Finite Group Databasebeta

← #29592661

Subgroups — #29592661

Order 15616.

544 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 59 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#21446945C211yesmaximal, characteristic
2#21444838C211yesmaximal, characteristic, complemented
3#21444804C211yesmaximal, characteristic, complemented
4#21443843C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443747C211yesmaximal, characteristic, complemented
7C61×#2735C211yesmaximal, characteristic, complemented
8#16840324C2211yescharacteristic
9C2×#14519746—21no—
10#16840080—21no—
11#16840075—21no—
12C2×#14519691—21no—
13#16839529C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#399C2211yescharacteristic
19C61×#397—21no—
20C61×#397C2211yescharacteristic
21C61×#396—21no—
22C61×#388—21no—
23C61×#388—21no—
24C61×#388—21no—
25C61×#379—21no—
26C61×#379C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61—41no—
29#14519761—41no—
30#14519751—21no—
31#14519751—21no—
32#14519747—41no—
33#14519746—42no—
34#14519746—42no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—41no—
37#14519710—41no—
38#14519708—41no—
39#14519697—41no—
40#14519697—41no—
41#14519691—42no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C25×C61D411yescharacteristic
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic, complemented
48C2×C4⋊C4×C61D411yescharacteristic, complemented
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61D411yescharacteristic
58C2×C22⋊C4×C61C2311yescharacteristic
59C2×C42×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic, complemented
64#95×C61D411yescharacteristic, complemented
65C24×C61—21no—
66C24×C61—21no—
67C24×C61—21no—
68C24×C61—41no—
69C24×C61—42no—
70C24×C61—41no—
71C24×C61—81no—
72C24×C61C2×D411yescharacteristic
73C23×D61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—44no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—82no—
89C2×C22⋊D61—82no—
90C22×Dic61—21no—
91C22×Dic61—41no—
92C2×D244—21no—
93C2×D244—21no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—81no—
97C4⋊C4×C61—81no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—81no—
105C22⋊C4×C61—81no—
106C22⋊C4×C61—81no—
107C22⋊C4×C61—81no—
108C22⋊C4×C61—81no—
109C42×C61—81no—
110C22⋊Dic61—22no—
111C22⋊Dic61—44no—
112C22⋊Dic61—41no—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C2×#92418—41no—
118C2×#92418—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—22no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—42no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—42no—
129C23×C61—42no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—81no—
134C23×C61—82no—
135C23×C61—81no—
136C23×C61—84no—
137C23×C61—82no—
138C23×C61—81no—
139C23×C61#12011yescharacteristic
140C23×C61#13511yescharacteristic
141C23×C61AGL(1,ℤ/8)11yescharacteristic
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—81no—
146C22×D61—81no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C22⋊D61—81no—
167C22⋊D61—81no—
168C22⋊D61—88no—
169C22⋊D61—81no—
170C22⋊D61—81no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177D244—81no—
178D244—81no—
179#92418—81no—
180#92418—81no—
181#12192—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—44no—
193C22×C61—42no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—82no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61#44911yescharacteristic
203C22×C61#45311yescharacteristic
204C22×C61B(4,𝔽2)11yescharacteristic
205C2×D61—82no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—161no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—81no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217Dic61—82no—
218Dic61—81no—
219#2735D6111yescharacteristic, complemented
220#2021—611no—
221#1613—611no—
222#1607—611no—
223#1352—611no—
224#1344—611no—
225#1316—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—41no—
229C2×C61—41no—
230C2×C61—82no—
231C2×C61#160011yescharacteristic
232C2×C61#219711yescharacteristic
233C2×C61#220011yescharacteristic
234D61—161no—
235#534—611no—
236C2×#120—1221no—
237#481—1221no—
238#480—1221no—
239C2×#99—1221no—
240#399C2×D6111yescharacteristic
241#397—21no—
242#397C2×D6111yescharacteristic
243#396—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247#379—21no—
248#379C2×D6111yescharacteristic
249#342—611no—
250#327—1221no—
251#327—1221no—
252#323—611no—
253#323—611no—
254C61#1219211yescharacteristic, complemented, Sylow
255C25C22⋊D6111yescharacteristic
256C22×D4—1221no—
257C22×D4—2441no—
258#123—2441no—
259#121—1221no—
260#121—1221no—
261#120—2441no—
262#120—2442no—
263#120—2442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
267C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
268C2×C22⋊C4—21no—
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—21no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—2441no—
278C2×C22⋊C4C22⋊D6111yescharacteristic
279C2×C22⋊C4C22×D6111yescharacteristic
280C2×C42—21no—
281#107—2441no—
282#106—2441no—
283#102—2441no—
284#102—2441no—
285#99—2442no—
286C22⋊C8—1221no—
287C22⋊C8—1221no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95C22⋊D6111yescharacteristic, complemented
292#95C22⋊D6111yescharacteristic, complemented
293C24—21no—
294C24—21no—
295C24—21no—
296C24—41no—
297C24—41no—
298C24—42no—
299C24—81no—
300C24—1221no—
301C24C2×C22⋊D6111yescharacteristic
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—4882no—
305C2×D4—4882no—
306C2×D4—2441no—
307C2×D4—2441no—
308C2×D4—2441no—
309C2×D4—2444no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—1221no—
319C22×C4—2441no—
320C22×C4C2×C22⋊D6111yescharacteristic
321C22×C4C2×C22⋊D6111yescharacteristic
322C2×C8—2441no—
323C2×C8—2441no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—81no—
327C4⋊C4—81no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—81no—
337C22⋊C4—81no—
338C22⋊C4—81no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C22⋊C4—1222no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2444no—
345C22⋊C4—2441no—
346C42—81no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—81no—
362C23—82no—
363C23—81no—
364C23—82no—
365C23—84no—
366C23—81no—
367C23—4881no—
368C23—4881no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23#1451974611yescharacteristic
373C23#1451979711yescharacteristic
374C23#1451980211yescharacteristic
375D4—4881no—
376D4—4881no—
377D4—4881no—
378D4—4881no—
379D4—4888no—
380D4—4881no—
381D4—4881no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C8—4881no—
408C8—4881no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—41no—
414C22—41no—
415C22—42no—
416C22—42no—
417C22—41no—
418C22—41no—
419C22—44no—
420C22—42no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—9761no—
430C22—4882no—
431C22—4881no—
432C22—4881no—
433C22—4881no—
434C22#1683990711yescharacteristic
435C22#1683993011yescharacteristic
436C22#1683994911yescharacteristic
437C4—41no—
438C4—41no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—4882no—
445C4—4881no—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—41no—
450C2—82no—
451C2—9761no—
452C2#2144476511yescharacteristic
453C2#2144780911yescharacteristic
454C2#2144782611yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2735C2
socleC22×C61B(4,𝔽2)
prime radical#21446945C2
hypercenter#2735D61
hypocenterC61#12192
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2735

Complements

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

NH ≅ G/Ntype
2. #21444838C2semidirect
3. #21444804C2semidirect
4. #21443843C2semidirect
5. #21443819C2semidirect
6. #21443747C2semidirect
7. C61×#2735C2semidirect
47. C2×C4⋊C4×C61D4semidirect
48. C2×C4⋊C4×C61D4semidirect
63. #95×C61D4semidirect
64. #95×C61D4semidirect
219. #2735D61semidirect
254. C61#12192semidirect
266. C2×C4⋊C4C22⋊D61semidirect
267. C2×C4⋊C4C22⋊D61semidirect
291. #95C22⋊D61semidirect
292. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214469452
#214448382
#214448042
#214438432
#214438192
#214437472
C61×#27352
#1219261