Finite Group Databasebeta

← #25013359

Subgroups — #25013359

Order 11008.

524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137731C211yesmaximal, characteristic
2#19135009C211yesmaximal, characteristic
3#19134878C211yesmaximal, characteristic
4#19134807C211yesmaximal, characteristic
5#19132719C211yesmaximal, characteristic
6#19132714C211yesmaximal, characteristic
7C2×C43×#352C211yesmaximal, characteristic
8#14583374C2211yescharacteristic
9#14582941—21no—
10C2×#13063240C2211yescharacteristic
11#14582802C2211yescharacteristic
12#14582792—21no—
13#14582792—21no—
14#14582785—21no—
15#14582779C2211yescharacteristic
16#14582774—21no—
17#14582762—21no—
18C4⋊C4×Dic43—21no—
19C22⋊C4×Dic43—21no—
20C4×C22⋊Dic43—21no—
21#14582665—21no—
22#14582665—21no—
23#14582660—21no—
24C2×#123×C43C2211yescharacteristic
25C2×#100×C43C2211yescharacteristic
26C2×#99×C43C2211yescharacteristic
27C43×#352C414yescomplemented
28C23×Dic43D411yescharacteristic
29D4×Dic43—41no—
30D4×Dic43—41no—
31#13063284—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—41no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43D411yescharacteristic
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43D411yescharacteristic
46#13063259—41no—
47#13063257—41no—
48#13063240—21no—
49#13063240—21no—
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
59C23×C4×C43D411yescharacteristic
60C2×M16×C43—21no—
61#123×C43—21no—
62#123×C43—21no—
63#123×C43C2×C412yes—
64#123×C43Q812yes—
65C2×C4⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43D411yescharacteristic
69#100×C43—21no—
70#100×C43C2×C412yes—
71#99×C43—21no—
72#99×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—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C4⋊C412yescomplemented
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—41no—
98C22×Dic43—41no—
99C22×Dic43—42no—
100M16×C43—22no—
101M16×C43—41no—
102C2×C8×C43—41no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—21no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43C4⋊C412yescomplemented
111C22⋊Dic43—41no—
112C22⋊Dic43—41no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115C22⋊Dic43—42no—
116C22⋊Dic43—42no—
117C22⋊Dic43—42no—
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—42no—
123C4⋊Dic43—41no—
124C4⋊Dic43—82no—
125C4×Dic43—42no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128C4×Dic43—81no—
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—22no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—81no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43C22⋊Q811yescharacteristic
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—81no—
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#12959—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—42no—
209C4×C43—42no—
210C4×C43—82no—
211Dic43—42no—
212Dic43—42no—
213Dic43—81no—
214Dic43—81no—
215Dic43—81no—
216Dic43—81no—
217Dic43—161no—
218#2374—431no—
219C2×#352D4311yescharacteristic
220#1890—431no—
221#1867—431no—
222#1856—431no—
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#219711yescharacteristic
233C2×C43#219811yescharacteristic
234C2×#123C2×D4311yescharacteristic
235#518—431no—
236#428—861no—
237C2×#100C2×D4311yescharacteristic
238C2×#99—431no—
239C2×#99C2×D4311yescharacteristic
240#390—431no—
241#388—861no—
242#388—861no—
243#387—861no—
244#386—431no—
245#385—861no—
246#381—861no—
247C4×C4⋊C4—861no—
248C4×C22⋊C4—861no—
249C4×C22⋊C4—861no—
250#352Dic4314yescomplemented
251#342—861no—
252#342—861no—
253#339—861no—
254C43#1295911yescharacteristic, complemented, Sylow
255C22×D4C22×D4311yescharacteristic
256C23×C4—431no—
257C23×C4D17211yescharacteristic
258C2×M16—21no—
259#123—21no—
260#123—21no—
261#123Dic8612yes—
262#123C2×Dic4312yes—
263C4×D4—1721no—
264C4×D4—1721no—
265#117—861no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—1721no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—431no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4—861no—
277C2×C22⋊C4—861no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4D17211yescharacteristic
280C2×C42—431no—
281C2×C42—861no—
282C2×C42—861no—
283C2×C42—861no—
284#107—1721no—
285#106—1721no—
286#100—21no—
287#100C2×Dic4312yes—
288#99—21no—
289#99—861no—
290#99—861no—
291#99C2×Dic4312yes—
292#95—861no—
293#95—861no—
294#95—861no—
295#95—861no—
296#95—861no—
297#95—1721no—
298#95—1721no—
299#95—1721no—
300C24C2×D17211yescharacteristic
301C24D4×D4311yescharacteristic
302C2×D4—41no—
303C2×D4—41no—
304C2×D4C2×Dic8611yescharacteristic
305C2×D4#1062190011yescharacteristic
306C2×D4#1062190011yescharacteristic
307C2×D4C22×Dic4311yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—1722no—
323C22×C4—1721no—
324C22×C4—1721no—
325C22×C4C4⋊Dic4312yescomplemented
326C22×C4D4×D4311yescharacteristic
327M16—22no—
328M16—41no—
329C2×C8—41no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—3442no—
335C4⋊C4—1721no—
336C4⋊C4—1722no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—21no—
340C22⋊C4—22no—
341C22⋊C4—41no—
342C22⋊C4—1722no—
343C22⋊C4—1722no—
344C22⋊C4—1722no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C22⋊C4C4⋊Dic4312yescomplemented
352C42—3441no—
353C42—3441no—
354C42—1721no—
355C42—1721no—
356C42—1722no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C2×C4⋊Dic4311yescharacteristic
366C23D4×Dic4311yescharacteristic
367C23#1306329511yescharacteristic
368C23#1306330211yescharacteristic
369C23#1306330911yescharacteristic
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—862no—
388C2×C4—862no—
389C2×C4—3441no—
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—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1722no—
410C2×C4D4×Dic4311yescharacteristic
411C2×C4#1306330211yescharacteristic
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#1458277411yescharacteristic
430C22#1458308711yescharacteristic
431C22#1458309011yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4—3441no—
438C4—3441no—
439C4—3441no—
440C4—3441no—
441C4—1722no—
442C4—1722no—
443C4—6881no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—41no—
450C2#1913487811yescharacteristic
451C2#1913658611yescharacteristic
452C2#1913659211yescharacteristic
subgroupG/H
centerC22#14583087
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#352C2
socleC22×C43B(4,𝔽2)
prime radical, cosocleC22×D4×C43C23
hypercenterC2×#352D43
hypocenterC43#12959
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
27. C43×#352C4semidirect
87. C22×C4×C43C4⋊C4semidirect
110. C22⋊C4×C43C4⋊C4semidirect
250. #352Dic43semidirect
254. C43#12959semidirect
325. C22×C4C4⋊Dic43semidirect
351. C22⋊C4C4⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
#191377312
#191350092
#191348782
#191348072
#191327192
#191327142
C2×C43×#3522
#1295943