Finite Group Databasebeta

← #28393816

Subgroups — #28393816

Order 14464.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
3C2×#16813581C211yesmaximal, characteristic, complemented
4#20298531C211yesmaximal, characteristic, complemented
5#20298526C211yesmaximal, characteristic, complemented
6#20298521C211yesmaximal, characteristic, complemented
7#20298520C211yesmaximal, characteristic, complemented
8#20298514C211yesmaximal, characteristic, complemented
9#20298513C211yesmaximal, characteristic, complemented
10#20298512C211yesmaximal, characteristic, complemented
11#20298506C211yesmaximal, characteristic
12C4×#14268626C211yesmaximal, characteristic, complemented
13C4×#14268624C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic113C211yesmaximal, characteristic, complemented
15C2×C4×D4×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C4×C22⋊D113—24no—
20C4×C22⋊D113—24no—
21#16813581—24no—
22C2×C4⋊Dic113C2211yescharacteristic
23C2×C4⋊Dic113C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×C22⋊Dic113C2211yescharacteristic
29C2×C22⋊Dic113C2211yescharacteristic
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
48C23×C4×C113C2211yescharacteristic
49C23×C4×C113C2211yescharacteristic
50C4×D4×C113—24no—
51C2×C4⋊C4×C113C2211yescharacteristic
52C2×C22⋊C4×C113C2211yescharacteristic
53C2×C22⋊C4×C113C2211yescharacteristic
54C2×C42×C113C2211yescharacteristic
55C23×D113C2311yescharacteristic
56C2×C22⋊D113—22no—
57C2×C22⋊D113—22no—
58C2×C22⋊D113—22no—
59C2×C22⋊D113—22no—
60C2×C22⋊D113—22no—
61C2×C22⋊D113—22no—
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C22×Dic113C2311yescharacteristic
69C2×C4×D113—22no—
70C2×C4×D113—22no—
71C2×C4×D113—22no—
72C4⋊Dic113—22no—
73C4⋊Dic113—22no—
74#14268626—22no—
75#14268626—22no—
76#14268626—22no—
77#14268626—22no—
78C22⋊Dic113—22no—
79C22⋊Dic113—22no—
80C22⋊Dic113—22no—
81C22⋊Dic113—22no—
82C22⋊Dic113—22no—
83C22⋊Dic113—22no—
84#14268624—22no—
85#14268624—22no—
86#14268624—22no—
87#14268624—22no—
88C4×Dic113—22no—
89C4×Dic113—22no—
90C4×Dic113D414yescomplemented
91C24×C113C2311yescharacteristic
92C24×C113C2311yescharacteristic
93C2×D4×C113—22no—
94C2×D4×C113—22no—
95C2×D4×C113—22no—
96C22×C4×C113—22no—
97C22×C4×C113—22no—
98C22×C4×C113—22no—
99C22×C4×C113—22no—
100C22×C4×C113—22no—
101C22×C4×C113D414yescomplemented
102C22×C4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105C22×C4×C113C2311yescharacteristic
106C22×C4×C113C2311yescharacteristic
107C4⋊C4×C113—22no—
108C22⋊C4×C113—22no—
109C22⋊C4×C113—22no—
110C42×C113—22no—
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×C113—21no—
123C23×C113C2×D412yes—
124C23×C113#4112yes—
125C23×C113C2411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—21no—
131C22×D113—21no—
132C22×D113#4112yes—
133D4×C113—28no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—28no—
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—44no—
146C2×C4×C113C2×D412yes—
147C2×C4×C113C2×D412yes—
148C2×C4×C113C2×D412yes—
149C2×C4×C113#4112yes—
150C2×C4×C113#4112yes—
151C22⋊D113—28no—
