Finite Group Databasebeta

← #25013370

Subgroups — #25013370

Order 11008.

504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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#19137745C211yesmaximal, characteristic
2C2×#14582690C211yesmaximal, characteristic
3#19135008C211yesmaximal, characteristic
4#19134876C211yesmaximal, characteristic
5#19132720C211yesmaximal, characteristic
6#19132714C211yesmaximal, characteristic
7C43×#1856C211yesmaximal, characteristic
8C2×#13063306C2211yescharacteristic
9C2×#13063240C2211yescharacteristic
10C2×#13063240C2211yescharacteristic
11#14582794—21no—
12#14582793—21no—
13#14582787—21no—
14#14582783—21no—
15#14582779C2211yescharacteristic
16#14582771—21no—
17#14582771—21no—
18#14582760—21no—
19#14582757—21no—
20#14582690C414yescomplemented
21#14582666—21no—
22#14582666—21no—
23C43×#518C2211yescharacteristic
24C43×#428—21no—
25C2×#100×C43C2211yescharacteristic
26C43×#390C2211yescharacteristic
27C43×#339—21no—
28C23×Dic43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30#13063306—21no—
31#13063306—21no—
32#13063306C2×C412yes—
33#13063306Q812yes—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—41no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43D411yescharacteristic
44C2×C22⋊Dic43D411yescharacteristic
45C2×C4×Dic43—21no—
46#13063240—21no—
47#13063240—21no—
48#13063240—21no—
49#13063240C2×C412yes—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—41no—
56C43⋊#95—41no—
57C43⋊#95—41no—
58C22×D4×C43C2311yescharacteristic
59C2×M16×C43—21no—
60C4×D4×C43—41no—
61C4×D4×C43—41no—
62#117×C43—21no—
63C2×C4⋊C4×C43D411yescharacteristic
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C42×C43D411yescharacteristic
69#107×C43—41no—
70#106×C43—41no—
71#100×C43—21no—
72#100×C43C2×C412yes—
73C24×C43C2×D411yescharacteristic
74C24×C43C2×D411yescharacteristic
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43C22×C411yescharacteristic
78C2×D4×C43C2×Q811yescharacteristic
79C2×D4×C43#4111yescharacteristic
80C2×D4×C43#4111yescharacteristic
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—41no—
94C22×Dic43—41no—
95C22×Dic43—41no—
96C22×Dic43—41no—
97C22×Dic43—41no—
98C22×Dic43—81no—
99C22×Dic43C4⋊C412yescomplemented
100M16×C43—22no—
101M16×C43—41no—
102C2×C8×C43—41no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—81no—
110C22⋊C4×C43—81no—
111C42×C43—41no—
112C42×C43—41no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115C22⋊Dic43—22no—
116C22⋊Dic43—21no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C22⋊Dic43—81no—
122C22⋊Dic43C4⋊C412yescomplemented
123Dic43⋊C4—22no—
124Dic43⋊C4—22no—
125Dic43⋊C4—81no—
126Dic43⋊C4—81no—
127Dic43⋊C4—81no—
128Dic43⋊C4—82no—
129C4×Dic43—81no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43C2×C4⋊C411yescharacteristic
139C23×C43C4×D411yescharacteristic
140C23×C43#12011yescharacteristic
141C23×C43C22⋊Q811yescharacteristic
142C23×C43#12311yescharacteristic
143D4×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—41no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—81no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43C22⋊Q811yescharacteristic
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—42no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—42no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—81no—
179C2×Dic43—81no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185C8×C43—42no—
186#12961—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43#38511yescharacteristic
204C22×C43B(4,𝔽2)11yescharacteristic
205C22×C43#45811yescharacteristic
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—81no—
209C4×C43—81no—
210C4×C43—81no—
211C4×C43—81no—
212Dic43—42no—
213Dic43—42no—
214Dic43—81no—
215Dic43—82no—
216Dic43—81no—
217Dic43—161no—
218#2376—431no—
219C2×#352—431no—
220#1890—431no—
221#1867—431no—
222#1856D4311yescharacteristic
223#1393—431no—
224#1390—431no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—41no—
