Finite Group Databasebeta

← #29584365

Subgroups — #29584365

Order 15616.

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

normal subgroups only

This group has 448 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#21456591C211yesmaximal, characteristic
2#21446288C211yesmaximal, characteristic
3#21446285C211yesmaximal, characteristic
4#21446004C211yesmaximal, characteristic
5#21444338C211yesmaximal, characteristic
6#21443695C211yesmaximal, characteristic
7C61×#1508C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9C2×#14519756C2211yescharacteristic
10#16840097—21no—
11#16840095—21no—
12#16840001—21no—
13#16840001—21no—
14#16839918—21no—
15#16839917—21no—
16C2×C4⋊#92418—21no—
17C2×#14519696—21no—
18C2×#14519695—21no—
19#16839726C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21#16839531—21no—
22#16839530—21no—
23#16839517—21no—
24#16839498—21no—
25#16839498—21no—
26C2×C22⋊Q8×C61C2211yescharacteristic
27C61×#407C2211yescharacteristic
28C4×C22⋊C4×C61C2211yescharacteristic
29C61×#328—21no—
30C61×#328—21no—
31C22×Dic122D411yescharacteristic
32C2×#11758202—21no—
33C2×#11758202—21no—
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×#11758194—21no—
37C2×#11758194—42no—
38C22×#92418—21no—
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41#14519756—21no—
42#14519756—21no—
43#14519756—21no—
44#14519756—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48#14519710—21no—
49#14519710—21no—
50C4⋊#92418—42no—
51#14519701—21no—
52#14519701—21no—
53#14519700—21no—
54#14519700—21no—
55#14519696—42no—
56#14519695—42no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61C22×Q8×C61D411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C2×M16×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C42×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75#95×C61D411yescharacteristic
76#95×C61D411yescharacteristic
77C24×C61#4111yescharacteristic
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×Dic61—21no—
95C22×Dic61—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C42×C61—41no—
111C42×C61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114#11758202—81no—
115#11758202—81no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118#11758196—41no—
119#11758196—41no—
120#11758194—22no—
121#11758194—22no—
122#11758194—41no—
123#11758194—41no—
124#11758194—41no—
125#11758194—41no—
126C2×#92418—22no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61#12111yescharacteristic
139C23×C61#12311yescharacteristic
140C23×C61#12311yescharacteristic
141Q8×C61—41no—
142Q8×C61—41no—
143Q8×C61—81no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—22no—
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—42no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12411yescharacteristic
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171Dic122—41no—
172Dic122—41no—
173Dic122—81no—
174C8×C61—81no—
175#92418—42no—
176#92418—41no—
177#92418—41no—
178#92418—81no—
179#10559—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61#39411yescharacteristic
191C22×C61#47311yescharacteristic
192C22×C61#47311yescharacteristic
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61—81no—
200C4×C61B(4,𝔽2)11yescharacteristic
201C4×C61#45811yescharacteristic
202Dic61—81no—
203Dic61—81no—
204#3189—611no—
205#1901—611no—
206#1901—611no—
207#1851—611no—
208#1508—611no—
209#1508D6111yescharacteristic
210#1293—611no—
211C2×C61—21no—
212C2×C61—21no—
213C2×C61—41no—
214C2×C61—41no—
215C2×C61#204411yescharacteristic
216C2×C61#204711yescharacteristic
217C2×C61#205011yescharacteristic
218C22×M16—611no—
219C2×C22⋊Q8—611no—
220C2×C22⋊Q8C2×D6111yescharacteristic
221#484—1221no—
222#484—1221no—
223#467—1221no—
224#467—1221no—
225#451—1221no—
226#451—1221no—
227C2×C4⋊C8—1221no—
228C2×#101—1221no—
229C2×#101—1221no—
230#407—611no—
231#407C2×D6111yescharacteristic
232C2×C22⋊C8—611no—
233C4×C22⋊C4C2×D6111yescharacteristic
234#343—1221no—
235#343—1221no—
236#336—1221no—
237#328—21no—
238#328—21no—
239#328—1221no—
240#328—1221no—
241C61#1055911yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×Q8D24411yescharacteristic
244C23×C4C22×D6111yescharacteristic
245C2×Q16—1221no—
246C2×Q16—1221no—
247C2×M16—21no—
248C2×M16—1221no—
249C2×M16—1221no—
250C2×M16—1221no—
251C2×M16—2442no—
252C22×C8—611no—
253C22×C8—611no—
254C22×C8—1221no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—1221no—
260C22⋊Q8—1221no—
261C22⋊Q8—1221no—
262C22⋊Q8—1221no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4D24411yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—1221no—
270C2×C42—21no—
271#107—1221no—
272#107—1221no—
273C4⋊C8—2442no—
274#103—1221no—
275#103—1221no—
276#103—1221no—
277#103—1221no—
278#101—2442no—
279#101—2442no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286#95C22⋊D6111yescharacteristic
287#95C22⋊D6111yescharacteristic
288C24#1175822411yescharacteristic
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—1221no—
294C2×Q8—1221no—
295C2×Q8—2441no—
296C2×Q8—2441no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4C2×D24411yescharacteristic
306C22×C4#1175822211yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309C22×C4#1175822411yescharacteristic
310C22×C4C2×C22⋊D6111yescharacteristic
311Q16—4881no—
312Q16—4881no—
313M16—41no—
314M16—41no—
315M16—1222no—
316M16—1222no—
317M16—2441no—
318M16—2441no—
319M16—2441no—
320M16—2441no—
321C2×C8—41no—
322C2×C8—1222no—
323C2×C8—1221no—
324C2×C8—1221no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C42—41no—
344C42—41no—
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23#1451974911yescharacteristic
350C23#1451975911yescharacteristic
351C23#1451976111yescharacteristic
352Q8—41no—
353Q8—41no—
354Q8—81no—
355Q8—4881no—
356Q8—2441no—
357Q8—2441no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—4881no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451974711yescharacteristic
382C2×C4#1451974811yescharacteristic
383C2×C4#1451975111yescharacteristic
384C2×C4#1451976311yescharacteristic
385C8—81no—
386C8—4881no—
387C8—2442no—
388C8—2441no—
389C8—2441no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1683967811yescharacteristic
401C22#1684003511yescharacteristic
402C22#1684003511yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—4881no—
411C4—4881no—
412C4#1683995011yescharacteristic
413C4#1683995311yescharacteristic
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2#2144706911yescharacteristic
419C2#2144708611yescharacteristic
420C2#2144710511yescharacteristic
subgroupG/H
centerC22#16839678
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1508C2
socleC22×C61#394
prime radicalC24×C61#41
hypercenter#1508D61
hypocenterC61#10559
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
241. C61#10559semidirect

Maximal subgroups

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

subgroupindex
#214565912
#214462882
#214462852
#214460042
#214443382
#214436952
C61×#15082
#1055961