Finite Group Databasebeta

← #29580316

Subgroups — #29580316

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840098C211yesmaximal, characteristic
2#21451632C211yesmaximal, characteristic
3C2×#16839701C211yesmaximal, characteristic
4#21445910C211yesmaximal, characteristic
5C2×#16839500C211yesmaximal, characteristic
6#21443699C211yesmaximal, characteristic
7C2×C61×#324C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10#16840098—22no—
11#16840098—22no—
12C2×#14519711—21no—
13C2×#14519702—21no—
14#16839701—22no—
15#16839701—21no—
16#16839701—22no—
17#16839695—22no—
18#16839682—21no—
19#16839635—21no—
20#16839625—21no—
21#16839622C2211yescharacteristic
22C2×#14519684—21no—
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839525—22no—
26#16839500—22no—
27C22×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#324—22no—
31C22×Dic122D411yescharacteristic
32C23×Dic61—21no—
33C23×Dic61—21no—
34#14519756—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D412yes—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D412yes—
46C2×#11758196—21no—
47C2×#11758196—22no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50#14519711—24no—
51#14519702—24no—
52#14519684—22no—
53#14519684—22no—
54#14519684—22no—
55#14519684—24no—
56#14519684—24no—
57#14519684—21no—
58#14519684—21no—
59#14519684D412yes—
60C23×C4×C61D411yescharacteristic
61C23×C4×C61D411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75C24×C61C2×D411yescharacteristic
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—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61Q1612yes—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C22×Dic61—44no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—42no—
109C2×C8×C61—22no—
110C2×C8×C61—42no—
111C2×C8×C61—42no—
112C2×C8×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C4⋊Dic61—22no—
122C4⋊Dic61—21no—
123C4⋊Dic61—22no—
124C4⋊Dic61—21no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127C4⋊Dic61—42no—
128#11758196—41no—
129#11758196—41no—
130#11758196—82no—
131C23×C61—22no—
132C23×C61—22no—
133C23×C61#12011yescharacteristic
134C23×C61#12011yescharacteristic
135C23×C61#12111yescharacteristic
136C23×C61C2×Q1611yescharacteristic
137C23×C61#13511yescharacteristic
138C23×C61#13711yescharacteristic
139C23×C61#13711yescharacteristic
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
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—42no—
154C2×C4×C61—41no—
155C2×C4×C61—42no—
156C2×C4×C61—81no—
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12711yescharacteristic
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—44no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—82no—
174C2×Dic61—82no—
175C2×Dic61—82no—
176C2×Dic61—82no—
177Dic122—42no—
178Dic122—81no—
179C8×C61—42no—
180C8×C61—81no—
181#9929—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61#39211yescharacteristic
191C22×C61#45111yescharacteristic
192C22×C61#45111yescharacteristic
193C22×C61#45211yescharacteristic
194C22×C61#45211yescharacteristic
195C22×C61#45412yes—
196C22×C61#45812yes—
197C22×C61#46711yescharacteristic
198C22×C61#47011yescharacteristic
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—42no—
204C4×C61—81no—
205Dic61—82no—
206Dic61—82no—
207Dic61—81no—
208Dic61—82no—
209Dic61—81no—
210C2×#484—611no—
211#2627—611no—
212C2×#400—611no—
213#1824—611no—
214C2×#328—611no—
215C2×#324D6111yescharacteristic
216#1294—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—21no—
220C2×C61—21no—
221C2×C61#161512yes—
222C2×C61#161712yes—
223C2×C61#200111yescharacteristic
224C2×C61#200311yescharacteristic
225C2×C61#202211yescharacteristic
226C2×C22⋊Q8—611no—
227C22×C4⋊C4—611no—
228C22×C4⋊C4C2×D6111yescharacteristic
229#484—1222no—
230#484—1222no—
231C2×#107—1221no—
232C2×#103—1221no—
233C2×C22⋊C8C2×D6111yescharacteristic
234C2×C22⋊C8C2×D6111yescharacteristic
235#400—1222no—
236#400—1221no—
237#400—1222no—
238#398—1222no—
239#395—1221no—
240#385—1221no—
241#381—1221no—
242#380—611no—
243C2×#95—611no—
244C2×#95—1221no—
245C2×#95—1221no—
246#340—1222no—
247#328—1222no—
248#324—22no—
249C61#992911yescharacteristic, complemented, Sylow
250C22×Q8—611no—
251C23×C4—1221no—
252C23×C4—1221no—
253C23×C4D24411yescharacteristic
254C23×C4D24411yescharacteristic
255C23×C4C22×D6111yescharacteristic
256C22×C8—21no—
257C22×C8—21no—
258C22⋊Q8—1221no—
259C22⋊Q8—1221no—
260C22⋊Q8—1221no—
261C22⋊Q8—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—612no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—612no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1222no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280#107—1224no—
281#103—1224no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8C22⋊D6112yes—
286#95—612no—
287#95—1224no—
288#95—1224no—
289#95—1222no—
290#95—1222no—
291#95—1222no—
292#95—1221no—
293#95—1221no—
294C24C2×D24411yescharacteristic
295C2×Q8—1221no—
296C2×Q8—1221no—
297C2×Q8—2442no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1221no—
312C22×C4—1222no—
313C22×C4—1221no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2444no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4Dic24412yes—
322C22×C4#1175822211yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C22×C4C2×C22⋊D6111yescharacteristic
328C2×C8—22no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—1222no—
337C4⋊C4—1221no—
338C4⋊C4—1222no—
339C4⋊C4—1221no—
340C4⋊C4—4882no—
341C4⋊C4—2442no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C23—22no—
351C23—22no—
352C23#1451974711yescharacteristic
353C23#1451974711yescharacteristic
354C23#1451975111yescharacteristic
355C23C2×Dic24411yescharacteristic
356C23#1451979911yescharacteristic
357C23#1451981011yescharacteristic
358C23#1451981011yescharacteristic
359Q8—4881no—
360Q8—2442no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—4882no—
379C2×C4—4882no—
380C2×C4—4882no—
381C2×C4—4882no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2444no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2442no—
394C2×C4#1451974511yescharacteristic
395C2×C4#1451975011yescharacteristic
396C2×C4#1451975011yescharacteristic
397C2×C4#1451977311yescharacteristic
398C8—42no—
399C8—81no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22#1683967111yescharacteristic
409C22#1683992011yescharacteristic
410C22#1683992011yescharacteristic
411C22#1683992611yescharacteristic
412C22#1683992611yescharacteristic
413C22#1683993712yes—
414C22#1683995312yes—
415C22#1684000311yescharacteristic
416C22#1684002011yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—4882no—
424C4—4881no—
425C4—4882no—
426C4—4881no—
427C4—4882no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#2144485212yes—
433C2#2144486312yes—
434C2#2144682911yescharacteristic
435C2#2144684311yescharacteristic
436C2#2144694911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#324D61
hypocenterC61#9929
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
249. C61#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#168400982
#214516322
C2×#168397012
#214459102
C2×#168395002
#214436992
C2×C61×#3242
#992961