Finite Group Databasebeta

← #24993059

Subgroups — #24993059

Order 11008.

566 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#14583218C211yesmaximal, characteristic
2#19137474C211yesmaximal, characteristic, complemented
3#19135430C211yesmaximal, characteristic
4#19134683C211yesmaximal, characteristic, complemented
5#19133162C211yesmaximal, characteristic
6#19132442C211yesmaximal, characteristic, complemented
7C43×#1289C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14583218—21no—
11#14583218—22no—
12#14583218—21no—
13C2×#13063257C412yescomplemented
14C2×#13063247C412yescomplemented
15C2×#13063239—21no—
16C2×#13063239—21no—
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18#14582795—21no—
19#14582784—22no—
20#14582757—21no—
21C4⋊C4×Dic43—21no—
22C22⋊C4×Dic43—21no—
23C4×C22⋊Dic43C2211yescharacteristic
24#14582661—22no—
25#14582632—22no—
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#380C2211yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43—21no—
32C22×C43⋊C8—21no—
33#13063299—21no—
34#13063299—21no—
35#13063299—21no—
36#13063299—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×C4⋊Dic43C2×C412yes—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D412yes—
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—22no—
46C2×C22⋊Dic43D411yescharacteristic
47C2×C22⋊Dic43D411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—22no—
51#13063257—22no—
52#13063257—22no—
53#13063247—22no—
54#13063247—22no—
55#13063239—42no—
56#13063239—42no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C43⋊#95—22no—
60C43⋊#95—22no—
61C43⋊#95—21no—
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43C2×C412yes—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70#95×C43—21no—
71#95×C43D412yes—
72C24×C43C2×D411yescharacteristic
73C23×D43—21no—
74C22×C4×C43—22no—
75C22×C4×C43—42no—
76C22×C4×C43—41no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C22×Dic43—22no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—22no—
96C22×Dic43—82no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—42no—
100C2×C8×C43—22no—
101C2×C8×C43—42no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—42no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊Dic43—21no—
109C22⋊Dic43—21no—
110C22⋊Dic43—21no—
111C22⋊Dic43SD1612yes—
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43C22⋊C412yes—
121C4⋊Dic43C22⋊C412yes—
122Dic43⋊C4—82no—
123C4×Dic43—42no—
124C4×Dic43—82no—
125C2×C43⋊C8—42no—
126C2×C43⋊C8—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43C4×D411yescharacteristic
130C23×C43#12011yescharacteristic
131C23×C43#12111yescharacteristic
132C23×C43C2×SD1611yescharacteristic
133C23×C43#13511yescharacteristic
134C23×C43AGL(1,ℤ/8)11yescharacteristic
135C23×C43#13711yescharacteristic
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—81no—
140C22×D43—81no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C22⋊D43—81no—
158C22⋊D43—81no—
159C22⋊D43—81no—
160C22⋊D43—81no—
161C2×Dic43—22no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—82no—
175C2×Dic43—82no—
176D172—42no—
177D172—81no—
178C8×C43—42no—
179C43⋊C8—81no—
180#9261—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43#38611yescharacteristic
192C22×C43C4×SD1611yescharacteristic
193C22×C43#44011yescharacteristic
194C22×C43#44811yescharacteristic
195C22×C43#44911yescharacteristic
196C22×C43#46011yescharacteristic
197C22×C43#46411yescharacteristic
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—161no—
202C2×D43—161no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—82no—
207C4×C43—161no—
208C4×C43#41012yes—
209Dic43—42no—
210Dic43—42no—
211Dic43—42no—
212Dic43—81no—
213Dic43—81no—
214C2×#481—431no—
215#2345—431no—
216#1964—431no—
217#1824—431no—
218#1519—431no—
219#1289D4311yescharacteristic, complemented
220#1282—431no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43#188011yescharacteristic
228C2×C43#189911yescharacteristic
229C2×C43#190411yescharacteristic
230D43—161no—
231C2×#121—431no—
232C22×C4⋊C4—431no—
