Finite Group Databasebeta

← #29574119

Subgroups — #29574119

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454867C211yesmaximal, characteristic
2#21446122C211yesmaximal, characteristic
3#21446026C211yesmaximal, characteristic, complemented
4#21446004C211yesmaximal, characteristic, complemented
5#21443705C211yesmaximal, characteristic, complemented
6#21443665C211yesmaximal, characteristic, complemented
7C61×#1501C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9#16839840—21no—
10#16839834—21no—
11#16839834—21no—
12D4×#92418—21no—
13#16839823—21no—
14C2×#14519713—21no—
15C2×C4⋊#92418—21no—
16C2×#14519704—21no—
17#16839729—21no—
18#16839726C2211yescharacteristic
19C2×C22⋊#92418C2211yescharacteristic
20C4×C22⋊Dic61C2211yescharacteristic
21#16839527—21no—
22#16839521—21no—
23#16839517—21no—
24C61×#525C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C61×#328C411yescharacteristic, complemented
28C61×#328C411yescharacteristic, complemented
29C61×#327C411yescharacteristic, complemented
30C61×#327C411yescharacteristic, complemented
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758194—42no—
35C2×#11758194D411yescharacteristic
36C2×#11758194D411yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61—21no—
43#14519713—42no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—42no—
47#14519704—42no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519688—21no—
55C4×#92418—21no—
56#14519684—21no—
57C2×#41×C61D411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C22×C8×C61—21no—
60#123×C61—21no—
61C22⋊Q8×C61C2×C411yescharacteristic
62C22⋊Q8×C61Q811yescharacteristic
63#121×C61C2×C411yescharacteristic
64#121×C61Q811yescharacteristic
65#120×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68#117×C61D411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C42×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61C2×C411yescharacteristic
73C22⋊C8×C61C2×C411yescharacteristic
74#95×C61C2×C411yescharacteristic
75#95×C61C2×C411yescharacteristic
76C24×C61#4111yescharacteristic
77#41×C61—41no—
78#41×C61—41no—
79C2×Q8×C61C4⋊C411yescharacteristic
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61C4⋊C411yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×Q811yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×Dic61—41no—
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61C4⋊C411yescharacteristic
103C4⋊C4×C61C4⋊C411yescharacteristic
104C22⋊C4×C61—21no—
105C22⋊C4×C61—21no—
106C22⋊C4×C61—21no—
107C22⋊C4×C61—21no—
108C22⋊C4×C61—21no—
109C22⋊C4×C61—42no—
110C42×C61—21no—
111C42×C61—41no—
112C42×C61—41no—
113C22⋊Dic61—22no—
114C22⋊Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117#11758194—22no—
118#11758194—22no—
119#11758194—41no—
120#11758194—41no—
121#11758194—41no—
122#11758194—41no—
123#11758194—81no—
124C2×#92418—22no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—81no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C4×D411yescharacteristic
140C23×C61C22⋊Q811yescharacteristic
141C23×C61#12311yescharacteristic
142Q8×C61—41no—
143D4×C61—41no—
144D4×C61—41no—
145D4×C61—41no—
146D4×C61—81no—
147D4×C61—81no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—22no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61C2×C4⋊C411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61C22⋊Q811yescharacteristic
172C2×Dic61—42no—
173C2×Dic61—81no—
174C2×Dic61—81no—
175C8×C61—41no—
176C8×C61—41no—
177#92418—42no—
178#92418—41no—
179#92418—41no—
180#92418—41no—
181#92418—41no—
182#8874—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61#38511yescharacteristic
197C22×C61#44311yescharacteristic
198C22×C61#44411yescharacteristic
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—42no—
203C4×C61—41no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—81no—
207C4×C61B(4,𝔽2)11yescharacteristic
208C4×C61#45811yescharacteristic
209Dic61—82no—
210#2976—611no—
211#1871—611no—
212#1855—611no—
213#1851—611no—
214#1501D6111yescharacteristic
215#1297—611no—
216#1282—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61—81no—
222C2×C61#186111yescharacteristic
223C2×C61#186611yescharacteristic
224C2×C61#186711yescharacteristic
