Finite Group Databasebeta

← #16822876

Subgroups — #16822876

Order 3712.

786 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745256C211yesmaximal, characteristic, complemented
2C2×#11745244C211yesmaximal, characteristic
3C2×#11745234C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D29C211yesmaximal, characteristic, complemented
5#14271087C211yesmaximal, characteristic, complemented
6#14271086C211yesmaximal, characteristic, complemented
7#14271081C211yesmaximal, characteristic, complemented
8#14271078C211yesmaximal, characteristic, complemented
9#14271065C211yesmaximal, characteristic, complemented
10#14271063C211yesmaximal, characteristic, complemented
11#14271053C211yesmaximal, characteristic, complemented
12#14271041C211yesmaximal, characteristic, complemented
13#14271037C211yesmaximal, characteristic, complemented
14#14271018C211yesmaximal, characteristic, complemented
15C29×#388C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C22×C22⋊D29C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C22×C4×D29C2211yescharacteristic
21C22×C4×D29C2211yescharacteristic
22C2×C4⋊C4×C29C2211yescharacteristic, complemented
23C2×C22⋊C4×C29C2211yescharacteristic
24C2×C22⋊C4×C29C2211yescharacteristic
25C2×C22⋊C4×C29C2211yescharacteristic
26C2×C42×C29C2211yescharacteristic, complemented
27C2×C22⋊Dic29C2211yescharacteristic
28C2×C22⋊Dic29C2211yescharacteristic
29C2×#90781C2211yescharacteristic
30C2×#90781C2211yescharacteristic
31C2×#90781C2211yescharacteristic
32C2×#90781C2211yescharacteristic
33C2×#90781C2211yescharacteristic
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×#90781C2211yescharacteristic
37C2×#90781C2211yescharacteristic, complemented
38C2×#90781C2211yescharacteristic, complemented
39C2×#90781C2211yescharacteristic, complemented
40C2×#90781C2211yescharacteristic, complemented
41C2×C4⋊Dic29C2211yescharacteristic, complemented
42C2×#90779C2211yescharacteristic, complemented
43C2×#90779C2211yescharacteristic, complemented
44C2×#90779C2211yescharacteristic, complemented
45C2×#90779C2211yescharacteristic, complemented
46C2×C4×Dic29C2211yescharacteristic, complemented
47#11745256—24no—
48#11745244—24no—
49C22⋊C4×D29—24no—
50#11745234—24no—
51C29×#95C2211yescharacteristic, complemented
52C29×#95C2211yescharacteristic, complemented
53#11745179C2211yescharacteristic, complemented
54#11745179C2211yescharacteristic, complemented
55C24×C29C2311yescharacteristic
56C23×D29—22no—
57C23×D29—22no—
58C23×D29—22no—
59C23×D29—22no—
60C23×D29—22no—
61C23×D29—41no—
62C23×D29—41no—
63C23×D29C2311yescharacteristic
64C23×D29C2311yescharacteristic
65C23×D29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C22×C4×C29C2311yescharacteristic
69C22×C4×C29C2311yescharacteristic
70C22×C4×C29C2311yescharacteristic
71C22×C4×C29C2311yescharacteristic
72C2×C22⋊D29—22no—
73C2×C22⋊D29—22no—
74C2×C22⋊D29—41no—
75C22×Dic29C2311yescharacteristic
76C22×Dic29C2311yescharacteristic
