Finite Group Databasebeta

← #29598717

Subgroups — #29598717

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519722C211yesmaximal, characteristic, complemented
2C2×#16840003C211yesmaximal, characteristic, complemented
3C2×#16839998C211yesmaximal, characteristic
4C2×#16839567C211yesmaximal, characteristic, complemented
5C2×#16839564C211yesmaximal, characteristic, complemented
6#21443911C211yesmaximal, characteristic, complemented
7C2×C61×C22⋊C16C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C2×#14519756—21no—
11C2×#14519751—21no—
12C2×#14519722—22no—
13C2×#14519722—22no—
14C2×#14519722—22no—
15#16840003—22no—
16#16840003—22no—
17#16839998—22no—
18#16839998—22no—
19C2×#14519711C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519702—21no—
22C2×#14519699—21no—
23#16839567—22no—
24#16839564—22no—
25C23×C8×C61C2211yescharacteristic
26C22×C16×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic
28C61×C22⋊C16—22no—
29C22×Dic122—21no—
30C22×D244—21no—
31C22×C22⋊D61—41no—
32C2×Dic244—21no—
33C2×Dic244—21no—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×Dic244—21no—
37C2×Dic244D412yescomplemented
38C2×D488—21no—
39C2×D488—21no—
40C2×D488—21no—
41C2×D488—21no—
42C2×D488—21no—
43C2×D488D412yes—
44#14519756—24no—
45#14519756—42no—
46#14519751—24no—
47#14519751—42no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×#11758196—41no—
51C2×C22⋊Dic61—41no—
52C2×#11758198—41no—
53#14519722—28no—
54#14519711—21no—
55#14519711—21no—
56#14519711D412yes—
57#14519711D412yescomplemented
58#14519702—24no—
59#14519699—24no—
60C23×C4×C61D411yescharacteristic
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C22×C8×C61—21no—
67C22×C8×C61D411yescharacteristic
68C22×C8×C61C2311yescharacteristic
69C2×C16×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61—21no—
73C2×C16×C61—21no—
74C2×C16×C61D412yescomplemented
75C24×C61D811yescharacteristic
76C23×D61—41no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61D811yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—44no—
86C2×C22⋊D61—82no—
87C2×C22⋊D61—82no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C2×D244—22no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×Dic122—22no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×Dic122—41no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C22⋊Dic61—44no—
117#11758198—44no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122#11758196—44no—
123Dic244—22no—
124Dic244—22no—
125Dic244—41no—
126Dic244—41no—
127D488—22no—
128D488—22no—
129D488—41no—
130D488—41no—
131C16×C61—22no—
132C16×C61—41no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61SD3212yescomplemented
140C23×C61C2×D811yescharacteristic
141C22×D61—42no—
142C22×D61—81no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61—81no—
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#12011yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C22⋊D61—88no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171D244—42no—
172D244—42no—
173D244—81no—
174D244—81no—
175Dic122—42no—
176Dic122—42no—
177Dic122—81no—
178Dic122—81no—
179C8×C61—41no—
180C8×C61#12011yescharacteristic
181C8×C61#12111yescharacteristic
182C8×C61#12111yescharacteristic
183C8×C61#12711yescharacteristic
184#13305—611nomaximal, Sylow
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61#44711yescharacteristic
193C22×C61#44711yescharacteristic
194C22×C61#46611yescharacteristic
195C22×C61C2×SD3211yescharacteristic
196C22×C61#50811yescharacteristic
197C22×C61#50911yescharacteristic
198C22×C61#51011yescharacteristic
199C2×D61—82no—
200C2×D61—82no—
201C2×D61—82no—
202C2×D61—161no—
203C2×D61—161no—
204C2×D61—161no—
205C2×D61—161no—
206C4×C61—41no—
207C4×C61#39211yescharacteristic
208C4×C61#44911yescharacteristic
209C4×C61#44911yescharacteristic
210C4×C61#46911yescharacteristic
211Dic61—82no—
212Dic61—82no—
213Dic61—82no—
214C22×SD32—611no—
215C2×#467—611no—
216C2×#466—611no—
217C2×#358—611no—
218C2×#357—611no—
219C2×C22⋊C16D6111yescharacteristic, complemented
220#1380—611no—
221C2×C61—42no—
222C2×C61#199911yescharacteristic
223C2×C61#218511yescharacteristic
224C2×C61#218611yescharacteristic
225C2×C61#218711yescharacteristic
226C2×C61#218911yescharacteristic
227C2×C61#221711yescharacteristic
228C2×C61#222011yescharacteristic
229D61—162no—
230C22×Q16—611no—
231C22×D8—611no—
232C23×C8C2×D6111yescharacteristic
233C2×C22⋊Q8—1221no—
234C2×#121—1221no—
235C2×SD32—1222no—
236C2×SD32—1222no—
