Finite Group Databasebeta

← #28393553

Subgroups — #28393553

Order 14464.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813591C211yesmaximal, characteristic
2C2×C4×C22⋊D113C211yesmaximal, characteristic, complemented
3C2×#16813582C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic113C211yesmaximal, characteristic, complemented
5#20298498C211yesmaximal, characteristic, complemented
6#20298492C211yesmaximal, characteristic, complemented
7#20298486C211yesmaximal, characteristic, complemented
8#20298477C211yesmaximal, characteristic, complemented
9#20298475C211yesmaximal, characteristic, complemented
10#20298474C211yesmaximal, characteristic, complemented
11#20298471C211yesmaximal, characteristic, complemented
12#20298470C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic113C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic113C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C22×C22⋊D113C2211yescharacteristic
19C23×Dic113C2211yescharacteristic
20C23×Dic113C2211yescharacteristic
21C22×C4×D113C2211yescharacteristic, complemented
22#16813591C418yescomplemented
23C4×C22⋊D113—24no—
24#16813582—24no—
25C2×#14268626C2211yescharacteristic, complemented
26C2×#14268626C2211yescharacteristic, complemented
27C2×#14268626C2211yescharacteristic, complemented
28C2×C22⋊Dic113—24no—
29C2×C22⋊Dic113C2211yescharacteristic
30C2×C22⋊Dic113C2211yescharacteristic
31C2×C22⋊Dic113C2211yescharacteristic
32C2×C22⋊Dic113C2211yescharacteristic
33C2×C22⋊Dic113C2211yescharacteristic
34C2×C22⋊Dic113C2211yescharacteristic
35C2×C22⋊Dic113C2211yescharacteristic
36C2×#14268624C2211yescharacteristic, complemented
37C2×#14268624C2211yescharacteristic, complemented
38C2×#14268624C2211yescharacteristic, complemented
39C2×C4×Dic113C2211yescharacteristic, complemented
40C2×C4×Dic113C2211yescharacteristic, complemented
41C2×C4×Dic113C2211yescharacteristic, complemented
42#16813529C2211yescharacteristic, complemented
43#16813529C2211yescharacteristic, complemented
44#16813529C2211yescharacteristic, complemented
45#16813529C2211yescharacteristic, complemented
46#16813529C2211yescharacteristic, complemented
47#16813529C2211yescharacteristic, complemented
48C25×C113C2211yescharacteristic
49C23×C4×C113C2211yescharacteristic
50C23×C4×C113C2211yescharacteristic
51C2×C22⋊C4×C113—24no—
52C2×C22⋊C4×C113C2211yescharacteristic
53C2×C22⋊C4×C113C2211yescharacteristic
54C2×C22⋊C4×C113C2211yescharacteristic
55C2×C22⋊C4×C113C2211yescharacteristic
56C23×D113C2311yescharacteristic
57C2×C22⋊D113—22no—
58C2×C22⋊D113—22no—
59C2×C22⋊D113—22no—
60C2×C22⋊D113—22no—
61C2×C22⋊D113—41no—
62C2×C22⋊D113—41no—
63C2×C22⋊D113C2×C414yescomplemented
64C2×C22⋊D113C2×C414yescomplemented
65C2×C22⋊D113C2×C414yescomplemented
66C22×Dic113—22no—
67C22×Dic113—22no—
68C22×Dic113—22no—
69C22×Dic113—22no—
70C22×Dic113—41no—
71C22×Dic113—41no—
72C22×Dic113C2311yescharacteristic
73C22×Dic113C2311yescharacteristic
74C22×Dic113C2311yescharacteristic
75C22×Dic113C2311yescharacteristic
76C22×Dic113C2311yescharacteristic
77C22×Dic113C2311yescharacteristic
78C22×Dic113C2311yescharacteristic
79C2×C4×D113—22no—
80C2×C4×D113—22no—
81C2×C4×D113—41no—
82#14268626—22no—
83#14268626—22no—
84#14268626—41no—
85C22⋊Dic113—22no—
86C22⋊Dic113—22no—