152C22⋊D113—28no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113—21no—
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—21no—
167C2×Dic113—21no—
168C2×Dic113—21no—
169C2×Dic113—21no—
170C2×Dic113—21no—
171C2×Dic113C2×D412yes—
172C2×Dic113C2×D412yes—
173C2×Dic113#4112yes—
174C4×D113—44no—
175C22×C113—22no—
176C22×C113—22no—
177C22×C113—22no—
178C22×C113—22no—
179C22×C113—22no—
180C22×C113—22no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113—41no—
189C22×C113C22×D411yescharacteristic
190C22×C113C22×D411yescharacteristic
191C22×C113C2×#4111yescharacteristic
192C22×C113C2×#4111yescharacteristic
193C22×C113C2×#4111yescharacteristic
194C22×C113C2×#4111yescharacteristic
195C22×C113C2×#4111yescharacteristic
196C2×D113—22no—
197C2×D113—22no—
198C2×D113—22no—
199C2×D113—41no—
200C2×D113—41no—
201C2×D113—41no—
202C2×D113—41no—
203C4×C113—22no—
204C4×C113—22no—
205C4×C113—41no—
206C4×C113—41no—
207C4×C113#12114yes—
208Dic113—22no—
209Dic113—22no—
210Dic113—22no—
211Dic113—41no—
212Dic113—41no—
213Dic113—41no—
214Dic113—41no—
215C2×C113—42no—
216C2×C113—42no—
217C2×C113C2×#12111yescharacteristic
218C2×C113#52511yescharacteristic
219C2×C113#52511yescharacteristic
220C2×C113#52511yescharacteristic
221C2×C113#52911yescharacteristic
222C2×C113#52911yescharacteristic
223C2×C113#53211yescharacteristic
224D113—42no—
225#2392—1131nomaximal, Sylow
226C113#239211yescharacteristic, complemented, Sylow
227C2×C4×D4—1131no—
228C2×C4×D4—1131no—
229C2×C4×D4D11311yescharacteristic, complemented
230C2×#117—1131no—
231#398—1131no—
232#397—1131no—
233#396—1131no—
234#396—1131no—
235#394—1131no—
236#394—1131no—
237#394—1131no—
238#392—1131no—
239C4×C4⋊C4—1131no—
240C4×C22⋊C4—1131no—
241C4×C22⋊C4—1131no—
242C22×D4—1131no—
243C22×D4—1131no—
244C22×D4C2×D11311yescharacteristic
245C23×C4—1131no—
246C23×C4C2×D11311yescharacteristic
247C23×C4C2×D11311yescharacteristic
248C4×D4—24no—
249C4×D4—2264no—
250C4×D4—2264no—
251#117—2264no—
252C2×C4⋊C4—1131no—
253C2×C4⋊C4—1131no—
254C2×C4⋊C4—1131no—
255C2×C4⋊C4—1131no—
256C2×C4⋊C4—1131no—
257C2×C4⋊C4—1131no—
258C2×C4⋊C4C2×D11311yescharacteristic
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⋊C4—1131no—
266C2×C22⋊C4—1131no—
267C2×C22⋊C4—1131no—
268C2×C22⋊C4—1131no—
269C2×C22⋊C4C2×D11311yescharacteristic
270C2×C22⋊C4C2×D11311yescharacteristic
271C2×C42—1131no—
272C2×C42—1131no—
273C2×C42—1131no—
274C2×C42C2×D11311yescharacteristic
275#95—1131no—
276#95—1131no—
277#95—1131no—
278#95—1131no—
279#95—1131no—
280#95—1131no—
281C24—1131no—
282C24C22×D11311yescharacteristic
283C24C22×D11311yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—2262no—
288C2×D4—2262no—
289C2×D4—2262no—
290C2×D4—2262no—
291C2×D4—2262no—
292C2×D4—2262no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—1131no—
299C22×C4—1131no—
300C22×C4—1131no—
301C22×C4—1131no—
302C22×C4—1131no—
303C22×C4—1131no—
304C22×C4—1131no—
305C22×C4—2262no—
306C22×C4—2262no—
307C22×C4—2262no—
308C22×C4C22⋊D11314yescomplemented
309C22×C4C22×D11311yescharacteristic
