Finite Group Databasebeta

← #24995614

Subgroups — #24995614

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142968C211yesmaximal, characteristic
2#19134449C211yesmaximal, characteristic, complemented
3#19134343C211yesmaximal, characteristic, complemented
4C2×#14582641C211yesmaximal, characteristic, complemented
5C2×#14582638C211yesmaximal, characteristic
6C2×#14582638C211yesmaximal, characteristic
7C2×C43×#330C211yesmaximal, characteristic, complemented
8C2×#13063313C2211yescharacteristic
9C2×Dic43⋊C8—21no—
10C2×#13063236C2211yescharacteristic
11C2×#13063236C2211yescharacteristic
12#14582804C411yescharacteristic
13#14582804C411yescharacteristic
14#14582800C411yescharacteristic
15#14582800C411yescharacteristic
16#14582789—21no—
17#14582789—21no—
18#14582789—21no—
19#14582789—21no—
20C42×Dic43C2211yescharacteristic
21#14582653—21no—
22#14582653—21no—
23#14582653—21no—
24#14582641—22no—
25#14582638—22no—
26#14582638—22no—
27C2×#125×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#330—22no—
31C22×Dic86C2×C411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063313—21no—
36#13063313—21no—
37#13063313—21no—
38#13063313—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43C2×C411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51Dic43⋊C8—24no—
52#13063236—21no—
53#13063236—21no—
54#13063236—21no—
55#13063236D412yes—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C22×C8×C43—21no—
61C22×C8×C43—21no—
62#125×C43—21no—
63#125×C43—21no—
64#125×C43—21no—
65#125×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43C2×C411yescharacteristic
69C2×C4⋊C4×C43C2×C411yescharacteristic
70C2×C42×C43C2311yescharacteristic
71#97×C43—21no—
72#97×C43—21no—
73#97×C43—21no—
74#97×C43D412yes—
75C23×D43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×Dic43—21no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—41no—
89C2×D172—41no—
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43#4111yescharacteristic
111C42×C43#4111yescharacteristic
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114(C2×D43)⋊C4—42no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—42no—
120C4×Dic43—22no—
121C4×Dic43—41no—
122C4×Dic43—41no—
123C4×Dic43—41no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C23×C43C2×C22⋊C411yescharacteristic
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12411yescharacteristic
157C2×C4×C43#12711yescharacteristic
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43#10412yes—
173D172—81no—
174D172—81no—
175Dic86—81no—
176Dic86—81no—
177C8×C43—42no—
178C8×C43—42no—
179C43⋊C8—42no—
180C43⋊C8—42no—
181#9688—431nomaximal, Sylow
182C22×C43#39011yescharacteristic
183C22×C43#41311yescharacteristic
184C22×C43#41311yescharacteristic
185C22×C43C2×#10411yescharacteristic
186C22×C43#42111yescharacteristic
187C22×C43#42111yescharacteristic
188C22×C43#42111yescharacteristic
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C2×D43—81no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—81no—
203C4×C43—81no—
204Dic43—22no—
205Dic43—41no—
206Dic43—41no—
207Dic43—41no—
208Dic43—81no—
209#2861—431no—
210#1767—431no—
211#1745—431no—
212C2×#330—431no—
213C2×#330D4311yescharacteristic, complemented
214C2×#329—431no—
215C2×#329—431no—
216C2×C43#152911yescharacteristic
217C2×C43#153211yescharacteristic
218C2×C43#153511yescharacteristic
219C2×C43#153511yescharacteristic
220C2×C43#196311yescharacteristic
221C2×C43#196711yescharacteristic
222C2×C43#198011yescharacteristic
223D43—161no—
224C2×#125C2×D4311yescharacteristic
225C2×#124—431no—
226C2×C4⋊C8—861no—
227C2×#97—431no—
228C2×#97—431no—
229C2×#97C2×D4311yescharacteristic
230C2×#97C2×D4311yescharacteristic
231#391—431no—
232#391—431no—
233#390—431no—
234#390—431no—
235#388—861no—
236#388—861no—
237#388—861no—
238#388—861no—
239C43—431no—
240#336—861no—
241#336—861no—
242#336—861no—
243#330—22no—
244#330—862no—
245#329—862no—
246#329—862no—
247C43#968811yescharacteristic, complemented, Sylow
248C22×Q8—431no—
249C22×D4—431no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—861no—
253C22×C8—861no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#124—861no—
259#124—861no—
260#124—861no—
261#124—861no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C4×D4311yescharacteristic
265C2×C4⋊C4C4×D4311yescharacteristic
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C42—431no—
273C2×C42—431no—
274C2×C42—431no—
275C2×C42—431no—
276C2×C42—431no—
277C2×C42—431no—
278C2×C42C22×D4311yescharacteristic
279C4⋊C8—864no—
280#97—21no—
281#97—21no—
282#97—21no—
283#97—432no—
284#97—861no—
285#97—861no—
286#97—861no—
287#97C22⋊D4312yes—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—861no—
292C24—861no—
293C2×Q8—861no—
294C2×Q8—861no—
295C2×Q8—1721no—
296C2×Q8—1721no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—1721no—
300C2×D4—1721no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—431no—
304C22×C4—431no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—861no—
308C22×C4C2×C4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—862no—
318C2×C8—862no—
319C2×C8—1721no—
320C2×C8—1721no—
321C2×C8—1721no—
322C2×C8—1721no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—1722no—
332C22⋊C4—1722no—
333C22⋊C4—1722no—
334C22⋊C4—1722no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C42—862no—
340C42—1721no—
341C42—1721no—
342C42—1721no—
343C42—1721no—
344C42—1721no—
345C42#1062189811yescharacteristic
346C42D4×D4311yescharacteristic
347C42#1062190011yescharacteristic
348C42C2×C22⋊D4311yescharacteristic
349C23—1721no—
350C23—1721no—
351C23—1721no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23C22⋊C4×D4311yescharacteristic
357Q8—3441no—
358Q8—3441no—
359D4—3441no—
360D4—3441no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—432no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4(C22⋊D43)⋊C411yescharacteristic
389C2×C4C4×C22⋊D4311yescharacteristic
390C2×C4#1306329711yescharacteristic
391C2×C4#1306329811yescharacteristic
392C2×C4#1306331111yescharacteristic
393C2×C4#1306332111yescharacteristic
394C8—42no—
395C8—42no—
396C8—1722no—
397C8—1722no—
398C22—3441no—
399C22—3441no—
400C22—3441no—
401C22—3441no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22#1458279911yescharacteristic
406C22#1458288211yescharacteristic
407C22#1458288211yescharacteristic
408C22#104×D4311yescharacteristic
409C22#1458291411yescharacteristic
410C22#1458291411yescharacteristic
411C22#1458291411yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—862no—
421C4—3441no—
422C4—1721no—
423C4—1721no—
424C4—1721no—
425C2—6881no—
426C2#1913320111yescharacteristic
427C2#1913321411yescharacteristic
428C2#1913322511yescharacteristic
429C2#1913322511yescharacteristic
430C2#1913542511yescharacteristic
431C2#1913544311yescharacteristic
432C2#1913551211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#330C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC2×#330D43
hypocenterC43#9688
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. #19134449C2semidirect
3. #19134343C2semidirect
4. C2×#14582641C2semidirect
7. C2×C43×#330C2semidirect
213. C2×#330D43semidirect
247. C43#9688semidirect

Maximal subgroups

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

subgroupindex
#191429682
#191344492
#191343432
C2×#145826412
C2×#145826382
C2×C43×#3302
#968843