Finite Group Databasebeta

← #25012581

Subgroups — #25012581

Order 11008.

544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063312C211yesmaximal, characteristic
2C2×#14582693C212yesmaximal
3#19134583C211yesmaximal, characteristic
4#19132719C212yesmaximal
5C43×#1799C211yesmaximal, characteristic
6C2×#13063312C2211yescharacteristic
7C2×C4×Dic86C411yescharacteristic, complemented
8C2×#13063240C2212yes—
9#14582804C411yescharacteristic, complemented
10#14582802C2211yescharacteristic
11#14582793—21no—
12#14582793—21no—
13#14582764C411yescharacteristic, complemented
14#14582759—21no—
15C4×C22⋊Dic43—21no—
16C4×C22⋊Dic43—21no—
17C42×Dic43C411yescharacteristic, complemented
18#14582693—24no—
19#14582666—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C2×#99×C43C2212yes—
22C43×#380—21no—
23C43×#342—21no—
24C22×Dic86C2×C411yescharacteristic
25#13063312—21no—
26#13063312—21no—
27#13063312D412yes—
28#13063312Q812yes—
29C4×Dic86—41no—
30C4×Dic86—41no—
31C2×C4⋊Dic43—41no—
32C2×C4⋊Dic43C2×C411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43C2×C411yescharacteristic
44#13063240—22no—
45#13063240—22no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—41no—
51C22×D4×C43C2311yescharacteristic
52C23×C4×C43D411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C4×D4×C43—41no—
55C4×D4×C43—41no—
56C2×C4⋊C4×C43—41no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—22no—
59C2×C22⋊C4×C43D411yescharacteristic
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C42×C43C2×C411yescharacteristic
62#99×C43—22no—
63#99×C43—22no—
64#95×C43—41no—
65C24×C43C2×D411yescharacteristic
66C24×C43C2×D411yescharacteristic
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43C2×D411yescharacteristic
70C2×D4×C43C2×Q811yescharacteristic
71C2×D4×C43#4111yescharacteristic
72C2×D4×C43#4111yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22×C411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—42no—
90C2×Dic86—21no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86C4⋊C412yescomplemented
94C4⋊C4×C43—41no—
95C4⋊C4×C43—82no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—42no—
100C42×C43—21no—
101C42×C43—21no—
102C22⋊Dic43—22no—
103C22⋊Dic43—22no—
104C22⋊Dic43—22no—
105C22⋊Dic43—22no—
106C22⋊Dic43—42no—
107C22⋊Dic43—42no—
108C22⋊Dic43—42no—
109C22⋊Dic43—42no—
110C4⋊Dic43—41no—
111C4⋊Dic43—82no—
112Dic43⋊C4—42no—
113C4×Dic43—21no—
114C4×Dic43—42no—
115C4×Dic43—42no—
116C4×Dic43—41no—
117C4×Dic43—41no—
118C4×Dic43—41no—
119C4×Dic43C4⋊C412yescomplemented
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43C2×C22⋊C411yescharacteristic
129C23×C43#12111yescharacteristic
130C23×C43#12111yescharacteristic
131C23×C43C22⋊Q811yescharacteristic
132C23×C43C22⋊Q811yescharacteristic
133D4×C43—41no—
134D4×C43—41no—
135D4×C43—41no—
136D4×C43—41no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—22no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43—82no—
151C2×C4×C43—82no—
152C2×C4×C43—82no—
153C2×C4×C43#9911yescharacteristic
154C2×C4×C43#9911yescharacteristic
155C2×C4×C43C2×C4⋊C411yescharacteristic
156C2×C4×C43#11711yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—82no—
170C2×Dic43—82no—
171C2×Dic43—82no—
172Dic86—42no—
173Dic86—42no—
174#12798—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43#38011yescharacteristic
192C22×C43C2×#9911yescharacteristic
193C22×C43#41011yescharacteristic
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—162no—
201C4×C43#35412yescomplemented
202Dic43—42no—
203Dic43—42no—
204Dic43—42no—
205Dic43—81no—
206Dic43—162no—
207C4×#124—431no—
208C2×#354—432no—
209#1799—431no—
210#1799D4311yescharacteristic
211#1393—432no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—41no—
215C2×C43—41no—
216C2×C43—41no—
217C2×C43—41no—
