Finite Group Databasebeta

← #25011745

Subgroups — #25011745

Order 11008.

636 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 123 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#19137249C211yesmaximal, characteristic
2C2×#14582685C212yesmaximal
3C4×#13063242C211yesmaximal, characteristic, complemented
4#19132712C212yesmaximal, complemented
5C4×#99×C43C211yesmaximal, characteristic, complemented
6C2×#13063293C2211yescharacteristic
7C22×(C2×D43)⋊C4C411yescharacteristic, complemented
8C2×#13063242C2212yes—
9C4×#10621877—21no—
10#14582799—21no—
11#14582790—21no—
12#14582789—21no—
13#14582779C2211yescharacteristic
14#14582778—21no—
15#14582771C411yescharacteristic, complemented
16#14582754C411yescharacteristic, complemented
17C4×C22⋊Dic43C411yescharacteristic, complemented
18#14582685C418yescomplemented
19#14582668—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C2×#99×C43C2212yes—
22C4×C22⋊C4×C43—21no—
23C43×#342—21no—
24C24×D43C2×C411yescharacteristic
25C22×C22⋊D43—21no—
26C23×Dic43C2×C411yescharacteristic
27C2×#10621877—22no—
28#13063293—22no—
29#13063293C2×C414yes—
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43C2×C411yescharacteristic
33C2×C22⋊Dic43C2×C411yescharacteristic
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—41no—
40C2×(C2×D43)⋊C4—41no—
41C2×C4×Dic43—21no—
42#13063242—22no—
43#13063242C2×C414yes—
44#13063236—41no—
45C4×C43⋊C8—41no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C22×D4×C43C2311yescharacteristic
50C23×C4×C43C2×C411yescharacteristic
51C23×C4×C43D411yescharacteristic
52C4×D4×C43—41no—
53C4×D4×C43—41no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43—22no—
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43—41no—
59C2×C42×C43D411yescharacteristic
60#99×C43—22no—
61#99×C43C2×C414yes—
62#95×C43—41no—
63C24×C43C22×C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C23×D43—21no—
66C23×D43—21no—
67C23×D43—41no—
68C23×D43—41no—
69C23×D43—81no—
70C23×D43—81no—
71C23×D43C4212yescomplemented
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43C22×C412yes—
75C2×D4×C43#4112yes—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—42no—
81C22×C4×C43—81no—
82C22×C4×C43—81no—
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C2×C22⋊D43—24no—
89C2×C22⋊D43—81no—
90C2×C22⋊D43—81no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—41no—
95C22×Dic43—81no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—24no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—42no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43—82no—
104C22⋊Dic43—21no—
105C22⋊Dic43—41no—
106C22⋊Dic43—81no—
107C22⋊Dic43C4212yescomplemented
108(C2×D43)⋊C4—24no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—81no—
113(C2×D43)⋊C4—81no—
114Dic43⋊C4—81no—
115C4×Dic43—81no—
116#10621877—24no—
117#10621877—42no—
118C2×C43⋊C8—42no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43C2×C4211yescharacteristic
128C23×C43C2×C22⋊C411yescharacteristic
129C23×C43#11711yescharacteristic
130C23×C43C4×D412yes—
131C22×D43—22no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—42no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—42no—
140C22×D43—82no—
141C22×D43—82no—
142C22×D43—84no—
143C22×D43—82no—
144C22×D43—82no—
145D4×C43—42no—
146D4×C43—42no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—44no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—82no—
162C2×C4×C43—82no—
163C2×C4×C43#9911yescharacteristic
164C2×C4×C43#9911yescharacteristic
165C2×C4×C43C4×D412yes—
166C22⋊D43—84no—
167C2×Dic43—22no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—82no—
177C43⋊C8—44no—
178#12622—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—22no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—81no—
193C22×C43C4×C22⋊C411yescharacteristic
194C22×C43C2×#9911yescharacteristic
195C22×C43#41011yescharacteristic
196C2×D43—42no—
197C2×D43—42no—
198C2×D43—42no—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—84no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43—84no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—22no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—84no—
212Dic43—42no—
213Dic43—81no—
214Dic43—81no—
215#2321—431no—
216C2×AΣL(1,𝔽16)—432no—
217C4×#100—431no—
218C4×#99D4311yescharacteristic, complemented
219#1390—432no—
220C2×C43—21no—
221C2×C43—21no—
222C2×C43—42no—
223C2×C43—41no—
