Finite Group Databasebeta

← #25013404

Subgroups — #25013404

Order 11008.

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

normal subgroups only

This group has 516 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#19137765C211yesmaximal, characteristic
2C2×#14582693C211yesmaximal, characteristic
3#19134983C211yesmaximal, characteristic
4#19134876C211yesmaximal, characteristic
5#19132713C211yesmaximal, characteristic
6#19132712C211yesmaximal, characteristic
7C43×#1867C211yesmaximal, characteristic
8C2×#13063312C2211yescharacteristic
9#14582907—21no—
10C2×#13063242C2211yescharacteristic
11C2×#13063240C2211yescharacteristic
12#14582803—21no—
13#14582793—21no—
14#14582787—21no—
15#14582779C2211yescharacteristic
16#14582772—21no—
17#14582771—21no—
18#14582771—21no—
19#14582763—21no—
20#14582693C414yescomplemented
21#14582666—21no—
22#14582658—21no—
23C43×#518C2211yescharacteristic
24C2×#99×C43C2211yescharacteristic
25C43×#386C2211yescharacteristic
26C43×#385—21no—
27C43×#342—21no—
28C22×Dic86D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C2×#10621877—21no—
31#13063312—21no—
32#13063312—21no—
33#13063312C2×C412yes—
34#13063312Q812yes—
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×C4×Dic43—21no—
45C2×C4×Dic43D411yescharacteristic
46#13063248—41no—
47#13063248—41no—
48#13063242—21no—
49#13063242—21no—
50#13063240—21no—
51#13063240C2×C412yes—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—41no—
58C22×D4×C43C2311yescharacteristic
59C23×C4×C43D411yescharacteristic
60C4×D4×C43—41no—
61C4×D4×C43—41no—
62#117×C43—21no—
63C2×C4⋊C4×C43—41no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43D411yescharacteristic
69#99×C43—21no—
70#99×C43C2×C412yes—
71#95×C43—21no—
72#95×C43—41no—
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×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—81no—
90C22×C4×C43C2×D411yescharacteristic
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—41no—
96C22×Dic43—41no—
97C22×Dic43—81no—
98C2×Dic86—21no—
99C2×Dic86—41no—
100C2×Dic86—41no—
101C2×Dic86C4⋊C412yescomplemented
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—82no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—81no—
112C42×C43—41no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115C22⋊Dic43—22no—
116C22⋊Dic43—22no—
117C22⋊Dic43—22no—
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—81no—
121Dic43⋊C4—81no—
122Dic43⋊C4—81no—
123Dic43⋊C4—81no—
124Dic43⋊C4—82no—
125C4×Dic43—21no—
126C4×Dic43—81no—
127C4×Dic43C4⋊C412yescomplemented
128#10621877—41no—
129#10621877—41no—
130C2×C43⋊C8—41no—
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×C43C4×D411yescharacteristic
140C23×C43C4×D411yescharacteristic
141C23×C43#12011yescharacteristic
142C23×C43C22⋊Q811yescharacteristic
143C23×C43C22⋊Q811yescharacteristic
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—41no—
147D4×C43—41no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C2×C4×C43C2×C4⋊C411yescharacteristic
168C2×C4×C43#12311yescharacteristic
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—42no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185C2×Dic43—81no—
186Dic86—42no—
187Dic86—81no—
188C43⋊C8—81no—
189#12967—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—81no—
205C22×C43—81no—
206C22×C43#38511yescharacteristic
207C22×C43B(4,𝔽2)11yescharacteristic
208C22×C43#45811yescharacteristic
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43—82no—
213C4×C43—81no—
214C4×C43—81no—
215C4×C43—81no—
216Dic43—42no—
217Dic43—42no—
218Dic43—81no—
219Dic43—82no—
220Dic43—81no—
221#2379—431no—
222C2×#354—431no—
223#1885—431no—
224#1867—431no—
225#1867D4311yescharacteristic
226#1390—431no—
227#1390—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—41no—
231C2×C43—41no—
232C2×C43—41no—
233C2×C43—41no—
234C2×C43#186711yescharacteristic
