Finite Group Databasebeta

← #29599681

Subgroups — #29599681

Order 15616.

540 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#21452192C211yesmaximal, characteristic
2#21446100C211yesmaximal, characteristic
3#21446029C211yesmaximal, characteristic
4#21443943C211yesmaximal, characteristic
5#21443937C211yesmaximal, characteristic
6#21443936C211yesmaximal, characteristic
7C61×#1867C211yesmaximal, characteristic
8C2×#14519756—21no—
9C2×#14519754—21no—
10#16839805—21no—
11C2×#14519694C2211yescharacteristic
12C2×#14519692C2211yescharacteristic
13#16839685—21no—
14#16839685—21no—
15#16839683—21no—
16#16839665C2211yescharacteristic
17#16839659—21no—
18#16839642C2211yescharacteristic
19#16839634—21no—
20#16839529—21no—
21#16839521—21no—
22C61×#518C2211yescharacteristic
23C2×#99×C61C2211yescharacteristic
24C61×#386C2211yescharacteristic
25C61×#385—21no—
26C61×#342—21no—
27C22×Dic122—21no—
28C23×Dic61D411yescharacteristic
29C2×#11758194—21no—
30#14519756—44no—
31#14519754—44no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—41no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519710—41no—
47#14519708—41no—
48#14519694—21no—
49#14519694Q812yescomplemented
50#14519692—21no—
51#14519692Q812yescomplemented
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55C22×D4×C61C2311yescharacteristic
56C23×C4×C61D411yescharacteristic
57C4×D4×C61—41no—
58C4×D4×C61—41no—
59#117×C61—21no—
60C2×C4⋊C4×C61—41no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61D411yescharacteristic
66#99×C61—21no—
67#99×C61Q812yescomplemented
68#95×C61—21no—
69#95×C61—41no—
70C24×C61C2×D411yescharacteristic
71C24×C61C2×D411yescharacteristic
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61C2×Q811yescharacteristic
75C2×D4×C61C2×Q811yescharacteristic
76C2×D4×C61C2×Q811yescharacteristic
77C2×D4×C61#4111yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—42no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C2×Dic122—42no—
96C2×Dic122—42no—
97C2×Dic122—81no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—82no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—42no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C42×C61—41no—
109C22⋊Dic61—22no—
110C22⋊Dic61—42no—
111C22⋊Dic61—42no—
112C22⋊Dic61—42no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C4⋊Dic61—42no—
116C4⋊Dic61—42no—
117C4⋊Dic61—41no—
118#11758196—24no—
119#11758196—42no—
120#11758196—42no—
121#11758196—81no—
122#11758196—82no—
123C4×Dic61—41no—
124#11758194—22no—
125#11758194—41no—
126C2×#92418—41no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61#12011yescharacteristic
136C23×C61C22⋊Q811yescharacteristic
137C23×C61C22⋊Q811yescharacteristic
138C23×C61C4⋊Q811yescharacteristic
139C23×C61C4⋊Q811yescharacteristic
140D4×C61—41no—
141D4×C61—41no—
142D4×C61—41no—
143D4×C61—41no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—42no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61C22⋊Q811yescharacteristic
164C2×C4×C61C4⋊Q811yescharacteristic
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182Dic122—84no—
183#92418—42no—
184#13461—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61#39511yescharacteristic
202C22×C61B(4,𝔽2)11yescharacteristic
203C22×C61#45811yescharacteristic
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—42no—
207C4×C61—81no—
208C4×C61—82no—
209C4×C61—81no—
210C4×C61—81no—
211Dic61—42no—
212Dic61—42no—
213Dic61—81no—
214Dic61—82no—
215Dic61—81no—
216#2683—611no—
217#1867—611no—
218#1867D6111yescharacteristic
219#1856—611no—
220#1393—611no—
221#1390—611no—
222#1390—611no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—41no—
