Finite Group Databasebeta

← #16018424

Subgroups — #16018424

Order 3328.

474 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#13125373C211yesmaximal, characteristic
2#13125369C211yesmaximal, characteristic
3#13117122C211yesmaximal, characteristic, complemented
4#13117121C211yesmaximal, characteristic, complemented
5#13117120C211yesmaximal, characteristic, complemented
6#13117114C211yesmaximal, characteristic, complemented
7#13117112C211yesmaximal, characteristic, complemented
8#13117110C211yesmaximal, characteristic, complemented
9#13117109C211yesmaximal, characteristic, complemented
10#13116623C211yesmaximal, characteristic
11#13116621C211yesmaximal, characteristic
12#13116619C211yesmaximal, characteristic
13D13×#366C211yesmaximal, characteristic
14#13116434C211yesmaximal, characteristic
15C13×#2255C211yesmaximal, characteristic, complemented
16#11719434—21no—
17#11719394—21no—
18C13×#500C2211yescharacteristic
19C13×#499C2211yescharacteristic
20#11718741—21no—
21#11718726—21no—
22C2×#88038C2211yescharacteristic
23C2×C16×D13C2211yescharacteristic
24#11718542—21no—
25#11718541C2211yescharacteristic
26#11718541C2211yescharacteristic
27D13×#107C2211yescharacteristic
28D13×#107C2211yescharacteristic
29#11718539C2211yescharacteristic
30#11718539C2211yescharacteristic
31#11718537—21no—
32#11718535C2211yescharacteristic
33#11718535C2211yescharacteristic
34#11718522—21no—
35#11718517—21no—
36#11718350C2211yescharacteristic
37#11718344C2211yescharacteristic
38#11718343C2211yescharacteristic
39C13×#367C2211yescharacteristic
40C13×#367C2211yescharacteristic
41C13×#366C2211yescharacteristic
42C13×#366C2211yescharacteristic
43C13×#346C2211yescharacteristic
44#11718097C2211yescharacteristic
45#11718097C2211yescharacteristic
46#11718096C2211yescharacteristic
47#11718096C2211yescharacteristic
48#11718094C2211yescharacteristic
49C16×Dic13C2211yescharacteristic
50#11718082C2211yescharacteristic
51#11718082C2211yescharacteristic
52#11718081C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55#11718081C2211yescharacteristic
56#11718081C2211yescharacteristic
57#11718081C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C13×C4⋊Q8—21no—
60C13×#125—21no—
61#88200—41no—
62#88198—41no—
63C2×#6094D411yescharacteristic
64C2×C8×D13C2311yescharacteristic
65#88151—41no—
66#88150—41no—
67#88150—41no—
68#88146—21no—
69#88146—21no—
70C4⋊C4×D13—21no—
71C4⋊C4×D13—21no—
72#88144—21no—
73#88144—21no—
74#88143—41no—
75#88143—41no—
76#88142—21no—
77#88142—21no—
78#88142—41no—
79#88126D411yescharacteristic
80#88124—21no—
81#88123—21no—
82C2×C13×C16C2311yescharacteristic
83C2×C13×C16C2311yescharacteristic
84C13×#107—21no—
85C13×#107C2311yescharacteristic
86C13×#107C2311yescharacteristic
87C13×#107C2311yescharacteristic
88C13×#107C2311yescharacteristic
89C13×#106—21no—
90C4×C8×C13C2311yescharacteristic
91#88058—21no—
92#88058C2311yescharacteristic
93#88058C2311yescharacteristic
94#88058C2311yescharacteristic
95#88058C2311yescharacteristic
96#88057—21no—
97#88055D411yescharacteristic
98C8×Dic13C2311yescharacteristic
99C2×#6090C2311yescharacteristic
100C2×#6090C2311yescharacteristic
101#88048—21no—
102#88048—21no—
103#88048—21no—
104#88048—21no—
105#88047—21no—
106#88047—21no—
107#88047—21no—
108#88047—21no—
109#88043D411yescharacteristic
110#88038Q814yescomplemented
111C16×D13Q814yescomplemented
112#33729—131nomaximal, Sylow
