Finite Group Databasebeta

← #29576338

Subgroups — #29576338

Order 15616.

478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16840083C211yesmaximal, characteristic
2#21454479C211yesmaximal, characteristic, complemented
3#21445919C211yesmaximal, characteristic, complemented
4#21444179C211yesmaximal, characteristic
5#21443695C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#1507C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9#16840083—21no—
10#16840083—21no—
11#16840083—21no—
12#16840083—21no—
13#16839820—22no—
14#16839816—21no—
15#16839812—21no—
16C2×#14519710C411yescharacteristic, complemented
17C2×#14519708C411yescharacteristic, complemented
18#16839790—21no—
19C2×#14519698C411yescharacteristic, complemented
20C2×#14519698C411yescharacteristic, complemented
21#16839726C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24#16839720—21no—
25#16839522—21no—
26#16839522—21no—
27#16839486—21no—
28#16839486—21no—
29C2×#121×C61C2211yescharacteristic
30C61×#407C2211yescharacteristic
31C4×C22⋊C4×C61C2211yescharacteristic
32C61×#327—22no—
33C2×#11758194—21no—
34C22×#92418—21no—
35C22×#92418C2×C411yescharacteristic
36C22×#92418C2×C411yescharacteristic
37#14519736—21no—
38#14519736—21no—
39#14519736D411yescharacteristic
40#14519736D411yescharacteristic
41#14519736D411yescharacteristic
42#14519736D411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C4×Dic61—21no—
47#14519710—21no—
48#14519710—21no—
49#14519708—21no—
50#14519708—21no—
51#14519706—22no—
52#14519706—22no—
53#14519698—21no—
54#14519698—21no—
55#14519698—21no—
56#14519698—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62C22⋊#92418D411yescharacteristic
63C22⋊#92418D411yescharacteristic
64#14519687—22no—
65C8×Dic61—22no—
66C22×D4×C61—21no—
67C22×D4×C61C2×C411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C42×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61D412yes—
80#95×C61—21no—
81C24×C61—21no—
82C24×C61#4111yescharacteristic
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—82no—
90C22×C4×C61—21no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C22×Dic61—21no—
101C22×Dic61—21no—
102M16×C61—41no—
103M16×C61—41no—
104C2×C8×C61—22no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C42×C61—41no—
112C42×C61—41no—
113C22⋊Dic61—21no—
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116C22⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61C22⋊C411yescharacteristic
120C4⋊Dic61C22⋊C411yescharacteristic
121C4⋊Dic61C22⋊C411yescharacteristic
122C4⋊Dic61C22⋊C411yescharacteristic
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127#11758194—41no—
128#11758194—41no—
129C2×#92418—21no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—21no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—81no—
146C23×C61—81no—
147C23×C61C4×D411yescharacteristic
148C23×C61#12111yescharacteristic
149C23×C61#12311yescharacteristic
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—81no—
153D4×C61—82no—
154D4×C61—82no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—81no—
180C8×C61—42no—
181#92418—41no—
182#92418—41no—
183#92418—41no—
184#92418—41no—
185#92418—81no—
186#9242—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—161no—
201C22×C61—161no—
202C22×C61#38611yescharacteristic
203C22×C61#44311yescharacteristic
204C22×C61#44411yescharacteristic
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—82no—
209C4×C61—81no—
210C4×C61#41011yescharacteristic
211C4×C61#41011yescharacteristic
212Dic61—41no—
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216C2×#482—611no—
217#2924—611no—
218#1826—611no—
219#1507D6111yescharacteristic
220#1471—611no—
221#1293—611no—
222#1282—611no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—41no—
226C2×C61—41no—
227C2×C61—161no—
228C2×C61#187611yescharacteristic
229C2×C61#189911yescharacteristic
