Finite Group Databasebeta

← #29596789

Subgroups — #29596789

Order 15616.

504 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448967C211yesmaximal, characteristic
2#21446233C211yesmaximal, characteristic
3#21446102C211yesmaximal, characteristic
4#21446031C211yesmaximal, characteristic
5#21443943C211yesmaximal, characteristic
6#21443938C211yesmaximal, characteristic
7C2×C61×#352C211yesmaximal, characteristic
8#16840237C2211yescharacteristic
9#16839804—21no—
10C2×#14519692C2211yescharacteristic
11#16839665C2211yescharacteristic
12#16839661—21no—
13#16839655—21no—
14#16839655—21no—
15#16839648—21no—
16#16839642C2211yescharacteristic
17#16839637—21no—
18#16839637—21no—
19#16839625—21no—
20#16839622—21no—
21#16839528—21no—
22#16839528—21no—
23#16839523—21no—
24C2×#123×C61C2211yescharacteristic
25C2×#100×C61C2211yescharacteristic
26C2×#99×C61C2211yescharacteristic
27C61×#352C414yescomplemented
28C23×Dic61D411yescharacteristic
29D4×Dic61—41no—
30D4×Dic61—41no—
31#14519736—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—41no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61D411yescharacteristic
46#14519711—41no—
47#14519709—41no—
48#14519692—21no—
49#14519692—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—41no—
56#14519684—41no—
57#14519684—41no—
58C22×D4×C61C2311yescharacteristic
59C23×C4×C61D411yescharacteristic
60C2×M16×C61—21no—
61#123×C61—21no—
62#123×C61—21no—
63#123×C61C2×C412yes—
64#123×C61Q812yes—
65C2×C4⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61D411yescharacteristic
69#100×C61—21no—
70#100×C61C2×C412yes—
71#99×C61—21no—
72#99×C61C2×C412yes—
73C24×C61C2×D411yescharacteristic
74C24×C61C2×D411yescharacteristic
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61C22×C411yescharacteristic
78C2×D4×C61C2×Q811yescharacteristic
79C2×D4×C61#4111yescharacteristic
80C2×D4×C61#4111yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C4⋊C412yescomplemented
88C22×C4×C61C2×D411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C22×Dic61—81no—
100M16×C61—22no—
101M16×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—22no—
105C22⋊C4×C61—22no—
106C22⋊C4×C61—22no—
107C22⋊C4×C61—21no—
108C22⋊C4×C61—22no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61C4⋊C412yescomplemented
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117C22⋊Dic61—81no—
118C22⋊Dic61—81no—
119C22⋊Dic61—81no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—41no—
123C4⋊Dic61—81no—
124C4⋊Dic61—81no—
125C4⋊Dic61—81no—
126C4⋊Dic61—82no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129C4×Dic61—81no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61C2×C4⋊C411yescharacteristic
139C23×C61C4×D411yescharacteristic
140C23×C61#12011yescharacteristic
141C23×C61C22⋊Q811yescharacteristic
142C23×C61#12311yescharacteristic
143D4×C61—41no—
144D4×C61—41no—
145D4×C61—41no—
146D4×C61—41no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61C22⋊Q811yescharacteristic
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—81no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184C2×Dic61—81no—
185C8×C61—42no—
186#12961—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61#38511yescharacteristic
204C22×C61B(4,𝔽2)11yescharacteristic
205C22×C61#45811yescharacteristic
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—42no—
209C4×C61—42no—
210C4×C61—82no—
211Dic61—81no—
212Dic61—81no—
213Dic61—81no—
214Dic61—81no—
215Dic61—81no—
216Dic61—81no—
217Dic61—161no—
218#2376—611no—
219C2×#352D6111yescharacteristic
220#1890—611no—
221#1867—611no—
222#1856—611no—
223#1393—611no—
224#1390—611no—
225C2×C61—21no—
226C2×C61—21no—
