Finite Group Databasebeta

← #24993020

Subgroups — #24993020

Order 11008.

552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#14583227C211yesmaximal, characteristic
2#19137466C211yesmaximal, characteristic
3#19135581C211yesmaximal, characteristic
4#19134682C211yesmaximal, characteristic
5#19132462C211yesmaximal, characteristic
6#19132441C211yesmaximal, characteristic
7C43×#1520C211yesmaximal, characteristic
8C2×#13063281—21no—
9C22×C4⋊Dic43C2211yescharacteristic
10#14583227—21no—
11#14583227—22no—
12#14583227—21no—
13C2×#13063256C412yescomplemented
14C2×#13063249C412yescomplemented
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582795—21no—
17#14582782—22no—
18#14582760—21no—
19#14582759C2211yescharacteristic
20C4⋊C4×Dic43—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582666—21no—
23#14582666—21no—
24#14582662—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#328—22no—
29C23×Dic43—21no—
30C22×C43⋊C8C2×C412yes—
31#13063281—42no—
32#13063281—42no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2×C412yes—
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D412yes—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43D411yescharacteristic
44C2×C22⋊Dic43D411yescharacteristic
45C2×C4×Dic43—22no—
46C2×C4×Dic43—21no—
47#13063256—22no—
48#13063256—22no—
49#13063249—22no—
50#13063249—22no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C22×Q8×C43C2×C411yescharacteristic
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43C2×C411yescharacteristic
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71#95×C43D412yes—
72C24×C43C2×D411yescharacteristic
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—42no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—22no—
79C22×C4×C43—42no—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43#4111yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—41no—
93C22×Dic43—41no—
94C22×Dic43—41no—
95C22×Dic43—41no—
96C22×Dic43—41no—
97C2×C8×C43—42no—
98C2×C8×C43—41no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊Dic43—21no—
109C22⋊Dic43—21no—
110C22⋊Dic43—21no—
111C22⋊Dic43—41no—
112C22⋊Dic43—41no—
113C22⋊Dic43SD1612yes—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—42no—
119C4⋊Dic43C22⋊C412yes—
120C4⋊Dic43C22⋊C412yes—
121Dic43⋊C4—44no—
122C4×Dic43—44no—
123C4×Dic43—42no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—42no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43C4×D411yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12111yescharacteristic
131C23×C43C2×SD1611yescharacteristic
132C23×C43#13511yescharacteristic
133C23×C43AGL(1,ℤ/8)11yescharacteristic
134C23×C43#13711yescharacteristic
135Q8×C43—42no—
136Q8×C43—81no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43C2×C22⋊C411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12311yescharacteristic
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43—22no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—81no—
171C2×Dic43—81no—
172C2×Dic43—81no—
173C8×C43—81no—
174C43⋊C8—42no—
175#9256—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43#38611yescharacteristic
187C22×C43C4×SD1611yescharacteristic
188C22×C43#44011yescharacteristic
189C22×C43#45011yescharacteristic
190C22×C43#45211yescharacteristic
191C22×C43#46111yescharacteristic
192C22×C43#46311yescharacteristic
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—82no—
197C4×C43—81no—
198C4×C43—81no—
199C4×C43#41012yes—
200Dic43—42no—
201Dic43—42no—
202Dic43—42no—
203Dic43—81no—
204Dic43—161no—
205C2×#483—431no—
206#2344—431no—
207#1996—431no—
208#1823—431no—
209#1520D4311yescharacteristic
210#1289—431no—
211#1282—431no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43#187711yescharacteristic
219C2×C43#189911yescharacteristic
220C2×C43#190511yescharacteristic
221C2×C22⋊Q8C2×D4311yescharacteristic
222C2×#117—861no—
223C22×C4⋊C4—431no—
224#483—862no—
225#483—861no—
226#483—861no—
227C2×#106—432no—
228C2×#103—432no—
229C2×C22⋊C8—431no—
230C2×C22⋊C8C2×D4311yescharacteristic
231#389—861no—
232#387—862no—
233#381—861no—
234#380—431no—
235#380C2×D4311yescharacteristic
236C4×C4⋊C4—861no—
237C4×C22⋊C4—431no—
238#342—861no—
239#342—861no—
240#340—862no—
241#328—22no—
242C43#925611yescharacteristic, complemented, Sylow
243C22×Q8C4×D4311yescharacteristic
244C23×C4—861no—
245C23×C4C22×D4311yescharacteristic
246C22×C8—21no—
247C22×C8—432no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252#117—1722no—
253#117—1722no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—432no—
257C2×C4⋊C4—432no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—862no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C4×D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—431no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—861no—
271C2×C42—862no—
272C2×C42—861no—
273#106—862no—
274#106—862no—
275#103—862no—
276#103—862no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—861no—
280C22⋊C8—861no—
281#95—862no—
282#95—862no—
283#95—861no—
284#95—861no—
285#95C22⋊D4312yes—
286C24D4×D4311yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—862no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4—862no—
299C22×C4—861no—
300C22×C4—1721no—
301C22×C4—1721no—
302C22×C4—1721no—
303C22×C4—1721no—
304C22×C4—1721no—
305C22×C4C2×C4×D4311yescharacteristic
306C22×C4#1062189811yescharacteristic
307C22×C4D4×D4311yescharacteristic
308C22×C4D4×D4311yescharacteristic
309C22×C4#1062190011yescharacteristic
310C22×C4C2×C22⋊D4311yescharacteristic
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—862no—
314C2×C8—1722no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—432no—
321C4⋊C4—432no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—1722no—
327C4⋊C4—1724no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—432no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C22⋊C4—1721no—
337C22⋊C4—1721no—
338C42—1722no—
339C42—1724no—
340C23—41no—
341C23—41no—
342C23(C22⋊D43)⋊C411yescharacteristic
343C23#1306329311yescharacteristic
344C23#1306329811yescharacteristic
345C23SD16×D4311yescharacteristic
346C23#1306334811yescharacteristic
347C23#1306335211yescharacteristic
348C23#1306335711yescharacteristic
349Q8—42no—
350Q8—81no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—862no—
365C2×C4—862no—
366C2×C4—862no—
367C2×C4—3441no—
368C2×C4—3441no—
369C2×C4—3441no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4C22⋊C4×D4311yescharacteristic
384C2×C4C4×C22⋊D4311yescharacteristic
385C2×C4#1306329611yescharacteristic
386C2×C4#1306330711yescharacteristic
387C8—81no—
388C8—1722no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22#1458277511yescharacteristic
400C22#1458298411yescharacteristic
401C22#1458300211yescharacteristic
402C22#1458304811yescharacteristic
403C22#1458306011yescharacteristic
404C22#1458310311yescharacteristic
405C22#1458311711yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—82no—
410C4—81no—
411C4—81no—
412C4—3441no—
413C4—1722no—
414C4—1722no—
415C4—1722no—
416C4—6881no—
417C4#1458287112yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2#1913492611yescharacteristic
425C2#1913505011yescharacteristic
426C2#1913508611yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1520C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1520D43
hypocenterC43#9256
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
13. C2×#13063256C4semidirect
14. C2×#13063249C4semidirect
242. C43#9256semidirect

Maximal subgroups

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

subgroupindex
C2×#145832272
#191374662
#191355812
#191346822
#191324622
#191324412
C43×#15202
#925643