Finite Group Databasebeta

← #24991668

Subgroups — #24991668

Order 11008.

484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#19143679C211yesmaximal, characteristic
2#19137886C211yesmaximal, characteristic
3C4×#13063243C211yesmaximal, characteristic
4#19133042C211yesmaximal, characteristic
5#19132489C211yesmaximal, characteristic
6#19132487C211yesmaximal, characteristic
7C43×#1491C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583028—22no—
10#14583027—22no—
11#14582956C2211yescharacteristic
12#14582953—21no—
13#14582949—21no—
14C2×#13063243—21no—
15C4×#10621877C2211yescharacteristic
16#14582830C411yescharacteristic
17#14582830C411yescharacteristic
18#14582829—21no—
19#14582819—21no—
20#14582818C411yescharacteristic
21#14582818C411yescharacteristic
22C4×Dic43⋊C4—21no—
23C4×Dic43⋊C4—21no—
24#14582745C2211yescharacteristic
25#14582667—21no—
26Q8⋊(C43⋊C8)—22no—
27C2×C4×Q8×C43C2211yescharacteristic
28C43×#432C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×Dic86D411yescharacteristic
32C2×#10621877—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C2×C4⋊Dic43D411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×Dic43⋊C4C2×C411yescharacteristic
44C2×C4×Dic43—21no—
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C4⋊(C43⋊C8)D412yes—
48Dic43⋊C8—22no—
49Dic43⋊C8—22no—
50#13063243—24no—
51C22⋊(C43⋊C8)—21no—
52#13063236—21no—
53#13063236—21no—
54#13063235—22no—
55C4×C43⋊C8—21no—
56C8×Dic43—22no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95C2×C411yescharacteristic
63C43⋊#95C2×C411yescharacteristic
64C22×Q8×C43C2×C411yescharacteristic
65C2×M16×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43D412yes—
75C22⋊C8×C43—21no—
76#97×C43—21no—
77#97×C43—21no—
78C4×C8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—42no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C22×Dic43C22⋊C411yescharacteristic
92C22×Dic43C22⋊C411yescharacteristic
93C2×Dic86—21no—
94C2×Dic86—21no—
95C2×Dic86—22no—
96C2×Dic86—41no—
97M16×C43—22no—
98M16×C43—41no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C42×C43—41no—
106C42×C43—41no—
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116Dic43⋊C4—21no—
117Dic43⋊C4—42no—
118Dic43⋊C4—42no—
119Dic43⋊C4—42no—
120Dic43⋊C4—42no—
121C4×Dic43—24no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126#10621877—22no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C23×C43C2×C22⋊C411yescharacteristic
131Q8×C43—22no—
132Q8×C43—22no—
133Q8×C43—41no—
134Q8×C43—41no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12311yescharacteristic
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43#10412yes—
167Dic86—42no—
168Dic86—42no—
169C8×C43—42no—
170C8×C43—42no—
171C43⋊C8—42no—
172C43⋊C8—42no—
173#9030—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43#38611yescharacteristic
177C22×C43C2×#10411yescharacteristic
178C22×C43#42111yescharacteristic
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—42no—
185C4×C43—81no—
186C4×C43#45612yes—
187Dic43—22no—
188Dic43—42no—
189Dic43—42no—
190Dic43—41no—
191Dic43—41no—
192Dic43—41no—
193#2983—431no—
194#2399—431no—
195C4×#101—431no—
196#1491—431no—
197#1491D4311yescharacteristic
198#1300—431no—
199#1300—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43#187111yescharacteristic
203C2×C43#188611yescharacteristic
204C2×C43#189111yescharacteristic
205C2×C4×Q8—431no—
206C2×C4×Q8C2×D4311yescharacteristic
207#446—862no—
208#446—862no—
209#432—431no—
210#432—861no—
211#432C2×D4311yescharacteristic
212#431—861no—
213C2×#101—861no—
214C4×M16—431no—
215C4×M16C2×D4311yescharacteristic
216#398—431no—
217#398—431no—
218#398—861no—
219#395—431no—
220#395—431no—
221#395—861no—
222C4×C4⋊C4—861no—
223C4×C4⋊C4—861no—
224#376—431no—
225#343—861no—
226Q8⋊C8—22no—
227Q8⋊C8—862no—
228C43#903011yescharacteristic, complemented, Sylow
229C22×Q8—431no—
230C22×Q8C4×D4311yescharacteristic
231C2×M16—21no—
232C2×M16—861no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×Q8—861no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—431no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4C4×D4311yescharacteristic
250C2×C42—21no—
251C2×C42—431no—
252C2×C42—431no—
253C2×C42—861no—
254C2×C42C22×D4311yescharacteristic
255C4⋊C8—432no—
256C4⋊C8—862no—
257C4⋊C8—862no—
258C4⋊C8C22⋊D4312yes—
259#101—864no—
260C22⋊C8—21no—
261C22⋊C8—861no—
262#97—21no—
263#97—21no—
264#97—862no—
265#97—861no—
266#97—861no—
267C4×C8—21no—
268C4×C8—862no—
269C4×C8—861no—
270#95—431no—
271#95—431no—
272#95—861no—
273#95—861no—
274#95—861no—
275#95—861no—
276#95—861no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—42no—
280C2×Q8—862no—
281C2×Q8—861no—
282C2×Q8—861no—
283C2×Q8—1721no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4C2×C4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295M16—22no—
296M16—41no—
297M16—862no—
298M16—1721no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—862no—
302C2×C8—1721no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1722no—
314C4⋊C4—1722no—
315C4⋊C4—1722no—
316C4⋊C4—1722no—
317C42—41no—
318C42—41no—
319C42—864no—
320C42—861no—
321C42—861no—
322C42—861no—
323C42—861no—
324C42#1062189811yescharacteristic
325C42D4×D4311yescharacteristic
326C42#1062190011yescharacteristic
327C42C2×C22⋊D4311yescharacteristic
328C23C22⋊C4×D4311yescharacteristic
329Q8—22no—
330Q8—22no—
331Q8—41no—
332Q8—41no—
333Q8—1722no—
334Q8—1722no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—432no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4(C22⋊D43)⋊C411yescharacteristic
362C2×C4C4×C22⋊D4311yescharacteristic
363C2×C4#1306329311yescharacteristic
364C2×C4#1306329611yescharacteristic
365C2×C4#1306329811yescharacteristic
366C2×C4#1306330711yescharacteristic
367C8—42no—
368C8—42no—
369C8—1722no—
370C8—1722no—
371C22—21no—
372C22—21no—
373C22#1458277511yescharacteristic
374C22#104×D4311yescharacteristic
375C22#1458291411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—862no—
384C4—1722no—
385C4—1722no—
386C4—1721no—
387C4—1721no—
388C4—1721no—
389C4#1458308012yes—
390C2—21no—
391C2—21no—
392C2#1913489411yescharacteristic
393C2#1913498511yescharacteristic
394C2#1913501011yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1491C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1491D43
hypocenterC43#9030
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
228. C43#9030semidirect

Maximal subgroups

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

subgroupindex
#191436792
#191378862
C4×#130632432
#191330422
#191324892
#191324872
C43×#14912
#903043