Finite Group Databasebeta

← #15773100

Subgroups — #15773100

Order 3328.

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

normal subgroups only

This group has 670 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
1C2×#11718118C211yesmaximal, characteristic, complemented
2C2×#11718117C211yesmaximal, characteristic, complemented
3#13112836C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2617C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic, complemented
7C2×C13×#120—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C13×#397C411yescharacteristic, complemented
11C13×#397C2211yescharacteristic
12C13×#394—21no—
13C13×#394—21no—
14C13×#392C411yescharacteristic, complemented
15C13×#392C2211yescharacteristic
16C13×#386—21no—
17C13×#380C411yescharacteristic, complemented
18C2×C22⋊#1055—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic, complemented
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×Dic13—41no—
31C13×#121—41no—
32C13×#121—41no—
33C13×#120—42no—
34C13×#120—42no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—41no—
44C2×C13×C22⋊C4—41no—
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C13×C22⋊C4C2311yescharacteristic
49C2×C22⋊Dic13—24no—
50C2×C22⋊Dic13—22no—
51C2×C22⋊Dic13—41no—
52C2×C22⋊Dic13—42no—
53C22×#1055—41no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95C2×C411yescharacteristic, complemented
57C13×#95C2×C411yescharacteristic, complemented
58C22⋊#1055—22no—
59C22⋊#1055—41no—
60#11692—131nomaximal, Sylow
61C24×C13—21no—
62C24×C13—21no—
63C24×C13—22no—
64C24×C13—21no—
65C24×C13—81no—
66C24×C13—81no—
67C24×C13C22⋊C411yescharacteristic
68C24×C13C22⋊C411yescharacteristic
69C24×C13D812yes—
70C24×C13SD1612yes—
71C24×C13C2×D411yescharacteristic
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—42no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—81no—
81C2×D4×C13—81no—
82C2×D4×C13—81no—
83C2×D4×C13—81no—
84C2×D4×C13—81no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—81no—
93C22×C4×C13—81no—
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22×C411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×Dic13—44no—
99C22×Dic13—42no—
100C22×Dic13—82no—
101C22×Dic13—82no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—81no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—81no—
114C13×C22⋊C4—81no—
115C22⋊Dic13—24no—
116C22⋊Dic13—44no—
117C22⋊Dic13—42no—
118C2×#1055—42no—
119C2×#1055—82no—
120#2617D1311yescharacteristic
121C2×#342—131no—
122C2×#323—131no—
123#1344—132no—
124#1343—132no—
125C23×C13—22no—
126C23×C13—22no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—22no—
130C23×C13—22no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—42no—
136C23×C13—42no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—81no—
149C23×C13—81no—
150C23×C13—82no—
151C23×C13—82no—
152C23×C13—84no—
153C23×C13#9911yescharacteristic
154C23×C13#9911yescharacteristic
155C23×C13#10212yes—
156C23×C13#10212yes—
157C23×C13#10412yes—
158C23×C13C2×C22⋊C411yescharacteristic
159C23×C13C2×D811yescharacteristic
160C23×C13C2×SD1611yescharacteristic
161D4×C13—82no—
162D4×C13—84no—
163D4×C13—82no—
164D4×C13—82no—
165D4×C13—82no—
166D4×C13—82no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—42no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—81no—
186C2×C4×C13—81no—
187C2×C4×C13—81no—
188C2×Dic13—44no—
189C2×Dic13—88no—
190C2×Dic13—82no—
191C2×Dic13—82no—
192#1055—82no—
193C2×#121Dic1311yescharacteristic, complemented
194C2×#120—21no—
195C22×C22⋊C4—261no—
196C22×C22⋊C4C2×D1311yescharacteristic
197C2×C22⋊C8—261no—
198#397Dic1311yescharacteristic, complemented
199#397C2×D1311yescharacteristic
200#394—21no—
201#394—21no—
202#392Dic1311yescharacteristic, complemented
203#392C2×D1311yescharacteristic
204#386—21no—
205#380Dic1311yescharacteristic, complemented
206#342—132no—
207#342—261no—
208#323—132no—
209#323—261no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—22no—
218C22×C13—21no—
219C22×C13—42no—
220C22×C13—42no—
221C22×C13—42no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—44no—
225C22×C13—44no—
226C22×C13—41no—
227C22×C13—41no—
228C22×C13—41no—
229C22×C13—41no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13—82no—
233C22×C13—82no—
234C22×C13—81no—
235C22×C13—81no—
236C22×C13—81no—
237C22×C13—81no—
238C22×C13—81no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13#32712yes—
242C22×C13#32712yes—
