Finite Group Databasebeta

← #24991670

Subgroups — #24991670

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#19137888C211yesmaximal, characteristic
3C4×#13063243C211yesmaximal, characteristic
4#19133043C211yesmaximal, characteristic
5#19133041C211yesmaximal, characteristic
6#19132488C211yesmaximal, characteristic
7C43×#1300C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583028—22no—
11#14583027—22no—
12#14582956C2211yescharacteristic
13#14582953—21no—
14#14582949—21no—
15C2×#13063243—21no—
16C4×#10621877C2211yescharacteristic
17#14582831—21no—
18#14582831C411yescharacteristic
19#14582831C411yescharacteristic
20#14582820—21no—
21#14582820C411yescharacteristic
22#14582820C411yescharacteristic
23C4×C4⋊Dic43—21no—
24C4×C4⋊Dic43—21no—
25#14582667—21no—
26#14582631—22no—
27#14582629—22no—
28C43×#432C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C43×#376C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×Dic86D411yescharacteristic
33C2×#10621877—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×C4⋊Dic43D411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4C2×C411yescharacteristic
50C2×Dic43⋊C4C2×C411yescharacteristic
51C2×C4×Dic43—21no—
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C4⋊(C43⋊C8)D412yes—
55Dic43⋊C8—22no—
56Dic43⋊C8—22no—
57#13063243—24no—
58C22⋊(C43⋊C8)—21no—
59#13063236—21no—
60#13063236—21no—
61#13063235—22no—
62C4×C43⋊C8—21no—
63C8×Dic43—22no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C2×M16×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43D412yes—
72C22⋊C8×C43—21no—
73#97×C43—21no—
74#97×C43—21no—
75C4×C8×C43—21no—
76#95×C43—21no—
77#95×C43C2×C411yescharacteristic
78#95×C43C2×C411yescharacteristic
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—22no—
95C2×Dic86—42no—
96C2×Dic86—41no—
97M16×C43—22no—
98M16×C43—41no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C42×C43—24no—
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C42×C43#4111yescharacteristic
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—42no—
111C4⋊Dic43—42no—
112C4⋊Dic43—42no—
113C4⋊Dic43—42no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116Dic43⋊C4—21no—
117Dic43⋊C4—21no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126#10621877—22no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C23×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C4×D411yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12311yescharacteristic
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—22no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43#10412yes—
163Dic86—22no—
164Dic86—22no—
165Dic86—42no—
166Dic86—42no—
167Dic86—41no—
168Dic86—41no—
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—42no—
186C4×C43#45612yes—
187Dic43—22no—
188Dic43—41no—
189Dic43—42no—
190Dic43—41no—
191Dic43—41no—
192Dic43—81no—
193#2983—431no—
194#2399—431no—
195C4×#101—431no—
196#1491—431no—
197#1491—431no—
198#1300—431no—
199#1300D4311yescharacteristic
200C2×C43—21no—
201C2×C43—21no—
202C2×C43#187111yescharacteristic
203C2×C43#188611yescharacteristic
204C2×C43#189111yescharacteristic
205C2×C4×Q8—431no—
206C2×C4×Q8—431no—
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#376C2×D4311yescharacteristic
225#343—861no—
226Q8⋊C8—862no—
227Q8⋊C8—862no—
228C43#903011yescharacteristic, complemented, Sylow
229C22×Q8—431no—
230C22×Q8—431no—
231C2×M16—21no—
232C2×M16—861no—
233C4×Q8—861no—
234C4×Q8—861no—
235C4×Q8—861no—
236C4×Q8—861no—
237C4×Q8—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×Q8—861no—
241C2×C4⋊C4—431no—
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⋊C4—861no—
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⋊C8D17212yes—
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—21no—
271#95—861no—
272#95—861no—
273#95—861no—
274#95—861no—
275#95C4×D4311yescharacteristic
276#95C4×D4311yescharacteristic
277C2×Q8—862no—
278C2×Q8—861no—
279C2×Q8—861no—
280C2×Q8—861no—
281C2×Q8—861no—
282C2×Q8—1721no—
283C2×Q8—1722no—
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—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—1722no—
312C4⋊C4—1722no—
313C4⋊C4—1722no—
314C4⋊C4—1722no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C42—24no—
318C42—861no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42—1721no—
323C42—1721no—
324C42C2×D17211yescharacteristic
325C42#1062189811yescharacteristic
326C42D4×D4311yescharacteristic
327C42#1062190211yescharacteristic
328C23C22⋊C4×D4311yescharacteristic
329Q8—862no—
330Q8—862no—
331Q8—1722no—
332Q8—1722no—
333Q8—1721no—
334Q8—1721no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
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—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4#1306328711yescharacteristic
362C2×C4C4×D17211yescharacteristic
363C2×C4#1306329511yescharacteristic
364C2×C4#1306329811yescharacteristic
365C2×C4#1306330011yescharacteristic
366C2×C4#1306331011yescharacteristic
367C8—42no—
368C8—42no—
369C8—1722no—
370C8—1722no—
371C22—21no—
372C22—21no—
373C22#1458277711yescharacteristic
374C22#104×D4311yescharacteristic
375C22#1458291411yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—42no—
383C4—862no—
384C4—3441no—
385C4—1722no—
386C4—1721no—
387C4—1721no—
388C4—1721no—
389C4#1458308312yes—
390C2—21no—
391C2—21no—
392C2#1913489611yescharacteristic
393C2#1913498711yescharacteristic
394C2#1913501211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1300C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1300D43
hypocenterC43#9030
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

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
#191378882
C4×#130632432
#191330432
#191330412
#191324882
C43×#13002
#903043