic, complemented
6#20298493C211yesmaximal, characteristic, complemented
7#20298492C211yesmaximal, characteristic, complemented
8#20298489C211yesmaximal, characteristic, complemented
9#20298478C211yesmaximal, characteristic, complemented
10#20298474C211yesmaximal, characteristic, complemented
11#20298470C211yesmaximal, characteristic, complemented
12#20298469C211yesmaximal, characteristic, complemented
13#20298456C211yesmaximal, characteristic, complemented
14C4×#14268626C211yesmaximal, characteristic, complemented
15#390×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C23×Dic113C2211yescharacteristic
19C23×Dic113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813594C418yescomplemented
22#16813582—24no—
23#16813578—24no—
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×#14268626C2211yescharacteristic
29C2×#14268626C2211yescharacteristic
30C2×C22⋊Dic113C2211yescharacteristic
31C2×C22⋊Dic113C2211yescharacteristic
32C2×C22⋊Dic113C2211yescharacteristic
33C2×C22⋊Dic113C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×#14268624C2211yescharacteristic
37C2×#14268624C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39C2×C4×Dic113C2211yescharacteristic
40C2×C4×Dic113C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47C22×D4×C113C2211yescharacteristic
48C2×C4⋊C4×C113C2211yescharacteristic
49C2×C22⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C22⋊C4×C113C2211yescharacteristic
52C2×C22⋊C4×C113C2211yescharacteristic
53C2×C42×C113C2211yescharacteristic
54C23×D113C2311yescharacteristic
55C2×C22⋊D113—22no—
56C2×C22⋊D113—22no—
57C2×C22⋊D113—41no—
58C2×C22⋊D113—41no—
59C2×C22⋊D113C2×C414yes—
60C2×C22⋊D113C2×C414yescomplemented
61C22×Dic113—22no—
62C22×Dic113—22no—
63C22×Dic113—22no—
64C22×Dic113—41no—
65C22×Dic113—41no—
66C22×Dic113C2×C414yescomplemented
67C22×Dic113C2311yescharacteristic
68C22×Dic113C2311yescharacteristic
69C22×Dic113C2311yescharacteristic
70C22×Dic113C2311yescharacteristic
71C22×Dic113C2311yescharacteristic
72C22×Dic113C2311yescharacteristic
73C22×Dic113C2311yescharacteristic
74C2×C4×D113—22no—
75C2×C4×D113—41no—
76C2×C4×D113—41no—
77#14268626—22no—
78#14268626—22no—
79#14268626—22no—
80#14268626—22no—
81#14268626—41no—
82#14268626C2×C414yescomplemented
83C22⋊Dic113—22no—
84C22⋊Dic113—41no—
85C22⋊Dic113—41no—
86C22⋊Dic113C2×C414yescomplemented
87#14268624—22no—
88#14268624—41no—
89#14268624—41no—
90#14268624C2×C414yescomplemented
91C4×Dic113—22no—
92C4×Dic113—41no—
93C4×Dic113D414yescomplemented
94C24×C113C2311yescharacteristic
95C24×C113C2311yescharacteristic
96C2×D4×C113—41no—
97C2×D4×C113—41no—
98C2×D4×C113C2×C414yescomplemented
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102C22×C4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C4⋊C4×C113—41no—
105C22⋊C4×C113—22no—
106C22⋊C4×C113—22no—
107C22⋊C4×C113—41no—
108C22⋊C4×C113—41no—
109C42×C113—41no—
110C23×C113—21no—
111C23×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C23×C113—21no—
118C23×C113—21no—
119C23×C113—21no—
120C23×C113—21no—
121C23×C113—21no—
122C23×C113C22×C412yes—
123C23×C113C22×C412yes—
124C23×C113C2411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—21no—
131C22×D113C22×C412yes—
132D4×C113—44no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113C22×C412yes—
