Finite Group Databasebeta

← #24997850

Subgroups — #24997850

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583295C211yesmaximal, characteristic, complemented
2C2×#14583180C211yesmaximal, characteristic
3#19139591C211yesmaximal, characteristic
4#19135517C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic
6#19132434C211yesmaximal, characteristic, complemented
7C2×C43×#332C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×#13063314—21no—
10C2×C4×D172C2211yescharacteristic
11#14583295—22no—
12#14583295—22no—
13#14583180—22no—
14#14583180—22no—
15C2×#13063259—21no—
16C2×#13063256—22no—
17C2×#13063250—22no—
18C2×#13063247—21no—
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582825—22no—
21#14582806—21no—
22#14582756—22no—
23C4×C4⋊Dic43C2211yescharacteristic
24#14582626—22no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C2×C4⋊C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C43×#332—22no—
29C22×Dic86—21no—
30C22×D172D411yescharacteristic
31C22×C4×D43—21no—
32C22×C43⋊C8—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325D412yes—
37#13063314—42no—
38#13063314—42no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×C4⋊Dic43D412yes—
47C2×(C2×D43)⋊C4—24no—
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43—21no—
50#13063259—24no—
51#13063256—28no—
52#13063250—44no—
53#13063247—24no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8D412yes—
56C43⋊#95—24no—
57C43⋊#95—21no—
58C22×Q8×C43—21no—
59C22×C8×C43—21no—
60C22×C8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43D412yes—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43D412yes—
72C23×D43—21no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C22×C4×C43—22no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×Dic43—21no—
84C22×Dic43—22no—
85C22×Dic43—41no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×D172—21no—
90C2×D172—21no—
91C2×D172SD1612yes—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C4×D43—42no—
95C2×C4×D43—42no—
96C2×Dic86—22no—
97C2×Dic86—42no—
98C2×Dic86—42no—
99C2×Dic86—41no—
100C2×C8×C43—22no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—42no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113(C2×D43)⋊C4—48no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—22no—
121C4⋊Dic43—22no—
122C4⋊Dic43—41no—
123C4⋊Dic43—41no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C2×C43⋊C8—24no—
127C2×C43⋊C8—22no—
128C23×C43#12011yescharacteristic
129C22×D43—22no—
130C22×D43—41no—
131C22×D43—42no—
132C22×D43—41no—
133C22×D43—42no—
134Q8×C43—81no—
135Q8×C43—81no—
136Q8×C43—81no—
137Q8×C43—81no—
138C2×C4×C43—22no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12711yescharacteristic
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43#13512yes—
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)12yes—
153C2×C4×C43#13711yescharacteristic
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—82no—
161D172—22no—
162D172—22no—
163D172—41no—
164D172—41no—
165C4×D43—82no—
166C4×D43—81no—
167C4×D43—81no—
168Dic86—44no—
169Dic86—81no—
170Dic86—81no—
171C8×C43—42no—
172C8×C43—81no—
173C43⋊C8—24no—
174#10074—431nomaximal, Sylow
175C22×C43#39211yescharacteristic
176C22×C43#44912yes—
177C22×C43#45011yescharacteristic
178C22×C43#45211yescharacteristic
179C22×C43#45612yes—
180C2×D43—44no—
181C2×D43—42no—
182C2×D43—82no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—82no—
188C4×C43#44811yescharacteristic
189C4×C43#44911yescharacteristic
190C4×C43#46312yes—
191C4×C43#46511yescharacteristic
192C4×C43#46811yescharacteristic
193C4×C43#49511yescharacteristic
194C4×C43#49611yescharacteristic
195Dic43—82no—
196Dic43—82no—
197Dic43—81no—
198C2×#498—431no—
199C2×#474—431no—
200#2547—431no—
201#1981—431no—
202C2×#332D4311yescharacteristic, complemented
203C2×D4⋊C8—431no—
204#1279—431no—
205C2×C43#165212yes—
206C2×C43#165412yes—
207C2×C43#200011yescharacteristic
208C2×C43#200511yescharacteristic
209C2×C43#201211yescharacteristic
210D43—82no—
211C2×C4⋊Q8—431no—
212C2×C4⋊Q8C2×D4311yescharacteristic
213C2×#124—861no—
214C2×C4×D4—431no—
215#498—862no—
216#498—862no—
217#474—862no—
