Finite Group Databasebeta

← #24993642

Subgroups — #24993642

Order 11008.

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

normal subgroups only

This group has 520 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#19145401C211yesmaximal, characteristic
2#19137758C211yesmaximal, characteristic, complemented
3#19133124C211yesmaximal, characteristic
4#19133114C211yesmaximal, characteristic, complemented
5#19132501C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1964C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583234C412yescomplemented
10#14583210—21no—
11#14583143—22no—
12#14583050C412yescomplemented
13#14583037—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582803—21no—
17#14582794—21no—
18#14582793—21no—
19#14582787—21no—
20#14582782—21no—
21#14582780—21no—
22#14582762C2211yescharacteristic
23#14582635—22no—
24#14582633—21no—
25#14582633—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#99×C43—21no—
28C2×#99×C43—21no—
29C43×#380C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621883—22no—
33C2×#10621877—21no—
34C2×#10621877—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304C2×C412yes—
38#13063304D412yes—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47#13063258—22no—
48#13063248—22no—
49#13063246—22no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)C2×C412yes—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95D411yescharacteristic
60C43⋊#95D411yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43C2×C411yescharacteristic
63C23×C4×C43C2311yescharacteristic
64#121×C43—21no—
65#121×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43C2×C411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75#99×C43—42no—
76#99×C43—42no—
77#95×C43—21no—
78#95×C43—21no—
79C24×C43—21no—
80C24×C43C2×D411yescharacteristic
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—81no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—41no—
94C22×C4×C43—81no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×Dic43—21no—
102C22×Dic43—21no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C2×Dic86—21no—
106C2×Dic86—81no—
107C2×Dic86C22⋊C412yes—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—81no—
111C22⋊C4×C43—22no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43—81no—
118C22⋊Dic43—22no—
119C22⋊Dic43—22no—
120C22⋊Dic43—81no—
121#10621883—82no—
122C4⋊Dic43—21no—
123C4⋊Dic43C22⋊C412yes—
124Dic43⋊C4—22no—
125Dic43⋊C4—22no—
126Dic43⋊C4—81no—
127Dic43⋊C4—81no—
128C4×Dic43—81no—
129C4×Dic43—81no—
130#10621877—81no—
131#10621877—81no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—41no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—81no—
142C23×C43—81no—
143C23×C43C4×D411yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—81no—
149D4×C43—81no—
150D4×C43—81no—
151D4×C43—81no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43C2×C22⋊C411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C2×Dic43—22no—
175C2×Dic43—22no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186Dic86—42no—
187Dic86—81no—
188C43⋊C8—42no—
189C43⋊C8—81no—
190#9344—431nomaximal, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43—81no—
204C22×C43—161no—
205C22×C43—161no—
206C22×C43#38611yescharacteristic
207C22×C43#45311yescharacteristic
208C22×C43#45411yescharacteristic
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—81no—
214C4×C43—81no—
215C4×C43—82no—
216C4×C43—81no—
217Dic43—42no—
218Dic43—42no—
219Dic43—81no—
220Dic43—81no—
221#3193—431no—
222#2378—431no—
223#1964D4311yescharacteristic
224#1510—431no—
225#1508—431no—
226#1305—431no—
227#1284—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—41no—
231C2×C43—41no—
232C2×C43—161no—
233C2×C43#188311yescharacteristic
234C2×C43#190511yescharacteristic
235C2×C43#191311yescharacteristic
236C2×C22⋊Q8—431no—
237C2×#121C2×D4311yescharacteristic
238#484—432no—
239#480—861no—
240#468—862no—
241#450—432no—
242#448—861no—
243C2×#99—21no—
244C2×#99—21no—
245#407—431no—
246#407—431no—
247#391—861no—
248#389—861no—
249#388—861no—
250#388—861no—
251#387—861no—
252#387—861no—
253#381—431no—
254#380C2×D4311yescharacteristic
255C4×C22⋊C4C2×D4311yescharacteristic
256#328—862no—
257#327—861no—
258#327—861no—
259C43#934411yescharacteristic, complemented, Sylow
260C22×Q8—431no—
261C22×D4—21no—
262C22×D4C4×D4311yescharacteristic
263C23×C4C22×D4311yescharacteristic
264C2×SD16—862no—
265C2×M16—861no—
266C2×M16—861no—
267C22⋊Q8—432no—
268C22⋊Q8—432no—
269C22⋊Q8—861no—
270C22⋊Q8—861no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—861no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4C4×D4311yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4C22⋊D4311yescharacteristic
286C2×C22⋊C4C22⋊D4311yescharacteristic
287C2×C42—21no—
288C2×C42—861no—
289C2×C42—861no—
290#107—862no—
291#103—862no—
292#102—862no—
293#99—42no—
294#99—42no—
295C22⋊C8—432no—
296C22⋊C8—861no—
297C22⋊C8—861no—
298C22⋊C8—861no—
299#95—21no—
300#95—21no—
301#95—431no—
302#95—431no—
303#95—861no—
304#95—861no—
305#95—861no—
306#95—861no—
307#95—861no—
308C24—21no—
309C24C2×C22⋊D4311yescharacteristic
310C2×Q8—432no—
311C2×Q8—861no—
312C2×Q8—3441no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—81no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4C2×C4×D4311yescharacteristic
332C22×C4#1062189811yescharacteristic
333C22×C4D4×D4311yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190011yescharacteristic
337SD16—3442no—
338M16—3441no—
339M16—3441no—
340C2×C8—862no—
341C2×C8—1721no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—81no—
345C4⋊C4—432no—
346C4⋊C4—862no—
347C4⋊C4—862no—
348C4⋊C4—861no—
349C4⋊C4—3441no—
350C4⋊C4—3441no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—862no—
358C22⋊C4—862no—
359C22⋊C4—3441no—
360C42—81no—
361C42—3441no—
362C42—3441no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C4×C22⋊D4311yescharacteristic
373C23#1306329311yescharacteristic
374C23#1306329611yescharacteristic
375Q8—3441no—
376Q8—1722no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—862no—
402C2×C4—862no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C22⋊C4×D4311yescharacteristic
414C2×C4(C22⋊D43)⋊C411yescharacteristic
415C2×C4#1306329811yescharacteristic
416C2×C4#1306330711yescharacteristic
417C8—3441no—
418C8—1722no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22#1458277511yescharacteristic
435C22#1458306611yescharacteristic
436C22#1458307111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—82no—
444C4—81no—
445C4—3441no—
446C4—3441no—
447C4—1722no—
448C4—1722no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2#1913497411yescharacteristic
455C2#1913509211yescharacteristic
456C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1964C2
socleC22×C43#386
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenter#1964D43
hypocenterC43#9344
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19137758C2semidirect
4. #19133114C2semidirect
5. #19132501C2semidirect
6. #19132448C2semidirect
9. #14583234C4semidirect
12. #14583050C4semidirect
259. C43#9344semidirect

Maximal subgroups

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

subgroupindex
#191454012
#191377582
#191331242
#191331142
#191325012
#191324482
C43×#19642
#934443