113C2×Q8×C13—41no—
114C2×C4×D13—41no—
115C2×C4×D13—41no—
116C2×C4×D13C2×D411yescharacteristic
117C2×Dic26—41no—
118C2×Dic26—41no—
119C2×Dic26—41no—
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2411yescharacteristic
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—41no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—41no—
129C42×C13C2×D411yescharacteristic
130#6103—41no—
131#6103—41no—
132#6103D811yescharacteristic
133#6103D811yescharacteristic
134C4⋊Dic13—21no—
135C4⋊Dic13—21no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13—41no—
139C4⋊Dic13—41no—
140C4⋊Dic13—41no—
141#6101—41no—
142#6101—41no—
143#6101—41no—
144#6101—41no—
145#6101—41no—
146#6101—41no—
147#6101—41no—
148#6101—41no—
149#6101D811yescharacteristic
150#6101D811yescharacteristic
151C4×Dic13—41no—
152C4×Dic13—41no—
153C4×Dic13C2×D411yescharacteristic
154C2×#1055C2×D411yescharacteristic
155C2×#1055C2×D411yescharacteristic
156#6094Q1614yes—
157C8×D13C2×Q812yes—
158C8×D13C2×Q812yes—
159C13×C16C2×Q812yes—
160C13×C16C2×Q812yes—
161#6090C2×Q812yes—
162#6090C2×Q812yes—
163#3164—131no—
164#3164—131no—
165#2255—131no—
166#2255—131no—
167#2255—131no—
168#2255D1311yescharacteristic, complemented
169#2253—131no—
170#2253—131no—
171#2252—131no—
172#2252—131no—
173#2159—131no—
174#2159—131no—
175#2158—131no—
176C2×#366—131no—
177#2108—131no—
178C22×D13C2×D811yescharacteristic
179Q8×C13—161no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13C2×D811yescharacteristic
185C2×C4×C13C2×D811yescharacteristic
186C2×C4×C13C22×D411yescharacteristic
187C2×Dic13—41no—
188C2×Dic13—41no—
189C2×Dic13—41no—
190C2×Dic13—41no—
191C2×Dic13C2×D811yescharacteristic
192C2×Dic13C2×D811yescharacteristic
193C2×Dic13C2×D811yescharacteristic
194C4×D13—161no—
195C4×D13—161no—
196C4×D13C4⋊Q812yes—
197C4×D13C2×Q1612yes—
198Dic26—161no—
199Dic26—161no—
200Dic26—161no—
201C8×C13C2×Q1612yes—
202C8×C13C22×Q811yescharacteristic
203C8×C13C22×Q811yescharacteristic
204#1055C4⋊Q812yes—
205#1055C2×Q1612yes—
206#544—261no—
207#544—261no—
208C2×M32—131no—
209C22×C16—131no—
210#501—261no—
211#501—261no—
212#501—261no—
213#501—261no—
214#500—131no—
215#500—131no—
216#500—131no—
217#500C2×D1311yescharacteristic
218#499—131no—
219#499—131no—
220#499—131no—
221#499C2×D1311yescharacteristic
222#428—261no—
223#428—261no—
224#427—131no—
225#427—131no—
226C2×#107—131no—
227C2×#107—131no—
228#405—131no—
229#367—131no—
230#367—131no—
231#367—131no—
232#367—131no—
233#367C2×D1311yescharacteristic
234#367C2×D1311yescharacteristic
235#366—131no—
236#366—131no—
237#366—131no—
238#366—131no—
239#366—131no—
240#366—131no—
241#366—131no—
242#366—131no—
243#366C2×D1311yescharacteristic
244#366C2×D1311yescharacteristic
245#346—131no—
246#346C2×D1311yescharacteristic
247C4×C16—131no—
248C4×C16—131no—
249C22×C13C22×D811yescharacteristic
250C2×D13—21no—
251C2×D13—21no—
252C2×D13#50012yes—
253C4×C13—21no—
254C4×C13—21no—
255C4×C13—81no—
256C4×C13—81no—
257C4×C13—81no—
258C4×C13—81no—
259C4×C13C2×C4⋊Q811yescharacteristic
260C4×C13C22×Q1611yescharacteristic
261Dic13—21no—
262Dic13—21no—
263Dic13—81no—
264Dic13—81no—
265Dic13—81no—
266Dic13—81no—
267Dic13#50012yes—
268C2×M16—131no—
269C22×C8—131no—
270C4⋊Q8—21no—
271C4⋊Q8—261no—
272C4⋊Q8—261no—
273C4⋊Q8—261no—
274C4⋊Q8—521no—
275C4⋊Q8—521no—
276#125—21no—
277#125—261no—
278#125—261no—
279#125—261no—
280#125—521no—
