Finite Group Databasebeta

← #26116579

Subgroups — #26116579

Order 12032.

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×#15689458C211yesmaximal, characteristic
2#20249201C211yesmaximal, characteristic
3#20243478C211yesmaximal, characteristic
4C2×#15688859C211yesmaximal, characteristic
5C2×#15688849C211yesmaximal, characteristic
6#20241267C211yesmaximal, characteristic
7C2×C47×#400C211yesmaximal, characteristic
8C2×#13094003C2211yescharacteristic
9#15689458—22no—
10#15689458—22no—
11C2×#13093957—21no—
12C2×#13093947—21no—
13C2×C22⋊(C47⋊C8)C2211yescharacteristic
14C2×C22⋊(C47⋊C8)C2211yescharacteristic
15#15689062—21no—
16#15689056—22no—
17#15689043—21no—
18#15688996—21no—
19#15688986—21no—
20#15688983C2211yescharacteristic
21#15688885—22no—
22#15688859—22no—
23#15688849—22no—
24C22×C4⋊C4×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C47×#400—22no—
27C47×#400—22no—
28C2×#95×C47—21no—
29C2×#95×C47—21no—
30C2×#95×C47C2211yescharacteristic
31C22×Dic94D411yescharacteristic
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34#13094003—21no—
35#13094003—21no—
36#13094003—21no—
37#13094003—21no—
38C2×C4⋊Dic47D411yescharacteristic
39C2×C4⋊Dic47D412yes—
40C2×Dic47⋊C4—21no—
41C2×Dic47⋊C4—22no—
42C2×C22⋊Dic47—21no—
43C2×C22⋊Dic47—21no—
44#13093957—24no—
45#13093947—24no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)D412yes—
50C47⋊#95—22no—
51C47⋊#95—22no—
52C47⋊#95—22no—
53C47⋊#95—21no—
54C23×C4×C47—21no—
55C23×C4×C47—21no—
56C23×C4×C47D411yescharacteristic
57C23×C4×C47D411yescharacteristic
58C23×C4×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47—21no—
68C2×C4⋊C4×C47—21no—
69C2×C4⋊C4×C47—21no—
70C2×C4⋊C4×C47D412yes—
71#95×C47—24no—
72#95×C47—24no—
73#95×C47—21no—
74#95×C47D412yes—
75C24×C47C2×D411yescharacteristic
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47—21no—
83C22×C4×C47—21no—
84C22×C4×C47—22no—
85C22×C4×C47—22no—
86C22×C4×C47—21no—
87C22×C4×C47—42no—
88C22×C4×C47—42no—
89C22×C4×C47—42no—
90C22×C4×C47—42no—
91C22×C4×C47—44no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47Q1612yes—
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47#4111yescharacteristic
103C22×Dic47—21no—
104C22×Dic47—22no—
105C22×Dic47—21no—
106C2×Dic94—21no—
107C2×Dic94—21no—
108C2×Dic94—42no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47—22no—
111C4⋊C4×C47—41no—
112C4⋊C4×C47—41no—
113C4⋊C4×C47—41no—
114C4⋊C4×C47—41no—
115C4⋊C4×C47—41no—
116C4⋊C4×C47—41no—
117C22⋊Dic47—41no—
118C22⋊Dic47—41no—
119C22⋊Dic47—41no—
120C22⋊Dic47—41no—
121C4⋊Dic47—21no—
122C4⋊Dic47—21no—
123C4⋊Dic47—42no—
124Dic47⋊C4—41no—
125Dic47⋊C4—41no—
126Dic47⋊C4—82no—
127C2×C47⋊C8—22no—
128C2×C47⋊C8—42no—
129C2×C47⋊C8—42no—
130C2×C47⋊C8—41no—
131C23×C47—22no—
132C23×C47—22no—
133C23×C47#12011yescharacteristic
134C23×C47#12011yescharacteristic
135C23×C47#12111yescharacteristic
136C23×C47C2×Q1611yescharacteristic
137C23×C47#13511yescharacteristic
138C23×C47#13711yescharacteristic
139C23×C47#13711yescharacteristic
140C2×C4×C47—22no—
141C2×C4×C47—22no—
142C2×C4×C47—22no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—44no—
156C2×C4×C47—42no—
157C2×C4×C47—42no—
158C2×C4×C47—41no—
159C2×C4×C47—42no—
160C2×C4×C47—42no—
161C2×C4×C47—82no—
162C2×C4×C47—82no—
163C2×C4×C47—82no—
164C2×C4×C47—82no—
165C2×C4×C47—81no—
166C2×C4×C47#12011yescharacteristic
167C2×C4×C47#12111yescharacteristic
168C2×C4×C47#12111yescharacteristic
169C2×C4×C47#12711yescharacteristic
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—42no—
173C2×Dic47—42no—
174C2×Dic47—42no—
175C2×Dic47—42no—
176C2×Dic47—42no—
177Dic94—42no—
178Dic94—81no—
179C47⋊C8—42no—
180C47⋊C8—81no—
181#9929—471nomaximal, Sylow
182C22×C47—22no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—22no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—21no—
190C22×C47#39211yescharacteristic
191C22×C47#45111yescharacteristic
192C22×C47#45111yescharacteristic
193C22×C47#45211yescharacteristic
194C22×C47#45211yescharacteristic
195C22×C47#45412yes—
196C22×C47#45812yes—
197C22×C47#46711yescharacteristic
198C22×C47#47011yescharacteristic
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—21no—
