Finite Group Databasebeta

← #28393907

Subgroups — #28393907

Order 14464.

864 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14268647C211yesmaximal, characteristic
2C2×#16813607C211yesmaximal, characteristic, complemented
3C2×#16813604C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D113C211yesmaximal, characteristic, complemented
5#20298519C211yesmaximal, characteristic, complemented
6#20298518C211yesmaximal, characteristic, complemented
7#20298514C211yesmaximal, characteristic, complemented
8#20298513C211yesmaximal, characteristic, complemented
9#20298476C211yesmaximal, characteristic, complemented
10#20298474C211yesmaximal, characteristic, complemented
11#20298472C211yesmaximal, characteristic, complemented
12#20298471C211yesmaximal, characteristic, complemented
13#20298469C211yesmaximal, characteristic, complemented
14#20298460C211yesmaximal, characteristic, complemented
15#385×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—24no—
17C2×#14268647—24no—
18C2×#14268647—24no—
19C22×Dic226C2211yescharacteristic
20C22×D452C2211yescharacteristic
21C22×C22⋊D113C2211yescharacteristic
22C22×C22⋊D113C2211yescharacteristic
23C22×C4×D113C2211yescharacteristic
24C22×C4×D113C2211yescharacteristic
25C22×C4×D113C2211yescharacteristic
26C22×C4×D113C2211yescharacteristic
27#16813607—24no—
28#16813604—24no—
29C2×C4⋊Dic113C2211yescharacteristic
30C2×C4⋊Dic113C2211yescharacteristic
31C2×#14268626C2211yescharacteristic
32C2×#14268626C2211yescharacteristic
33C2×#14268626C2211yescharacteristic
34C2×#14268626C2211yescharacteristic
35C4⋊C4×D113—24no—
36C2×C22⋊Dic113C2211yescharacteristic
37C2×C22⋊Dic113C2211yescharacteristic
38C2×#14268624C2211yescharacteristic
39C2×#14268624C2211yescharacteristic
40C2×#14268624C2211yescharacteristic
41C2×#14268624C2211yescharacteristic
42C2×#14268624C2211yescharacteristic
43C2×#14268624C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47#16813529C2211yescharacteristic
48#16813529C2211yescharacteristic
49#16813529C2211yescharacteristic
50C23×C4×C113C2211yescharacteristic
51C2×C4⋊C4×C113C2211yescharacteristic
52C2×C4⋊C4×C113C2211yescharacteristic
53C2×C22⋊C4×C113C2211yescharacteristic
54C2×C22⋊C4×C113C2211yescharacteristic
55#95×C113C2211yescharacteristic
56#95×C113C2211yescharacteristic
57C23×D113C2311yescharacteristic
58C23×D113C2311yescharacteristic
59#14268647—232no—
60C2×Dic226—22no—
61C2×Dic226—22no—
62C2×Dic226—22no—
63C2×D452—22no—
64C2×D452—22no—
65C2×D452D414yes—
66C2×C22⋊D113—22no—
67C2×C22⋊D113—22no—
68C2×C22⋊D113—22no—
69C2×C22⋊D113—22no—
70C2×C22⋊D113—22no—
71C2×C22⋊D113D414yes—
72C22×Dic113C2311yescharacteristic
73C22×Dic113C2311yescharacteristic
74C22×Dic113C2311yescharacteristic
75C22×Dic113C2311yescharacteristic
76C22×Dic113C2311yescharacteristic
77C22×Dic113C2311yescharacteristic
78C2×C4×D113—22no—
79C2×C4×D113—22no—
80C2×C4×D113—22no—
81C2×C4×D113—22no—
82C2×C4×D113—22no—
83C2×C4×D113—22no—
84C2×C4×D113—22no—
85C2×C4×D113—22no—
86C2×C4×D113—22no—
87C2×C4×D113—22no—
88C2×C4×D113—22no—
89C2×C4×D113D414yes—
90C4⋊Dic113—22no—
91C4⋊Dic113—22no—
92#14268626—22no—
93#14268626—22no—
94#14268626—22no—
95#14268626—22no—
96C22⋊Dic113—22no—
97C22⋊Dic113—22no—
98#14268624—22no—
99#14268624—22no—
100#14268624—22no—
101#14268624—22no—
102#14268624—22no—
103#14268624—22no—
104C24×C113C2311yescharacteristic
105C22×C4×C113—22no—
106C22×C4×C113—22no—
107C22×C4×C113—22no—
108C22×C4×C113C2311yescharacteristic
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C22×C4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114C4⋊C4×C113—22no—
115C4⋊C4×C113—22no—
116C22⋊C4×C113—22no—
117C22⋊C4×C113—22no—
118C23×C113—21no—
119C23×C113—21no—
