Finite Group Databasebeta

← #29584393

Subgroups — #29584393

Order 15616.

438 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 79 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#21456640C211yesmaximal, characteristic
2#21446288C211yesmaximal, characteristic
3#21446250C211yesmaximal, characteristic
4#21446026C211yesmaximal, characteristic
5#21444182C211yesmaximal, characteristic
6#21443725C211yesmaximal, characteristic
7C61×#1520C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9C2×#14519756C2211yescharacteristic
10#16840092—21no—
11#16840090—21no—
12#16840018—21no—
13#16840018—21no—
14#16839918—21no—
15#16839917—21no—
16C2×#14519713—21no—
17C2×#14519700—21no—
18C2×#14519696—21no—
19#16839726C2211yescharacteristic
20#16839726C2211yescharacteristic
21#16839531—21no—
22#16839527—21no—
23#16839524—21no—
24#16839487—22no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#328—22no—
29C22×Dic122D411yescharacteristic
30C2×#11758202—21no—
31C2×#11758202—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758194—21no—
35C2×#11758194—42no—
36C2×#11758194D411yescharacteristic
37C2×#11758194D411yescharacteristic
38C22×#92418—21no—
39#14519756—21no—
40#14519756—21no—
41#14519756—21no—
42#14519756—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46#14519713—42no—
47#14519708—21no—
48#14519708—21no—
49#14519701—21no—
50#14519701—21no—
51#14519700—21no—
52#14519700—21no—
53#14519700—42no—
54#14519696—42no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22×Q8×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61D412yes—
73#95×C61—21no—
74C24×C61#4111yescharacteristic
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—81no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110#11758202—81no—
111#11758202—81no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114#11758196—41no—
115#11758196—41no—
116#11758194—22no—
117#11758194—22no—
118#11758194—41no—
119#11758194—41no—
120#11758194—41no—
121#11758194—41no—
122#11758194—41no—
123#11758194—41no—
124C2×#92418—22no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61#12111yescharacteristic
135C23×C61#12311yescharacteristic
136C23×C61#12411yescharacteristic
137Q8×C61—41no—
138Q8×C61—41no—
139Q8×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—81no—
165Dic122—42no—
166Dic122—41no—
167Dic122—41no—
168C8×C61—42no—
169#92418—42no—
170#92418—41no—
171#92418—41no—
172#92418—81no—
173#10563—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61#39411yescharacteristic
185C22×C61#47111yescharacteristic
186C22×C61#47311yescharacteristic
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—81no—
191C4×C61—81no—
192C4×C61—161no—
193C4×C61B(4,𝔽2)11yescharacteristic
194C4×C61#45811yescharacteristic
195Dic61—81no—
196Dic61—81no—
197#3195—611no—
198#1901—611no—
199#1894—611no—
200#1855—611no—
201#1520D6111yescharacteristic
202#1472—611no—
203#1305—611no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—41no—
207C2×C61—41no—
208C2×C61#204411yescharacteristic
209C2×C61#204911yescharacteristic
210C2×C61#205211yescharacteristic
211C22×M16—611no—
212C2×C22⋊Q8—611no—
213C2×C22⋊Q8C2×D6111yescharacteristic
214#483—1221no—
215#483—1221no—
216#470—1221no—
217#470—1221no—
218#451—1221no—
219#451—1221no—
220C2×#108—1221no—
221C2×#103—1221no—
222C2×#101—1221no—
223#407—611no—
224#407—611no—
225C2×C22⋊C8C2×D6111yescharacteristic
226#380C2×D6111yescharacteristic
227#343—1221no—
228#341—1221no—
229#340—1221no—
230#328—22no—
231#324—1222no—
232C61#1056311yescharacteristic, complemented, Sylow
233C22×Q8—611no—
234C22×Q8D24411yescharacteristic
235C23×C4C22×D6111yescharacteristic
236C2×Q16—1221no—
237C2×Q16—1221no—
238C2×M16—611no—
239C2×M16—611no—
240C2×M16—1221no—
241C2×M16—1221no—
242C2×M16—1221no—
243C2×M16—2442no—
244C22×C8—21no—
245C22×C8—1221no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—1221no—
251C22⋊Q8—1221no—
252C22⋊Q8—1221no—
253C22⋊Q8—1221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4D24411yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—1221no—
262#108—2442no—
263#106—1221no—
264#106—1221no—
265#103—1221no—
266#103—1221no—
267#103—1221no—
268#103—1221no—
269#103—2442no—
270#101—2442no—
271C22⋊C8—21no—
272C22⋊C8—1221no—
273C22⋊C8—1221no—
274C22⋊C8—1221no—
275C22⋊C8—1221no—
276C22⋊C8C22⋊D6112yes—
277#95—21no—
278C24#1175822411yescharacteristic
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—1221no—
284C2×Q8—1221no—
285C2×Q8—2441no—
286C2×Q8—2441no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4C2×D24411yescharacteristic
295C22×C4#1175822211yescharacteristic
296C22×C4D4×D6111yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4#1175822411yescharacteristic
299C22×C4C2×C22⋊D6111yescharacteristic
300Q16—4881no—
301Q16—4881no—
302M16—1222no—
303M16—1222no—
304M16—2441no—
305M16—2441no—
306M16—2441no—
307M16—2441no—
308M16—2441no—
309M16—2441no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1222no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#1451974811yescharacteristic
339C23#1451976111yescharacteristic
340C23#1451976311yescharacteristic
341Q8—41no—
342Q8—41no—
343Q8—81no—
344Q8—2442no—
345Q8—2441no—
346Q8—2441no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—4881no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4#1451974711yescharacteristic
369C2×C4#1451974911yescharacteristic
370C2×C4#1451975111yescharacteristic
371C2×C4#1451975911yescharacteristic
372C8—42no—
373C8—4881no—
374C8—2442no—
375C8—2441no—
376C8—2441no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1683967811yescharacteristic
388C22#1684002211yescharacteristic
389C22#1684003411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—161no—
396C4—4881no—
397C4—4881no—
398C4#1683995011yescharacteristic
399C4#1683995311yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#2144706911yescharacteristic
405C2#2144710011yescharacteristic
406C2#2144711911yescharacteristic
subgroupG/H
centerC22#16839678
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1520C2
socleC22×C61#394
prime radicalC24×C61#41
hypercenter#1520D61
hypocenterC61#10563
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
232. C61#10563semidirect

Maximal subgroups

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

subgroupindex
#214566402
#214462882
#214462502
#214460262
#214441822
#214437252
C61×#15202
#1056361