Finite Group Databasebeta

← #15760103

Subgroups — #15760103

Order 3328.

732 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 115 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#13117677C211yesmaximal, characteristic
2#13115822C211yesmaximal, characteristic, complemented
3#13114780C211yesmaximal, characteristic
4#13113356C211yesmaximal, characteristic, complemented
5#13112741C211yesmaximal, characteristic, complemented
6#13112721C211yesmaximal, characteristic, complemented
7C13×#3007C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C2×C13×#137C412yescomplemented
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×Q8×Dic13—21no—
12C13×#452—22no—
13C13×#451—21no—
14C13×#450—21no—
15C13×#417C412yescomplemented
16C13×#407C2211yescharacteristic
17C2×#88077—22no—
18#11718882—21no—
19#11718882—22no—
20#11718873—21no—
21#11718873C2211yescharacteristic
22C4×C22⋊Dic13—21no—
23C4×C22⋊Dic13C2211yescharacteristic
24C4×C22⋊Dic13C2211yescharacteristic
25#11718868C2211yescharacteristic
26#11718130—21no—
27#11718130—21no—
28#11718118—22no—
29C2×C13×#41—21no—
30C2×C13×#41—21no—
31C2×C13×#41—44no—
32C2×C13×#41C2×C412yes—
33C2×C13×#41D412yes—
34C22×Q8×C13C2×C411yescharacteristic
35C22×Q8×C13D411yescharacteristic
36C22×D4×C13—21no—
37C22×D4×C13D411yescharacteristic
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C13×#137—44no—
41C2×C13×Q16—22no—
42C2×C13×SD16—22no—
43C2×C13×M16C2×C412yes—
44C13×C22⋊Q8—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—21no—
54C2×C22⋊Dic13—22no—
55C2×C22⋊Dic13D412yes—
56Q8×Dic13—44no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—21no—
59C2×C4×Dic13—22no—
60C2×C4×Dic13—21no—
61C2×C4×Dic13—21no—
62C2×#6099—21no—
63C13×#103—22no—
64C13×#102—22no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8—21no—
67#88077—44no—
68#88071—21no—
69#88071—21no—
70#88071D411yescharacteristic
71#88071D411yescharacteristic
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74#9364—131nomaximal, Sylow
75C24×C13—21no—
76C24×C13C2×D411yescharacteristic
77C13×#41—24no—
78C13×#41—24no—
79C13×#41—42no—
80C13×#41—42no—
81C13×#41—44no—
82C13×#41—44no—
83C2×Q8×C13—24no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—42no—
88C2×Q8×C13C22⋊C412yes—
89C2×D4×C13—22no—
90C2×D4×C13—22no—
91C2×D4×C13—21no—
92C2×D4×C13—42no—
93C2×D4×C13—44no—
94C2×D4×C13C22⋊C412yes—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—42no—
101C22×C4×C13—44no—
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×Dic13—21no—
109C22×Dic13—22no—
110C22×Dic13—21no—
111C22×Dic13—41no—
112C13×Q16—44no—
113C13×SD16—44no—
114C13×M16—42no—
115C2×C8×C13—22no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C22⋊Dic13—22no—
123C22⋊Dic13—42no—
124C22⋊Dic13—44no—
125C22⋊Dic13—41no—
126C22⋊Dic13—42no—
127C22⋊Dic13—82no—
128C4⋊Dic13—44no—
129C4⋊Dic13—42no—
130C4×Dic13—44no—
131C4×Dic13—42no—
132C4×Dic13—42no—
133#6099—42no—
134C2×#1055—41no—
135#3007D1311yescharacteristic
136#2341—131no—
137#1996—131no—
138#1789—131no—
139#1508—131no—
140#1305—131no—
141#1297—131no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—22no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—42no—
148C23×C13—42no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13C4×D411yescharacteristic
152C23×C13#12011yescharacteristic
153C23×C13#12111yescharacteristic
154Q8×C13—24no—
155Q8×C13—22no—
156Q8×C13—42no—
157Q8×C13—81no—
158Q8×C13#9914yes—
159D4×C13—22no—
160D4×C13—22no—
161D4×C13—44no—
162D4×C13—44no—
163D4×C13—42no—
164C2×C4×C13—24no—
165C2×C4×C13—22no—
166C2×C4×C13—22no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—44no—
173C2×C4×C13—44no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13C2×C22⋊C411yescharacteristic
179C2×C4×C13C4×D411yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12311yescharacteristic
182C2×Dic13—22no—
183C2×Dic13—41no—
184C2×Dic13—41no—
185C2×Dic13—42no—
186C2×Dic13—41no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—41no—
190C2×Dic13—42no—
191C2×Dic13—41no—
192C2×Dic13—81no—
193C2×Dic13—81no—
194C8×C13—42no—
195#1055—81no—
196C22×#41C2×D1311yescharacteristic
197C2×#137Dic1312yescomplemented
198C2×C22⋊Q8C2×D1311yescharacteristic
199C2×C4×Q8—261no—
200#452—22no—
201#451—21no—
202#450—21no—
203C2×#104—262no—
204#417Dic1312yescomplemented
205#407—131no—
206#407C2×D1311yescharacteristic
207#390—262no—
208#390—261no—
209#380—131no—
210#380—261no—
