Finite Group Databasebeta

← #24995617

Subgroups — #24995617

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142950C211yesmaximal, characteristic
2#19134449C211yesmaximal, characteristic, complemented
3#19134343C211yesmaximal, characteristic, complemented
4C2×#14582639C211yesmaximal, characteristic, complemented
5C2×#14582638C211yesmaximal, characteristic, complemented
6C2×#14582638C211yesmaximal, characteristic, complemented
7C2×C43×#329C211yesmaximal, characteristic, complemented
8C2×#13063323C411yescharacteristic
9C2×#13063321C411yescharacteristic
10C2×#13063314C411yescharacteristic
11C2×#13063313C2211yescharacteristic
12C2×#13063312C411yescharacteristic
13C2×Dic43⋊C8—21no—
14C2×#13063236C2211yescharacteristic
15C2×#13063236C2211yescharacteristic
16#14582799—21no—
17#14582799—21no—
18#14582799—21no—
19#14582799—21no—
20C42×Dic43C2211yescharacteristic
21#14582653—21no—
22#14582653—21no—
23#14582653—21no—
24#14582639—22no—
25#14582638—22no—
26#14582638—22no—
27C2×#124×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#329—22no—
31C22×Dic86C2×C411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8—21no—
37#13063323—42no—
38#13063321—42no—
39#13063314—42no—
40#13063313—21no—
41#13063313—21no—
42#13063313—21no—
43#13063313—21no—
44#13063312—42no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×C4×Dic43C2×C411yescharacteristic
54C2×C4×Dic43C2×C411yescharacteristic
55C2×C4×Dic43D411yescharacteristic
56C2×C4×Dic43D411yescharacteristic
57C2×C4×Dic43D411yescharacteristic
58C2×C4×Dic43D411yescharacteristic
59Dic43⋊C8—24no—
60#13063236—21no—
61#13063236—21no—
62#13063236—21no—
63#13063236D412yescomplemented
64C22×Q8×C43C2×C411yescharacteristic
65C22×D4×C43C2×C411yescharacteristic
66C22×C8×C43—21no—
67C22×C8×C43—21no—
68#124×C43—21no—
69#124×C43—21no—
70#124×C43—21no—
71#124×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C42×C43C2311yescharacteristic
75#97×C43—21no—
76#97×C43—21no—
77#97×C43—21no—
78#97×C43D412yescomplemented
79C24×C43—21no—
80C23×D43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—41no—
84C2×Q8×C43—41no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C22×C4×C43—21no—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C2×C22⋊D43—42no—
94C2×C22⋊D43—42no—
95C2×C22⋊D43—42no—
96C2×C22⋊D43—42no—
97C2×C22⋊D43—42no—
98C2×C22⋊D43—42no—
99C22×Dic43—21no—
100C22×Dic43C22⋊C411yescharacteristic
101C22×Dic43C22⋊C411yescharacteristic
102C22×Dic43C22⋊C411yescharacteristic
103C22×Dic43C22⋊C411yescharacteristic
104C2×D172—21no—
105C2×D172—21no—
106C2×D172—41no—
107C2×D172—41no—
108C2×Dic86—21no—
109C2×Dic86—21no—
110C2×Dic86—41no—
111C2×Dic86—41no—
112C2×C8×C43—22no—
113C2×C8×C43—22no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43#4111yescharacteristic
125C42×C43#4111yescharacteristic
126C22⋊Dic43—42no—
127C22⋊Dic43—42no—
128(C2×D43)⋊C4—42no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4—41no—
133(C2×D43)⋊C4—42no—
134Dic43⋊C4—42no—
135Dic43⋊C4—42no—
136C4×Dic43—22no—
137C4×Dic43—22no—
138C4×Dic43—22no—
139C4×Dic43—41no—
140C4×Dic43—41no—
141C4×Dic43—41no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—22no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43C2×C22⋊C411yescharacteristic
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—41no—
160C22×D43—41no—
161C22×D43—41no—
162C22×D43—41no—
163Q8×C43—81no—
164Q8×C43—81no—
165D4×C43—81no—
166D4×C43—81no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43C4×D411yescharacteristic
177C2×C4×C43C4×D411yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12411yescharacteristic
181C2×C4×C43#12711yescharacteristic
182C22⋊D43—84no—
183C22⋊D43—84no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43#10012yes—
197C2×Dic43#10012yes—
198C2×Dic43#10412yes—
199D172—81no—
200D172—81no—
201Dic86—81no—
202Dic86—81no—
203C8×C43—42no—
204C8×C43—42no—
205C43⋊C8—42no—
206C43⋊C8—42no—
207#9689—431nomaximal, Sylow
208C22×C43—81no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43#39011yescharacteristic
216C22×C43C2×#10011yescharacteristic
217C22×C43C2×#10011yescharacteristic
218C22×C43C2×#10411yescharacteristic
219C22×C43#42111yescharacteristic
220C22×C43#42111yescharacteristic
221C22×C43#42111yescharacteristic
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—81no—
236Dic43—22no—
237Dic43—22no—
238Dic43—22no—
239Dic43—41no—
240Dic43—81no—
241#2858—431no—
242#1767—431no—
243#1745—431no—
244C2×#329—431no—
245C2×#329—431no—
246C2×#329—431no—
247C2×#329D4311yescharacteristic, complemented
248C2×C43—161no—
249C2×C43#152711yescharacteristic
250C2×C43#153011yescharacteristic
251C2×C43#153311yescharacteristic
252C2×C43#153611yescharacteristic
253C2×C43#196311yescharacteristic
254C2×C43#196511yescharacteristic