147C2×C4×C113C2×D412yes—
148C22⋊D113—28no—
149C22⋊D113—44no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113—28no—
157C2×Dic113—21no—
158C2×Dic113—21no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—21no—
162C2×Dic113—21no—
163C2×Dic113—21no—
164C2×Dic113—21no—
165C2×Dic113—21no—
166C2×Dic113—44no—
167C2×Dic113C22×C412yes—
168C2×Dic113C22×C412yes—
169C2×Dic113C22×C412yes—
170C2×Dic113C2×D412yes—
171C2×Dic113C2×D412yes—
172C2×Dic113#4112yes—
173C4×D113—44no—
174C22×C113—22no—
175C22×C113—22no—
176C22×C113—22no—
177C22×C113—22no—
178C22×C113—22no—
179C22×C113—22no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113C23×C411yescharacteristic
189C22×C113C22×D411yescharacteristic
190C22×C113C2×#4111yescharacteristic
191C22×C113H(5,𝔽2)11yescharacteristic
192C22×C113H(5,𝔽2)11yescharacteristic
193C22×C113H(5,𝔽2)11yescharacteristic
194C22×C1132−1+411yescharacteristic
195C2×D113—22no—
196C2×D113—22no—
197C2×D113—22no—
198C2×D113—41no—
199C2×D113—41no—
200C2×D113—41no—
201C2×D113—41no—
202C4×C113—22no—
203C4×C113—22no—
204C4×C113—41no—
205C4×C113—41no—
206C4×C113—41no—
207Dic113—22no—
208Dic113—22no—
209Dic113—22no—
210Dic113—41no—
211Dic113—41no—
212Dic113—41no—
213Dic113C4×D414yes—
214C2×C113—42no—
215C2×C113—42no—
216C2×C113C2×C4×D411yescharacteristic
217C2×C113#51811yescharacteristic
218C2×C113#52011yescharacteristic
219C2×C113#53511yescharacteristic
220C2×C113#53711yescharacteristic
221C2×C113#54011yescharacteristic
222C2×C113#54211yescharacteristic
223D113—42no—
224#2324—1131nomaximal, Sylow
225C113#232411yescharacteristic, complemented, Sylow
226C2×#121—1131no—
227C2×C4×D4—1131no—
228C2×#117—1131no—
229#390—1131no—
230#390—1131no—
231#390D11311yescharacteristic, complemented
232#389—1131no—
233#388—1131no—
234#388—1131no—
235#386—1131no—
236#386—1131no—
237#385—1131no—
238#385—1131no—
239#380—1131no—
240C4×C4⋊C4—1131no—
241C22×D4—1131no—
242C22×D4—1131no—
243C22×D4C2×D11311yescharacteristic
244C23×C4—1131no—
245C23×C4—1131no—
246C23×C4—1131no—
247#121—1138no—
248C4×D4—2264no—
249#117—2264no—
250C2×C4⋊C4—1131no—
251C2×C4⋊C4—1131no—
252C2×C4⋊C4—1131no—
253C2×C4⋊C4—1131no—
254C2×C4⋊C4—1131no—
255C2×C4⋊C4—1131no—
256C2×C4⋊C4C2×D11311yescharacteristic
257C2×C22⋊C4—1131no—
258C2×C22⋊C4—1131no—
259C2×C22⋊C4—1131no—
260C2×C22⋊C4—1131no—
261C2×C22⋊C4—1131no—
262C2×C22⋊C4—1131no—
263C2×C22⋊C4—1131no—
264C2×C22⋊C4—1131no—
265C2×C22⋊C4C2×D11311yescharacteristic
266C2×C22⋊C4C2×D11311yescharacteristic
267C2×C22⋊C4C2×D11311yescharacteristic
268C2×C22⋊C4C2×D11311yescharacteristic
269C2×C42—1131no—
270C2×C42—1131no—
271C2×C42—1131no—
272C2×C42C2×D11311yescharacteristic
273#95—1131no—
274#95—1131no—
275#95—1131no—
276#95—1131no—
277#95—1131no—
278#95—1131no—
279C24—1131no—
280C24C22×D11311yescharacteristic
281C24C22×D11311yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—1134no—
285C2×D4—1134no—
286C2×D4—4521no—
287C2×D4—4521no—
288C2×D4—2262no—
289C2×D4—2262no—
290C2×D4C4×D11314yescomplemented
291C22×C4—1131no—
292C22×C4—1134no—
293C22×C4—1131no—
294C22×C4—1131no—
295C22×C4—1131no—
296C22×C4—1131no—
297C22×C4—1131no—
298C22×C4—1131no—
299C22×C4—4521no—
300C22×C4—4521no—
301C22×C4—4521no—
302C22×C4—4521no—
303C22×C4—2262no—
304C22×C4—2262no—
305C22×C4—2262no—
306C22×C4—2262no—