77C22×Dic29C2311yescharacteristic
78C22×Dic29C2311yescharacteristic
79C22×Dic29C2311yescharacteristic
80C2×D116—22no—
81C2×D116—22no—
82C2×D116—22no—
83C2×D116—22no—
84C2×D116—22no—
85C2×D116—41no—
86C2×C4×D29—22no—
87C2×C4×D29—22no—
88C2×C4×D29—22no—
89C2×C4×D29—41no—
90C2×C4×D29—41no—
91C2×C4×D29D414yescomplemented
92C4⋊C4×C29—22no—
93C22⋊C4×C29—22no—
94C22⋊C4×C29—22no—
95C22⋊C4×C29—22no—
96C42×C29—22no—
97C22⋊Dic29—22no—
98C22⋊Dic29—41no—
99#90781—22no—
100#90781—22no—
101#90781—22no—
102#90781—22no—
103#90781—22no—
104#90781—22no—
105#90781—22no—
106#90781—22no—
107#90781—41no—
108#90781—41no—
109#90781—41no—
110#90781D414yes—
111C4⋊Dic29—41no—
112#90779—22no—
113#90779—22no—
114#90779—22no—
115#90779—41no—
116C4×Dic29—22no—
117C23×C29—21no—
118C23×C29—21no—
119C23×C29—21no—
120C23×C29—21no—
121C23×C29—21no—
122C23×C29—21no—
123C23×C29#4112yes—
124C23×C29C2411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—28no—
130C22×D29—21no—
131C22×D29—21no—
132C22×D29—21no—
133C22×D29—21no—
134C22×D29—21no—
135C22×D29—21no—
136C22×D29—21no—
137C22×D29—21no—
138C22×D29—21no—
139C22×D29—21no—
140C22×D29—21no—
141C22×D29—21no—
142C22×D29—21no—
143C22×D29—44no—
144C22×D29—44no—
145C22×D29—44no—
146C22×D29—44no—
147C22×D29—44no—
148C22×D29—44no—
149C22×D29C2×D412yes—
150C22×D29C2×D412yes—
151C22×D29#4112yes—
152C22×D29#4112yes—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—21no—
168C2×C4×C29—21no—
169C2×C4×C29C2×D412yes—
170C2×C4×C29C2×D412yes—
171C22⋊D29—44no—
172C2×Dic29—21no—
173C2×Dic29—21no—
174C2×Dic29—21no—
175C2×Dic29—21no—
176C2×Dic29—21no—
177C2×Dic29—21no—
178C2×Dic29—21no—
179C2×Dic29—21no—
180C2×Dic29—21no—
181C2×Dic29—21no—
182C2×Dic29—21no—
183C2×Dic29—21no—
184C2×Dic29—21no—
185C2×Dic29C2×D412yes—
186C2×Dic29C2×D412yes—
187D116—44no—
188D116—44no—
189C4×D29—28no—
190C4×D29—44no—
191#2411—291nomaximal, Sylow
192C22×C29—22no—
193C22×C29—22no—
194C22×C29—22no—
195C22×C29—41no—
196C22×C29—41no—
197C22×C29—41no—
198C22×C29—41no—
199C22×C29C22×D411yescharacteristic
200C22×C29C22×D411yescharacteristic
201C22×C29C2×#4111yescharacteristic
202C22×C29C2×#4111yescharacteristic
203C22×C29C2×#4111yescharacteristic
204C22×C29H(5,𝔽2)11yescharacteristic
205C22×C29H(5,𝔽2)11yescharacteristic
206C2×D29—22no—
207C2×D29—22no—
208C2×D29—22no—
209C2×D29—22no—
210C2×D29—22no—
211C2×D29—22no—
212C2×D29—22no—
213C2×D29—22no—
214C2×D29—22no—
215C2×D29—416no—
216C2×D29—41no—
217C2×D29—41no—
218C2×D29—41no—
219C2×D29—41no—
220C2×D29—41no—
221C2×D29—41no—
222C2×D29—41no—
223C2×D29—41no—
224C2×D29—41no—
225C2×D29—41no—
226C2×D29—41no—
227C2×D29#12114yes—
228C4×C29—22no—
229C4×C29—22no—
230C4×C29—41no—
231C4×C29—41no—
232C4×C29—41no—
233C4×C29—41no—
234Dic29—22no—
235Dic29—22no—
236Dic29—41no—
237Dic29—41no—
238Dic29—41no—
239C2×#123—291no—
240C2×#120—291no—
241C2×#117—291no—
242C22×C22⋊C4—291no—
243#396—291no—
244#396—291no—
245#394—291no—
246#394—291no—