281#125—521no—
282C22⋊Q8—521no—
283C22⋊Q8—521no—
284C22⋊Q8—521no—
285C22⋊Q8—521no—
286#117—131no—
287#117—261no—
288#117—261no—
289C2×C4⋊C4—261no—
290C2×C4⋊C4—261no—
291M32—134no—
292C2×C16—131no—
293C2×C16—131no—
294C2×C16—134no—
295C2×C16C22×D1311yescharacteristic
296C2×C16C22×D1311yescharacteristic
297#107—21no—
298#107—131no—
299#107—131no—
300#107—131no—
301#107—131no—
302#107—261no—
303#107—261no—
304#107—261no—
305#107—261no—
306#107—261no—
307#107C22×D1311yescharacteristic
308#107C22×D1311yescharacteristic
309#107C22×D1311yescharacteristic
310#107C22×D1311yescharacteristic
311#106—21no—
312#106—261no—
313#106—261no—
314#106—261no—
315#106—261no—
316#106—261no—
317#97—131no—
318#97—131no—
319C4×C8—131no—
320C4×C8C22×D1311yescharacteristic
321C2×C13C2×#50011yescharacteristic
322C2×C13#341511yescharacteristic
323C2×C13#341711yescharacteristic
324D13—22no—
325C2×Q8—41no—
326C2×Q8—521no—
327C2×Q8—521no—
328C2×Q8—521no—
329C22×C4—131no—
330C22×C4—521no—
331C22×C4—521no—
332M16—134no—
333C2×C8—131no—
334C2×C8—131no—
335C2×C8—132no—
336C2×C8—132no—
337C2×C8D4×D1311yescharacteristic
338C2×C8C23×D1311yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—131no—
347C4⋊C4—131no—
348C4⋊C4—261no—
349C4⋊C4—261no—
350C4⋊C4—261no—
351C4⋊C4—261no—
352C4⋊C4—521no—
353C4⋊C4—521no—
354C4⋊C4—521no—
355C4⋊C4—521no—
356C4⋊C4—521no—
357C4⋊C4—521no—
358C4⋊C4—521no—
359C4⋊C4—521no—
360C4⋊C4—521no—
361C4⋊C4—521no—
362C4⋊C4—521no—
363C22⋊C4—131no—
364C22⋊C4—131no—
365C22⋊C4—521no—
366C22⋊C4—521no—
367C42—131no—
368C42—521no—
369C42—521no—
370C42D4×D1311yescharacteristic
371C16—132no—
372C16—132no—
373C16Q8×D1312yes—
374C16Q8×D1312yes—
375C13#3372911yescharacteristic, complemented, Sylow
376C23—131no—
377Q8—161no—
378Q8—2081no—
379Q8—2081no—
380Q8—2081no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—131no—
386C2×C4—132no—
387C2×C4—132no—
388C2×C4—131no—
389C2×C4—131no—
390C2×C4—521no—
391C2×C4—521no—
392C2×C4—521no—
393C2×C4—521no—
394C2×C4—2081no—
395C2×C4—2081no—
396C2×C4D8×D1311yescharacteristic
397C2×C4D8×D1311yescharacteristic
398C2×C4C2×D4×D1311yescharacteristic
399C8—132no—
400C8—132no—
401C8Q16×D1312yes—
402C8C2×Q8×D1311yescharacteristic
403C8C2×Q8×D1311yescharacteristic
404C22—132no—
405C22—261no—
406C22—261no—
407C22C2×D8×D1311yescharacteristic
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—81no—
414C4—132no—
415C4—261no—
416C4—261no—
417C4—1041no—
418C4—1041no—
419C4—1041no—
420C4—1041no—
421C4D13×C4⋊Q811yescharacteristic
422C4C2×Q16×D1311yescharacteristic
423C2—262no—
424C2D13×#50011yescharacteristic
425C2#1312797611yescharacteristic
426C2#1312798811yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2255C2
socleC22×C13C22×D8
prime radicalC22×D13C2×D8
hypercenter#2255D13
hypocenterC13#33729
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13117122C2semidirect
4. #13117121C2semidirect
5. #13117120C2semidirect
6. #13117114C2semidirect
7. #13117112C2semidirect
8. #13117110C2semidirect
9. #13117109C2semidirect
15. C13×#2255C2semidirect
110. #88038Q8semidirect
111. C16×D13Q8semidirect
168. #2255D13semidirect
375. C13#33729semidirect

Maximal subgroups

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

subgroupindex
#131253732
#131253692
#131171222
#131171212
#131171202
#131171142
#131171122
#131171102
#131171092
#131166232
#131166212
#131166192
D13×#3662
#131164342
C13×#22552
#3372913