227C2×C61—41no—
228C2×C61—41no—
229C2×C61—41no—
230C2×C61—41no—
231C2×C61#186711yescharacteristic
232C2×C61#220011yescharacteristic
233C2×C61#220111yescharacteristic
234C2×#123C2×D6111yescharacteristic
235#518—611no—
236#428—1221no—
237C2×#100C2×D6111yescharacteristic
238C2×#99—611no—
239C2×#99C2×D6111yescharacteristic
240#390—611no—
241#389—1221no—
242#388—1221no—
243#388—1221no—
244#387—1221no—
245#386—611no—
246#385—1221no—
247#385—1221no—
248#381—1221no—
249#380—1221no—
250#352Dic6114yescomplemented
251#342—1221no—
252#342—1221no—
253#339—1221no—
254C61#1296111yescharacteristic, complemented, Sylow
255C22×D4C22×D6111yescharacteristic
256C23×C4—611no—
257C23×C4D24411yescharacteristic
258C2×M16—21no—
259#123—21no—
260#123—21no—
261#123Dic12212yes—
262#123C2×Dic6112yes—
263C4×D4—2441no—
264C4×D4—2441no—
265#117—1221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—2441no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4D24411yescharacteristic
282C2×C42—611no—
283C2×C42—1221no—
284#107—2441no—
285#106—2441no—
286#100—21no—
287#100C2×Dic6112yes—
288#99—21no—
289#99—1221no—
290#99—1221no—
291#99C2×Dic6112yes—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297#95—2441no—
298#95—2441no—
299#95—2441no—
300C24C2×D24411yescharacteristic
301C24D4×D6111yescharacteristic
302C2×D4—41no—
303C2×D4—41no—
304C2×D4C2×Dic12211yescharacteristic
305C2×D4#1175822411yescharacteristic
306C2×D4#1175822411yescharacteristic
307C2×D4C22×Dic6111yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—4881no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4C4⋊Dic6112yescomplemented
326C22×C4D4×D6111yescharacteristic
327M16—22no—
328M16—41no—
329C2×C8—41no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—4881no—
335C4⋊C4—4881no—
336C4⋊C4—4881no—
337C4⋊C4—4882no—
338C4⋊C4—2441no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—21no—
342C22⋊C4—22no—
343C22⋊C4—41no—
344C22⋊C4—4881no—
345C22⋊C4—4881no—
346C22⋊C4—4881no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4C4⋊Dic6112yescomplemented
354C42—4881no—
355C42—2441no—
356C42—2441no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C2×C4⋊Dic6111yescharacteristic
366C23D4×Dic6111yescharacteristic
367C23#1451974711yescharacteristic
368C23#1451975411yescharacteristic
369C23#1451976111yescharacteristic
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—4881no—
390C2×C4—4881no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—4881no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4D4×Dic6111yescharacteristic
411C2×C4#1451975411yescharacteristic
412C8—42no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—81no—
428C22—81no—
429C22#1683963711yescharacteristic
430C22#1683995011yescharacteristic
431C22#1683995311yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4—9761no—
438C4—4881no—
439C4—4881no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—4881no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—41no—
450C2#2144610211yescharacteristic
451C2#2144782711yescharacteristic
452C2#2144783311yescharacteristic
subgroupG/H
centerC22#16839950
commutatorC2×D4×C61C22×C4
FrattiniC22×D4C22×D61
FittingC2×C61×#352C2
socleC22×C61B(4,𝔽2)
prime radical, cosocleC22×D4×C61C23
hypercenterC2×#352D61
hypocenterC61#12961
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
27. C61×#352C4semidirect
87. C22×C4×C61C4⋊C4semidirect
110. C22⋊C4×C61C4⋊C4semidirect
250. #352Dic61semidirect
254. C61#12961semidirect
325. C22×C4C4⋊Dic61semidirect
353. C22⋊C4C4⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
#214489672
#214462332
#214461022
#214460312
#214439432
#214439382
C2×C61×#3522
#1296161