Finite Group Databasebeta

← #15755899

Subgroups — #15755899

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123531C211yesmaximal, characteristic
2#13114872C211yesmaximal, characteristic, complemented
3#13114863C211yesmaximal, characteristic, complemented
4#13113379C211yesmaximal, characteristic
5#13112743C211yesmaximal, characteristic, complemented
6#13112742C211yesmaximal, characteristic, complemented
7C13×#1513C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C2×#88202C411yescharacteristic, complemented
10C23×#1055C2211yescharacteristic
11C13×#407C2211yescharacteristic
12C13×#380C2211yescharacteristic
13#11718895C411yescharacteristic, complemented
14#11718873C2211yescharacteristic
15#11718868C2211yescharacteristic
16#11718868C2211yescharacteristic
17C2×#88062—21no—
18#11718672—21no—
19#11718672—21no—
20D4×#1055—21no—
21D4×#1055—21no—
22#11718660C411yescharacteristic, complemented
23#11718658C411yescharacteristic, complemented
24C2×#88047—21no—
25C13×#328—21no—
26C13×#327—21no—
27#11718150—21no—
28#11718130—21no—
29#11718129—21no—
30#11718121—21no—
31C2×C13×#41C2×C411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C2×C13×M16—21no—
34C13×#123—21no—
35C13×C22⋊Q8D411yescharacteristic
36C13×C22⋊Q8Q811yescharacteristic
37C13×#121D411yescharacteristic
38C13×#121Q811yescharacteristic
39C13×#120—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C13×#117C2×C411yescharacteristic
43C2×C13×C4⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C22⋊Dic13—21no—
46#88202—42no—
47C2×C4⋊Dic13—21no—
48C2×#6099—21no—
49C2×#6099—21no—
50C2×#6099C2×C411yescharacteristic
51C2×#6099C2×C411yescharacteristic
52C22×#1055—21no—
53C22×#1055—42no—
54C22×#1055C2×C411yescharacteristic
55C22×#1055C2×C411yescharacteristic
56C22×#1055D411yescharacteristic
57C22×#1055D411yescharacteristic
58C22×#1055D411yescharacteristic
59C22×#1055D411yescharacteristic
60C13×C22⋊C8—21no—
61C13×C22⋊C8—21no—
62C13×#95—21no—
63#88071—21no—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70#88062—42no—
71#88047—42no—
72C4⋊#1055—21no—
73C4⋊#1055—21no—
74#88043—21no—
75C4×#1055—21no—
76#8628—131nomaximal, Sylow
77C24×C13#4111yescharacteristic
78C13×#41—41no—
79C13×#41—41no—
80C2×Q8×C13C4⋊C411yescharacteristic
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13C4⋊C411yescharacteristic
85C22×C4×C13—21no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×Q811yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×Dic13—41no—
96C13×M16—41no—
97C13×M16—41no—
98C2×C8×C13—41no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4C4⋊C411yescharacteristic
104C13×C4⋊C4C4⋊C411yescharacteristic
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—21no—
108C13×C22⋊C4—21no—
109C13×C22⋊C4—21no—
110C13×C22⋊C4—81no—
111C42×C13—21no—
112C22⋊Dic13—81no—
113C4⋊Dic13—41no—
114C4⋊Dic13—41no—
115#6099—42no—
116#6099—41no—
117#6099—41no—
118#6099—41no—
119#6099—41no—
120C2×#1055—22no—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—21no—
124C2×#1055—21no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055—42no—
129C2×#1055—41no—
130C2×#1055C22⋊C411yescharacteristic
131C2×#1055C22⋊C411yescharacteristic
132C2×#1055C22⋊C411yescharacteristic
133C2×#1055C22⋊C411yescharacteristic
134#2929—131no—
135#1810—131no—
136#1808—131no—
137#1513—131no—
138#1513D1311yescharacteristic
139#1305—131no—
140#1305—131no—
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13#11711yescharacteristic
147C23×C13#12111yescharacteristic
148C23×C13C22⋊Q811yescharacteristic
149Q8×C13—41no—
150D4×C13—41no—
151D4×C13—42no—
152D4×C13—42no—
153D4×C13—41no—
154D4×C13—41no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13C2×C22⋊C411yescharacteristic
173C2×C4×C13C2×C4⋊C411yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13C22⋊Q811yescharacteristic
176C2×Dic13—81no—
177C2×Dic13—81no—
178C2×Dic13—81no—
179C8×C13—81no—
180#1055—21no—
181#1055—21no—
182#1055—21no—
183#1055—41no—
184#1055—41no—
185#1055—81no—
186#1055#9912yes—
187C2×#131—131no—
188C23×C8—131no—
189#525C2×D1311yescharacteristic
190#435—261no—
191#435—261no—
192C8×D4—261no—
193C8×D4—261no—
194C2×#108—261no—
195C2×#107—261no—
196#424—131no—
197#408—131no—
198#407—131no—
199#407—131no—
200#407C2×D1311yescharacteristic
201#405—131no—