247#390—291no—
248#390—291no—
249#388—291no—
250#388D2911yescharacteristic, complemented
251#386—291no—
252#385—291no—
253#379—291no—
254C2×C29—42no—
255C2×C29C2×#12111yescharacteristic
256C2×C29#52511yescharacteristic
257C2×C29#53511yescharacteristic
258C2×C29#54611yescharacteristic
259C2×C29#54611yescharacteristic
260C2×C29#55111yescharacteristic
261C2×C29#55111yescharacteristic
262D29—24no—
263D29—42no—
264D29—81no—
265C25—291no—
266C22×D4—291no—
267C22×D4—291no—
268C22×D4—291no—
269C23×C4—291no—
270C23×C4—291no—
271#123—584no—
272#120—584no—
273#117—584no—
274C2×C4⋊C4—291no—
275C2×C4⋊C4—291no—
276C2×C4⋊C4—291no—
277C2×C4⋊C4—291no—
278C2×C4⋊C4—291no—
279C2×C4⋊C4C2×D2911yescharacteristic, complemented
280C2×C22⋊C4—291no—
281C2×C22⋊C4—291no—
282C2×C22⋊C4—291no—
283C2×C22⋊C4—291no—
284C2×C22⋊C4—291no—
285C2×C22⋊C4—291no—
286C2×C22⋊C4—291no—
287C2×C22⋊C4—291no—
288C2×C22⋊C4—291no—
289C2×C22⋊C4—291no—
290C2×C22⋊C4—291no—
291C2×C22⋊C4—291no—
292C2×C22⋊C4—291no—
293C2×C22⋊C4—291no—
294C2×C22⋊C4—584no—
295C2×C22⋊C4C2×D2911yescharacteristic
296C2×C22⋊C4C2×D2911yescharacteristic
297C2×C22⋊C4C2×D2911yescharacteristic
298C2×C42—291no—
299C2×C42C2×D2911yescharacteristic, complemented
300#95—291no—
301#95—291no—
302#95C2×D2911yescharacteristic, complemented
303#95C2×D2911yescharacteristic, complemented
304C29#241111yescharacteristic, complemented, Sylow
305C24—291no—
306C24—291no—
307C24—291no—
308C24—582no—
309C24—582no—
310C24—582no—
311C24—582no—
312C24—582no—
313C24—1161no—
314C24—1161no—
315C24C22×D2911yescharacteristic
316C2×D4—582no—
317C2×D4—582no—
318C2×D4—582no—
319C2×D4—582no—
320C2×D4—582no—
321C2×D4—582no—
322C2×D4—582no—
323C2×D4—1161no—
324C2×D4—1161no—
325C22×C4—291no—
326C22×C4—291no—
327C22×C4—294no—
328C22×C4—291no—
329C22×C4—291no—
330C22×C4—291no—
331C22×C4—582no—
332C22×C4—582no—
333C22×C4—582no—
334C22×C4—1161no—
335C22×C4—1161no—
336C22×C4C22×D2911yescharacteristic
337C22×C4C22×D2911yescharacteristic
338C22×C4C22×D2911yescharacteristic
339C22×C4C22×D2911yescharacteristic
340C22×C4C22×D2911yescharacteristic
341C22×C4C22×D2911yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—582no—
344C4⋊C4—582no—
345C4⋊C4—582no—
346C4⋊C4—1161no—
347C4⋊C4—1161no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—294no—
352C22⋊C4—582no—
353C22⋊C4—582no—
354C22⋊C4—582no—
355C22⋊C4—582no—
356C22⋊C4—582no—
357C22⋊C4—582no—
358C22⋊C4—582no—
359C22⋊C4—582no—
360C22⋊C4—582no—
361C22⋊C4—1161no—
362C22⋊C4—1161no—
363C22⋊C4—1161no—
364C22⋊C4—1161no—
365C42—22no—
366C42—582no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—292no—
374C23—292no—
375C23—292no—
376C23—292no—
377C23—588no—
378C23—581no—
379C23—581no—
380C23—581no—
381C23—581no—
382C23—581no—
383C23—581no—
384C23—581no—
385C23—581no—
386C23—581no—
387C23—581no—
388C23—581no—
389C23—581no—
390C23—581no—
391C23—581no—
392C23—581no—
393C23—581no—
394C23—581no—
395C23—1164no—
396C23—1164no—
397C23—1164no—
