Finite Group Databasebeta

← #15773205

Subgroups — #15773205

Order 3328.

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

normal subgroups only

This group has 592 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
1#13120641C211yesmaximal, characteristic
2C2×#11718118C211yesmaximal, characteristic
3#13112861C212yesmaximal, complemented
4#13112858C212yesmaximal, complemented
5C2×C13×#323C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic13—21no—
8C2×#88178C411yescharacteristic, complemented
9C2×C13×C22⋊C8—21no—
10#11718908—21no—
11#11718873C411yescharacteristic, complemented
12#11718871—21no—
13#11718610C411yescharacteristic, complemented
14#11718610C2211yescharacteristic
15#11718609—21no—
16#11718609—21no—
17#11718608C411yescharacteristic, complemented
18#11718608C2211yescharacteristic
19C13×#323—21no—
20C13×#323C2212yes—
21#11718118—21no—
22#11718118C2212yes—
23C25×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13—41no—
27C22×Dic26C2×C411yescharacteristic, complemented
28C22×C8×C13—41no—
29C2×C13×C22⋊C4—41no—
30C2×C13×C22⋊C4—41no—
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic13—24no—
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C22⋊Dic13—21no—
42C2×C22⋊Dic13—21no—
43C2×C22⋊Dic13—41no—
44C2×C22⋊Dic13—42no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13C2×C411yescharacteristic, complemented
47#88178—41no—
48#88178—41no—
49C2×#6101—21no—
50C2×#6101—21no—
51C2×#6101—21no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8—41no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic, complemented
57#88071C2×C411yescharacteristic, complemented
58#11716—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—81no—
63C24×C13—81no—
64C24×C13C22⋊C411yescharacteristic
65C24×C13C22⋊C411yescharacteristic
66C24×C13SD1612yes—
67C24×C13Q1612yes—
68C24×C13C2×D411yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—44no—
84C22×Dic13—42no—
85C22×Dic13—82no—
86C22×Dic13—82no—
87C2×Dic26—41no—
88C2×Dic26—81no—
89C2×C8×C13—42no—
90C2×C8×C13—82no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C22⋊Dic13—24no—
96C22⋊Dic13—44no—
97C22⋊Dic13—41no—
98C22⋊Dic13—41no—
99C22⋊Dic13—42no—
100C22⋊Dic13—42no—
101C22⋊Dic13—81no—
102C22⋊Dic13—81no—
103C22⋊Dic13—81no—
104C22⋊Dic13—81no—
105C4⋊Dic13—41no—
106C4⋊Dic13—81no—
107#6101—42no—
108#6101—81no—
109#6101—81no—
110#2626—131no—
111C2×#342—131no—
112C2×#323D1311yescharacteristic
113#1352—132no—
114#1351—132no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—81no—
132C23×C13—81no—
133C23×C13—82no—
134C23×C13—82no—
135C23×C13—84no—
136C23×C13#9911yescharacteristic
137C23×C13#9911yescharacteristic
138C23×C13#10312yes—
139C23×C13#10312yes—
140C23×C13#10412yes—
141C23×C13C2×C22⋊C411yescharacteristic
142C23×C13C2×SD1611yescharacteristic
143C23×C13C2×Q1611yescharacteristic
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—81no—
154C2×C4×C13—81no—
155C2×C4×C13—81no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—44no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—88no—
170C2×Dic13—82no—
171C2×Dic13—82no—
172Dic26—82no—
173C8×C13—82no—
174C2×C22⋊Q8—131no—
175C22×C22⋊C4—261no—
176C22×C22⋊C4C2×D1311yescharacteristic
177C2×C22⋊C8—21no—
178#399—131no—
179#399—131no—
180#396—261no—
181#396—261no—
182#393—131no—
183#393—131no—
184#385—261no—
185#380—131no—
186#379—261no—
187#342—132no—
188#342—261no—
189#323—21no—
190#323C2×D1312yes—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—22no—
199C22×C13—21no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—44no—
206C22×C13—44no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—82no—
214C22×C13—82no—
215C22×C13#32812yes—
216C22×C13#32812yes—
217C22×C13C2×#9911yescharacteristic
218C22×C13C2×#10311yescharacteristic
219C22×C13C2×#10411yescharacteristic
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224Dic13—81no—
225Dic13—81no—