243C22×C13C2×#9911yescharacteristic
244C22×C13C2×#10211yescharacteristic
245C22×C13C2×#10411yescharacteristic
246C4×C13—41no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13—41no—
250C4×C13—81no—
251C4×C13—81no—
252C4×C13—81no—
253Dic13—84no—
254C25C22⋊D1311yescharacteristic
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4C2×Dic1311yescharacteristic, complemented
259C23×C4—521no—
260C23×C4C2×Dic1311yescharacteristic
261C23×C4C22⋊D1311yescharacteristic
262C22×C8—521no—
263#121—41no—
264#121—41no—
265#120—42no—
266#120—42no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—41no—
276C2×C22⋊C4—41no—
277C2×C22⋊C4—264no—
278C2×C22⋊C4—262no—
279C2×C22⋊C4—521no—
280C2×C22⋊C4—522no—
281C2×C22⋊C4C2×Dic1311yescharacteristic
282C2×C22⋊C4C22⋊D1311yescharacteristic
283C2×C22⋊C4C22⋊D1311yescharacteristic
284C2×C22⋊C4C22×D1311yescharacteristic
285C22⋊C8—262no—
286C22⋊C8—521no—
287#95—21no—
288#95—21no—
289#95C2×Dic1311yescharacteristic, complemented
290#95C2×Dic1311yescharacteristic, complemented
291C2×C13—21no—
292C2×C13—22no—
293C2×C13—21no—
294C2×C13—22no—
295C2×C13—41no—
296C2×C13—42no—
297C2×C13—41no—
298C2×C13—161no—
299C2×C13C2×#32711yescharacteristic
300C2×C13#212111yescharacteristic
301C2×C13#212711yescharacteristic
302C24—21no—
303C24—21no—
304C24—22no—
305C24—21no—
306C24—81no—
307C24—81no—
308C24#610412yes—
309C24#610512yes—
310C24C22⋊Dic1311yescharacteristic
311C24C22⋊Dic1311yescharacteristic
312C24C2×C22⋊D1311yescharacteristic
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C2×D4—81no—
323C2×D4—81no—
324C2×D4—81no—
325C2×D4—81no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—81no—
334C22×C4—81no—
335C22×C4—522no—
336C22×C4—524no—
337C22×C4—1042no—
338C22×C4—1042no—
339C22×C4C22⋊Dic1311yescharacteristic
340C22×C4C22⋊Dic1311yescharacteristic
341C22×C4C22×Dic1311yescharacteristic
342C22×C4C2×C22⋊D1311yescharacteristic
343C2×C8—522no—
344C2×C8—1042no—
345C4⋊C4—41no—
346C4⋊C4—81no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C22⋊C4—81no—
358C22⋊C4—264no—
359C22⋊C4—524no—
360C22⋊C4—522no—
361C13#1169211yescharacteristic, complemented, Sylow
362C23—21no—
363C23—21no—
364C23—22no—
365C23—22no—
366C23—21no—
367C23—21no—
368C23—22no—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—81no—
386C23—81no—
387C23—82no—
388C23—82no—
389C23—84no—
390C23#8807212yes—
391C23#8807212yes—
392C23#8807411yescharacteristic
393C23#8807411yescharacteristic
394C23#8807712yes—
395C23C2×#610411yescharacteristic
396C23C2×#610511yescharacteristic
397C23C2×C22⋊Dic1311yescharacteristic
398D4—82no—
399D4—84no—
400D4—82no—
401D4—82no—
402D4—82no—
403D4—82no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—524no—
426C2×C4—1048no—
427C2×C4—1042no—
428C2×C4—1042no—
429C8—1042no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—21no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—41no—
443C22—41no—
444C22—44no—
445C22—44no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—81no—
451C22—81no—
452C22—82no—
453C22—82no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1171812912yes—
462C22#1171812912yes—
463C22C2×#8807211yescharacteristic
464C22C2×#8807411yescharacteristic
465C22C2×#8807711yescharacteristic
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—81no—
471C4—81no—
472C4—81no—
473C4—1044no—
474C2—21no—
475C2—22no—
476C2—21no—
477C2—22no—
478C2—41no—
479C2—42no—
480C2—41no—
481C2—161no—
482C2C2×#1171812911yescharacteristic
483C2#1311648211yescharacteristic
484C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2617C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2617D13
hypocenterC13#11692
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#11718118C2semidirect
2. C2×#11718117C2semidirect
3. #13112836C2semidirect
4. #13112833C2semidirect
6. C2×C13×#121C4semidirect
10. C13×#397C4semidirect
14. C13×#392C4semidirect
17. C13×#380C4semidirect
27. C22×D4×C13C2×C4semidirect
36. C2×C13×C4⋊C4C2×C4semidirect
56. C13×#95C2×C4semidirect
57. C13×#95C2×C4semidirect
193. C2×#121Dic13semidirect
198. #397Dic13semidirect
202. #392Dic13semidirect
205. #380Dic13semidirect
258. C22×D4C2×Dic13semidirect
268. C2×C4⋊C4C2×Dic13semidirect
289. #95C2×Dic13semidirect
290. #95C2×Dic13semidirect
361. C13#11692semidirect

Maximal subgroups

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

subgroupindex
C2×#117181182
C2×#117181172
#131128362
#131128332
C13×#26172
#1169213