Finite Group Databasebeta

← #15763490

Subgroups — #15763490

Order 3328.

658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11718631C211yesmaximal, characteristic, complemented
2#13120769C211yesmaximal, characteristic
3C2×#11718059C211yesmaximal, characteristic, complemented
4C2×#11718129C211yesmaximal, characteristic
5#13113104C211yesmaximal, characteristic, complemented
6#13112678C211yesmaximal, characteristic, complemented
7C2×C13×#481C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88178C2211yescharacteristic
11C13×#481—22no—
12C13×#481—22no—
13C2×C13×#106—21no—
14C2×C13×#102—21no—
15C2×C13×C22⋊C8C2211yescharacteristic
16#11718883—21no—
17#11718881—22no—
18C2×#88071—22no—
19C2×#88071C2211yescharacteristic
20C2×#88071C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22#11718643—21no—
23#11718631—22no—
24#11718631—22no—
25C2×#88050—21no—
26C2×#88047—21no—
27#11718614—21no—
28#11718608—21no—
29#11718129—22no—
30#11718059—22no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C23×C4×C13C2311yescharacteristic
35C23×Dic13—21no—
36C23×Dic13D412yes—
37C22×Dic26D411yescharacteristic
38C22×C8×C13—21no—
39C13×#121—21no—
40C13×#121—21no—
41C13×#121—21no—
42C13×#121—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D412yes—
50C2×C13×C22⋊C4—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—22no—
54C2×C4⋊Dic13D411yescharacteristic
55#88178—21no—
56#88178—21no—
57#88178—21no—
58#88178—21no—
59C2×#6101—21no—
60C22×#1055—21no—
61C13×#106—24no—
62C13×#102—24no—
63C13×C22⋊C8—21no—
64C13×C22⋊C8D412yes—
65#88071—22no—
66#88071—22no—
67#88071—21no—
68#88071—21no—
69#88071—21no—
70#88071—21no—
71#88071—44no—
72C22⋊#1055—21no—
73C22⋊#1055D412yes—
74#88050—24no—
75#88047—24no—
76#9969—131nomaximal, Sylow
77C24×C13—21no—
78C24×C13C2×D411yescharacteristic
79C2×D4×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—42no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—42no—
85C2×D4×C13—42no—
86C22×C4×C13—21no—
87C22×C4×C13—22no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—42no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13#4111yescharacteristic
99C22×Dic13—22no—
100C22×Dic13—22no—
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—22no—
104C22×Dic13—22no—
105C22×Dic13—42no—
106C22×Dic13—42no—
107C22×Dic13—41no—
108C22×Dic13—42no—
109C22×Dic13—41no—
110C22×Dic13—42no—
111C2×Dic26—21no—
112C2×Dic26—21no—
113C2×Dic26—42no—
114C2×C8×C13—22no—
115C2×C8×C13—42no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C22⋊Dic13—41no—
125C22⋊Dic13—41no—
126C22⋊Dic13—82no—
127C22⋊Dic13—82no—
128C4⋊Dic13—21no—
129C4⋊Dic13—21no—
130#6101—41no—
131#6101—41no—
132C2×#1055—22no—
133C2×#1055—42no—
134C2×#484—131no—
135C2×#481D1311yescharacteristic
136#2639—131no—
137C2×#328—131no—
138C2×#327—131no—
139#1445—131no—
140#1280—131no—
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—22no—
144C23×C13—41no—
145C23×C13—42no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—42no—
149C23×C13#12011yescharacteristic
150C23×C13#12111yescharacteristic
151C23×C13#12711yescharacteristic
152C23×C13#13512yes—
153C23×C13#13712yes—
154D4×C13—42no—
155D4×C13—81no—
156D4×C13—82no—
157D4×C13—81no—
158D4×C13—81no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—44no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—82no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12111yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×Dic13—44no—
177C2×Dic13—42no—
178C2×Dic13—44no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—42no—
182C2×Dic13—41no—
183C2×Dic13—42no—
184C2×Dic13—41no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—82no—
188C2×Dic13—81no—
189C2×Dic13—81no—
190C2×Dic13—82no—
191Dic26—42no—
192Dic26—81no—
193C8×C13—42no—
194#1055—42no—
195C2×C22⋊Q8—131no—
196C2×#121C2×D1311yescharacteristic
197C22×C4⋊C4C2×D1311yescharacteristic
198#484—262no—
199#484—262no—
200#481—22no—
201#481—22no—
202C2×#107—261no—
203C2×#106—21no—
204C2×#103—261no—
205C2×#102—21no—
206C2×C22⋊C8—131no—
207C2×C22⋊C8C2×D1311yescharacteristic
208#400—261no—
209#397—261no—
210#394—261no—
211#393—261no—
212#386—262no—
213C2×#95—131no—
214C2×#95—131no—
215C2×#95—262no—
216#328—262no—
217#327—262no—
218C22×C13—22no—
219C22×C13—22no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—82no—
