Finite Group Databasebeta

← #25005774

Subgroups — #25005774

Order 11008.

562 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 115 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#19137207C211yesmaximal, characteristic
2C2×#14582623C211yesmaximal, characteristic
3#19132544C212yesmaximal, complemented
4#19132542C212yesmaximal, complemented
5C2×C43×#323C211yesmaximal, characteristic
6C22×C22⋊Dic43C411yescharacteristic
7C22×C22⋊Dic43C411yescharacteristic
8C2×C22⋊(C43⋊C8)—21no—
9#14582772—21no—
10#14582772—21no—
11#14582771C411yescharacteristic
12#14582771C411yescharacteristic
13#14582771C2211yescharacteristic
14#14582771C2211yescharacteristic
15#14582757—21no—
16#14582757—21no—
17#14582623—21no—
18#14582623C2212yes—
19C22×C22⋊C4×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C43×#323—21no—
22C43×#323C2212yes—
23C23×Dic43—21no—
24C23×Dic43C2×C411yescharacteristic
25C23×Dic43C2×C411yescharacteristic
26C22×C43⋊C8—41no—
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—41no—
36C2×C22⋊Dic43—41no—
37C2×C22⋊Dic43C814yescomplemented
38C2×C22⋊Dic43C2×C411yescharacteristic
39C2×C22⋊Dic43C2×C411yescharacteristic
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)—41no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C25×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C22×C8×C43—41no—
50C2×C22⋊C4×C43—41no—
51C2×C22⋊C4×C43—41no—
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43C2311yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43—21no—
59C24×C43—21no—
60C24×C43—22no—
61C24×C43—81no—
62C24×C43—81no—
63C24×C43C22⋊C411yescharacteristic
64C24×C43C22⋊C411yescharacteristic
65C24×C43C2×C812yes—
66C24×C43M1612yes—
67C24×C43C22×C411yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—81no—
73C22×C4×C43—81no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—24no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—41no—
84C22×Dic43—41no—
85C22×Dic43—81no—
86C22×Dic43—81no—
87C22×Dic43—81no—
88C22×Dic43—81no—
89C2×C8×C43—42no—
90C2×C8×C43—82no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊Dic43—24no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—42no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43C2×C812yescomplemented
102C22⋊Dic43C2×C812yescomplemented
103Dic43⋊C4—81no—
104Dic43⋊C4—81no—
105Dic43⋊C4—81no—
106Dic43⋊C4—81no—
107C2×C43⋊C8—42no—
108C2×C43⋊C8—82no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—22no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43—81no—
126C23×C43—81no—
127C23×C43—82no—
128C23×C43—82no—
129C23×C43—84no—
130C23×C43C22⋊C812yes—
131C23×C43C22⋊C812yes—
132C23×C43#9911yescharacteristic
133C23×C43#9911yescharacteristic
134C23×C43#10112yes—
135C23×C43C2×C22⋊C411yescharacteristic
136C23×C43C22×C811yescharacteristic
137C23×C43C2×M1611yescharacteristic
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—84no—
163C2×Dic43—82no—
164C2×Dic43—82no—
165C8×C43—82no—
166C43⋊C8—82no—
167#11453—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—22no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—42no—
183C22×C43—42no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—82no—
189C22×C43—82no—
190C22×C43—82no—
191C22×C43—82no—
192C22×C43#32412yes—
193C22×C43#32412yes—
194C22×C43C2×C22⋊C811yescharacteristic
195C22×C43C2×#9911yescharacteristic
196C22×C43C2×#10111yescharacteristic
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201Dic43—42no—
202Dic43—42no—
203Dic43—81no—
204Dic43—81no—
205#2315—431no—
206C2×#323—431no—
207C2×#323D4311yescharacteristic
208#1326—432no—
209#1326—432no—
210C2×C43—21no—
211C2×C43—21no—
212C2×C43—22no—
213C2×C43—22no—
214C2×C43—42no—
215C2×C43—41no—
216C2×C43—41no—