211C4×C22⋊C4—131no—
212C4×C22⋊C4—131no—
213C4×C22⋊C4—261no—
214#342—262no—
215#328—261no—
216#328—261no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—42no—
226C22×C13—42no—
227C22×C13—42no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—82no—
231C22×C13—82no—
232C22×C13#38611yescharacteristic
233C22×C13#45511yescharacteristic
234C22×C13#45611yescharacteristic
235C4×C13—21no—
236C4×C13—24no—
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—81no—
240C4×C13—81no—
241C4×C13C2×#9912yes—
242Dic13—42no—
243Dic13—82no—
244Dic13—81no—
245Dic13—82no—
246C2×#41—21no—
247C2×#41—21no—
248C2×#41—44no—
249C2×#41C2×Dic1312yes—
250C2×#41C22⋊D1312yes—
251C22×Q8C2×Dic1311yescharacteristic
252C22×Q8C22⋊D1311yescharacteristic
253C22×D4—21no—
254C22×D4C22⋊D1311yescharacteristic
255C23×C4—21no—
256C23×C4C22×D1311yescharacteristic
257#137—44no—
258C2×Q16—22no—
259C2×SD16—22no—
260C2×M16—261no—
261C2×M16C2×Dic1312yes—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C4×Q8—524no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—262no—
269C2×C4⋊C4—261no—
270C2×C4⋊C4C2×Dic1311yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—132no—
273C2×C22⋊C4—261no—
274C2×C22⋊C4—262no—
275C2×C22⋊C4—261no—
276C2×C22⋊C4—262no—
277C2×C42—262no—
278C2×C42—261no—
279C2×C42—261no—
280#104—524no—
281#103—22no—
282#102—22no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—261no—
286C22⋊C8—261no—
287#95—131no—
288#95—131no—
289#95—261no—
290#95—261no—
291C2×C13—21no—
292C2×C13—21no—
293C2×C13—41no—
294C2×C13—41no—
295C2×C13—82no—
296C2×C13#188211yescharacteristic
297C2×C13#189811yescharacteristic
298C2×C13#190611yescharacteristic
299C24—21no—
300C24D4×D1311yescharacteristic
301#41—24no—
302#41—24no—
303#41—42no—
304#41—42no—
305#41—44no—
306#41—44no—
307C2×Q8—24no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—42no—
312C2×Q8C22⋊Dic1312yes—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—42no—
317C2×D4—44no—
318C2×D4C22⋊Dic1312yes—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—44no—
326C22×C4—261no—
327C22×C4—261no—
328C22×C4—262no—
329C22×C4—521no—
330C22×C4D4×D1311yescharacteristic
331C22×C4#612911yescharacteristic
332C22×C4#612911yescharacteristic
333C22×C4C22×Dic1311yescharacteristic
334C22×C4C2×C22⋊D1311yescharacteristic
335C22×C4C2×C22⋊D1311yescharacteristic
336Q16—44no—
337SD16—44no—
338M16—42no—
339M16—522no—
340C2×C8—22no—
341C2×C8—521no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—524no—
347C4⋊C4—522no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—262no—
351C22⋊C4—522no—
352C22⋊C4—524no—
353C22⋊C4—521no—
354C22⋊C4—522no—
355C22⋊C4—1042no—
356C42—524no—
357C42—522no—
358C42—522no—
359C13#936411yescharacteristic, complemented, Sylow
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23D4×Dic1311yescharacteristic
370C23#8819111yescharacteristic
371C23#8819311yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—42no—
375Q8—81no—
376Q8#8807414yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—262no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—522no—
401C2×C4—522no—
402C2×C4—521no—
403C2×C4—522no—
404C2×C4—522no—
405C2×C4—521no—
406C2×C4—1041no—
407C2×C4—1041no—
408C2×C4D4×Dic1311yescharacteristic
409C2×C4#8818911yescharacteristic
410C2×C4#8819311yescharacteristic
411C2×C4C2×C22⋊Dic1311yescharacteristic
412C8—42no—
413C8—1041no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22#1171886311yescharacteristic
430C22#1171886611yescharacteristic
431C22#1171888111yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—522no—
439C4—1042no—
440C4—1041no—
441C4—1042no—
442C4C2×#8807412yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2#1311520711yescharacteristic
449C2#1311529011yescharacteristic
450C2#1311533911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#3007C2
socleC22×C13#386
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenter#3007D13
hypocenterC13#9364
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
2. #13115822C2semidirect
4. #13113356C2semidirect
5. #13112741C2semidirect
6. #13112721C2semidirect
9. C2×C13×#137C4semidirect
15. C13×#417C4semidirect
197. C2×#137Dic13semidirect
204. #417Dic13semidirect
359. C13#9364semidirect

Maximal subgroups

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

subgroupindex
#131176772
#131158222
#131147802
#131133562
#131127412
#131127212
C13×#30072
#936413