Finite Group Databasebeta

← #15778903

Subgroups — #15778903

Order 3328.

544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88190C211yesmaximal, characteristic
2C2×#11718065C212yesmaximal
3#13114824C211yesmaximal, characteristic
4#13112960C212yesmaximal
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88190C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic, complemented
9C2×C13×#99C2212yes—
10C13×#380—21no—
11#11718882C2211yescharacteristic
12C2×#88074C2212yes—
13#11718873—21no—
14C4×C22⋊Dic13—21no—
15C4×C22⋊Dic13—21no—
16#11718638C411yescharacteristic, complemented
17#11718635C411yescharacteristic, complemented
18#11718606—21no—
19#11718606—21no—
20C42×Dic13C411yescharacteristic, complemented
21C13×#342—21no—
22#11718118—21no—
23#11718065—24no—
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—22no—
41#88190—21no—
42#88190—21no—
43#88190D412yes—
44#88190Q812yes—
45C2×C4⋊Dic13—41no—
46C2×C4⋊Dic13C2×C411yescharacteristic
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—21no—
50C2×C4×Dic13—21no—
51C2×C4×Dic13C2×C411yescharacteristic
52C2×C4×Dic13C2×C411yescharacteristic
53C4×Dic26—41no—
54C4×Dic26—41no—
55C13×#99—22no—
56C13×#99—22no—
57C13×#95—41no—
58#88074—22no—
59#88074—22no—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63#88071—21no—
64#88071—41no—
65#12798—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13C2×D411yescharacteristic
71C2×D4×C13C2×Q811yescharacteristic
72C2×D4×C13#4111yescharacteristic
73C2×D4×C13#4111yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—42no—
91C2×Dic26—21no—
92C2×Dic26—41no—
93C2×Dic26—41no—
94C2×Dic26C4⋊C412yescomplemented
95C13×C4⋊C4—41no—
96C13×C4⋊C4—82no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C42×C13—21no—
102C42×C13—21no—
103C22⋊Dic13—22no—
104C22⋊Dic13—22no—
105C22⋊Dic13—22no—
106C22⋊Dic13—22no—
107C22⋊Dic13—42no—
108C22⋊Dic13—42no—
109C22⋊Dic13—42no—
110C22⋊Dic13—42no—
111C4⋊Dic13—41no—
112C4⋊Dic13—82no—
113#6101—42no—
114C4×Dic13—21no—
115C4×Dic13—42no—
116C4×Dic13—42no—
117C4×Dic13—41no—
118C4×Dic13—41no—
119C4×Dic13—41no—
120C4×Dic13C4⋊C412yescomplemented
121C4×#124—131no—
122C2×#354—132no—
123#1799—131no—
124#1799D1311yescharacteristic
125#1393—132no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13C2×C22⋊C411yescharacteristic
135C23×C13#12111yescharacteristic
136C23×C13#12111yescharacteristic
137C23×C13C22⋊Q811yescharacteristic
138C23×C13C22⋊Q811yescharacteristic
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—41no—
142D4×C13—41no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—22no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×C4×C13—82no—
157C2×C4×C13—82no—
158C2×C4×C13—82no—
159C2×C4×C13#9911yescharacteristic
160C2×C4×C13#9911yescharacteristic
161C2×C4×C13C2×C4⋊C411yescharacteristic
162C2×C4×C13#11711yescharacteristic
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—22no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—82no—
176C2×Dic13—82no—
177C2×Dic13—82no—
178Dic26—42no—
179Dic26—42no—
180C2×#124—131no—
181C2×C4×Q8—131no—
182C2×C4×D4C2×D1311yescharacteristic
183C2×#99—132no—
184C2×#99C2×D1312yes—
185#391—131no—
186#390—131no—
187#388—261no—
188#388—261no—
189#382—131no—
190#380—21no—
191#380—261no—
192C4×C22⋊C4—261no—
193C4×C22⋊C4—261no—
194C43—131no—
195#354—264no—
196#342—21no—
197#342—261no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13#38011yescharacteristic
215C22×C13C2×#9911yescharacteristic
216C22×C13#41011yescharacteristic
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—162no—
224C4×C13#35412yescomplemented
225Dic13—42no—
226Dic13—42no—
227Dic13—42no—
228Dic13—81no—
229Dic13—162no—
230C22×Q8—131no—
231C22×D4C22×D1311yescharacteristic