120C23×C113—21no—
121C23×C113—21no—
122C23×C113—21no—
123C23×C113—21no—
124C23×C113C2×D412yes—
125C23×C113C2411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—21no—
131C22×D113—21no—
132C22×D113—21no—
133C22×D113—21no—
134C22×D113—21no—
135C22×D113—21no—
136C22×D113C2×D412yes—
137C22×D113C2×D412yes—
138C22×D113C2×D412yes—
139C22×D113C2×D412yes—
140C2×C4×C113—28no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113—21no—
150C2×C4×C113—21no—
151C2×C4×C113—21no—
152C2×C4×C113—21no—
153C2×C4×C113—21no—
154C2×C4×C113—21no—
155C2×C4×C113—21no—
156C2×C4×C113C2×D412yes—
157C2×C4×C113C2×D412yes—
158C2×C4×C113#4112yescomplemented
159C22⋊D113—28no—
160C22⋊D113—28no—
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×Dic113—21no—
172C2×Dic113—21no—
173C2×Dic113—21no—
174C2×Dic113—21no—
175C2×Dic113—21no—
176C2×Dic113C2×D412yes—
177C2×Dic113C2×D412yes—
178C2×Dic113#4112yescomplemented
179D452—28no—
180C4×D113—28no—
181C4×D113—28no—
182C4×D113—28no—
183C4×D113—44no—
184Dic226—28no—
185C22×C113—22no—
186C22×C113—22no—
187C22×C113—22no—
188C22×C113—41no—
189C22×C113—41no—
190C22×C113—41no—
191C22×C113—41no—
192C22×C113C22×D411yescharacteristic
193C22×C113C22×D411yescharacteristic
194C22×C113C22×D411yescharacteristic
195C22×C113C2×#4111yescharacteristic
196C22×C113C2×#4111yescharacteristic
197C22×C1132−1+411yescharacteristic
198C22×C1132−1+411yescharacteristic
199C2×D113—22no—
200C2×D113—22no—
201C2×D113—22no—
202C2×D113—22no—
203C2×D113—22no—
204C2×D113—22no—
205C2×D113—22no—
206C2×D113—22no—
207C2×D113—22no—
208C2×D113—41no—
209C2×D113—41no—
210C2×D113—41no—
211C2×D113—41no—
212C2×D113#12014yes—
213C4×C113—22no—
214C4×C113—22no—
215C4×C113—22no—
216C4×C113—41no—
217C4×C113—41no—
218C4×C113—41no—
219Dic113—22no—
220Dic113—22no—
221Dic113—22no—
222Dic113—41no—
223Dic113—41no—
224Dic113—41no—
225C2×C113—42no—
226C2×C113C2×#12011yescharacteristic
227C2×C113#52511yescharacteristic
228C2×C113#53611yescharacteristic
229C2×C113#54711yescharacteristic
230C2×C113#54711yescharacteristic
231C2×C113#54711yescharacteristic
232C2×C113#54711yescharacteristic
233D113—24no—
234D113—42no—
235#2406—1131nomaximal, Sylow
236C113#240611yescharacteristic, complemented, Sylow
237C22×#41—1131no—
238C2×#123—1131no—
239C2×#123—1131no—
240C22×C4⋊C4—1131no—
241#395—1131no—
242#395—1131no—
243#394—1131no—
244#394—1131no—
245#386—1131no—
246#386—1131no—
247#385—1131no—
248#385—1131no—
249#385—1131no—
250#385D11311yescharacteristic, complemented
251#381—1131no—
252C2×#41—2264no—
253C2×#41—2264no—
254C2×#41—2264no—
255C22×Q8—1131no—
256C22×D4—1131no—
257C22×D4—1131no—
258C22×D4—1131no—
259C23×C4—1131no—
260C23×C4—1131no—
261C23×C4—1131no—
262C23×C4—1131no—
263C23×C4C2×D11311yescharacteristic
264#123—2264no—
265#123—2264no—
266C2×C4⋊C4—1131no—
267C2×C4⋊C4—1131no—
268C2×C4⋊C4—1131no—
269C2×C4⋊C4—1131no—
270C2×C4⋊C4—1131no—
271C2×C4⋊C4—1131no—
272C2×C4⋊C4—2264no—
273C2×C4⋊C4C2×D11311yescharacteristic
274C2×C4⋊C4C2×D11311yescharacteristic
275C2×C22⋊C4—1131no—
276C2×C22⋊C4—1131no—
277C2×C22⋊C4—1131no—
278C2×C22⋊C4—1131no—
279C2×C22⋊C4—1131no—
280C2×C22⋊C4—1131no—
281C2×C22⋊C4—1131no—
282C2×C22⋊C4—1131no—
283C2×C22⋊C4C2×D11311yescharacteristic
284C2×C22⋊C4C2×D11311yescharacteristic
285#95—1131no—
286#95—1131no—
287#95—1131no—
288#95—1131no—
289#95—1131no—
290#95—1131no—
291#95C2×D11311yescharacteristic
292#95C2×D11311yescharacteristic
293C24—1131no—
294C24—1131no—
295C24C22×D11311yescharacteristic
296#41—22632no—
297C2×Q8—2262no—
298C2×Q8—2262no—
299C2×Q8—2262no—
300C2×D4—1134no—
301C2×D4—1134no—
302C2×D4—2262no—
303C2×D4—2262no—
304C2×D4—2262no—
305C2×D4—2262no—
306C2×D4—2262no—
307C2×D4—2262no—
