Finite Group Databasebeta

← #15762643

Subgroups — #15762643

Order 3328.

484 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#11718712C211yesmaximal, characteristic
2#13114872C211yesmaximal, characteristic
3#13114615C211yesmaximal, characteristic
4#13113357C211yesmaximal, characteristic
5#13113356C211yesmaximal, characteristic
6#13113199C211yesmaximal, characteristic
7C13×#1472C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×#6107C411yescharacteristic, complemented
10C2×#88178C2211yescharacteristic
11C23×#1055C2211yescharacteristic
12C13×#407C2211yescharacteristic
13C2×C13×C22⋊C8C2211yescharacteristic
14C2×#88075C411yescharacteristic, complemented
15C4×C22⋊Dic13C2211yescharacteristic
16#11718868C2211yescharacteristic
17C2×#88062—21no—
18C2×#88055—21no—
19#11718712—21no—
20#11718712—21no—
21#11718712—21no—
22#11718712—21no—
23C2×#88050C411yescharacteristic, complemented
24C2×#88047C411yescharacteristic, complemented
25C13×#324—22no—
26#11718150—21no—
27#11718142—21no—
28#11718130—22no—
29#11718061—22no—
30#11718059—22no—
31C22×Q8×C13C2×C411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C22×Dic26C2×C411yescharacteristic
34C2×C13×M16—21no—
35C22×C8×C13—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C22⋊Dic13—21no—
44C2×C22⋊Dic13—21no—
45C2×#6107—21no—
46C2×#6107—21no—
47C2×#6107—42no—
48C2×C4⋊Dic13C2×C411yescharacteristic
49#88178—21no—
50#88178—21no—
51#88178—21no—
52#88178—21no—
53C2×#6101—21no—
54C2×C4×Dic13—21no—
55C2×#6099—21no—
56C22×#1055—42no—
57C22×#1055C2×C411yescharacteristic
58C22×#1055C2×C411yescharacteristic
59C22×#1055D411yescharacteristic
60C22×#1055D411yescharacteristic
61C22×#1055D411yescharacteristic
62C22×#1055D411yescharacteristic
63C13×C22⋊C8—21no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8D412yes—
67#88075—21no—
68#88075—21no—
69#88071D412yes—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72#88062—42no—
73#88055—42no—
74#88050—21no—
75#88050—21no—
76#88047—21no—
77#88047—21no—
78#9817—131nomaximal, Sylow
79C24×C13#4111yescharacteristic
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C22×Dic13—21no—
95C22×Dic13—22no—
96C22×Dic13—21no—
97C2×Dic26—21no—
98C2×Dic26—21no—
99C2×Dic26—41no—
100C2×Dic26—41no—
101C13×M16—41no—
102C13×M16—41no—
103C2×C8×C13—22no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C22⋊Dic13—42no—
114C22⋊Dic13—41no—
115C22⋊Dic13—41no—
116#6107—42no—
117#6107—42no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120#6101—41no—
121#6101—41no—
122C4×Dic13—41no—
123C4×Dic13—41no—
124#6099—41no—
125#6099—41no—
126C2×#1055—22no—
127C2×#1055—22no—
128C2×#1055—22no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055C22⋊C411yescharacteristic
134C2×#1055C22⋊C411yescharacteristic
135C2×#1055C22⋊C411yescharacteristic
136C2×#1055C22⋊C411yescharacteristic
137C2×#467—131no—
138#1810—131no—
139#1752—131no—
140#1508—131no—
141#1508—131no—
142#1472—131no—
143#1472D1311yescharacteristic
144C23×C13—22no—
145C23×C13—22no—
146C23×C13—41no—
147C23×C13C4×D411yescharacteristic
148C23×C13#12111yescharacteristic
149C23×C13#12411yescharacteristic
150Q8×C13—41no—
151Q8×C13—41no—
152Q8×C13—81no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—81no—
166C2×C4×C13C2×C22⋊C411yescharacteristic
167C2×C4×C13C4×D411yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12711yescharacteristic
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—42no—
175C2×Dic13—42no—
176C2×Dic13—81no—
177Dic26—41no—
178Dic26—41no—
179Dic26—81no—
180C8×C13—42no—
181C8×C13—81no—
182#1055—21no—
183#1055—21no—
184#1055—21no—
185#1055—81no—
186#1055#9912yes—
187C22×Q16—131no—
188C23×C8—131no—
189C2×C22⋊Q8—131no—
190C2×C22⋊Q8C2×D1311yescharacteristic
191#467—261no—
192#467—261no—
193#467—261no—
194#467—261no—
195C2×#108—261no—
196C2×#107—131no—
197C2×#103—131no—
198C2×#103—131no—
199#407—131no—
200#407C2×D1311yescharacteristic
201C2×C22⋊C8C2×D1311yescharacteristic
202C2×#97—261no—