218C2×C43#179911yescharacteristic
219C2×C43C2×#35411yescharacteristic
220C2×C43#212611yescharacteristic
221C2×#124—431no—
222C2×C4×Q8—431no—
223C2×C4×D4C2×D4311yescharacteristic
224C2×#99—432no—
225C2×#99C2×D4312yes—
226#391—431no—
227#390—431no—
228#388—861no—
229#388—861no—
230#382—431no—
231#380—21no—
232#380—861no—
233C4×C22⋊C4—861no—
234C4×C22⋊C4—861no—
235C43—431no—
236#354—864no—
237#342—21no—
238#342—861no—
239C43#1279811yescharacteristic, complemented, Sylow
240C22×Q8—431no—
241C22×D4C22×D4311yescharacteristic
242C23×C4D17211yescharacteristic
243C23×C4C22⋊D4311yescharacteristic
244#124—432no—
245#124—432no—
246#124—861no—
247#124—861no—
248C4×Q8—1721no—
249C4×Q8—1721no—
250C4×D4—41no—
251C4×D4—41no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—1721no—
256C2×C4⋊C4C4×D4311yescharacteristic
257C2×C22⋊C4—22no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—862no—
263C2×C22⋊C4D17211yescharacteristic
264C2×C22⋊C4C22⋊D4311yescharacteristic
265C2×C42—431no—
266C2×C42—431no—
267C2×C42—861no—
268C2×C42—861no—
269C2×C42—861no—
270C2×C42C4×D4311yescharacteristic
271#99—22no—
272#99—22no—
273#99—862no—
274#99—862no—
275#95—41no—
276#95—861no—
277#95—861no—
278#95—861no—
279#95—861no—
280#95—1721no—
281C24C2×D17211yescharacteristic
282C24C2×C22⋊D4311yescharacteristic
283C2×Q8—432no—
284C2×Q8—861no—
285C2×Q8—1721no—
286C2×Q8—1721no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4D4×D4311yescharacteristic
290C2×D4#1062190011yescharacteristic
291C2×D4Q8×D4311yescharacteristic
292C2×D4#1062190211yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—1722no—
305C22×C4(C2×D43)⋊C411yescharacteristic
306C22×C4(C2×D43)⋊C411yescharacteristic
307C22×C4(C2×D43)⋊C411yescharacteristic
308C22×C4(C2×D43)⋊C411yescharacteristic
309C22×C4C2×C4×D4311yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—82no—
312C4⋊C4—3442no—
313C4⋊C4—1721no—
314C4⋊C4—1722no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C22⋊C4—862no—
322C22⋊C4—862no—
323C22⋊C4—1722no—
324C22⋊C4—1722no—
325C22⋊C4—1722no—
326C22⋊C4—1722no—
327C42—21no—
328C42—21no—
329C42—432no—
330C42—861no—
331C42—1721no—
332C42—1722no—
333C42—1722no—
334C42—1721no—
335C42—1721no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23C2×(C2×D43)⋊C411yescharacteristic
345C23#1306329611yescharacteristic
346C23#1306330011yescharacteristic
347C23#1306330111yescharacteristic
348C23#1306330511yescharacteristic
349Q8—1722no—
350Q8—1722no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—862no—
372C2×C4—862no—
373C2×C4—862no—
374C2×C4—3442no—
375C2×C4—3442no—
376C2×C4—3442no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4#1306323911yescharacteristic
387C2×C4#1306323911yescharacteristic
388C2×C4C4⋊C4×D4311yescharacteristic
389C2×C4#1306328311yescharacteristic
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22#1458275611yescharacteristic
407C22C2×#1306323911yescharacteristic
408C22#1458287211yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—162no—
416C4—3441no—
417C4—1722no—
418C4—1722no—
419C4—1722no—
420C4—6882no—
421C4#1458269312yescomplemented
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2—41no—
427C2—41no—
428C2#1913458011yescharacteristic
429C2C2×#1458269311yescharacteristic
430C2#1913625811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#1799D43
hypocenterC43#12798
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic86C4semidirect
9. #14582804C4semidirect
13. #14582764C4semidirect
17. C42×Dic43C4semidirect
93. C2×Dic86C4⋊C4semidirect
119. C4×Dic43C4⋊C4semidirect
201. C4×C43#354semidirect
239. C43#12798semidirect
421. C4#14582693semidirect

Maximal subgroups

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

subgroupindex
C4×#130633122
C2×#145826932
#191345832
#191327192
C43×#17992
#1279843