310C22×C4C22×D11311yescharacteristic
311C22×C4C22×D11311yescharacteristic
312C22×C4C22×D11311yescharacteristic
313C22×C4C22×D11311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—2262no—
316C4⋊C4—2262no—
317C4⋊C4—2262no—
318C4⋊C4—2262no—
319C4⋊C4—2262no—
320C4⋊C4—2262no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—2262no—
324C22⋊C4—2262no—
325C22⋊C4—2262no—
326C22⋊C4—2262no—
327C22⋊C4—2262no—
328C22⋊C4—2262no—
329C22⋊C4—2262no—
330C22⋊C4—2262no—
331C22⋊C4—2262no—
332C22⋊C4—2262no—
333C42—22no—
334C42—1134no—
335C42—2262no—
336C42—2262no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—1132no—
350C23—2261no—
351C23—2261no—
352C23—2261no—
353C23—2261no—
354C23—2261no—
355C23—2261no—
356C23C2×C22⋊D11312yes—
357C23#1426864712yes—
358C23C23×D11311yescharacteristic
359D4—28no—
360D4—2268no—
361D4—2268no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—28no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—1132no—
375C2×C4—1132no—
376C2×C4—1132no—
377C2×C4—4524no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4—2261no—
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×C4D4×D11312yes—
397C2×C4C2×C22⋊D11312yes—
398C2×C4C2×C22⋊D11312yes—
399C2×C4#1426864612yes—
400C2×C4#1426864712yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—4521no—
416C22—4521no—
417C22—4521no—
418C22—4521no—
419C22—2262no—
420C22—2262no—
421C22—2262no—
422C22C2×D4×D11311yescharacteristic
423C22C22×C22⋊D11311yescharacteristic
424C22#41×D11311yescharacteristic
425C22#41×D11311yescharacteristic
426C22C2×#1426864611yescharacteristic
427C22C2×#1426864711yescharacteristic
428C22C2×#1426864711yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—4521no—
434C4—4521no—
435C4—4521no—
436C4—4521no—
437C4—2262no—
438C4—2262no—
439C4—2262no—
440C4#1681359414yes—
441C2—42no—
442C2—42no—
443C2—4522no—
444C2C2×#1681359411yescharacteristic
445C2#2029910511yescharacteristic
446C2#2029910711yescharacteristic
447C2#2029910911yescharacteristic
448C2#2029912811yescharacteristic
449C2#2029913011yescharacteristic
450C2#2029914511yescharacteristic
subgroupG/H
centerC22×C4C22×D113
commutator, socle, cosocleC23×C113C24
FrattiniC23C23×D113
FittingC2×C4×D4×C113C2
prime radical#20298506C2
hypercenterC2×C4×D4D113
hypocenterC113#2392
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D113C2semidirect
2. C2×C4×C22⋊D113C2semidirect
3. C2×#16813581C2semidirect
4. #20298531C2semidirect
5. #20298526C2semidirect
6. #20298521C2semidirect
7. #20298520C2semidirect
8. #20298514C2semidirect
9. #20298513C2semidirect
10. #20298512C2semidirect
12. C4×#14268626C2semidirect
13. C4×#14268624C2semidirect
14. C4×C22⋊Dic113C2semidirect
15. C2×C4×D4×C113C2semidirect
90. C4×Dic113D4semidirect
101. C22×C4×C113D4semidirect
226. C113#2392semidirect
229. C2×C4×D4D113semidirect
308. C22×C4C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1132
C2×#168135812
#202985312
#202985262
#202985212
#202985202
#202985142
#202985132
#202985122
#202985062
C4×#142686262
C4×#142686242
C4×C22⋊Dic1132
C2×C4×D4×C1132
#2392113