233#481—862no—
234#481—861no—
235#481—861no—
236C2×#106—432no—
237C2×#102—432no—
238C2×#99—861no—
239C2×#99—861no—
240C2×C22⋊C8—431no—
241C2×C22⋊C8C2×D4311yescharacteristic
242#389—861no—
243#387—862no—
244#380—861no—
245#380C2×D4311yescharacteristic
246#380C2×D4311yescharacteristic
247C4×C4⋊C4—861no—
248C4×C22⋊C4—431no—
249C4×C22⋊C4—861no—
250#340—862no—
251#327—862no—
252C43#926111yescharacteristic, complemented, Sylow
253C22×D4—431no—
254C22×D4—861no—
255C23×C4—861no—
256C23×C4C22×D4311yescharacteristic
257C22×C8—861no—
258C22×C8C4×D4312yes—
259#121—861no—
260#121—861no—
261#121—861no—
262#121—861no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—432no—
266C2×C4⋊C4—432no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—862no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—431no—
278C2×C22⋊C4—861no—
279C2×C42—862no—
280C2×C42—861no—
281#106—862no—
282#106—862no—
283#102—862no—
284#102—862no—
285#99—1722no—
286#99—1722no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291#95—21no—
292#95—862no—
293#95—862no—
294#95—861no—
295#95D17212yes—
296C24—861no—
297C24D4×D4311yescharacteristic
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—1722no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C22×C4—22no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—862no—
311C22×C4—862no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—3442no—
318C22×C4C2×C4×D4311yescharacteristic
319C22×C4C2×D17211yescharacteristic
320C22×C4#1062189811yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323C22×C4#1062190211yescharacteristic
324C2×C8—22no—
325C2×C8—42no—
326C2×C8—1722no—
327C2×C8—1721no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—432no—
331C4⋊C4—432no—
332C4⋊C4—862no—
333C4⋊C4—862no—
334C4⋊C4—861no—
335C4⋊C4—861no—
336C4⋊C4—861no—
337C4⋊C4—861no—
338C4⋊C4—3442no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—432no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—3442no—
350C42—1722no—
351C23—41no—
352C23—41no—
353C23—3441no—
354C23—3441no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23#1306328711yescharacteristic
359C23#1306329511yescharacteristic
360C23#1306329811yescharacteristic
361C23SD16×D4311yescharacteristic
362C23#1306334611yescharacteristic
363C23#1306334911yescharacteristic
364C23#1306335711yescharacteristic
365D4—3441no—
366D4—3441no—
367D4—3441no—
368D4—3441no—
369D4—3441no—
370D4—1722no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—862no—
384C2×C4—862no—
385C2×C4—862no—
386C2×C4—3442no—
387C2×C4—3442no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1722no—
396C2×C4—1721no—
397C2×C4—1722no—
398C2×C4C22⋊C4×D4311yescharacteristic
399C2×C4C4×D17211yescharacteristic
400C2×C4#1306330011yescharacteristic
401C2×C4#1306331011yescharacteristic
402C8—42no—
403C8—3441no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—3441no—
415C22—3441no—
416C22—3441no—
417C22—6881no—
418C22—6881no—
419C22#1458277711yescharacteristic
420C22#1458298611yescharacteristic
421C22#1458299811yescharacteristic
422C22#1458303911yescharacteristic
423C22#1458304511yescharacteristic
424C22#1458309811yescharacteristic
425C22#1458312411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—161no—
431C4—3441no—
432C4—3441no—
433C4—1722no—
434C4—1722no—
435C4—1722no—
436C4#1458287112yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—6881no—
444C2#1913495111yescharacteristic
445C2#1913505211yescharacteristic
446C2#1913508311yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1289C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1289D43
hypocenterC43#9261
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #19137474C2semidirect
4. #19134683C2semidirect
6. #19132442C2semidirect
7. C43×#1289C2semidirect
13. C2×#13063257C4semidirect
14. C2×#13063247C4semidirect
219. #1289D43semidirect
252. C43#9261semidirect

Maximal subgroups

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

subgroupindex
C2×#145832182
#191374742
#191354302
#191346832
#191331622
#191324422
C43×#12892
#926143