202C4×C47—21no—
203C4×C47—42no—
204C4×C47—82no—
205C4×C47—82no—
206C4×C47—81no—
207Dic47—82no—
208Dic47—81no—
209Dic47—81no—
210C2×#484—471no—
211#2627—471no—
212C2×#400D4711yescharacteristic
213#1824—471no—
214C2×#328—471no—
215C2×#324—471no—
216#1294—471no—
217C2×C47—21no—
218C2×C47—21no—
219C2×C47—21no—
220C2×C47—21no—
221C2×C47#161512yes—
222C2×C47#161712yes—
223C2×C47#200111yescharacteristic
224C2×C47#200311yescharacteristic
225C2×C47#202211yescharacteristic
226C2×C22⋊Q8—471no—
227C22×C4⋊C4C2×D4711yescharacteristic
228C22×C4⋊C4C2×D4711yescharacteristic
229#484—942no—
230#484—942no—
231C2×#107—941no—
232C2×#103—941no—
233C2×C22⋊C8—471no—
234C2×C22⋊C8—471no—
235#400—22no—
236#400—22no—
237#400—941no—
238#398—942no—
239#395—941no—
240#385—941no—
241#381—941no—
242#380—471no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95C2×D4711yescharacteristic
246#340—942no—
247#328—942no—
248#324—942no—
249C47#992911yescharacteristic, complemented, Sylow
250C22×Q8—471no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4C22⋊D4711yescharacteristic
254C23×C4C22⋊D4711yescharacteristic
255C23×C4C22×D4711yescharacteristic
256C22×C8—941no—
257C22×C8—941no—
258C22⋊Q8—941no—
259C22⋊Q8—941no—
260C22⋊Q8—941no—
261C22⋊Q8—941no—
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—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—471no—
274C2×C4⋊C4—472no—
275C2×C4⋊C4—942no—
276C2×C4⋊C4—941no—
277C2×C4⋊C4C22⋊D4712yes—
278C2×C22⋊C4—941no—
279C2×C22⋊C4—941no—
280#107—944no—
281#103—944no—
282C22⋊C8—472no—
283C22⋊C8—941no—
284C22⋊C8—941no—
285C22⋊C8—941no—
286#95—24no—
287#95—24no—
288#95—21no—
289#95—942no—
290#95—942no—
291#95—942no—
292#95—941no—
293#95C22⋊D4712yes—
294C24C2×C22⋊D4711yescharacteristic
295C2×Q8—941no—
296C2×Q8—941no—
297C2×Q8—1882no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—942no—
319C22×C4—941no—
320C22×C4—941no—
321C22×C4#1062533712yes—
322C22×C4D4×D4711yescharacteristic
323C22×C4D4×D4711yescharacteristic
324C22×C4D4×D4711yescharacteristic
325C22×C4#1062535211yescharacteristic
326C22×C4C2×C22⋊D4711yescharacteristic
327C22×C4C2×C22⋊D4711yescharacteristic
328C2×C8—942no—
329C2×C8—1882no—
330C2×C8—1881no—
331C2×C8—1882no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—941no—
341C4⋊C4—941no—
342C4⋊C4—3762no—
343C4⋊C4—1882no—
344C4⋊C4—1881no—
345C4⋊C4—1881no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C22⋊C4—1881no—
349C22⋊C4—1881no—
350C23—22no—
351C23—22no—
352C23#1309399211yescharacteristic
353C23#1309399311yescharacteristic
354C23#1309399611yescharacteristic
355C23C2×#1062533711yescharacteristic
356C23#1309404411yescharacteristic
357C23#1309405411yescharacteristic
358C23#1309405511yescharacteristic
359Q8—3761no—
360Q8—1882no—
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—42no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—1882no—
388C2×C4—1881no—
389C2×C4—1881no—
390C2×C4—1882no—
391C2×C4—1882no—
392C2×C4—1882no—
393C2×C4—1882no—
394C2×C4#1309399211yescharacteristic
395C2×C4#1309399511yescharacteristic
396C2×C4#1309399611yescharacteristic
397C2×C4#1309402011yescharacteristic
398C8—3761no—
399C8—1882no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22#1568903111yescharacteristic
409C22#1568927811yescharacteristic
410C22#1568927911yescharacteristic
411C22#1568928311yescharacteristic
412C22#1568928511yescharacteristic
413C22#1568929512yes—
414C22#1568931212yes—
415C22#1568936211yescharacteristic
416C22#1568937911yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—82no—
423C4—81no—
424C4—82no—
425C4—3761no—
426C4—3761no—
427C4—3762no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#2024241712yes—
433C2#2024242912yes—
434C2#2024439611yescharacteristic
435C2#2024441011yescharacteristic
436C2#2024451611yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC2×C47×#400C2
socleC23×C47#120
prime radicalC24×C47C2×D4
hypercenterC2×#400D47
hypocenterC47#9929
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
249. C47#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#156894582
#202492012
#202434782
C2×#156888592
C2×#156888492
#202412672
C2×C47×#4002
#992947