226Dic13—84no—
227Dic13—81no—
228Dic13—81no—
229C25D5211yescharacteristic
230C22×Q8—131no—
231C23×C4—521no—
232C23×C4C4×D1311yescharacteristic
233C23×C4C22⋊D1311yescharacteristic
234C22×C8—41no—
235C22⋊Q8—521no—
236C22⋊Q8—521no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—261no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4—41no—
244C2×C22⋊C4—264no—
245C2×C22⋊C4—262no—
246C2×C22⋊C4—261no—
247C2×C22⋊C4—261no—
248C2×C22⋊C4—261no—
249C2×C22⋊C4—261no—
250C2×C22⋊C4—261no—
251C2×C22⋊C4—261no—
252C2×C22⋊C4—521no—
253C2×C22⋊C4—522no—
254C2×C22⋊C4C4×D1311yescharacteristic
255C2×C22⋊C4D5211yescharacteristic
256C2×C22⋊C4C22⋊D1311yescharacteristic
257C2×C22⋊C4C22×D1311yescharacteristic
258C22⋊C8—22no—
259C22⋊C8—41no—
260#95—131no—
261#95—131no—
262#95—261no—
263#95—261no—
264C2×C13—21no—
265C2×C13—22no—
266C2×C13—21no—
267C2×C13—22no—
268C2×C13—41no—
269C2×C13—42no—
270C2×C13—41no—
271C2×C13C2×#32811yescharacteristic
272C2×C13#212111yescharacteristic
273C2×C13#212711yescharacteristic
274C24—21no—
275C24—22no—
276C24—21no—
277C24—81no—
278C24—81no—
279C24#609512yes—
280C24Dic5212yes—
281C24#610311yescharacteristic
282C24#610311yescharacteristic
283C24C2×D5211yescharacteristic
284C2×Q8—521no—
285C2×Q8—1041no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—261no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4—524no—
297C22×C4—522no—
298C22×C4—1042no—
299C22×C4—1042no—
300C22×C4#610311yescharacteristic
301C22×C4#610311yescharacteristic
302C22×C4C2×C4×D1311yescharacteristic
303C22×C4C2×C22⋊D1311yescharacteristic
304C2×C8—42no—
305C2×C8—82no—
306C4⋊C4—521no—
307C4⋊C4—522no—
308C4⋊C4—1041no—
309C4⋊C4—1041no—
310C4⋊C4—1041no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—264no—
316C22⋊C4—524no—
317C22⋊C4—522no—
318C22⋊C4—522no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C22⋊C4—1041no—
322C22⋊C4—1041no—
323C22⋊C4—1041no—
324C22⋊C4—1041no—
325C13#1171611yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—22no—
333C23—22no—
334C23—41no—
335C23—41no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—81no—
343C23—81no—
344C23—82no—
345C23—82no—
346C23—84no—
347C23#8804611yescharacteristic
348C23#8804611yescharacteristic
349C23#8805612yes—
350C23#8805612yes—
351C23#8806512yes—
352C23C2×#609511yescharacteristic
353C23C2×Dic5211yescharacteristic
354C23C2×#610311yescharacteristic
355Q8—1042no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—524no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—521no—
380C2×C4—521no—
381C2×C4—1048no—
382C2×C4—1042no—
383C2×C4—1042no—
384C8—82no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—42no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—42no—
399C22—44no—
400C22—44no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22#1171805912yes—
410C22#1171805912yes—
411C22C2×#8804611yescharacteristic
412C22C2×#8805611yescharacteristic
413C22C2×#8806511yescharacteristic
414C4—41no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—1041no—
419C4—1041no—
420C4—1044no—
421C4—1041no—
422C4—1041no—
423C2—21no—
424C2—21no—
425C2—22no—
426C2—22no—
427C2—41no—
428C2—41no—
429C2—42no—
430C2C2×#1171805911yescharacteristic
431C2#1311648311yescharacteristic
432C2#1311650311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC2×C13×#323C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenterC2×#323D13
hypocenterC13#11716
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #13112861C2semidirect
4. #13112858C2semidirect
8. C2×#88178C4semidirect
11. #11718873C4semidirect
13. #11718610C4semidirect
17. #11718608C4semidirect
27. C22×Dic26C2×C4semidirect
46. C2×C4⋊Dic13C2×C4semidirect
56. #88071C2×C4semidirect
57. #88071C2×C4semidirect
325. C13#11716semidirect

Maximal subgroups

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

subgroupindex
#131206412
C2×#117181182
#131128612
#131128582
C2×C13×#3232
#1171613