217C2×C43C2×#32411yescharacteristic
218C2×C43#212111yescharacteristic
219C2×C43#212111yescharacteristic
220C22×C22⋊C4—431no—
221C22×C22⋊C4—431no—
222C22×C22⋊C4C2×D4311yescharacteristic
223C2×C22⋊C8—21no—
224C2×C22⋊C8—861no—
225#385—431no—
226#385—431no—
227#385—431no—
228#385—431no—
229#385—861no—
230#385—861no—
231#380—861no—
232#380—861no—
233#323—21no—
234#323—432no—
235#323—861no—
236#323C2×D4312yes—
237C43#1145311yescharacteristic, complemented, Sylow
238C25C4×D4311yescharacteristic
239C23×C4—431no—
240C23×C4—431no—
241C23×C4—861no—
242C23×C4D17211yescharacteristic
243C23×C4C22⋊D4311yescharacteristic
244C22×C8—41no—
245C22×C8—1721no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C22⋊C4—41no—
251C2×C22⋊C4—41no—
252C2×C22⋊C4—434no—
253C2×C22⋊C4—431no—
254C2×C22⋊C4—431no—
255C2×C22⋊C4—862no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—1721no—
260C2×C22⋊C4—1721no—
261C2×C22⋊C4C4×D4311yescharacteristic
262C2×C22⋊C4D17211yescharacteristic
263C2×C22⋊C4C22⋊D4311yescharacteristic
264C2×C22⋊C4C22×D4311yescharacteristic
265C22⋊C8—22no—
266C22⋊C8—41no—
267C22⋊C8—862no—
268C22⋊C8—1721no—
269#95—861no—
270#95—861no—
271#95—861no—
272#95—861no—
273C24—21no—
274C24—21no—
275C24—22no—
276C24—81no—
277C24—81no—
278C24C8×D4312yes—
279C24#1062187212yes—
280C24(C2×D43)⋊C411yescharacteristic
281C24(C2×D43)⋊C411yescharacteristic
282C24C2×C4×D4311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4—864no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—3441no—
295C22×C4—3441no—
296C22×C4—3441no—
297C22×C4—3441no—
298C22×C4—1721no—
299C22×C4—1721no—
300C22×C4(C2×D43)⋊C411yescharacteristic
301C22×C4(C2×D43)⋊C411yescharacteristic
302C22×C4C2×D17211yescharacteristic
303C22×C4C2×C22⋊D4311yescharacteristic
304C2×C8—42no—
305C2×C8—82no—
306C2×C8—3442no—
307C2×C8—1722no—
308C4⋊C4—3441no—
309C4⋊C4—3441no—
310C4⋊C4—3441no—
311C4⋊C4—3441no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—432no—
317C22⋊C4—432no—
318C22⋊C4—864no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—1722no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—84no—
345C23(C2×D43)⋊C812yes—
346C23(C2×D43)⋊C812yes—
347C23#1306323911yescharacteristic
348C23#1306323911yescharacteristic
349C23#1306324312yes—
350C23C2×(C2×D43)⋊C411yescharacteristic
351C23C2×C8×D4311yescharacteristic
352C23C2×#1062187211yescharacteristic
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—862no—
366C2×C4—862no—
367C2×C4—3442no—
368C2×C4—3442no—
369C2×C4—3444no—
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—1721no—
380C8—82no—
381C8—3442no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22#1458262412yes—
407C22#1458262412yes—
408C22C2×(C2×D43)⋊C811yescharacteristic
409C22C2×#1306323911yescharacteristic
410C22C2×#1306324311yescharacteristic
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—3441no—
416C4—3441no—
417C4—1722no—
418C4—1722no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—22no—
423C2—42no—
424C2—41no—
425C2—41no—
426C2C2×#1458262411yescharacteristic
427C2#1913623911yescharacteristic
428C2#1913624211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC23×C43C22×C8
FrattiniC2×C22⋊C4C22×D43
FittingC2×C43×#323C2
socleC22×C43C2×#99
prime radicalC25×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenterC2×#323D43
hypocenterC43#11453
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #19132544C2semidirect
4. #19132542C2semidirect
37. C2×C22⋊Dic43C8semidirect
101. C22⋊Dic43C2×C8semidirect
102. C22⋊Dic43C2×C8semidirect
237. C43#11453semidirect

Maximal subgroups

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

subgroupindex
#191372072
C2×#145826232
#191325442
#191325422
C2×C43×#3232
#1145343