225C22×M16—611no—
226#525C2×D6111yescharacteristic
227#436—1221no—
228#435—1221no—
229#435—1221no—
230C8×D4—1221no—
231#433—1221no—
232C2×#108—1221no—
233C2×C4⋊C8—1221no—
234C2×#104—1221no—
235#408—1221no—
236#407—611no—
237C2×C22⋊C8—611no—
238C2×C22⋊C8C2×D6111yescharacteristic
239C4×C22⋊C4—611no—
240C4×C22⋊C4C2×D6111yescharacteristic
241#341—1221no—
242#339—1221no—
243#336—1221no—
244#328Dic6111yescharacteristic, complemented
245#328Dic6111yescharacteristic, complemented
246#327Dic6111yescharacteristic, complemented
247#327Dic6111yescharacteristic, complemented
248C61#887411yescharacteristic, complemented, Sylow
249C2×#41D24411yescharacteristic
250C23×C4C22×D6111yescharacteristic
251C2×M16—611no—
252C2×M16—611no—
253C2×M16—1221no—
254C2×M16—1221no—
255C2×M16—1221no—
256C2×M16—2442no—
257C22×C8—21no—
258C22×C8—611no—
259C22×C8—611no—
260C22×C8—1221no—
261C22×C8—1221no—
262#123—21no—
263C22⋊Q8Dic12211yescharacteristic
264C22⋊Q8C2×Dic6111yescharacteristic
265#121Dic12211yescharacteristic
266#121C2×Dic6111yescharacteristic
267#120—21no—
268C4×D4—21no—
269C4×D4—21no—
270#117D24411yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—1221no—
273C2×C42—21no—
274C2×C42—1221no—
275#108—2442no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—2442no—
279#104—2442no—
280C22⋊C8—21no—
281C22⋊C8—1221no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8—1221no—
287C22⋊C8C2×Dic6111yescharacteristic
288C22⋊C8C2×Dic6111yescharacteristic
289#97—1221no—
290C4×C8—1221no—
291#95—1221no—
292#95C2×Dic6111yescharacteristic
293#95C2×Dic6111yescharacteristic
294C24#1175822411yescharacteristic
295#41—41no—
296#41—41no—
297C2×Q8C4⋊Dic6111yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4C4⋊Dic6111yescharacteristic
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—2441no—
308C22×C4C2×Dic12211yescharacteristic
309C22×C4C2×D24411yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4#1175822411yescharacteristic
313C22×C4C22×Dic6111yescharacteristic
314M16—1222no—
315M16—1222no—
316M16—4881no—
317M16—2441no—
318M16—2441no—
319M16—2441no—
320M16—2441no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—1222no—
326C2×C8—1221no—
327C2×C8—1221no—
328C2×C8—1221no—
329C2×C8—1221no—
330C2×C8—4881no—
331C2×C8—2441no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4C4⋊Dic6111yescharacteristic
338C4⋊C4C4⋊Dic6111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—42no—
345C22⋊C4—1222no—
346C22⋊C4—2441no—
347C42—21no—
348C42—41no—
349C42—41no—
350C42—2441no—
351C42—2441no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23D4×Dic6111yescharacteristic
358C23#1451975411yescharacteristic
359C23#1451976111yescharacteristic
360Q8—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—4881no—
387C2×C4—4881no—
388C2×C4—2442no—
389C2×C4C2×C4⋊Dic6111yescharacteristic
390C2×C4D4×Dic6111yescharacteristic
391C2×C4#1451974711yescharacteristic
392C2×C4#1451975411yescharacteristic
393C8—41no—
394C8—41no—
395C8—2441no—
396C8—2441no—
397C8—2442no—
398C8—2441no—
399C8—2441no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1683963711yescharacteristic
414C22#1683987911yescharacteristic
415C22#1683988411yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—81no—
424C4—4882no—
425C4#1683995011yescharacteristic
426C4#1683995311yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—81no—
432C2#2144606111yescharacteristic
433C2#2144609611yescharacteristic
434C2#2144610211yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1501C2
socleC22×C61#385
prime radicalC61×#525C22
cosocleC23×C4×C61C23
hypercenter#1501D61
hypocenterC61#8874
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
3. #21446026C2semidirect
4. #21446004C2semidirect
5. #21443705C2semidirect
6. #21443665C2semidirect
27. C61×#328C4semidirect
28. C61×#328C4semidirect
29. C61×#327C4semidirect
30. C61×#327C4semidirect
244. #328Dic61semidirect
245. #328Dic61semidirect
246. #327Dic61semidirect
247. #327Dic61semidirect
248. C61#8874semidirect

Maximal subgroups

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

subgroupindex
#214548672
#214461222
#214460262
#214460042
#214437052
#214436652
C61×#15012
#887461