226C2×C61—41no—
227C2×C61—41no—
228C2×C61—41no—
229C2×C61#206211yescharacteristic
230C2×C61#219611yescharacteristic
231C2×C61#220111yescharacteristic
232C2×C22⋊Q8—1221no—
233C2×C22⋊Q8—1221no—
234#518C2×D6111yescharacteristic
235#428—1221no—
236C2×#100—611no—
237C2×#99—611no—
238C2×#99C2×D6111yescharacteristic
239#396—1221no—
240#396—1221no—
241#395—1221no—
242#390—611no—
243#389—1221no—
244#386—611no—
245#386C2×D6111yescharacteristic
246#385—21no—
247#385—1221no—
248#342—21no—
249#342—1221no—
250#339—1221no—
251C61#1346111yescharacteristic, complemented, Sylow
252C22×Q8—1221no—
253C22×D4C22×D6111yescharacteristic
254C23×C4—611no—
255C23×C4C22⋊D6111yescharacteristic
256C2×M16—1221no—
257C22⋊Q8—2444no—
258C22⋊Q8—2444no—
259C4×D4—41no—
260C4×D4—41no—
261#117—21no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—2441no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4C22⋊D6111yescharacteristic
281C2×C42—611no—
282#107—2441no—
283#106—2441no—
284#100—612no—
285#100—1221no—
286#99—21no—
287#99—612no—
288#99—1221no—
289#99Dic12212yescomplemented
290#95—21no—
291#95—41no—
292#95—1221no—
293#95—1221no—
294#95—2441no—
295C24D4×D6111yescharacteristic
296C24C2×C22⋊D6111yescharacteristic
297C2×Q8—4881no—
298C2×Q8—2442no—
299C2×Q8—2442no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4C2×Dic12211yescharacteristic
303C2×D4#1175822211yescharacteristic
304C2×D4Q8×D6111yescharacteristic
305C2×D4Q8×D6111yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—2442no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4D4×D6111yescharacteristic
323M16—1222no—
324M16—2441no—
325C2×C8—2441no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—82no—
329C4⋊C4—1224no—
330C4⋊C4—4881no—
331C4⋊C4—4882no—
332C4⋊C4—2441no—
333C4⋊C4—2442no—
334C4⋊C4—2442no—
335C4⋊C4—2442no—
336C4⋊C4—2442no—
337C22⋊C4—22no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—1222no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C22⋊C4—2442no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C42—41no—
351C42—2441no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23#1451974511yescharacteristic
361C23#1451975511yescharacteristic
362C23#1451975611yescharacteristic
363C23#1451977511yescharacteristic
364C23#1451977611yescharacteristic
365Q8—4884no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—2442no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2442no—
406C2×C4#1451975511yescharacteristic
407C2×C4#1451977611yescharacteristic
408C8—2442no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—81no—
424C22—81no—
425C22#1683968211yescharacteristic
426C22#1683994811yescharacteristic
427C22#1683995111yescharacteristic
428C4—21no—
429C4—21no—
430C4—42no—
431C4—81no—
432C4—82no—
433C4—81no—
434C4—81no—
435C4—4881no—
436C4—4882no—
437C4—4881no—
438C4—2442no—
439C4—2442no—
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2#2144717211yescharacteristic
447C2#2144780111yescharacteristic
448C2#2144783011yescharacteristic
subgroupG/H
centerC22#16839948
commutator, prime radical, cosocleC22×D4×C61C23
FrattiniC22×D4C22×D61
FittingC61×#1867C2
socleC22×C61B(4,𝔽2)
hypercenter#1867D61
hypocenterC61#13461
LCSG ▷ C22×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1867

Complements

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

NH ≅ G/Ntype
49. #14519694Q8semidirect
51. #14519692Q8semidirect
67. #99×C61Q8semidirect
251. C61#13461semidirect
289. #99Dic122semidirect

Maximal subgroups

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

subgroupindex
#214521922
#214461002
#214460292
#214439432
#214439372
#214439362
C61×#18672
#1346161