Finite Group Databasebeta

← #29592633

Subgroups — #29592633

Order 15616.

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

normal subgroups only

This group has 554 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#21444804C211yesmaximal, characteristic, complemented
3#21444770C211yesmaximal, characteristic, complemented
4#21443840C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443747C211yesmaximal, characteristic, complemented
7C61×#2736C211yesmaximal, characteristic, complemented
8#16840324C2211yescharacteristic
9C2×#14519746—21no—
10#16840075—21no—
11#16839901—21no—
12C2×#14519691—21no—
13#16839529C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#397—21no—
19C61×#397C2211yescharacteristic
20C61×#393—21no—
21C61×#393C2211yescharacteristic
22C61×#388—21no—
23C61×#388—21no—
24C61×#388—21no—
25C61×#379—21no—
26C61×#379C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61—41no—
29C2×#11758201—41no—
30#14519761—41no—
31#14519751—21no—
32#14519751—21no—
33#14519747—41no—
34#14519746—42no—
35#14519746—42no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—41no—
38#14519710—41no—
39#14519701—41no—
40#14519697—41no—
41#14519691—42no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C25×C61D411yescharacteristic
45C22×Q8×C61D411yescharacteristic, complemented
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic, complemented
48C2×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
57C2×C22⋊C4×C61C2311yescharacteristic
58C2×C42×C61—21no—
59#95×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—
74C2×Q8×C61—41no—
75C2×Q8×C61—81no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—44no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—82no—
91C2×C22⋊D61—82no—
92C22×Dic61—21no—
93C22×Dic61—41no—
94C2×D244—21no—
95C2×D244—21no—
96C4⋊C4×C61—41no—
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#11758201—82no—
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—22no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—42no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—42no—
130C23×C61—42no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—81no—
135C23×C61—82no—
136C23×C61—81no—
137C23×C61—84no—
138C23×C61—82no—
139C23×C61—81no—
140C23×C61#12011yescharacteristic
141C23×C61#13511yescharacteristic
142C23×C61AGL(1,ℤ/8)11yescharacteristic
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—81no—
147C22×D61—81no—
148Q8×C61—42no—
149Q8×C61—81no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
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—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C22⋊D61—81no—
170C22⋊D61—81no—
171C22⋊D61—88no—
172C22⋊D61—81no—
173C22⋊D61—81no—
174C2×Dic61—42no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180D244—81no—
181D244—81no—
182#92418—81no—
183#92418—81no—
184#12188—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—42no—
192C22×C61—42no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—44no—
196C22×C61—42no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61—82no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61#44911yescharacteristic
206C22×C61#45311yescharacteristic
207C22×C61B(4,𝔽2)11yescharacteristic
208C2×D61—82no—
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—161no—
213C4×C61—41no—
214C4×C61—41no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220Dic61—82no—
221Dic61—81no—
222#2736D6111yescharacteristic, complemented
223#2021—611no—
224#1607—611no—
225#1601—611no—
226#1351—611no—
227#1344—611no—
228#1316—611no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—41no—
232C2×C61—41no—
233C2×C61—82no—
234C2×C61#160011yescharacteristic
235C2×C61#219711yescharacteristic
236C2×C61#219911yescharacteristic
237D61—161no—
238#534—611no—
239C2×#120—1221no—
240#480—1221no—
241#448—1221no—
242C2×#99—1221no—
243#397—21no—
244#397C2×D6111yescharacteristic
245#393—21no—
246#393C2×D6111yescharacteristic
247#388—21no—
248#388—21no—
249#388—21no—
250#379—21no—
251#379C2×D6111yescharacteristic
252#342—611no—
253#327—1221no—
254#327—1221no—
255#323—611no—
256#323—611no—
257C61#1218811yescharacteristic, complemented, Sylow
258C25C22⋊D6111yescharacteristic
259C22×Q8C22⋊D6111yescharacteristic, complemented
260C22×D4—1221no—
261C22×D4—2441no—
262C2×SD16—2441no—
263#123—2441no—
264#121—1221no—
265#121—1221no—
266#120—2441no—
267#120—2442no—
268#120—2442no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—2441no—
281C2×C22⋊C4C22⋊D6111yescharacteristic
282C2×C22⋊C4C22×D6111yescharacteristic
283C2×C42—21no—
284#107—2441no—
285#103—2441no—
286#102—2441no—
287#99—2442no—
288C22⋊C8—1221no—
289C22⋊C8—1221no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95C22⋊D6111yescharacteristic, complemented
295#95C22⋊D6111yescharacteristic, complemented
296C24—21no—
297C24—21no—
298C24—21no—
299C24—41no—
300C24—41no—
301C24—42no—
302C24—81no—
303C24—1221no—
304C24C2×C22⋊D6111yescharacteristic
305C2×Q8—41no—
306C2×Q8—81no—
307C2×D4—1221no—
308C2×D4—1221no—
309C2×D4—4882no—
310C2×D4—4882no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2444no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—1221no—
324C22×C4—2441no—
325C22×C4C2×C22⋊D6111yescharacteristic
326C22×C4C2×C22⋊D6111yescharacteristic
327SD16—4882no—
328C2×C8—2441no—
329C2×C8—2441no—
330C4⋊C4—41no—
331C4⋊C4—81no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C22⋊C4—41no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—81no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C22⋊C4—81no—
345C22⋊C4—1222no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C22⋊C4—2444no—
349C22⋊C4—2441no—
350C42—81no—
351C23—21no—
352C23—21no—
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—42no—
359C23—41no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—82no—
367C23—81no—
368C23—82no—
369C23—84no—
370C23—81no—
371C23—4881no—
372C23—4881no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23#1451974611yescharacteristic
377C23#1451979711yescharacteristic
378C23#1451980211yescharacteristic
379Q8—42no—
380Q8—81no—
381D4—4881no—
382D4—4881no—
383D4—4881no—
384D4—4881no—
385D4—4888no—
386D4—4881no—
387D4—4881no—
388C2×C4—21no—
389C2×C4—21no—
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—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—2442no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C8—4881no—
414C8—4881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—44no—
426C22—42no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22—81no—
434C22—81no—
435C22—9761no—
436C22—4882no—
437C22—4881no—
438C22—4881no—
439C22—4881no—
440C22#1683990711yescharacteristic
441C22#1683993011yescharacteristic
442C22#1683994911yescharacteristic
443C4—41no—
444C4—41no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—4882no—
451C4—4881no—
452C2—21no—
453C2—21no—
454C2—41no—
455C2—41no—
456C2—82no—
457C2—9761no—
458C2#2144476511yescharacteristic
459C2#2144780911yescharacteristic
460C2#2144782011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2736C2
socleC22×C61B(4,𝔽2)
prime radical#21446945C2
hypercenter#2736D61
hypocenterC61#12188
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2736

Complements

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

NH ≅ G/Ntype
2. #21444804C2semidirect
3. #21444770C2semidirect
4. #21443840C2semidirect
5. #21443819C2semidirect
6. #21443747C2semidirect
7. C61×#2736C2semidirect
45. C22×Q8×C61D4semidirect
47. C2×C4⋊C4×C61D4semidirect
63. #95×C61D4semidirect
64. #95×C61D4semidirect
222. #2736D61semidirect
257. C61#12188semidirect
259. C22×Q8C22⋊D61semidirect
270. C2×C4⋊C4C22⋊D61semidirect
294. #95C22⋊D61semidirect
295. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214469452
#214448042
#214447702
#214438402
#214438192
#214437472
C61×#27362
#1218861