398C23—1164no—
399C23—1164no—
400C23—1164no—
401C23#9080512yes—
402C23C23×D2911yescharacteristic
403D4—1164no—
404D4—1164no—
405D4—1164no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—292no—
423C2×C4—292no—
424C2×C4—588no—
425C2×C4—581no—
426C2×C4—581no—
427C2×C4—581no—
428C2×C4—581no—
429C2×C4—581no—
430C2×C4—581no—
431C2×C4—581no—
432C2×C4—581no—
433C2×C4—581no—
434C2×C4—581no—
435C2×C4—581no—
436C2×C4—581no—
437C2×C4—581no—
438C2×C4—1164no—
439C2×C4D4×D2912yes—
440C2×C4D4×D2912yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—294no—
449C22—582no—
450C22—582no—
451C22—582no—
452C22—582no—
453C22—582no—
454C22—582no—
455C22—582no—
456C22—582no—
457C22—582no—
458C22—11616no—
459C22—1161no—
460C22—1161no—
461C22—1161no—
462C22—1161no—
463C22—1161no—
464C22—1161no—
465C22—1161no—
466C22—1161no—
467C22—1161no—
468C22—1161no—
469C22—1161no—
470C22C2×#9080511yescharacteristic
471C22C2×D4×D2911yescharacteristic
472C22C2×D4×D2911yescharacteristic
473C22#41×D2911yescharacteristic
474C22#41×D2911yescharacteristic
475C22#1174536411yescharacteristic
476C22#1174536411yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—582no—
484C4—582no—
485C4—1161no—
486C4—1161no—
487C4—1161no—
488C2—42no—
489C2—584no—
490C2—1162no—
491C2—2321no—
492C2#121×D2911yescharacteristic
493C2#1427167211yescharacteristic
494C2#1427173111yescharacteristic
495C2#1427180511yescharacteristic
496C2#1427180911yescharacteristic
497C2#1427183711yescharacteristic
498C2#1427183811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#388C2
prime radicalC2×#11745244C2
hypercenter#388D29
hypocenterC29#2411
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#11745256C2semidirect
3. C2×#11745234C2semidirect
4. C2×C22⋊C4×D29C2semidirect
5. #14271087C2semidirect
6. #14271086C2semidirect
7. #14271081C2semidirect
8. #14271078C2semidirect
9. #14271065C2semidirect
10. #14271063C2semidirect
11. #14271053C2semidirect
12. #14271041C2semidirect
13. #14271037C2semidirect
14. #14271018C2semidirect
15. C29×#388C2semidirect
22. C2×C4⋊C4×C29C22semidirect
26. C2×C42×C29C22semidirect
37. C2×#90781C22semidirect
38. C2×#90781C22semidirect
39. C2×#90781C22semidirect
40. C2×#90781C22semidirect
41. C2×C4⋊Dic29C22semidirect
42. C2×#90779C22semidirect
43. C2×#90779C22semidirect
44. C2×#90779C22semidirect
45. C2×#90779C22semidirect
46. C2×C4×Dic29C22semidirect
51. C29×#95C22semidirect
52. C29×#95C22semidirect
53. #11745179C22semidirect
54. #11745179C22semidirect
91. C2×C4×D29D4semidirect
250. #388D29semidirect
279. C2×C4⋊C4C2×D29semidirect
299. C2×C42C2×D29semidirect
302. #95C2×D29semidirect
303. #95C2×D29semidirect
304. C29#2411semidirect

Maximal subgroups

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

subgroupindex
C2×#117452562
C2×#117452442
C2×#117452342
C2×C22⋊C4×D292
#142710872
#142710862
#142710812
#142710782
#142710652
#142710632
#142710532
#142710412
#142710372
#142710182
C29×#3882
#241129