Finite Group Databasebeta

← #29579737

Subgroups — #29579737

Order 15616.

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×#16840001C211yesmaximal, characteristic
2#21445855C211yesmaximal, characteristic
3#21445598C211yesmaximal, characteristic
4#21444340C211yesmaximal, characteristic
5#21444339C211yesmaximal, characteristic
6#21444182C211yesmaximal, characteristic
7C61×#1472C211yesmaximal, characteristic
8C22×#11758202C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10C2×#14519756C2211yescharacteristic
11#16840001—21no—
12#16840001—21no—
13#16840001—21no—
14#16840001—21no—
15C2×#14519712—21no—
16C2×#14519710C411yescharacteristic, complemented
17C2×#14519701C411yescharacteristic, complemented
18C2×#14519700C411yescharacteristic, complemented
19#16839726C2211yescharacteristic
20C2×#14519687—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839526—21no—
23#16839516—21no—
24#16839500—22no—
25#16839499—22no—
26#16839487—22no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#324—22no—
31C22×Dic122C2×C411yescharacteristic
32C2×#11758202—21no—
33C2×#11758202—21no—
34C2×#11758202—42no—
35C2×#11758194—21no—
36C22×#92418—42no—
37C22×#92418C2×C411yescharacteristic
38C22×#92418C2×C411yescharacteristic
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C22×#92418D411yescharacteristic
43#14519756—21no—
44#14519756—21no—
45#14519756—21no—
46#14519756—21no—
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C4×Dic61—21no—
52#14519712—42no—
53#14519710—21no—
54#14519710—21no—
55#14519701—21no—
56#14519701—21no—
57#14519700—21no—
58#14519700—21no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61#14519687—42no—
62#14519684D412yes—
63C22×Q8×C61C2×C411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C2×M16×C61—21no—
66C22×C8×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C22⋊Q8×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61D412yes—
78C24×C61#4111yescharacteristic
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—22no—
95C22×Dic61—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊Dic61—42no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115#11758202—42no—
116#11758202—42no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119#11758196—41no—
120#11758196—41no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123#11758194—41no—
124#11758194—41no—
125C2×#92418—22no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418C22⋊C411yescharacteristic
133C2×#92418C22⋊C411yescharacteristic
134C2×#92418C22⋊C411yescharacteristic
135C2×#92418C22⋊C411yescharacteristic
136C23×C61—22no—
137C23×C61—22no—
138C23×C61—41no—
139C23×C61C4×D411yescharacteristic
140C23×C61#12111yescharacteristic
141C23×C61#12411yescharacteristic
142Q8×C61—41no—
143Q8×C61—41no—
144Q8×C61—81no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—81no—
158C2×C4×C61C2×C22⋊C411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12711yescharacteristic
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—81no—
169Dic122—41no—
170Dic122—41no—
171Dic122—81no—
172C8×C61—42no—
173C8×C61—81no—
174#92418—21no—
175#92418—21no—
176#92418—21no—
177#92418—81no—
178#92418#9912yes—
179#9817—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—44no—
188C22×C61#39011yescharacteristic
189C22×C61#44412yes—
190C22×C61#47312yes—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—81no—
195C4×C61—81no—
196C4×C61C2×#9911yescharacteristic
197C4×C61#41011yescharacteristic
198Dic61—82no—
199Dic61—81no—
200Dic61—81no—
201C2×#467—611no—
202#1810—611no—
203#1752—611no—
204#1508—611no—
205#1508—611no—
206#1472—611no—
207#1472D6111yescharacteristic
208C2×C61—22no—
209C2×C61—22no—
210C2×C61—41no—
211C2×C61#196411yescharacteristic
212C2×C61#197511yescharacteristic
213C2×C61#197911yescharacteristic
214C22×Q16—611no—
215C23×C8—611no—
216C2×C22⋊Q8—611no—
217C2×C22⋊Q8C2×D6111yescharacteristic
218#467—1221no—
219#467—1221no—
220#467—1221no—
221#467—1221no—
222C2×#108—1221no—
223C2×#107—611no—
224C2×#103—611no—
225C2×#103—611no—
226#407—611no—
227#407C2×D6111yescharacteristic
228C2×C22⋊C8C2×D6111yescharacteristic
229C2×#97—1221no—
230C4×C22⋊C4—611no—
231#341—1221no—
232#336—1221no—
233#328—1222no—
234#328—1222no—
235#324—22no—
236#324—1222no—
237C61#981711yescharacteristic, complemented, Sylow
238C22×Q8—611no—
239C22×Q8C4×D6111yescharacteristic
240C23×C4C22×D6111yescharacteristic
241C2×Q16—1221no—
242C2×Q16—1221no—
243C2×Q16—2442no—
244C2×M16—21no—
245C2×M16—1221no—
246C22×C8—21no—
247C22×C8—611no—
248C22×C8—611no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—611no—
252C22×C8—611no—
253C22×C8—2442no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—1221no—
259C22⋊Q8—1221no—
260C22⋊Q8—1221no—
261C22⋊Q8—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4C4×D6111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42—1221no—
270#108—2442no—
271#107—1221no—
272#107—1221no—
273#103—1221no—
274#103—1221no—
275#103—1221no—
276#103—1221no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—1221no—
281C22⋊C8—1221no—
282C22⋊C8C22⋊D6112yes—
283#97—2442no—
284#95—612no—
285C24#1175822211yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—1221no—
291C2×Q8—1221no—
292C2×Q8—2441no—
293C2×Q8—2441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1222no—
301C22×C4C2×C4×D6111yescharacteristic
302C22×C4D4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305C22×C4#1175822411yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307Q16—2442no—
308Q16—2442no—
309M16—41no—
310M16—41no—
311M16—2441no—
312M16—2441no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—611no—
320C2×C8—611no—
321C2×C8—1222no—
322C2×C8—1222no—
323C2×C8—1222no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8—2441no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—2442no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C42—2441no—
342C42—2441no—
343C23—22no—
344C23—22no—
345C23—41no—
346C23C4×C22⋊D6111yescharacteristic
347C23#1451975011yescharacteristic
348C23#1451976311yescharacteristic
349Q8—41no—
350Q8—41no—
351Q8—81no—
352Q8—4881no—
353Q8—2441no—
354Q8—2441no—
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—4881no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4C22⋊C4×D6111yescharacteristic
376C2×C4#1451973711yescharacteristic
377C2×C4#1451974911yescharacteristic
378C2×C4#1451977311yescharacteristic
379C8—42no—
380C8—81no—
381C8—612no—
382C8—1221no—
383C8—1221no—
384C8—1221no—
385C8—4881no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22#1683966211yescharacteristic
395C22#1683988212yes—
396C22#1684003612yes—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—4882no—
403C4—4881no—
404C4—4881no—
405C4#99×D6111yescharacteristic
406C4#1683973411yescharacteristic
407C2—22no—
408C2—22no—
409C2—41no—
410C2#2144665311yescharacteristic
411C2#2144671111yescharacteristic
412C2#2144673111yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1472C2
socleC22×C61#390
prime radicalC24×C61#41
cosocleC23×C4×C61C23
hypercenter#1472D61
hypocenterC61#9817
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
8. C22×#11758202C4semidirect
16. C2×#14519710C4semidirect
17. C2×#14519701C4semidirect
18. C2×#14519700C4semidirect
237. C61#9817semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
#214458552
#214455982
#214443402
#214443392
#214441822
C61×#14722
#981761