Finite Group Databasebeta

← #29592682

Subgroups — #29592682

Order 15616.

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

normal subgroups only

This group has 458 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#21446865C211yesmaximal, characteristic, complemented
2#21444855C211yesmaximal, characteristic, complemented
3#21444753C211yesmaximal, characteristic
4#21443846C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443753C211yesmaximal, characteristic, complemented
7C61×#2572C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9#16840343C2211yescharacteristic
10#16840080—21no—
11#16839896—21no—
12C2×#14519705—21no—
13#16839531C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#400C2211yescharacteristic
19C61×#394C2211yescharacteristic
20C61×#393—21no—
21C61×#391C2211yescharacteristic
22C61×#388—21no—
23C61×#386—21no—
24C61×#383—21no—
25C61×#381—21no—
26C4×C22⋊C4×C61—21no—
27C2×#11758222—21no—
28#14519808—42no—
29#14519808—42no—
30C2×#11758202—41no—
31C2×#11758201—41no—
32C2×#11758199—41no—
33C2×#11758194—21no—
34#14519757—41no—
35#14519752—41no—
36#14519751—21no—
37#14519751—21no—
38#14519708—41no—
39#14519705—42no—
40#14519698—41no—
41#14519697—41no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22×Q8×C61D411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61C2311yescharacteristic
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×C42×C61—21no—
55C2×C42×C61D411yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C24×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—21no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—42no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—42no—
78C22×C4×C61—42no—
79C22×C4×C61—81no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C2×C22⋊D61—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—81no—
100C22⋊C4×C61—81no—
101C42×C61—42no—
102C42×C61—41no—
103#11758202—44no—
104#11758201—44no—
105#11758199—82no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758194—22no—
111#11758194—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61#12011yescharacteristic
123C22×D61—41no—
124Q8×C61—42no—
125Q8×C61—81no—
126D4×C61—42no—
127D4×C61—81no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—84no—
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C22⋊D61—81no—
153C22⋊D61—81no—
154C2×Dic61—41no—
155D244—41no—
156D244—41no—
157D244—81no—
158D244—81no—
159C4×D61—81no—
160C4×D61—81no—
161Dic122—41no—
162Dic122—41no—
163#92418—42no—
164#92418—81no—
165#92418—81no—
166#12195—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61#44911yescharacteristic
177C22×C61#45311yescharacteristic
178C22×C61B(4,𝔽2)11yescharacteristic
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—42no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—81no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61—81no—
191Dic61—81no—
192#2572D6111yescharacteristic, complemented
193#2007—611no—
194#1616—611no—
195#1598—611no—
196#1353—611no—
197#1345—611no—
198#1319—611no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—82no—
202C2×C61#160011yescharacteristic
203C2×C61#219711yescharacteristic
204C2×C61#220411yescharacteristic
205D61—161no—
206C2×#137—1221no—
207#537—611no—
208#481—1221no—
209#447—1221no—
210C2×#104—1221no—
211#400C2×D6111yescharacteristic
212#394C2×D6111yescharacteristic
213#393—21no—
214#391C2×D6111yescharacteristic
215#388—21no—
216#386—21no—
217#383—21no—
218#381—21no—
219C4×C22⋊C4—21no—
220#343—611no—
221#327—1221no—
222#327—1221no—
223#324—611no—
224#324—611no—
225C61#1219511yescharacteristic, complemented, Sylow
226C2×#41—1221no—
227C22×Q8C22⋊D6111yescharacteristic
228C22×D4C22⋊D6111yescharacteristic
229C23×C4—21no—
230#137—2442no—
231#137—2442no—
232C2×Q16—2441no—
233C2×SD16—2441no—
234C2×D8—2441no—
235C2×M16—1221no—
236C22⋊Q8—2441no—
237#121—1221no—
238#121—1221no—
239#121—2441no—
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C4⋊C4C22×D6111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—21no—
248C2×C42C22⋊D6111yescharacteristic
249#106—2441no—
250#104—2442no—
251#102—2441no—
252#102—2441no—
253C22⋊C8—1221no—
254C22⋊C8—1221no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95C22⋊D6111yescharacteristic
263#95C22⋊D6111yescharacteristic
264C24—21no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268#41—2441no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—1221no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4—2441no—
289C22×C4C2×C22⋊D6111yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292Q16—2444no—
293SD16—2444no—
294D8—4882no—
295M16—1222no—
296M16—2441no—
297C2×C8—2441no—
298C2×C8—2441no—
299C2×C8—2441no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C42—41no—
313C42—42no—
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—2441no—
322C23#1451974611yescharacteristic
323Q8—42no—
324Q8—81no—
325Q8—2441no—
326Q8—2441no—
327D4—42no—
328D4—81no—
329D4—4881no—
330D4—4881no—
331D4—4881no—
332D4—4881no—
333D4—2441no—
334D4—2441no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—2441no—
360C2×C4#1451979711yescharacteristic
361C2×C4#1451980211yescharacteristic
362C8—4881no—
363C8—4881no—
364C8—2442no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—4881no—
375C22—4881no—
376C22—4881no—
377C22#1683990711yescharacteristic
378C22#1683993011yescharacteristic
379C22#1683994911yescharacteristic
380C4—21no—
381C4—21no—
382C4—42no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—4881no—
390C2—21no—
391C2—21no—
392C2—82no—
393C2—9761no—
394C2#2144476511yescharacteristic
395C2#2144780911yescharacteristic
396C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2572C2
socleC22×C61B(4,𝔽2)
prime radical#21444753C2
hypercenter#2572D61
hypocenterC61#12195
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2572

Complements

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

NH ≅ G/Ntype
1. #21446865C2semidirect
2. #21444855C2semidirect
4. #21443846C2semidirect
5. #21443822C2semidirect
6. #21443753C2semidirect
7. C61×#2572C2semidirect
192. #2572D61semidirect
225. C61#12195semidirect

Maximal subgroups

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

subgroupindex
#214468652
#214448552
#214447532
#214438462
#214438222
#214437532
C61×#25722
#1219561