307C22×C4C22×D11311yescharacteristic
308C22×C4C22×D11311yescharacteristic
309C22×C4C22×D11311yescharacteristic
310C22×C4C22×D11311yescharacteristic
311C22×C4C22×D11311yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—1134no—
314C4⋊C4—4521no—
315C4⋊C4—2262no—
316C4⋊C4—2262no—
317C4⋊C4—2262no—
318C4⋊C4—2262no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—1134no—
324C22⋊C4—1134no—
325C22⋊C4—4521no—
326C22⋊C4—4521no—
327C22⋊C4—4521no—
328C22⋊C4—4521no—
329C22⋊C4—2262no—
330C22⋊C4—2262no—
331C42—41no—
332C42—1134no—
333C42—4521no—
334C42—2262no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—1132no—
348C23—2261no—
349C23—2261no—
350C23—2261no—
351C23—2261no—
352C23—2261no—
353C23—2261no—
354C23C2×C4×D11312yes—
355C23C2×C4×D11312yes—
356C23C23×D11311yescharacteristic
357D4—44no—
358D4—4524no—
359D4—2268no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—1132no—
374C2×C4—1132no—
375C2×C4—1132no—
376C2×C4—1132no—
377C2×C4—1132no—
378C2×C4—1132no—
379C2×C4—4524no—
380C2×C4—4524no—
381C2×C4—2268no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4—2261no—
385C2×C4—2261no—
386C2×C4—2261no—
387C2×C4—2261no—
388C2×C4—2261no—
389C2×C4—2261no—
390C2×C4—2261no—
391C2×C4—2261no—
392C2×C4—2261no—
393C2×C4—2261no—
394C2×C4—2261no—
395C2×C4—2261no—
396C2×C4—2261no—
397C2×C4C2×C4×D11312yes—
398C2×C4D4×D11312yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—4521no—
414C22—4521no—
415C22—4521no—
416C22—4521no—
417C22—2262no—
418C22—2262no—
419C22—2262no—
420C22C22×C4×D11311yescharacteristic
421C22C2×D4×D11311yescharacteristic
422C22#41×D11311yescharacteristic
423C22#1681366711yescharacteristic
424C22#1681366711yescharacteristic
425C22#1681366711yescharacteristic
426C22#1681366911yescharacteristic
427C4—22no—
428C4—22no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—1134no—
433C4—4521no—
434C4—4521no—
435C4—4521no—
436C4—2262no—
437C4—2262no—
438C4—2262no—
439C2—42no—
440C2—42no—
441C2—4522no—
442C2C4×D4×D11311yescharacteristic
443C2#2029907111yescharacteristic
444C2#2029907711yescharacteristic
445C2#2029916111yescharacteristic
446C2#2029917511yescharacteristic
447C2#2029919811yescharacteristic
448C2#2029921211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#390×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813594C2
hypercenter#390D113
hypocenterC113#2324
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#16813582C2semidirect
3. C2×#16813578C2semidirect
4. #20298498C2semidirect
5. #20298498C2semidirect
6. #20298493C2semidirect
7. #20298492C2semidirect
8. #20298489C2semidirect
9. #20298478C2semidirect
10. #20298474C2semidirect
11. #20298470C2semidirect
12. #20298469C2semidirect
13. #20298456C2semidirect
14. C4×#14268626C2semidirect
15. #390×C113C2semidirect
21. #16813594C4semidirect
60. C2×C22⋊D113C2×C4semidirect
66. C22×Dic113C2×C4semidirect
82. #14268626C2×C4semidirect
86. C22⋊Dic113C2×C4semidirect
90. #14268624C2×C4semidirect
93. C4×Dic113D4semidirect
98. C2×D4×C113C2×C4semidirect
225. C113#2324semidirect
231. #390D113semidirect
290. C2×D4C4×D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168135942
C2×#168135822
C2×#168135782
#202984982
#202984932
#202984922
#202984892
#202984782
#202984742
#202984702
#202984692
#202984562
C4×#142686262
#390×C1132
#2324113