Finite Group Databasebeta

← #29599685

Subgroups — #29599685

Order 15616.

476 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 81 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#21446099C211yesmaximal, characteristic
2#21446099C211yesmaximal, characteristic
3#21446028C211yesmaximal, characteristic
4#21443944C211yesmaximal, characteristic
5#21443937C211yesmaximal, characteristic
6#21443937C211yesmaximal, characteristic
7C61×#2748C211yesmaximal, characteristic
8#16840237C2211yescharacteristic
9#16839802—21no—
10C2×#14519694C2211yescharacteristic
11C2×#14519692C2211yescharacteristic
12C2×#14519692C2211yescharacteristic
13#16839635—21no—
14#16839635—21no—
15#16839528—21no—
16#16839528—21no—
17#16839522—21no—
18C61×#399—21no—
19C61×#398—21no—
20C61×#396—21no—
21C61×#390C2211yescharacteristic
22C61×#387—21no—
23C61×#386C2211yescharacteristic
24C61×#386C2211yescharacteristic
25C61×#385—21no—
26C61×#380—21no—
27C2×#11758194—21no—
28D4×Dic61—41no—
29D4×Dic61—41no—
30#14519736—21no—
31C2×#11758196—41no—
32C2×#11758196—41no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37#14519710—41no—
38#14519708—41no—
39#14519694—21no—
40#14519694Q812yes—
41#14519692—21no—
42#14519692—21no—
43#14519692Q812yes—
44#14519692Q812yes—
45#14519684—41no—
46#14519684—41no—
47C22×D4×C61C2311yescharacteristic
48C23×C4×C61D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C22⋊C4×C61D411yescharacteristic
62C2×C42×C61D411yescharacteristic
63#95×C61—21no—
64#95×C61—21no—
65#95×C61—21no—
66#95×C61—21no—
67#95×C61—21no—
68C24×C61C2×D411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61C2×Q811yescharacteristic
73C2×D4×C61C2×Q811yescharacteristic
74C2×D4×C61C2×Q811yescharacteristic
75C2×D4×C61#4111yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—42no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—81no—
86C22×C4×C61C2×D411yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C4⋊C4×C61—42no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—81no—
96C4⋊C4×C61—81no—
97C4⋊C4×C61—81no—
98C4⋊C4×C61—81no—
99C22⋊C4×C61—42no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—81no—
103C22⋊C4×C61—81no—
104C22⋊C4×C61—81no—
105C42×C61—41no—
106C22⋊Dic61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115#11758196—82no—
116#11758196—82no—
117C4×Dic61—41no—
118#11758194—22no—
119#11758194—41no—
120C2×#92418—41no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61#12011yescharacteristic
130C23×C61C22⋊Q811yescharacteristic
131C23×C61C22⋊Q811yescharacteristic
132C23×C61C4⋊Q811yescharacteristic
133C23×C61C4⋊Q811yescharacteristic
134D4×C61—41no—
135D4×C61—41no—
136D4×C61—41no—
137D4×C61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61C22⋊Q811yescharacteristic
163C2×C4×C61C4⋊Q811yescharacteristic
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174C2×Dic61—81no—
175C2×Dic61—81no—
176#92418—42no—
177#13462—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61#39511yescharacteristic
195C22×C61B(4,𝔽2)11yescharacteristic
196C22×C61#45811yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—42no—
200C4×C61—81no—
201C4×C61—81no—
202C4×C61—81no—
203C4×C61—81no—
204C4×C61—81no—
205Dic61—82no—
206Dic61—82no—
207Dic61—81no—
208Dic61—81no—
209#2748D6111yescharacteristic
210#1867—611no—
211#1867—611no—
212#1856—611no—
213#1393—611no—
214#1390—611no—
215#1390—611no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—41no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61—41no—
222C2×C61#206211yescharacteristic
223C2×C61#219711yescharacteristic
224C2×C61#220011yescharacteristic
225#518—611no—
226#428—1221no—
227C2×#100—611no—
228C2×#99—611no—
229C2×#99—611no—
230#399—21no—
231#398—21no—
232#396—21no—
233#390C2×D6111yescharacteristic
234#387—21no—
235#386C2×D6111yescharacteristic
236#386C2×D6111yescharacteristic
237#385—21no—
238#385—1221no—
239#385—1221no—
240#380—21no—
241#342—1221no—
242#342—1221no—
243#339—1221no—
244C61#1346211yescharacteristic, complemented, Sylow
245C22×D4C22×D6111yescharacteristic
246C23×C4C22⋊D6111yescharacteristic
247C23×C4C22⋊D6111yescharacteristic
248C2×M16—1221no—
249C4×D4—2441no—
250C4×D4—2441no—
251#117—1221no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—2441no—
258C2×C4⋊C4—2441no—
259C2×C4⋊C4C22⋊D6111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4C22⋊D6111yescharacteristic
269C2×C22⋊C4C22⋊D6111yescharacteristic
270C2×C42C22⋊D6111yescharacteristic
271#107—2441no—
272#106—2441no—
273#100—612no—
274#100—1221no—
275#99—612no—
276#99—612no—
277#99—1221no—
278#99—1221no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—2441no—
285#95—2441no—
286C24C2×C22⋊D6111yescharacteristic
287C24C2×C22⋊D6111yescharacteristic
288C2×D4—41no—
289C2×D4—41no—
290C2×D4Q8×D6111yescharacteristic
291C2×D4Q8×D6111yescharacteristic
292C2×D4Q8×D6111yescharacteristic
293C2×D4#1175822611yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—81no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4C2×C22⋊D6111yescharacteristic
311M16—1222no—
312M16—2441no—
313C2×C8—2441no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C4⋊C4—81no—
317C4⋊C4—81no—
318C4⋊C4—81no—
319C4⋊C4—81no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—4882no—
323C4⋊C4—4882no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C42—41no—
338C42—2441no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#1451974611yescharacteristic
348C23#1451975311yescharacteristic
349C23#1451975311yescharacteristic
350C23#1451977511yescharacteristic
351C23#1451977511yescharacteristic
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
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—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—4881no—
386C2×C4—4881no—
387C2×C4—4881no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4#1451975311yescharacteristic
393C2×C4#1451977511yescharacteristic
394C8—2442no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22#1683968111yescharacteristic
412C22#1683994911yescharacteristic
413C22#1683995211yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—4882no—
423C4—4882no—
424C4—4881no—
425C4—4881no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—41no—
431C2—41no—
432C2#2144717111yescharacteristic
433C2#2144780911yescharacteristic
434C2#2144782611yescharacteristic
subgroupG/H
centerC22#16839949
commutator, prime radical, cosocleC22×D4×C61C23
FrattiniC22×D4C22×D61
FittingC61×#2748C2
socleC22×C61B(4,𝔽2)
hypercenter#2748D61
hypocenterC61#13462
LCSG ▷ C22×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2748

Complements

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

NH ≅ G/Ntype
244. C61#13462semidirect

Maximal subgroups

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

subgroupindex
#214460992
#214460282
#214439442
#214439372
C61×#27482
#1346261