Finite Group Databasebeta

← #29580314

Subgroups — #29580314

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840097C211yesmaximal, characteristic
2#21451632C211yesmaximal, characteristic
3#21445909C211yesmaximal, characteristic
4C2×#16839498C211yesmaximal, characteristic
5C2×#16839488C211yesmaximal, characteristic
6#21443698C211yesmaximal, characteristic
7C2×C61×#400C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840097—22no—
10#16840097—22no—
11C2×#14519710—21no—
12C2×#14519700—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C2×C22⋊#92418C2211yescharacteristic
15#16839701—21no—
16#16839695—22no—
17#16839682—21no—
18#16839635—21no—
19#16839625—21no—
20#16839622C2211yescharacteristic
21#16839524—22no—
22#16839498—22no—
23#16839488—22no—
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C61×#400—22no—
27C61×#400—22no—
28C2×#95×C61—21no—
29C2×#95×C61—21no—
30C2×#95×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34#14519756—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D412yes—
40C2×#11758196—21no—
41C2×#11758196—22no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44#14519710—24no—
45#14519700—24no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49C22⋊#92418D412yes—
50#14519684—22no—
51#14519684—22no—
52#14519684—22no—
53#14519684—21no—
54C23×C4×C61—21no—
55C23×C4×C61—21no—
56C23×C4×C61D411yescharacteristic
57C23×C4×C61D411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61D412yes—
71#95×C61—24no—
72#95×C61—24no—
73#95×C61—21no—
74#95×C61D412yes—
75C24×C61C2×D411yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—42no—
91C22×C4×C61—44no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61Q1612yes—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—22no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—42no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—42no—
124#11758196—41no—
125#11758196—41no—
126#11758196—82no—
127C2×#92418—22no—
128C2×#92418—42no—
129C2×#92418—42no—
130C2×#92418—41no—
131C23×C61—22no—
132C23×C61—22no—
133C23×C61#12011yescharacteristic
134C23×C61#12011yescharacteristic
135C23×C61#12111yescharacteristic
136C23×C61C2×Q1611yescharacteristic
137C23×C61#13511yescharacteristic
138C23×C61#13711yescharacteristic
139C23×C61#13711yescharacteristic
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—44no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—82no—
162C2×C4×C61—82no—
163C2×C4×C61—82no—
164C2×C4×C61—82no—
165C2×C4×C61—81no—
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12711yescharacteristic
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177Dic122—42no—
178Dic122—81no—
179#92418—42no—
180#92418—81no—
181#9929—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61#39211yescharacteristic
191C22×C61#45111yescharacteristic
192C22×C61#45111yescharacteristic
193C22×C61#45211yescharacteristic
194C22×C61#45211yescharacteristic
195C22×C61#45412yes—
196C22×C61#45812yes—
197C22×C61#46711yescharacteristic
198C22×C61#47011yescharacteristic
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—42no—
204C4×C61—82no—
205C4×C61—82no—
206C4×C61—81no—
207Dic61—82no—
208Dic61—81no—
209Dic61—81no—
210C2×#484—611no—
211#2627—611no—
212C2×#400D6111yescharacteristic
213#1824—611no—
214C2×#328—611no—
215C2×#324—611no—
216#1294—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—21no—
220C2×C61—21no—
221C2×C61#161512yes—
222C2×C61#161712yes—
223C2×C61#200111yescharacteristic
224C2×C61#200311yescharacteristic
225C2×C61#202211yescharacteristic
226C2×C22⋊Q8—611no—
227C22×C4⋊C4C2×D6111yescharacteristic
228C22×C4⋊C4C2×D6111yescharacteristic
229#484—1222no—
230#484—1222no—
231C2×#107—1221no—
232C2×#103—1221no—
233C2×C22⋊C8—611no—
234C2×C22⋊C8—611no—
235#400—22no—
236#400—22no—
237#400—1221no—
238#398—1222no—
239#395—1221no—
240#385—1221no—
241#381—1221no—
242#380—611no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95C2×D6111yescharacteristic
246#340—1222no—
247#328—1222no—
248#324—1222no—
249C61#992911yescharacteristic, complemented, Sylow
250C22×Q8—611no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4C22⋊D6111yescharacteristic
254C23×C4C22⋊D6111yescharacteristic
255C23×C4C22×D6111yescharacteristic
256C22×C8—1221no—
257C22×C8—1221no—
258C22⋊Q8—1221no—
259C22⋊Q8—1221no—
260C22⋊Q8—1221no—
261C22⋊Q8—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—612no—
275C2×C4⋊C4—1222no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4C22⋊D6112yes—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280#107—1224no—
281#103—1224no—
282C22⋊C8—612no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286#95—24no—
287#95—24no—
288#95—21no—
289#95—1222no—
290#95—1222no—
291#95—1222no—
292#95—1221no—
293#95C22⋊D6112yes—
294C24C2×C22⋊D6111yescharacteristic
295C2×Q8—1221no—
296C2×Q8—1221no—
297C2×Q8—2442no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—1222no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4#1175820212yes—
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4#1175822411yescharacteristic
326C22×C4C2×C22⋊D6111yescharacteristic
327C22×C4C2×C22⋊D6111yescharacteristic
328C2×C8—1222no—
329C2×C8—2442no—
330C2×C8—2441no—
331C2×C8—2442no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—4882no—
343C4⋊C4—2442no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C23—22no—
351C23—22no—
352C23#1451974511yescharacteristic
353C23#1451974611yescharacteristic
354C23#1451974911yescharacteristic
355C23C2×#1175820211yescharacteristic
356C23#1451979711yescharacteristic
357C23#1451980711yescharacteristic
358C23#1451980811yescharacteristic
359Q8—4881no—
360Q8—2442no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4#1451974511yescharacteristic
395C2×C4#1451974811yescharacteristic
396C2×C4#1451974911yescharacteristic
397C2×C4#1451977311yescharacteristic
398C8—4881no—
399C8—2442no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22#1683967011yescharacteristic
409C22#1683991711yescharacteristic
410C22#1683991811yescharacteristic
411C22#1683992211yescharacteristic
412C22#1683992411yescharacteristic
413C22#1683993412yes—
414C22#1683995112yes—
415C22#1684000111yescharacteristic
416C22#1684001811yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—82no—
423C4—81no—
424C4—82no—
425C4—4881no—
426C4—4881no—
427C4—4882no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#2144484812yes—
433C2#2144486012yes—
434C2#2144682711yescharacteristic
435C2#2144684111yescharacteristic
436C2#2144694711yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#400C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#400D61
hypocenterC61#9929
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
249. C61#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#168400972
#214516322
#214459092
C2×#168394982
C2×#168394882
#214436982
C2×C61×#4002
#992961