87C22⋊Dic113—22no—
88C22⋊Dic113C2×C414yescomplemented
89C22⋊Dic113C2×C414yescomplemented
90C22⋊Dic113C2×C414yescomplemented
91C22⋊Dic113D414yescomplemented
92#14268624—22no—
93#14268624—22no—
94#14268624—41no—
95C4×Dic113—22no—
96C4×Dic113—22no—
97C4×Dic113—41no—
98C24×C113—22no—
99C24×C113—22no—
100C24×C113—22no—
101C24×C113—22no—
102C24×C113—41no—
103C24×C113—41no—
104C24×C113C2×C414yescomplemented
105C24×C113C2311yescharacteristic
106C24×C113C2311yescharacteristic
107C24×C113C2311yescharacteristic
108C22×C4×C113—22no—
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—22no—
112C22×C4×C113—41no—
113C22×C4×C113—41no—
114C22×C4×C113C2311yescharacteristic
115C22×C4×C113C2311yescharacteristic
116C22×C4×C113C2311yescharacteristic
117C22×C4×C113C2311yescharacteristic
118C22⋊C4×C113—22no—
119C22⋊C4×C113—22no—
120C22⋊C4×C113—22no—
121C22⋊C4×C113D414yescomplemented
122C23×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C23×C113—21no—
128C23×C113—21no—
129C23×C113—21no—
130C23×C113—28no—
131C23×C113—28no—
132C23×C113—21no—
133C23×C113—21no—
134C23×C113—21no—
135C23×C113—21no—
136C23×C113—21no—
137C23×C113—21no—
138C23×C113—44no—
139C23×C113—44no—
140C23×C113—44no—
141C23×C113—44no—
142C23×C113—44no—
143C23×C113C22×C412yes—
144C23×C113C22×C412yes—
145C23×C113C22×C412yes—
146C23×C113C2×D412yes—
147C23×C113C2×D412yes—
148C23×C113#4112yes—
149C23×C113#4112yes—
150C23×C113C2411yescharacteristic
151C22×D113—21no—
152C22×D113—21no—
153C22×D113—21no—
154C22×D113—21no—
155C22×D113—21no—
156C22×D113—21no—
157C22×D113C22×C412yes—
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113—21no—
167C2×C4×C113—21no—
168C2×C4×C113—44no—
169C2×C4×C113—44no—
170C2×C4×C113C2×D412yes—
171C2×C4×C113C2×D412yes—
172C22⋊D113—28no—
173C22⋊D113—28no—
174C22⋊D113—44no—
175C2×Dic113—21no—
176C2×Dic113—21no—
177C2×Dic113—21no—
178C2×Dic113—21no—
179C2×Dic113—21no—
180C2×Dic113—21no—
181C2×Dic113—21no—
182C2×Dic113—21no—
183C2×Dic113—21no—
184C2×Dic113—21no—
185C2×Dic113—21no—
186C2×Dic113—21no—
187C2×Dic113—21no—
188C2×Dic113—21no—
189C2×Dic113—21no—
190C2×Dic113—21no—
191C2×Dic113—44no—
192C2×Dic113—44no—
193C2×Dic113C22×C412yes—
194C2×Dic113C22×C412yes—
195C2×Dic113C22×C412yes—
196C2×Dic113C2×D412yes—
197C2×Dic113C2×D412yes—
198C4×D113—44no—
199C22×C113—22no—
200C22×C113—22no—
201C22×C113—22no—
202C22×C113—22no—
203C22×C113—22no—
204C22×C113—22no—
205C22×C113—22no—
206C22×C113—22no—
207C22×C113—22no—
208C22×C113—22no—
209C22×C113—22no—
210C22×C113—22no—
211C22×C113—22no—
212C22×C113—22no—
213C22×C113—22no—
214C22×C113—416no—
215C22×C113—41no—
216C22×C113—41no—
217C22×C113—41no—
218C22×C113—41no—
219C22×C113C4×D414yescomplemented
220C22×C113C4×D414yescomplemented
221C22×C113C23×C411yescharacteristic
222C22×C113C22×D411yescharacteristic
223C22×C113C22×D411yescharacteristic
224C22×C113C2×#4111yescharacteristic
225C22×C113C2×#4111yescharacteristic
226C22×C113H(5,𝔽2)11yescharacteristic
227C22×C113H(5,𝔽2)11yescharacteristic
228C2×D113—22no—
229C2×D113—22no—
230C2×D113—22no—
231C2×D113—41no—
232C2×D113—41no—
233C2×D113—41no—
234C2×D113—41no—
235C4×C113—22no—
236C4×C113—22no—
237C4×C113—41no—
238C4×C113—41no—
239Dic113—22no—
240Dic113—22no—
241Dic113—22no—
242Dic113—22no—
243Dic113—22no—
244Dic113—41no—
245Dic113—41no—