224C2×C43—41no—
225C2×C43C4×#9911yescharacteristic
226C2×C43#212111yescharacteristic
227C2×C43#212211yescharacteristic
228D43—82no—
229C2×#120—431no—
230C2×C4×D4C2×D4311yescharacteristic
231C22×C22⋊C4—431no—
232C2×#100—432no—
233C2×#99C2×D4312yes—
234C4×M16—861no—
235#390—861no—
236#388—861no—
237#388—861no—
238#386—431no—
239#386—861no—
240#385—431no—
241#379—431no—
242C4×C22⋊C4—21no—
243C4×C22⋊C4—431no—
244AΣL(1,𝔽16)—438no—
245#343—861no—
246#342—21no—
247C43#1262211yescharacteristic, complemented, Sylow
248C25—431no—
249C22×D4—861no—
250C22×D4C22×D4311yescharacteristic
251C23×C4—431no—
252C23×C4C4×D4311yescharacteristic
253C23×C4C22⋊D4311yescharacteristic
254C2×M16—862no—
255#120—434no—
256#120—862no—
257C4×D4—41no—
258C4×D4—41no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4D17211yescharacteristic
261C2×C22⋊C4—22no—
262C2×C22⋊C4—431no—
263C2×C22⋊C4—431no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—1721no—
271C2×C22⋊C4—1721no—
272C2×C22⋊C4C4×D4311yescharacteristic
273C2×C22⋊C4C22⋊D4311yescharacteristic
274C2×C42—41no—
275C2×C42—861no—
276C2×C42D17211yescharacteristic
277#100—434no—
278#100—862no—
279#99—22no—
280#99C4×D4314yes—
281#97—1721no—
282C4×C8—1721no—
283#95—41no—
284#95—861no—
285#95—861no—
286#95—861no—
287C24—432no—
288C24—861no—
289C24—861no—
290C24—3441no—
291C24—3441no—
292C24—1721no—
293C24—1721no—
294C24C2×C4×D4311yescharacteristic
295C24C2×C22⋊D4311yescharacteristic
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—864no—
299C2×D4—3441no—
300C2×D4—3441no—
301C2×D4C2×C4×D4312yes—
302C2×D4#1062189812yes—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—3441no—
314C22×C4—1721no—
315C22×C4(C2×D43)⋊C411yescharacteristic
316C22×C4(C2×D43)⋊C411yescharacteristic
317C22×C4(C2×D43)⋊C411yescharacteristic
318C22×C4(C2×D43)⋊C411yescharacteristic
319C22×C4C2×D17211yescharacteristic
320M16—864no—
321M16—1722no—
322C2×C8—1722no—
323C4⋊C4—41no—
324C4⋊C4—3441no—
325C22⋊C4—24no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—432no—
330C22⋊C4—861no—
331C22⋊C4—864no—
332C22⋊C4—3441no—
333C22⋊C4—3441no—
334C22⋊C4—3441no—
335C22⋊C4—1722no—
336C22⋊C4—1721no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C42—21no—
340C42—21no—
341C42—82no—
342C42—3441no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—862no—
352C23—3442no—
353C23—3442no—
354C23—3444no—
355C23—3442no—
356C23—3442no—
357C23—1722no—
358C23—1721no—
359C23—1721no—
360C23—1721no—
361C23—1721no—
362C23—1722no—
363C23—1721no—
364C23—1721no—
365C23C42×D4311yescharacteristic
366C23C2×(C2×D43)⋊C411yescharacteristic
367C23#1306328211yescharacteristic
368C23C4×C22⋊D4312yes—
369D4—42no—
370D4—42no—
371D4—3444no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—44no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—862no—
389C2×C4—3442no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4#1306323911yescharacteristic
399C2×C4#1306323911yescharacteristic
400C2×C4C4×D17212yes—
401C8—1724no—
402C22—21no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—41no—
409C22—41no—
410C22—42no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—3441no—
417C22—3441no—
418C22—3444no—
419C22—3444no—
420C22—3441no—
421C22—3441no—
422C22—1722no—
423C22—1722no—
424C22—1722no—
425C22C4×(C2×D43)⋊C411yescharacteristic
426C22C2×#1306323911yescharacteristic
427C22#1458287211yescharacteristic
428C4—22no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—84no—
435C4—3441no—
436C4—3441no—
437C4—1722no—
438C2—21no—
439C2—21no—
440C2—42no—
441C2—41no—
442C2—41no—
443C2—3442no—
444C2C4×#1306323911yescharacteristic
445C2#1913623911yescharacteristic
446C2#1913624411yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC23×C43C2×C42
FrattiniC22×D4C22×D43
FittingC4×#99×C43C2
socleC22×C43C2×#99
prime radicalC2×#13063293C22
cosocleC22×D4×C43C23
hypercenterC4×#99D43
hypocenterC43#12622
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×#13063242C2semidirect
4. #19132712C2semidirect
5. C4×#99×C43C2semidirect
7. C22×(C2×D43)⋊C4C4semidirect
15. #14582771C4semidirect
16. #14582754C4semidirect
17. C4×C22⋊Dic43C4semidirect
18. #14582685C4semidirect
71. C23×D43C42semidirect
107. C22⋊Dic43C42semidirect
218. C4×#99D43semidirect
247. C43#12622semidirect

Maximal subgroups

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

subgroupindex
#191372492
C2×#145826852
C4×#130632422
#191327122
C4×#99×C432
#1262243