235C2×C43#219911yescharacteristic
236C2×C43#220111yescharacteristic
237C2×#124—431no—
238#518C2×D4311yescharacteristic
239#419—861no—
240C2×#100—431no—
241C2×#99—431no—
242C2×#99C2×D4311yescharacteristic
243#391—861no—
244#388—861no—
245#388—861no—
246#386—431no—
247#386C2×D4311yescharacteristic
248#385—21no—
249#385—861no—
250#385—861no—
251#385—861no—
252#382—861no—
253#354—434no—
254#342—21no—
255#342—861no—
256#339—861no—
257C43#1296711yescharacteristic, complemented, Sylow
258C22×Q8—431no—
259C22×D4C22×D4311yescharacteristic
260C23×C4—431no—
261C23×C4C22⋊D4311yescharacteristic
262C2×M16—861no—
263#124—432no—
264#124—432no—
265#124—861no—
266#124—861no—
267C4×D4—41no—
268C4×D4—41no—
269#117—21no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—1721no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—431no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4C22⋊D4311yescharacteristic
285C2×C42—431no—
286C2×C42—861no—
287#103—1721no—
288#103—1721no—
289#100—861no—
290#100—861no—
291#99—21no—
292#99—432no—
293#99—861no—
294#99C4×D4312yes—
295#95—21no—
296#95—41no—
297#95—861no—
298#95—861no—
299#95—861no—
300#95—861no—
301#95—861no—
302#95—1721no—
303C24D4×D4311yescharacteristic
304C24C2×C22⋊D4311yescharacteristic
305C2×Q8—432no—
306C2×Q8—861no—
307C2×Q8—1721no—
308C2×Q8—1721no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4C2×C4×D4311yescharacteristic
312C2×D4#1062189811yescharacteristic
313C2×D4Q8×D4311yescharacteristic
314C2×D4#1062190211yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—3441no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4D4×D4311yescharacteristic
332M16—1721no—
333M16—1721no—
334C2×C8—1721no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—82no—
338C4⋊C4—3441no—
339C4⋊C4—3441no—
340C4⋊C4—3441no—
341C4⋊C4—3442no—
342C22⋊C4—22no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—81no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C22⋊C4—862no—
352C22⋊C4—862no—
353C22⋊C4—862no—
354C22⋊C4—3441no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C42—41no—
358C42—432no—
359C42—861no—
360C42—3441no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23C4×C22⋊D4311yescharacteristic
370C23#1306328711yescharacteristic
371C23#1306329311yescharacteristic
372C23#1306330111yescharacteristic
373C23#1306330311yescharacteristic
374Q8—3441no—
375Q8—1722no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—41no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—862no—
400C2×C4—862no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—1722no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1722no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4C4⋊C4×D4311yescharacteristic
417C2×C4#1306331011yescharacteristic
418C8—3441no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22—81no—
435C22#1458277011yescharacteristic
436C22#1458308511yescharacteristic
437C22#1458308811yescharacteristic
438C4—21no—
439C4—21no—
440C4—81no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—3441no—
446C4—3442no—
447C4—3441no—
448C4—1722no—
449C4—1722no—
450C2—21no—
451C2—21no—
452C2—41no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2#1913487411yescharacteristic
457C2#1913659411yescharacteristic
458C2#1913660611yescharacteristic
subgroupG/H
centerC22#14583085
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1867C2
socleC22×C43B(4,𝔽2)
prime radical, cosocleC22×D4×C43C23
hypercenter#1867D43
hypocenterC43#12967
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1867

Complements

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

NH ≅ G/Ntype
20. #14582693C4semidirect
101. C2×Dic86C4⋊C4semidirect
127. C4×Dic43C4⋊C4semidirect
257. C43#12967semidirect

Maximal subgroups

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

subgroupindex
#191377652
C2×#145826932
#191349832
#191348762
#191327132
#191327122
C43×#18672
#1296743