246C2×C113—24no—
247C2×C113—24no—
248C2×C113—42no—
249C2×C113C2×C4×D411yescharacteristic
250C2×C113C2×C4×D411yescharacteristic
251C2×C113#51811yescharacteristic
252C2×C113D4211yescharacteristic
253C2×C113#54611yescharacteristic
254C2×C113#54611yescharacteristic
255C2×C113#55111yescharacteristic
256D113—42no—
257#2358—1131nomaximal, Sylow
258C113#235811yescharacteristic, complemented, Sylow
259C2×#120—1131no—
260C2×C4×D4—1131no—
261C2×C4×D4—1131no—
262C22×C22⋊C4—1131no—
263C22×C22⋊C4D11311yescharacteristic, complemented
264#390—1131no—
265#388—1131no—
266#388—1131no—
267#386—1131no—
268#386—1131no—
269#386—1131no—
270#385—1131no—
271#385—1131no—
272C4×C22⋊C4—1131no—
273C4×C22⋊C4—1131no—
274C25C2×D11311yescharacteristic
275C22×D4—1131no—
276C22×D4—1131no—
277C22×D4—1131no—
278C23×C4—1131no—
279C23×C4—1131no—
280C23×C4—1131no—
281C23×C4C2×D11311yescharacteristic
282C23×C4C2×D11311yescharacteristic
283#120—1138no—
284C4×D4—2264no—
285C4×D4—2264no—
286C2×C4⋊C4—1131no—
287C2×C4⋊C4—1131no—
288C2×C4⋊C4—1131no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—1131no—
291C2×C22⋊C4—1131no—
292C2×C22⋊C4—1131no—
293C2×C22⋊C4—1131no—
294C2×C22⋊C4—1131no—
295C2×C22⋊C4—1131no—
296C2×C22⋊C4—1131no—
297C2×C22⋊C4—1131no—
298C2×C22⋊C4—1131no—
299C2×C22⋊C4—1131no—
300C2×C22⋊C4—2264no—
301C2×C22⋊C4C2×D11311yescharacteristic
302C2×C22⋊C4C2×D11311yescharacteristic
303C2×C22⋊C4C2×D11311yescharacteristic
304C2×C22⋊C4C2×D11311yescharacteristic
305C2×C42—1131no—
306C2×C42—1131no—
307C2×C42—1131no—
308#95—1131no—
309#95—1131no—
310#95—1131no—
311#95—1131no—
312#95—1131no—
313#95—1131no—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—1131no—
321C24C4×D11314yescomplemented
322C24C22×D11311yescharacteristic
323C24C22×D11311yescharacteristic
324C24C22×D11311yescharacteristic
325C2×D4—1134no—
326C2×D4—1134no—
327C2×D4—1134no—
328C2×D4—4521no—
329C2×D4—4521no—
330C2×D4—2262no—
331C2×D4—2262no—
332C2×D4—2262no—
333C2×D4—2262no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—1131no—
341C22×C4—1131no—
342C22×C4—1131no—
343C22×C4—1131no—
344C22×C4—1131no—
345C22×C4—1131no—
346C22×C4—1131no—
347C22×C4—4521no—
348C22×C4—4521no—
349C22×C4—4521no—
350C22×C4—2262no—
351C22×C4—2262no—
352C22×C4—2262no—
353C22×C4—2262no—
354C22×C4—2262no—
355C22×C4—2262no—
356C22×C4C22×D11311yescharacteristic
357C22×C4C22×D11311yescharacteristic
358C22×C4C22×D11311yescharacteristic
359C22×C4C22×D11311yescharacteristic
360C4⋊C4—4521no—
361C4⋊C4—2262no—
362C4⋊C4—2262no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—1134no—
367C22⋊C4—1134no—
368C22⋊C4—1134no—
369C22⋊C4—1134no—
370C22⋊C4—4521no—
371C22⋊C4—2262no—
372C22⋊C4—2262no—
373C22⋊C4—2262no—
374C22⋊C4—2262no—
375C22⋊C4—2262no—
376C22⋊C4C22⋊D11314yescomplemented
377C42—4521no—
378C42—2262no—
379C42—2262no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—28no—
389C23—28no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—1132no—
402C23—2261no—
403C23—2261no—
404C23—2261no—
405C23—2261no—
406C23—2261no—
407C23—2261no—
408C23C2×C4×D11312yes—
409C23C2×C4×D11312yes—
410C23C2×C4×D11312yes—
411C23D4×D11312yes—
412C23C2×C22⋊D11312yes—
413C23#1426864612yes—
414C23#1426864712yes—
415C23C23×D11311yescharacteristic
416D4—4524no—
417D4—2268no—