237C2×SD32—1222no—
238C22×C16C2×D6111yescharacteristic
239C22×C16C2×D6111yescharacteristic
240#467—1222no—
241#467—1222no—
242#466—1222no—
243#466—1222no—
244C2×#107—611no—
245C2×#107—611no—
246C2×#103—1221no—
247C2×#102—1221no—
248#358—1222no—
249#357—1222no—
250C22⋊C16—22no—
251C61#1330511yescharacteristic, complemented, Sylow
252C22×Q8—1221no—
253C22×D4—1221no—
254C22×D4—2441no—
255C23×C4D24411yescharacteristic
256C2×Q16—612no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×Q16—1221no—
261C2×Q16—1221no—
262C2×D8—612no—
263C2×D8—1221no—
264C2×D8—1221no—
265C2×D8—1221no—
266C2×D8—1221no—
267C2×D8—1221no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8D24411yescharacteristic
275C22×C8C22×D6111yescharacteristic
276C22⋊Q8—1224no—
277C22⋊Q8—2442no—
278#121—1224no—
279#121—2442no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—2441no—
283C2×C22⋊C4—2441no—
284C2×C22⋊C4—2441no—
285SD32—1228no—
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—21no—
289C2×C16—21no—
290C2×C16—21no—
291C2×C16C22⋊D6112yescomplemented
292#107—612no—
293#107—612no—
294#107—1221no—
295#107—1221no—
296#103—1224no—
297#102—1224no—
298C24—2441no—
299C24D48811yescharacteristic
300C2×Q8—1222no—
301C2×Q8—2441no—
302C2×Q8—2441no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×D4—1222no—
307C2×D4—4882no—
308C2×D4—4882no—
309C2×D4—2444no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4D48811yescharacteristic
325C22×C4C2×D24411yescharacteristic
326Q16—1222no—
327Q16—1222no—
328Q16—2441no—
329Q16—2441no—
330D8—1222no—
331D8—1222no—
332D8—2441no—
333D8—2441no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8#1175822211yescharacteristic
342C2×C8D4×D6111yescharacteristic
343C2×C8D4×D6111yescharacteristic
344C2×C8D4×D6111yescharacteristic
345C2×C8D4×D6111yescharacteristic
346C2×C8C2×C22⋊D6111yescharacteristic
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—2444no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C22⋊C4—2444no—
353C22⋊C4—2444no—
354C16—22no—
355C16—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—4881no—
363C23—4881no—
364C23—4881no—
365C23—4881no—
366C23—4881no—
367C23—4881no—
368C23—2442no—
369C23#1451972212yescomplemented
370C23C2×D48811yescharacteristic
371Q8—4881no—
372Q8—4881no—
373Q8—2442no—
374Q8—2442no—
375D4—4888no—
376D4—4881no—
377D4—4881no—
378D4—2442no—
379D4—2442no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—4881no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4#1451974711yescharacteristic
397C2×C4#1451974711yescharacteristic
398C2×C4#1451975111yescharacteristic
399C2×C4#1451979911yescharacteristic
400C2×C4#1451980511yescharacteristic
401C2×C4#1451980511yescharacteristic
402C8—41no—
403C8#1451974511yescharacteristic
404C8#1451975011yescharacteristic
405C8#1451975011yescharacteristic
406C8#1451977311yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—9761no—
415C22—9761no—
416C22—9761no—
417C22—9761no—
418C22—4882no—
419C22—4882no—
420C22—4882no—
421C22#1683989811yescharacteristic
422C22#1683989811yescharacteristic
423C22#1683999811yescharacteristic
424C22C2×#1451972211yescharacteristic
425C22#1684019411yescharacteristic
426C22#1684020011yescharacteristic
427C22#1684020511yescharacteristic
428C4—41no—
429C4—4882no—
430C4—4882no—
431C4—4882no—
432C4#1683967111yescharacteristic
433C4#1683990911yescharacteristic
434C4#1683990911yescharacteristic
435C4#1684001511yescharacteristic
436C2—42no—
437C2—9762no—
438C2#2144681711yescharacteristic
439C2#2144773811yescharacteristic
440C2#2144774411yescharacteristic
441C2#2144775011yescharacteristic
442C2#2144776111yescharacteristic
443C2#2144791511yescharacteristic
444C2#2144793211yescharacteristic
subgroupG/H
centerC23C2×D488
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×C22⋊C16C2
socleC23×C61C2×D8
prime radicalC2×#16839998C2
hypercenterC2×C22⋊C16D61
hypocenterC61#13305
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C22×#14519722C2semidirect
2. C2×#16840003C2semidirect
4. C2×#16839567C2semidirect
5. C2×#16839564C2semidirect
6. #21443911C2semidirect
7. C2×C61×C22⋊C16C2semidirect
37. C2×Dic244D4semidirect
57. #14519711D4semidirect
74. C2×C16×C61D4semidirect
139. C23×C61SD32semidirect
219. C2×C22⋊C16D61semidirect
251. C61#13305semidirect
291. C2×C16C22⋊D61semidirect
369. C23#14519722semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×#168400032
C2×#168399982
C2×#168395672
C2×#168395642
#214439112
C2×C61×C22⋊C162
#1330561