230C2×C61#190311yescharacteristic
231C2×#121C2×D6111yescharacteristic
232C2×#117—611no—
233#482—1221no—
234#482—1221no—
235#482—1221no—
236#482—1221no—
237#433—1222no—
238#432—1221no—
239#431—1221no—
240C2×#107—611no—
241C2×#106—611no—
242#424—1221no—
243C2×#102—611no—
244C2×#102—611no—
245#407—611no—
246#407C2×D6111yescharacteristic
247C2×C22⋊C8—611no—
248C2×C22⋊C8—611no—
249#405—1221no—
250C4×C22⋊C4C2×D6111yescharacteristic
251#339—1221no—
252#339—1221no—
253#327—22no—
254#323—1221no—
255#323—1221no—
256C61#924211yescharacteristic, complemented, Sylow
257C22×D4—21no—
258C22×D4C4×D6111yescharacteristic
259C23×C4C22×D6111yescharacteristic
260C2×M16—21no—
261C2×M16—1221no—
262C22×C8—611no—
263C22×C8—611no—
264C22×C8—1221no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269#117—611no—
270#117—611no—
271#117—611no—
272#117—611no—
273#117—1221no—
274#117—1221no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4C4×D6111yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—1221no—
281C2×C42—21no—
282C2×C42—1221no—
283#107—1221no—
284#107—1221no—
285#106—1221no—
286#106—1221no—
287C4⋊C8—1222no—
288C4⋊C8—1222no—
289#102—1221no—
290#102—1221no—
291#102—1221no—
292#102—1221no—
293C22⋊C8—21no—
294C22⋊C8—611no—
295C22⋊C8—611no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298C22⋊C8—1221no—
299C22⋊C8—1221no—
300C22⋊C8—1221no—
301C22⋊C8C22⋊D6112yes—
302#97—1222no—
303C4×C8—1222no—
304#95—21no—
305C24—21no—
306C24#1175822411yescharacteristic
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—82no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4C2×C4×D6111yescharacteristic
321C22×C4#1175822211yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4C2×C22⋊D6111yescharacteristic
326M16—41no—
327M16—41no—
328M16—2441no—
329M16—2441no—
330C2×C8—22no—
331C2×C8—1221no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—611no—
343C4⋊C4—611no—
344C4⋊C4—611no—
345C4⋊C4—611no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—1221no—
353C22⋊C4—1221no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C42—41no—
357C42—41no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42—1221no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—81no—
370C23—81no—
371C23#1451973711yescharacteristic
372C23#1451974811yescharacteristic
373C23#1451975911yescharacteristic
374D4—41no—
375D4—41no—
376D4—81no—
377D4—82no—
378D4—82no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—4881no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4C22⋊C4×D6111yescharacteristic
401C2×C4C4×C22⋊D6111yescharacteristic
402C2×C4#1451974511yescharacteristic
403C2×C4#1451975011yescharacteristic
404C8—42no—
405C8—4881no—
406C8—2441no—
407C8—2441no—
408C8—2441no—
409C8—2441no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—161no—
424C22—161no—
425C22#1683963811yescharacteristic
426C22#1683987611yescharacteristic
427C22#1683988111yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—81no—
433C4—2441no—
434C4—2441no—
435C4—2441no—
436C4—2441no—
437C4#1683973411yescharacteristic
438C4#1683973411yescharacteristic
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—161no—
444C2#2144614311yescharacteristic
445C2#2144627411yescharacteristic
446C2#2144629611yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1507C2
socleC22×C61#386
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#1507D61
hypocenterC61#9242
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #21454479C2semidirect
3. #21445919C2semidirect
5. #21443695C2semidirect
6. #21443667C2semidirect
16. C2×#14519710C4semidirect
17. C2×#14519708C4semidirect
19. C2×#14519698C4semidirect
20. C2×#14519698C4semidirect
256. C61#9242semidirect

Maximal subgroups

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

subgroupindex
C2×#168400832
#214544792
#214459192
#214441792
#214436952
#214436672
C61×#15072
#924261