228C2×C43—41no—
229C2×C43—41no—
230C2×C43—41no—
231C2×C43#186711yescharacteristic
232C2×C43#220011yescharacteristic
233C2×C43#220111yescharacteristic
234C2×#123—431no—
235#518C2×D4311yescharacteristic
236#428—21no—
237C2×#100C2×D4311yescharacteristic
238C2×#99—431no—
239C2×#99—431no—
240#390C2×D4311yescharacteristic
241#389—861no—
242#388—861no—
243#388—861no—
244#387—861no—
245#386—431no—
246#385—861no—
247#385—861no—
248#381—861no—
249#380—861no—
250#352—434no—
251#342—861no—
252#342—861no—
253#339—21no—
254C43#1296111yescharacteristic, complemented, Sylow
255C22×D4C22×D4311yescharacteristic
256C23×C4—431no—
257C23×C4—431no—
258C2×M16—21no—
259#123—432no—
260#123—432no—
261#123—861no—
262#123—861no—
263C4×D4—41no—
264C4×D4—41no—
265#117—21no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—1721no—
271C2×C4⋊C4C22⋊D4311yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—431no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C42—861no—
283C2×C42C22⋊D4311yescharacteristic
284#107—41no—
285#106—41no—
286#100—21no—
287#100C4×D4312yes—
288#99—432no—
289#99—861no—
290#99—861no—
291#99—861no—
292#95—861no—
293#95—861no—
294#95—861no—
295#95—861no—
296#95—861no—
297#95—1721no—
298#95—1721no—
299#95—1721no—
300C24D4×D4311yescharacteristic
301C24D4×D4311yescharacteristic
302C2×D4—41no—
303C2×D4—41no—
304C2×D4C2×C4×D4311yescharacteristic
305C2×D4#1062189811yescharacteristic
306C2×D4Q8×D4311yescharacteristic
307C2×D4#1062190211yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—432no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—3441no—
321C22×C4—1721no—
322C22×C4—1721no—
323C22×C4—1721no—
324C22×C4—1721no—
325C22×C4—1721no—
326C22×C4C2×C22⋊D4311yescharacteristic
327M16—22no—
328M16—41no—
329C2×C8—41no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—862no—
334C4⋊C4—862no—
335C4⋊C4—3441no—
336C4⋊C4—3441no—
337C4⋊C4—3441no—
338C4⋊C4—3442no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C22⋊C4—432no—
345C22⋊C4—862no—
346C22⋊C4—862no—
347C22⋊C4—861no—
348C22⋊C4—862no—
349C22⋊C4—3441no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C42—41no—
355C42—41no—
356C42—3441no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C4⋊C4×D4311yescharacteristic
366C23#1306328711yescharacteristic
367C23#1306329311yescharacteristic
368C23#1306330311yescharacteristic
369C23#1306331011yescharacteristic
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—862no—
389C2×C4—862no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—3441no—
393C2×C4—3441no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—1721no—
398C2×C4—1722no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1722no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1722no—
410C2×C4C4×C22⋊D4311yescharacteristic
411C2×C4#1306330111yescharacteristic
412C8—42no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—81no—
428C22—81no—
429C22#1458277011yescharacteristic
430C22#1458308511yescharacteristic
431C22#1458308811yescharacteristic
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—3441no—
439C4—3442no—
440C4—3441no—
441C4—1722no—
442C4—1722no—
443C4—6881no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—41no—
450C2#1913487411yescharacteristic
451C2#1913660111yescharacteristic
452C2#1913660711yescharacteristic
subgroupG/H
centerC22#14583085
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1856C2
socleC22×C43B(4,𝔽2)
prime radical, cosocleC22×D4×C43C23
hypercenter#1856D43
hypocenterC43#12961
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1856

Complements

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

NH ≅ G/Ntype
20. #14582690C4semidirect
99. C22×Dic43C4⋊C4semidirect
122. C22⋊Dic43C4⋊C4semidirect
254. C43#12961semidirect

Maximal subgroups

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

subgroupindex
#191377452
C2×#145826902
#191350082
#191348762
#191327202
#191327142
C43×#18562
#1296143