227C22×C13—82no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13#39211yescharacteristic
232C22×C13#45212yes—
233C22×C13#45311yescharacteristic
234C22×C13#45411yescharacteristic
235C22×C13#45812yes—
236C22×C13#46412yes—
237C22×C13#49511yescharacteristic
238C22×C13#49711yescharacteristic
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—82no—
244C4×C13—81no—
245Dic13—82no—
246Dic13—82no—
247Dic13—81no—
248Dic13—81no—
249C22×Q8—131no—
250C22×D4—21no—
251C22×D4C22⋊D1311yescharacteristic
252C23×C4—21no—
253C23×C4—132no—
254C23×C4—261no—
255C23×C4C22×D1311yescharacteristic
256C22×C8—21no—
257C22×C8—261no—
258C22⋊Q8—261no—
259C22⋊Q8—261no—
260C22⋊Q8—261no—
261C22⋊Q8—261no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—131no—
272C2×C4⋊C4—261no—
273C2×C4⋊C4C22⋊D1312yes—
274C2×C4⋊C4C22⋊D1311yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—261no—
277C2×C22⋊C4—262no—
278C2×C22⋊C4—262no—
279#107—264no—
280#106—24no—
281#103—264no—
282#102—24no—
283C22⋊C8—21no—
284C22⋊C8—132no—
285C22⋊C8—261no—
286C22⋊C8C22⋊D1312yes—
287#95—262no—
288#95—262no—
289#95—261no—
290#95—261no—
291#95—261no—
292#95—261no—
293#95—524no—
294C2×C13—21no—
295C2×C13—22no—
296C2×C13—21no—
297C2×C13—161no—
298C2×C13#161512yes—
299C2×C13#161812yes—
300C2×C13#200611yescharacteristic
301C2×C13#201511yescharacteristic
302C2×C13#202211yescharacteristic
303C24—21no—
304C24D4×D1311yescharacteristic
305C2×Q8—261no—
306C2×Q8—261no—
307C2×Q8—522no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—42no—
311C2×D4—42no—
312C2×D4—42no—
313C2×D4—41no—
314C2×D4—41no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—262no—
323C22×C4—262no—
324C22×C4—262no—
325C22×C4—261no—
326C22×C4—261no—
327C22×C4—262no—
328C22×C4—522no—
329C22×C4—522no—
330C22×C4—522no—
331C22×C4—521no—
332C22×C4—522no—
333C22×C4—521no—
334C22×C4D4×D1311yescharacteristic
335C22×C4D4×D1311yescharacteristic
336C22×C4#612911yescharacteristic
337C22×C4C2×C22⋊D1311yescharacteristic
338C22×C4C2×C22⋊D1311yescharacteristic
339C22×C4C2×C22⋊D1311yescharacteristic
340C2×C8—22no—
341C2×C8—42no—
342C2×C8—262no—
343C2×C8—522no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—261no—
351C4⋊C4—261no—
352C4⋊C4—521no—
353C4⋊C4—521no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—521no—
357C22⋊C4—521no—
358C22⋊C4—1042no—
359C22⋊C4—1042no—
360C13#996911yescharacteristic, complemented, Sylow
361C23—22no—
362C23—21no—
363C23—21no—
364C23—42no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23#8816912yes—
370C23#8817012yes—
371C23#8819111yescharacteristic
372C23#8819311yescharacteristic
373C23#8819411yescharacteristic
374Q8—522no—
375Q8—1041no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—81no—
380D4—81no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—524no—
395C2×C4—522no—
396C2×C4—524no—
397C2×C4—522no—
398C2×C4—522no—
399C2×C4—522no—
400C2×C4—521no—
401C2×C4—522no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4—521no—
405C2×C4—1042no—
406C2×C4—1041no—
407C2×C4—1041no—
408C2×C4—1042no—
409C2×C4#8819111yescharacteristic
410C2×C4#8819211yescharacteristic
411C2×C4#8819311yescharacteristic
412C2×C4#8820711yescharacteristic
413C8—42no—
414C8—522no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—82no—
424C22—81no—
425C22—82no—
426C22—81no—
427C22—81no—
428C22#1171871412yes—
429C22#1171882712yes—
430C22#1171882811yescharacteristic
431C22#1171882911yescharacteristic
432C22#1171883412yes—
433C22#1171885911yescharacteristic
434C22#1171886211yescharacteristic
435C22#1171888411yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—82no—
442C4—1042no—
443C4—1042no—
444C4—1041no—
445C4—1041no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—161no—
450C2#1311386412yes—
451C2#1311388112yes—
452C2#1311587611yescharacteristic
453C2#1311592811yescharacteristic
454C2#1311596411yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#481C2
socleC23×C13#120
prime radicalC2×C13×#121C22
hypercenterC2×#481D13
hypocenterC13#9969
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#11718631C2semidirect
3. C2×#11718059C2semidirect
5. #13113104C2semidirect
6. #13112678C2semidirect
360. C13#9969semidirect

Maximal subgroups

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

subgroupindex
C2×#117186312
#131207692
C2×#117180592
C2×#117181292
#131131042
#131126782
C2×C13×#4812
#996913