Finite Group Databasebeta

← #24988251

Subgroups — #24988251

Order 11008.

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

normal subgroups only

This group has 814 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
1C2×#14583595C211yesmaximal, characteristic
2C4×#13063242C211yesmaximal, characteristic, complemented
3#19133198C212yesmaximal, complemented
4#19133037C212yesmaximal, complemented
5C43×#1466C211yesmaximal, characteristic, complemented
6#14583595—24no—
7#14583595—24no—
8C2×#13063320—21no—
9C2×#13063317C2211yescharacteristic
10C2×#13063307—21no—
11C2×#13063299C411yescharacteristic
12C2×#13063299C411yescharacteristic
13C2×#13063297—21no—
14C2×C4×D172C2211yescharacteristic
15C2×(C22⋊D43)⋊C4—21no—
16C2×#13063284C411yescharacteristic
17C22×C4⋊Dic43C411yescharacteristic
18C2×#13063242—21no—
19C4×#10621877C2212yes—
20#14582668—21no—
21#14582640—24no—
22#14582626—24no—
23C2×C4×D4×C43C2211yescharacteristic
24C43×#432C2212yes—
25C43×#323—21no—
26C43×#323—21no—
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C22⋊D43—21no—
30C23×Dic43—21no—
31C22×C4×D43—21no—
32C2×#10621877—22no—
33#13063320—28no—
34#13063317—22no—
35#13063317D414yes—
36#13063307—28no—
37#13063299—22no—
38#13063299—22no—
39#13063299—22no—
40#13063299—22no—
41#13063297—28no—
42C4×D172—22no—
43C4×D172D414yes—
44(C22⋊D43)⋊C4—28no—
45#13063284—22no—
46#13063284—22no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43C2×C411yescharacteristic
51C2×C4⋊Dic43C2×C411yescharacteristic
52C2×C4⋊Dic43C2×C411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×C22⋊Dic43—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59C2×C4×Dic43—21no—
60#13063242—24no—
61#13063236—22no—
62C4×C43⋊C8—22no—
63C22×D4×C43D411yescharacteristic
64C23×C4×C43C2×C411yescharacteristic
65C23×C4×C43C2×C411yescharacteristic
66C4×D4×C43—22no—
67C4×D4×C43—22no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43D411yescharacteristic
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—22no—
73C22⋊C8×C43—22no—
74#97×C43—22no—
75C24×C43C22⋊C411yescharacteristic
76C24×C43C22⋊C411yescharacteristic
77C23×D43—21no—
78C2×D4×C43—22no—
79C2×D4×C43—22no—
80C2×D4×C43—41no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43C22⋊C411yescharacteristic
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C2×C22⋊D43—24no—
93C2×C22⋊D43—24no—
94C2×C22⋊D43—42no—
95C2×C22⋊D43—42no—
96C2×C22⋊D43—82no—
97C22×Dic43—24no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—82no—
102C2×D172—21no—
103C2×D172—42no—
104C2×D172C22⋊C412yes—
105C2×C4×D43—24no—
106C2×C4×D43—82no—
107C2×C8×C43—42no—
108C4⋊C4×C43—22no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C42×C43C2×D412yes—
112C42×C43C2×D412yes—
113C22⋊Dic43—24no—
114(C2×D43)⋊C4—24no—
115(C2×D43)⋊C4—24no—
116(C2×D43)⋊C4—24no—
117C4⋊Dic43—24no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43C22⋊C412yes—
122C4⋊Dic43C22⋊C412yes—
123C4⋊Dic43C22⋊C412yes—
124Dic43⋊C4—24no—
125Dic43⋊C4—24no—
126C4×Dic43—24no—
127#10621877—24no—
128#10621877—42no—
129C2×C43⋊C8—42no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43#10412yes—
140C23×C43C2×C22⋊C411yescharacteristic
141C22×D43—22no—
142C22×D43—42no—
143C22×D43—42no—
144C22×D43—41no—
145C22×D43—41no—
146D4×C43—44no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43C2×C22⋊C411yescharacteristic
161C2×C4×C43#12012yes—
162C2×C4×C43#12012yes—
163C22⋊D43—48no—
164C22⋊D43—84no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—84no—
173D172—24no—
174D172—42no—
175C4×D43—84no—
176C8×C43—82no—
177C43⋊C8—44no—
178#8373—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—22no—
182C22×C43—42no—
183C22×C43—42no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43#37911yescharacteristic
192C22×C43C2×#10411yescharacteristic
193C22×C43#42111yescharacteristic
194C2×D43—42no—
195C2×D43—42no—
196C2×D43—42no—
197C2×D43—82no—
198C2×D43—82no—
199C4×C43—22no—
200C4×C43—21no—
201C4×C43—22no—
202C4×C43—41no—
203C4×C43—41no—
204C4×C43#41312yes—
205Dic43—42no—
206Dic43—42no—
207Dic43—42no—
208C2×#553—431no—
209C4×#100—431no—
210#1528—432no—
211#1490—432no—
212#1466D4311yescharacteristic, complemented