218#474—862no—
219C2×#107—861no—
220C2×#106—862no—
221C2×C4⋊C8C2×D4311yescharacteristic
222C2×C4⋊C8C2×D4311yescharacteristic
223C2×#103—862no—
224C2×#102—861no—
225C2×C4×C8—431no—
226#397—862no—
227#391—861no—
228#380—862no—
229C4×C4⋊C4—431no—
230#332—22no—
231D4⋊C8—862no—
232C43#1007411yescharacteristic, complemented, Sylow
233C22×Q8—21no—
234C22×Q8—861no—
235C22×D4—431no—
236C23×C4—861no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—861no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—432no—
245C4⋊Q8—861no—
246C4⋊Q8—861no—
247C4⋊Q8—861no—
248#124—1722no—
249#124—1722no—
250C4×D4—861no—
251C4×D4—861no—
252C4×D4—861no—
253C4×D4—861no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—432no—
257C2×C4⋊C4—861no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4D17212yes—
260C2×C22⋊C4—864no—
261C2×C22⋊C4—861no—
262C2×C42—861no—
263C2×C42C22×D4311yescharacteristic
264#107—864no—
265#106—868no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8C22⋊D4312yes—
270#103—1724no—
271#102—864no—
272C4×C8—432no—
273C4×C8—861no—
274#95—864no—
275#95—861no—
276C24—861no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—862no—
284C2×Q8—1722no—
285C2×Q8—1722no—
286C2×Q8—1721no—
287C2×D4—432no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—861no—
292C2×D4—861no—
293C22×C4—22no—
294C22×C4—861no—
295C22×C4—862no—
296C22×C4—1721no—
297C22×C4—1721no—
298C22×C4—1721no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4C2×D17211yescharacteristic
302C22×C4D4×D4311yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—42no—
309C2×C8—864no—
310C2×C8—862no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—862no—
316C4⋊C4—861no—
317C4⋊C4—862no—
318C4⋊C4—861no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C4⋊C4—1721no—
322C4⋊C4—1721no—
323C22⋊C4—1728no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C42—1721no—
327C42—1721no—
328C42#1062189811yescharacteristic
329C42D4×D4311yescharacteristic
330C42D4×D4311yescharacteristic
331C42C2×C22⋊D4311yescharacteristic
332C23—862no—
333C23—1722no—
334C23—1721no—
335C23—1721no—
336C23—1722no—
337C23#1306329511yescharacteristic
338Q8—81no—
339Q8—81no—
340Q8—81no—
341Q8—81no—
342Q8—3441no—
343Q8—3441no—
344Q8—1724no—
345D4—862no—
346D4—862no—
347D4—1721no—
348D4—1721no—
349C2×C4—22no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—3442no—
354C2×C4—3442no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1721no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4#1306329311yescharacteristic
364C2×C4#1306329511yescharacteristic
365C2×C4#1306329811yescharacteristic
366C2×C4#1306329811yescharacteristic
367C2×C4#1306329911yescharacteristic
368C2×C4#1306332111yescharacteristic
369C2×C4SD16×D4311yescharacteristic
370C2×C4#1306334411yescharacteristic
371C2×C4#1306334812yes—
372C2×C4#1306334911yescharacteristic
373C2×C4#1306335212yes—
374C2×C4#1306335411yescharacteristic
375C8—42no—
376C8—81no—
377C8—864no—
378C22—3441no—
379C22—3442no—
380C22—3441no—
381C22—1722no—
382C22—1724no—
383C22#1458280811yescharacteristic
384C22#1458304712yes—
385C22#1458305111yescharacteristic
386C22#1458306211yescharacteristic
387C22#1458308412yes—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—3442no—
392C4—3441no—
393C4—3442no—
394C4#1458303611yescharacteristic
395C4#1458304111yescharacteristic
396C4#1458311712yes—
397C4#1458312711yescharacteristic
398C4#1458314411yescharacteristic
399C4#1458328411yescharacteristic
400C4#1458328511yescharacteristic
401C2—3442no—
402C2#1913386612yes—
403C2#1913388012yes—
404C2#1913559911yescharacteristic
405C2#1913563311yescharacteristic
406C2#1913567311yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenterC2×#332D43
hypocenterC43#10074
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#14583295C2semidirect
4. #19135517C2semidirect
6. #19132434C2semidirect
7. C2×C43×#332C2semidirect
202. C2×#332D43semidirect
232. C43#10074semidirect

Maximal subgroups

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

subgroupindex
C2×#145832952
C2×#145831802
#191395912
#191355172
C2×#145826262
#191324342
C2×C43×#3322
#1007443