Finite Group Databasebeta

← #25251729

Subgroups — #25251729

Order 11008.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143472C211yesmaximal, characteristic
2#19136795C211yesmaximal, characteristic, complemented
3#19136790C211yesmaximal, characteristic, complemented
4#19136756C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136642C211yesmaximal, characteristic, complemented
7#19136637C211yesmaximal, characteristic, complemented
8#19136533C211yesmaximal, characteristic
9#19136533C211yesmaximal, characteristic
10#19136464C211yesmaximal, characteristic, complemented
11#19136457C211yesmaximal, characteristic, complemented
12C4×#13063271C211yesmaximal, characteristic, complemented
13C4×#13063268C211yesmaximal, characteristic, complemented
14#19136402C211yesmaximal, characteristic, complemented
15C43×#3177C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17#14583379—21no—
18C2×#13063271C2211yescharacteristic
19C2×#13063271C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
22#14583001—21no—
23#14583001—21no—
24C4×Dic172C2211yescharacteristic
25C4×Dic172C2211yescharacteristic
26C4×D344C2211yescharacteristic
27C4×D344C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29#14582901—21no—
30#14582726C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35C4⋊(C43⋊C16)C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582703C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44C22⋊(C43⋊C16)C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#541—21no—
49C43×#499C2211yescharacteristic
50C43×#494C2211yescharacteristic
51C43×#491—21no—
52C43×#470—21no—
53C43×#467C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#441—21no—
56C4×Q16×C43C2211yescharacteristic
57C4×Q16×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×#10621898—21no—
60#13063347—22no—
61#13063347—22no—
62C2×Dic172C2311yescharacteristic
63C2×#10621873—21no—
64C2×D344C2311yescharacteristic
65C4×Dic86—21no—
66C4×Dic86—21no—
67C4×D172—21no—
68C4×D172—21no—
69(C22⋊D43)⋊C4—41no—
70(C22⋊D43)⋊C4—41no—
71#13063283—41no—
72C2×C4⋊Dic43—21no—
73C4⋊C4×D43—41no—
74#13063271—22no—
75#13063271—22no—
76#13063268—22no—
77#13063268—22no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063250—21no—
86#13063250—21no—
87#13063247—21no—
88#13063247—21no—
89C2×Q16×C43—21no—
90C2×Q16×C43C2311yescharacteristic
91C2×Q16×C43C2311yescharacteristic
92C2×M16×C43D411yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C4⋊Q8×C43—21no—
95#126×C43—41no—
96#126×C43—41no—
97#125×C43—21no—
98#125×C43—41no—
99#125×C43—41no—
100C22⋊Q8×C43—21no—
101C22⋊Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43—21no—
104#117×C43D411yescharacteristic
105#107×C43C2311yescharacteristic
106#107×C43C2311yescharacteristic
107#106×C43—21no—
108#103×C43—21no—
109#103×C43—21no—
110#103×C43—21no—
111#103×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C2×C22⋊D43—41no—
120C22×Dic43—41no—
121#10621898—24no—
122#10621898—42no—
123C2×D172—21no—
124C2×C4×D43—41no—
125C2×C4×D43—41no—
126C2×C4×D43—41no—
127C2×Dic86—21no—
128Q16×C43—21no—
129Q16×C43—21no—
130Q16×C43—21no—
131Q16×C43—21no—
132Q16×C43—42no—
133M16×C43—41no—
134C2×C8×C43—21no—
135C2×C8×C43—21no—
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2×D411yescharacteristic
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C4⋊C4×C43—41no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43D811yescharacteristic
151C4⋊C4×C43D811yescharacteristic
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43D811yescharacteristic
155C22⋊C4×C43D811yescharacteristic
156C42×C43—41no—
157C42×C43—41no—
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169Dic172—21no—
170Dic172#4112yes—
171D344—21no—
172D344#4112yes—
173#10621873—24no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43C2×D811yescharacteristic
179C22×D43—41no—
180Q8×C43—41no—
181Q8×C43—41no—
182Q8×C43—41no—
183Q8×C43—41no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C22⋊D43—44no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—161no—
201D172—22no—
202D172—41no—
203C4×D43—44no—
204C4×D43—161no—
205C4×D43—161no—
206Dic86—22no—
207Dic86—41no—
208C8×C43—21no—
209C8×C43—21no—
210C8×C43—21no—
211C8×C43C2×#4111yescharacteristic
212C8×C43C2×#4111yescharacteristic
213#33680—431nomaximal, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43C22×D811yescharacteristic
218C2×D43—42no—
219C2×D43—81no—
220C2×D43—81no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43—81no—
230C4×C43#52511yescharacteristic
231C4×C43#57511yescharacteristic
232Dic43—42no—
233Dic43—81no—
234Dic43—81no—
235#3177D4311yescharacteristic, complemented
236#2951—431no—
237#2236—431no—
238#2235—431no—
239#2229—431no—
240#2228—431no—
241#2209—431no—
242#2208—431no—
243#2189—431no—
244#2189—431no—
245#2176—431no—
246#2175—431no—
247C4×Q32—431no—
248C4×SD32—431no—
249#2164—431no—
250C2×C43—41no—
251C2×C43#310011yescharacteristic