418D4—2268no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—1132no—
432C2×C4—1132no—
433C2×C4—1132no—
434C2×C4—1132no—
435C2×C4—1132no—
436C2×C4—4524no—
437C2×C4—4524no—
438C2×C4—4524no—
439C2×C4—2261no—
440C2×C4—2261no—
441C2×C4—2261no—
442C2×C4—2261no—
443C2×C4—2261no—
444C2×C4—2261no—
445C2×C4—2261no—
446C2×C4—2261no—
447C2×C4—2261no—
448C2×C4—2261no—
449C2×C4—2261no—
450C2×C4—2261no—
451C2×C4—2261no—
452C2×C4—2261no—
453C2×C4—2261no—
454C2×C4—2261no—
455C2×C4C2×C22⋊D11312yes—
456C2×C4C2×C22⋊D11312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—4521no—
478C22—4521no—
479C22—4521no—
480C22—4521no—
481C22—2262no—
482C22—2262no—
483C22—2262no—
484C22#1681358214yescomplemented
485C22C4×C22⋊D11314yescomplemented
486C22C22×C4×D11311yescharacteristic
487C22C2×D4×D11311yescharacteristic
488C22C22×C22⋊D11311yescharacteristic
489C22C2×#1426864611yescharacteristic
490C22C2×#1426864711yescharacteristic
491C22#1681366711yescharacteristic
492C22#1681366711yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—4521no—
498C4—4521no—
499C4—2262no—
500C4—2262no—
501C4—2262no—
502C4—2262no—
503C4—2262no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—4522no—
508C2C2×#1681358211yescharacteristic
509C2C2×C4×C22⋊D11311yescharacteristic
510C2#2029907111yescharacteristic
511C2D4×C22⋊D11311yescharacteristic
512C2#2029923811yescharacteristic
513C2#2029924211yescharacteristic
514C2#2029927411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC22×C22⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813591C2
hypercenterC22×C22⋊C4D113
hypocenterC113#2358
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D113C2semidirect
3. C2×#16813582C2semidirect
4. C22×C22⋊Dic113C2semidirect
5. #20298498C2semidirect
6. #20298492C2semidirect
7. #20298486C2semidirect
8. #20298477C2semidirect
9. #20298475C2semidirect
10. #20298474C2semidirect
11. #20298471C2semidirect
12. #20298470C2semidirect
13. C22⋊C4×Dic113C2semidirect
14. C4×C22⋊Dic113C2semidirect
15. C22×C22⋊C4×C113C2semidirect
21. C22×C4×D113C22semidirect
22. #16813591C4semidirect
25. C2×#14268626C22semidirect
26. C2×#14268626C22semidirect
27. C2×#14268626C22semidirect
36. C2×#14268624C22semidirect
37. C2×#14268624C22semidirect
38. C2×#14268624C22semidirect
39. C2×C4×Dic113C22semidirect
40. C2×C4×Dic113C22semidirect
41. C2×C4×Dic113C22semidirect
42. #16813529C22semidirect
43. #16813529C22semidirect
44. #16813529C22semidirect
45. #16813529C22semidirect
46. #16813529C22semidirect
47. #16813529C22semidirect
63. C2×C22⋊D113C2×C4semidirect
64. C2×C22⋊D113C2×C4semidirect
65. C2×C22⋊D113C2×C4semidirect
88. C22⋊Dic113C2×C4semidirect
89. C22⋊Dic113C2×C4semidirect
90. C22⋊Dic113C2×C4semidirect
91. C22⋊Dic113D4semidirect
104. C24×C113C2×C4semidirect
121. C22⋊C4×C113D4semidirect
219. C22×C113C4×D4semidirect
220. C22×C113C4×D4semidirect
258. C113#2358semidirect
263. C22×C22⋊C4D113semidirect
321. C24C4×D113semidirect
376. C22⋊C4C22⋊D113semidirect
484. C22#16813582semidirect
485. C22C4×C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135912
C2×C4×C22⋊D1132
C2×#168135822
C22×C22⋊Dic1132
#202984982
#202984922
#202984862
#202984772
#202984752
#202984742
#202984712
#202984702
C22⋊C4×Dic1132
C4×C22⋊Dic1132
C22×C22⋊C4×C1132
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