308C2×D4—2262no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—1131no—
313C22×C4—1131no—
314C22×C4—1131no—
315C22×C4—1134no—
316C22×C4—1131no—
317C22×C4—1131no—
318C22×C4—1131no—
319C22×C4—2262no—
320C22×C4—2262no—
321C22×C4—2262no—
322C22×C4—2262no—
323C22×C4—2262no—
324C22×C4—2262no—
325C22×C4—2262no—
326C22×C4—2262no—
327C22×C4—2262no—
328C22×C4—2262no—
329C22×C4—2262no—
330C22×C4C22×D11311yescharacteristic
331C22×C4C22×D11311yescharacteristic
332C22×C4C22×D11311yescharacteristic
333C22×C4C22×D11311yescharacteristic
334C22×C4C22×D11311yescharacteristic
335C22×C4C22×D11311yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—2262no—
339C4⋊C4—2262no—
340C4⋊C4—2262no—
341C4⋊C4—2262no—
342C4⋊C4—2262no—
343C4⋊C4—2262no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—2262no—
347C22⋊C4—2262no—
348C22⋊C4—2262no—
349C22⋊C4—2262no—
350C22⋊C4—2262no—
351C22⋊C4—2262no—
352C22⋊C4—2262no—
353C22⋊C4—2262no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—1132no—
361C23—1132no—
362C23—1132no—
363C23—1132no—
364C23—2261no—
365C23—2261no—
366C23—2261no—
367C23—2261no—
368C23—2261no—
369C23—2261no—
370C23—2261no—
371C23—2261no—
372C23—2261no—
373C23—2261no—
374C23D4×D11312yes—
375C23C23×D11311yescharacteristic
376Q8—2268no—
377D4—2268no—
378D4—2268no—
379D4—2268no—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—1132no—
397C2×C4—1132no—
398C2×C4—1132no—
399C2×C4—4524no—
400C2×C4—2268no—
401C2×C4—2268no—
402C2×C4—2268no—
403C2×C4—2261no—
404C2×C4—2261no—
405C2×C4—2261no—
406C2×C4—2261no—
407C2×C4—2261no—
408C2×C4—2261no—
409C2×C4—2261no—
410C2×C4—2261no—
411C2×C4—2261no—
412C2×C4—2261no—
413C2×C4—2261no—
414C2×C4—2261no—
415C2×C4—2261no—
416C2×C4—2261no—
417C2×C4—2261no—
418C2×C4D4×D11312yes—
419C2×C4D4×D11312yes—
420C2×C4#1426864712yescomplemented
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—1134no—
429C22—4521no—
430C22—4521no—
431C22—4521no—
432C22—4521no—
433C22—2262no—
434C22—2262no—
435C22—2262no—
436C22—2262no—
437C22—2262no—
438C22—2262no—
439C22—2262no—
440C22—2262no—
441C22—2262no—
442C22C2×D4×D11311yescharacteristic
443C22C2×D4×D11311yescharacteristic
444C22C2×D4×D11311yescharacteristic
445C22#41×D11311yescharacteristic
446C22C2×#1426864711yescharacteristic
447C22#1681366911yescharacteristic
448C22#1681367011yescharacteristic
449C4—22no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—4521no—
456C4—4521no—
457C4—4521no—
458C4—2262no—
459C4—2262no—
460C4—2262no—
461C2—42no—
462C2—4522no—
463C2—2264no—
464C2#120×D11311yescharacteristic
465C2#2029910711yescharacteristic
466C2#2029917111yescharacteristic
467C2#2029924611yescharacteristic
468C2#2029924911yescharacteristic
469C2#2029925011yescharacteristic
470C2#2029925311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#385×C113C2
prime radicalC22×#14268647C2
hypercenter#385D113
hypocenterC113#2406
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#16813607C2semidirect
3. C2×#16813604C2semidirect
4. C2×C4⋊C4×D113C2semidirect
5. #20298519C2semidirect
6. #20298518C2semidirect
7. #20298514C2semidirect
8. #20298513C2semidirect
9. #20298476C2semidirect
10. #20298474C2semidirect
11. #20298472C2semidirect
12. #20298471C2semidirect
13. #20298469C2semidirect
14. #20298460C2semidirect
15. #385×C113C2semidirect
158. C2×C4×C113#41semidirect
178. C2×Dic113#41semidirect
236. C113#2406semidirect
250. #385D113semidirect
420. C2×C4#14268647semidirect

Maximal subgroups

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

subgroupindex
C22×#142686472
C2×#168136072
C2×#168136042
C2×C4⋊C4×D1132
#202985192
#202985182
#202985142
#202985132
#202984762
#202984742
#202984722
#202984712
#202984692
#202984602
#385×C1132
#2406113