232C23×C4D5211yescharacteristic
233C23×C4C22⋊D1311yescharacteristic
234#124—132no—
235#124—132no—
236#124—261no—
237#124—261no—
238C4×Q8—521no—
239C4×Q8—521no—
240C4×D4—41no—
241C4×D4—41no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—521no—
246C2×C4⋊C4C4×D1311yescharacteristic
247C2×C22⋊C4—22no—
248C2×C22⋊C4—261no—
249C2×C22⋊C4—261no—
250C2×C22⋊C4—261no—
251C2×C22⋊C4—261no—
252C2×C22⋊C4—262no—
253C2×C22⋊C4D5211yescharacteristic
254C2×C22⋊C4C22⋊D1311yescharacteristic
255C2×C42—131no—
256C2×C42—131no—
257C2×C42—261no—
258C2×C42—261no—
259C2×C42—261no—
260C2×C42C4×D1311yescharacteristic
261#99—22no—
262#99—22no—
263#99—262no—
264#99—262no—
265#95—41no—
266#95—261no—
267#95—261no—
268#95—261no—
269#95—261no—
270#95—521no—
271C2×C13—21no—
272C2×C13—21no—
273C2×C13—41no—
274C2×C13—41no—
275C2×C13—41no—
276C2×C13—41no—
277C2×C13#179911yescharacteristic
278C2×C13C2×#35411yescharacteristic
279C2×C13#212611yescharacteristic
280C24C2×D5211yescharacteristic
281C24C2×C22⋊D1311yescharacteristic
282C2×Q8—132no—
283C2×Q8—261no—
284C2×Q8—521no—
285C2×Q8—521no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4D4×D1311yescharacteristic
289C2×D4#612911yescharacteristic
290C2×D4Q8×D1311yescharacteristic
291C2×D4#613111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—261no—
300C22×C4—261no—
301C22×C4—261no—
302C22×C4—261no—
303C22×C4—522no—
304C22×C4#610311yescharacteristic
305C22×C4#610311yescharacteristic
306C22×C4#610311yescharacteristic
307C22×C4#610311yescharacteristic
308C22×C4C2×C4×D1311yescharacteristic
309C4⋊C4—41no—
310C4⋊C4—82no—
311C4⋊C4—521no—
312C4⋊C4—522no—
313C4⋊C4—1042no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—262no—
319C22⋊C4—262no—
320C22⋊C4—262no—
321C22⋊C4—262no—
322C22⋊C4—522no—
323C22⋊C4—522no—
324C22⋊C4—522no—
325C22⋊C4—522no—
326C42—21no—
327C42—21no—
328C42—132no—
329C42—261no—
330C42—521no—
331C42—522no—
332C42—522no—
333C42—521no—
334C42—521no—
335C13#1279811yescharacteristic, complemented, Sylow
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23#8814911yescharacteristic
345C23#8815111yescharacteristic
346C23C2×#610311yescharacteristic
347C23#8819211yescharacteristic
348C23#8820011yescharacteristic
349Q8—522no—
350Q8—522no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—262no—
372C2×C4—262no—
373C2×C4—262no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—521no—
380C2×C4—521no—
381C2×C4—521no—
382C2×C4—521no—
383C2×C4—1042no—
384C2×C4—1042no—
385C2×C4—1042no—
386C2×C4#8804611yescharacteristic
387C2×C4#8804611yescharacteristic
388C2×C4C4⋊C4×D1311yescharacteristic
389C2×C4#8814611yescharacteristic
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22C2×#8804611yescharacteristic
407C22#1171864811yescharacteristic
408C22#1171866711yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—162no—
416C4—522no—
417C4—522no—
418C4—522no—
419C4—1041no—
420C4—2082no—
421C4#1171806512yescomplemented
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2—41no—
427C2—41no—
428C2#1311482111yescharacteristic
429C2C2×#1171806511yescharacteristic
430C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#1799C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#1799D13
hypocenterC13#12798
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
8. C2×C4×Dic26C4semidirect
16. #11718638C4semidirect
17. #11718635C4semidirect
20. C42×Dic13C4semidirect
94. C2×Dic26C4⋊C4semidirect
120. C4×Dic13C4⋊C4semidirect
224. C4×C13#354semidirect
335. C13#12798semidirect
421. C4#11718065semidirect

Maximal subgroups

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

subgroupindex
C4×#881902
C2×#117180652
#131148242
#131129602
C13×#17992
#1279813