202#380—131no—
203#380C2×D1311yescharacteristic
204#341—261no—
205#340—261no—
206#328—21no—
207#328—261no—
208#327—21no—
209#327—261no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—42no—
219C22×C13—42no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13#38011yescharacteristic
224C22×C13#47211yescharacteristic
225C22×C13#47311yescharacteristic
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—41no—
230C4×C13—41no—
231C4×C13—41no—
232C4×C13—161no—
233C4×C13C2×#9911yescharacteristic
234C4×C13#41011yescharacteristic
235Dic13—161no—
236C2×#41C4×D1311yescharacteristic
237C23×C4C22×D1311yescharacteristic
238#131—522no—
239C2×M16—21no—
240C2×M16—131no—
241C2×M16—131no—
242C2×M16—261no—
243C2×M16—261no—
244C22×C8—131no—
245C22×C8—131no—
246C22×C8—131no—
247C22×C8—131no—
248C22×C8—131no—
249C22×C8—131no—
250C22×C8—261no—
251C22×C8—522no—
252#123—21no—
253C22⋊Q8Dic2611yescharacteristic
254C22⋊Q8C22⋊D1311yescharacteristic
255#121Dic2611yescharacteristic
256#121C22⋊D1311yescharacteristic
257#120—21no—
258C4×D4—21no—
259C4×D4—21no—
260#117C4×D1311yescharacteristic
261C2×C4⋊C4—21no—
262C2×C4⋊C4—261no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—261no—
265#108—522no—
266#107—522no—
267C4⋊C8—261no—
268C4⋊C8—261no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—261no—
272C22⋊C8—261no—
273C22⋊C8—261no—
274C22⋊C8—261no—
275C22⋊C8—261no—
276C22⋊C8—261no—
277#97—261no—
278C4×C8—261no—
279#95—21no—
280#95—261no—
281C2×C13—21no—
282C2×C13—21no—
283C2×C13—41no—
284C2×C13—41no—
285C2×C13—81no—
286C2×C13#179911yescharacteristic
287C2×C13#181411yescharacteristic
288C2×C13#181611yescharacteristic
289C24#612911yescharacteristic
290#41—41no—
291#41—41no—
292C2×Q8#610111yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4#610111yescharacteristic
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—521no—
302C22×C4C2×Dic2611yescharacteristic
303C22×C4C2×C4×D1311yescharacteristic
304C22×C4D4×D1311yescharacteristic
305C22×C4D4×D1311yescharacteristic
306C22×C4#612911yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308M16—41no—
309M16—41no—
310M16—522no—
311M16—521no—
312M16—521no—
313M16—521no—
314M16—521no—
315C2×C8—41no—
316C2×C8—131no—
317C2×C8—131no—
318C2×C8—131no—
319C2×C8—131no—
320C2×C8—262no—
321C2×C8—262no—
322C2×C8—262no—
323C2×C8—261no—
324C2×C8—261no—
325C2×C8—521no—
326C2×C8—521no—
327C2×C8—521no—
328C2×C8—522no—
329C2×C8—521no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—521no—
335C4⋊C4—521no—
336C4⋊C4#610111yescharacteristic
337C4⋊C4#610111yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—81no—
344C22⋊C4—1041no—
345C42—21no—
346C13#862811yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23#8813111yescharacteristic
353C23#8813211yescharacteristic
354C23#8819311yescharacteristic
355Q8—41no—
356D4—41no—
357D4—42no—
358D4—42no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—1041no—
379C2×C4—1041no—
380C2×C4—1041no—
381C2×C4#8813211yescharacteristic
382C2×C4C22⋊C4×D1311yescharacteristic
383C2×C4C2×#610111yescharacteristic
384C2×C4#8819311yescharacteristic
385C8—81no—
386C8—132no—
387C8—261no—
388C8—261no—
389C8—261no—
390C8—521no—
391C8—521no—
392C8—1041no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22#1171860311yescharacteristic
407C22#1171886011yescharacteristic
408C22#1171886511yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—161no—
416C4—2081no—
417C4#1171840111yescharacteristic
418C4D13×#9911yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—81no—
424C2#1311482211yescharacteristic
425C2#1311488811yescharacteristic
426C2#1311489811yescharacteristic
subgroupG/H
centerC22#11718603
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1513C2
socleC22×C13#380
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#1513D13
hypocenterC13#8628
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #13114872C2semidirect
3. #13114863C2semidirect
5. #13112743C2semidirect
6. #13112742C2semidirect
9. C2×#88202C4semidirect
13. #11718895C4semidirect
22. #11718660C4semidirect
23. #11718658C4semidirect
346. C13#8628semidirect

Maximal subgroups

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

subgroupindex
#131235312
#131148722
#131148632
#131133792
#131127432
#131127422
C13×#15132
#862813