203C4×C22⋊C4—131no—
204#341—261no—
205#336—261no—
206#328—262no—
207#328—262no—
208#324—22no—
209#324—262no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—44no—
218C22×C13#39011yescharacteristic
219C22×C13#44412yes—
220C22×C13#47312yes—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13C2×#9911yescharacteristic
227C4×C13#41011yescharacteristic
228Dic13—82no—
229Dic13—81no—
230Dic13—81no—
231C22×Q8—131no—
232C22×Q8C4×D1311yescharacteristic
233C23×C4C22×D1311yescharacteristic
234C2×Q16—261no—
235C2×Q16—261no—
236C2×Q16—522no—
237C2×M16—21no—
238C2×M16—261no—
239C22×C8—21no—
240C22×C8—131no—
241C22×C8—131no—
242C22×C8—131no—
243C22×C8—131no—
244C22×C8—131no—
245C22×C8—131no—
246C22×C8—522no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—261no—
252C22⋊Q8—261no—
253C22⋊Q8—261no—
254C22⋊Q8—261no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—261no—
258C2×C4⋊C4C4×D1311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—261no—
261C2×C22⋊C4—261no—
262C2×C42—261no—
263#108—522no—
264#107—261no—
265#107—261no—
266#103—261no—
267#103—261no—
268#103—261no—
269#103—261no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—261no—
274C22⋊C8—261no—
275C22⋊C8C22⋊D1312yes—
276#97—522no—
277#95—132no—
278C2×C13—22no—
279C2×C13—22no—
280C2×C13—41no—
281C2×C13#196411yescharacteristic
282C2×C13#197511yescharacteristic
283C2×C13#197911yescharacteristic
284C24#612711yescharacteristic
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—261no—
290C2×Q8—261no—
291C2×Q8—521no—
292C2×Q8—521no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—262no—
298C22×C4—261no—
299C22×C4—261no—
300C22×C4C2×C4×D1311yescharacteristic
301C22×C4D4×D1311yescharacteristic
302C22×C4D4×D1311yescharacteristic
303C22×C4D4×D1311yescharacteristic
304C22×C4#612911yescharacteristic
305C22×C4C2×C22⋊D1311yescharacteristic
306Q16—522no—
307Q16—522no—
308M16—41no—
309M16—41no—
310M16—521no—
311M16—521no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
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—521no—
324C2×C8—521no—
325C2×C8—521no—
326C2×C8—521no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—261no—
332C4⋊C4—261no—
333C4⋊C4—521no—
334C4⋊C4—521no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—522no—
338C22⋊C4—521no—
339C22⋊C4—521no—
340C42—521no—
341C42—521no—
342C13#981711yescharacteristic, complemented, Sylow
343C23—22no—
344C23—22no—
345C23—41no—
346C23#8813811yescharacteristic
347C23#8813911yescharacteristic
348C23C4×C22⋊D1311yescharacteristic
349Q8—41no—
350Q8—41no—
351Q8—81no—
352Q8—521no—
353Q8—521no—
354Q8—1041no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4—522no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—1041no—
375C2×C4C22⋊C4×D1311yescharacteristic
376C2×C4#8813511yescharacteristic
377C2×C4#8819311yescharacteristic
378C2×C4#8819411yescharacteristic
379C8—42no—
380C8—81no—
381C8—132no—
382C8—261no—
383C8—261no—
384C8—261no—
385C8—1041no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22#1171841612yes—
395C22#1171861811yescharacteristic
396C22#1171880612yes—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—1042no—
403C4—1041no—
404C4—1041no—
405C4#1171840111yescharacteristic
406C4D13×#9911yescharacteristic
407C2—22no—
408C2—22no—
409C2—41no—
410C2#1311567011yescharacteristic
411C2#1311572811yescharacteristic
412C2#1311574811yescharacteristic
subgroupG/H
centerC22#11718618
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1472C2
socleC22×C13#390
prime radicalC24×C13#41
cosocleC23×C4×C13C23
hypercenter#1472D13
hypocenterC13#9817
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
9. C22×#6107C4semidirect
14. C2×#88075C4semidirect
23. C2×#88050C4semidirect
24. C2×#88047C4semidirect
342. C13#9817semidirect

Maximal subgroups

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

subgroupindex
C2×#117187122
#131148722
#131146152
#131133572
#131133562
#131131992
C13×#14722
#981713