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—42no—
216C2×C43—81no—
217C2×C43#178511yescharacteristic
218C2×C43#178911yescharacteristic
219C2×C43#179511yescharacteristic
220D43—82no—
221#553—864no—
222#553—864no—
223C2×#126—861no—
224C2×#125—431no—
225C2×#123—861no—
226C2×#121—431no—
227C2×#121—431no—
228C2×#121—861no—
229C2×C4×D4—431no—
230C2×C4×D4—861no—
231C2×C4×D4C2×D4311yescharacteristic
232C2×#117—431no—
233C22×C4⋊C4—431no—
234#432C2×D4312yes—
235C2×#100—861no—
236C4×M16—432no—
237#343—861no—
238#330—864no—
239D4⋊C8—864no—
240#323—21no—
241#323—21no—
242C43#837311yescharacteristic, complemented, Sylow
243C22×D4—431no—
244C22×D4—861no—
245C22×D4—861no—
246C22×D4D17211yescharacteristic
247C23×C4—861no—
248C23×C4—861no—
249C23×C4C4×D4311yescharacteristic
250C23×C4C4×D4311yescharacteristic
251C2×M16—862no—
252#126—868no—
253#125—434no—
254#125—862no—
255#123—868no—
256#121—862no—
257#121—862no—
258#121—862no—
259#121—862no—
260#121—868no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—434no—
264C4×D4—868no—
265C4×D4—862no—
266#117—862no—
267#117—862no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—431no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4—862no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4D17211yescharacteristic
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4C22⋊D4311yescharacteristic
282C2×C22⋊C4C22⋊D4311yescharacteristic
283C2×C42—861no—
284C2×C42C22×D4311yescharacteristic
285C4⋊C8—22no—
286#100—864no—
287C22⋊C8—22no—
288#97—22no—
289#97—862no—
290C4×C8—862no—
291C24—861no—
292C24(C2×D43)⋊C411yescharacteristic
293C24(C2×D43)⋊C411yescharacteristic
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—432no—
298C2×D4—864no—
299C2×D4—864no—
300C2×D4—861no—
301C2×D4—3442no—
302C2×D4—1722no—
303C2×D4—1722no—
304C2×D4—1722no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—864no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—864no—
316C22×C4—3442no—
317C22×C4—3442no—
318C22×C4(C2×D43)⋊C411yescharacteristic
319C22×C4(C2×D43)⋊C411yescharacteristic
320C22×C4C2×C4×D4311yescharacteristic
321C22×C4C2×D17211yescharacteristic
322C22×C4C2×C22⋊D4311yescharacteristic
323M16—864no—
324M16—1722no—
325C2×C8—42no—
326C2×C8—1722no—
327C4⋊C4—22no—
328C4⋊C4—432no—
329C4⋊C4—432no—
330C4⋊C4—432no—
331C4⋊C4—864no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C4⋊C4—864no—
336C4⋊C4—864no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—864no—
340C22⋊C4—864no—
341C22⋊C4—864no—
342C22⋊C4—864no—
343C42—864no—
344C42D4×D4312yes—
345C42D4×D4312yes—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—862no—
356C23—1722no—
357C23—1722no—
358C23—1721no—
359C23—1721no—
360C23#1306325112yes—
361C23C2×(C2×D43)⋊C411yescharacteristic
362D4—44no—
363D4—864no—
364D4—3444no—
365D4—1722no—
366D4—1728no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—862no—
380C2×C4—862no—
381C2×C4—862no—
382C2×C4—3444no—
383C2×C4—3444no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4C22⋊C4×D4311yescharacteristic
389C2×C4C22⋊C4×D4311yescharacteristic
390C2×C4#1306329312yes—
391C2×C4#1306329512yes—
392C8—82no—
393C8—1724no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22—3442no—
407C22—3442no—
408C22—1722no—
409C22—1722no—
410C22—1722no—
411C22#1458275411yescharacteristic
412C22C2×#1306325111yescharacteristic
413C22#1458291511yescharacteristic
414C4—21no—
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—1722no—
420C4—1722no—
421C4—1722no—
422C4#1458288012yes—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—81no—
427C2—3442no—
428C2#1913452011yescharacteristic
429C2#1913453811yescharacteristic
430C2#1913456311yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1466C2
socleC22×C43#379
prime radicalC2×#14583595C2
cosocleC2×C42×C43C23
hypercenter#1466D43
hypocenterC43#8373
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. C4×#13063242C2semidirect
3. #19133198C2semidirect
4. #19133037C2semidirect
5. C43×#1466C2semidirect
212. #1466D43semidirect
242. C43#8373semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C4×#130632422
#191331982
#191330372
C43×#14662
#837343