252C2×C43#341611yescharacteristic
253C2×C43#341711yescharacteristic
254D43—82no—
255C2×#135—431no—
256#541—21no—
257#520—861no—
258C2×Q32—431no—
259C2×Q32—431no—
260C2×SD32—431no—
261C2×SD32—431no—
262#499C2×D4311yescharacteristic
263#494C2×D4311yescharacteristic
264#491—21no—
265#470—21no—
266#467C2×D4311yescharacteristic
267#467C2×D4311yescharacteristic
268#441—21no—
269#440—861no—
270#440—861no—
271C4×Q16—431no—
272C4×Q16—431no—
273C4×Q16C2×D4311yescharacteristic
274C4×Q16C2×D4311yescharacteristic
275C4×D8—431no—
276C4×D8—431no—
277C2×#107—431no—
278#417—861no—
279#405C2×D4311yescharacteristic
280#367—431no—
281#367—431no—
282#366—431no—
283#366—431no—
284C4⋊C16—431no—
285C4⋊C16—431no—
286#358—431no—
287#358—431no—
288#358—431no—
289#358—431no—
290#358—431no—
291#358—431no—
292#357—431no—
293#357—431no—
294C22⋊C16—431no—
295C22⋊C16—431no—
296#346—431no—
297C4×C16—431no—
298C43#3368011yescharacteristic, complemented, Sylow
299C2×#41—861no—
300#135—862no—
301#135—862no—
302C2×Q16—21no—
303C2×Q16—431no—
304C2×Q16C22×D4311yescharacteristic
305C2×Q16C22×D4311yescharacteristic
306C2×SD16—861no—
307C2×D8—431no—
308C2×M16C22⋊D4311yescharacteristic
309C22×C8C22×D4311yescharacteristic
310C4⋊Q8—21no—
311#126—41no—
312#126—41no—
313#125—21no—
314#125—41no—
315#125—41no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—861no—
321C4×Q8—861no—
322C4×D4—861no—
323C4×D4—861no—
324C4×D4—1721no—
325C4×D4—1721no—
326#117—1721no—
327#117C22⋊D4311yescharacteristic
328C2×C4⋊C4—861no—
329C2×C4⋊C4—1721no—
330Q32—862no—
331Q32—862no—
332SD32—862no—
333SD32—862no—
334C2×C16—431no—
335C2×C16—431no—
336C2×C16—431no—
337C2×C16—431no—
338#107—431no—
339#107—431no—
340#107—861no—
341#107C22×D4311yescharacteristic
342#107C22×D4311yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—861no—
349#103—861no—
350#102—861no—
351#102—861no—
352#97C22⋊D4311yescharacteristic
353#97C22⋊D4311yescharacteristic
354C4×C8C22×D4311yescharacteristic
355C4×C8C22×D4311yescharacteristic
356#41—864no—
357#41—1722no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—861no—
361C2×D4—861no—
362C2×D4—1721no—
363C22×C4—1721no—
364C22×C4—1721no—
365C22×C4—1721no—
366C22×C4—1721no—
367C22×C4C2×C22⋊D4311yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16—42no—
373Q16—432no—
374Q16—861no—
375SD16—864no—
376D8—432no—
377D8—861no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D4311yescharacteristic
382C2×C8C2×C22⋊D4311yescharacteristic
383C2×C8C2×C22⋊D4311yescharacteristic
384C2×C8C23×D4311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—861no—
396C4⋊C4—861no—
397C4⋊C4—1721no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C4⋊C4#1062188211yescharacteristic
401C4⋊C4#1062188211yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4#1062188211yescharacteristic
407C22⋊C4#1062188211yescharacteristic
408C42—41no—
409C42—41no—
410C42—1721no—
411C42—1721no—
412C42C2×C22⋊D4311yescharacteristic
413C42C2×C22⋊D4311yescharacteristic
414C16—861no—
415C16—861no—
416C16—861no—
417C16—861no—
418C23—1721no—
419C23C2×#1062188211yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—41no—
423Q8—41no—
424Q8—862no—
425Q8—1721no—
426D4—862no—
427D4—1724no—
428D4—1721no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—1724no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—6881no—
440C2×C4—6881no—
441C2×C4—6881no—
442C2×C4C2×#1062188211yescharacteristic
443C2×C4C2×#1062188211yescharacteristic
444C2×C4C2×#1062188211yescharacteristic
445C2×C4C2×#1062188211yescharacteristic
446C2×C4C2×#1062188211yescharacteristic
447C2×C4C22×C22⋊D4311yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8#41×D4311yescharacteristic
452C8#41×D4311yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—3441no—
457C22—3441no—
458C22—1722no—
459C22C22×#1062188211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—3441no—
470C4—3441no—
471C4—1722no—
472C4#1458340611yescharacteristic
473C4#1458369711yescharacteristic
474C2—41no—
475C2—3442no—
476C2#1914459111yescharacteristic
477C2#1914773911yescharacteristic
478C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3177C2
socleC22×C43C22×D8
prime radicalC2×#13063347C22
hypercenter#3177D43
hypocenterC43#33680
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #19136795C2semidirect
3. #19136790C2semidirect
4. #19136756C2semidirect
5. #19136749C2semidirect
6. #19136642C2semidirect
7. #19136637C2semidirect
10. #19136464C2semidirect
11. #19136457C2semidirect
12. C4×#13063271C2semidirect
13. C4×#13063268C2semidirect
14. #19136402C2semidirect
15. C43×#3177C2semidirect
235. #3177D43semidirect
298. C43#33680semidirect

Maximal subgroups

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

subgroupindex
#191434722
#191367952
#191367902
#191367562
#191367492
#191366422
#191366372
#191365332
#191364642
#191364572
C4×#130632712
C4×#130632682
#191364022
C43×#31772
#3368043