255C2×C43#198011yescharacteristic
256D43—161no—
257C2×C4⋊Q8—431no—
258C2×#127—431no—
259C2×#124—431no—
260C2×#124—431no—
261C2×#124—431no—
262C2×#124C2×D4311yescharacteristic
263C2×C4⋊C8—861no—
264C2×#97—431no—
265C2×#97—431no—
266C2×#97C2×D4311yescharacteristic
267C2×#97C2×D4311yescharacteristic
268#390—861no—
269#390—861no—
270#390—861no—
271#390—861no—
272C43—431no—
273#336—861no—
274#336—861no—
275#336—861no—
276#329—22no—
277#329—862no—
278#329—862no—
279#329—862no—
280C43#968911yescharacteristic, complemented, Sylow
281C22×Q8—431no—
282C22×Q8C4×D4311yescharacteristic
283C22×D4—431no—
284C22×D4—861no—
285C22×D4—861no—
286C22×D4C4×D4311yescharacteristic
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—861no—
290C22×C8—861no—
291C4⋊Q8—1722no—
292#127—1722no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—21no—
297#124—861no—
298#124—861no—
299#124—861no—
300#124—861no—
301#124—1722no—
302#124—1722no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4—861no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C42—431no—
314C2×C42—431no—
315C2×C42—431no—
316C2×C42—431no—
317C2×C42—431no—
318C2×C42—431no—
319C2×C42C22×D4311yescharacteristic
320C4⋊C8—864no—
321#97—21no—
322#97—21no—
323#97—21no—
324#97—432no—
325#97—861no—
326#97—861no—
327#97—861no—
328#97C22⋊D4312yescomplemented
329C24—21no—
330C24—861no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—861no—
336C2×Q8—861no—
337C2×Q8—1721no—
338C2×Q8—1721no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—861no—
344C2×D4—861no—
345C2×D4—1721no—
346C2×D4—1721no—
347C2×D4—1722no—
348C2×D4—1722no—
349C2×D4—1722no—
350C2×D4—1722no—
351C2×D4—1722no—
352C2×D4—1722no—
353C22×C4—21no—
354C22×C4—431no—
355C22×C4—431no—
356C22×C4—431no—
357C22×C4—431no—
358C22×C4—861no—
359C22×C4C2×C4×D4311yescharacteristic
360C22×C4D4×D4311yescharacteristic
361C22×C4D4×D4311yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—862no—
369C2×C8—862no—
370C2×C8—1721no—
371C2×C8—1721no—
372C2×C8—1721no—
373C2×C8—1721no—
374C4⋊C4—1722no—
375C4⋊C4—1722no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—1722no—
381C22⋊C4—1722no—
382C22⋊C4—1722no—
383C22⋊C4—1722no—
384C22⋊C4—1721no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C42—862no—
389C42—862no—
390C42—862no—
391C42—1721no—
392C42—1721no—
393C42—1721no—
394C42#1062189811yescharacteristic
395C42D4×D4311yescharacteristic
396C42#1062190011yescharacteristic
397C42C2×C22⋊D4311yescharacteristic
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—1721no—
406C23—1721no—
407C23—1721no—
408C23—1721no—
409C23—1721no—
410C23—1721no—
411C23—1721no—
412C23C22⋊C4×D4311yescharacteristic
413Q8—81no—
414Q8—81no—
415Q8—3441no—
416Q8—3441no—
417D4—81no—
418D4—81no—
419D4—3441no—
420D4—3441no—
421D4—3444no—
422D4—3444no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—432no—
433C2×C4—432no—
434C2×C4—432no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—861no—
438C2×C4—861no—
439C2×C4—861no—
440C2×C4—861no—
441C2×C4—861no—
442C2×C4—861no—
443C2×C4—861no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4(C22⋊D43)⋊C411yescharacteristic
448C2×C4C4×C22⋊D4311yescharacteristic
449C2×C4#1306329711yescharacteristic
450C2×C4#1306329811yescharacteristic
451C2×C4#1306331111yescharacteristic
452C2×C4#1306332111yescharacteristic
453C8—42no—
454C8—42no—
455C8—1722no—
456C8—1722no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—3441no—
465C22—3441no—
466C22—3441no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22#1458279911yescharacteristic
472C22#100×D4311yescharacteristic
473C22#100×D4311yescharacteristic
474C22#104×D4311yescharacteristic
475C22#1458291411yescharacteristic
476C22#1458291411yescharacteristic
477C22#1458291411yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—81no—
485C4—862no—
486C4—862no—
487C4—862no—
488C4—3441no—
489C4—1721no—
490C2—161no—
491C2—6881no—
492C2#1913319111yescharacteristic
493C2#1913320411yescharacteristic
494C2#1913321711yescharacteristic
495C2#1913322811yescharacteristic
496C2#1913542511yescharacteristic
497C2#1913543311yescharacteristic
498C2#1913551211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#329C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063321C4
cosocleC2×C42×C43C23
hypercenterC2×#329D43
hypocenterC43#9689
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #19134449C2semidirect
3. #19134343C2semidirect
4. C2×#14582639C2semidirect
5. C2×#14582638C2semidirect
6. C2×#14582638C2semidirect
7. C2×C43×#329C2semidirect
63. #13063236D4semidirect
78. #97×C43D4semidirect
247. C2×#329D43semidirect
280. C43#9689semidirect
328. #97C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191429502
#191344492
#191343432
C2×#145826392
C2×#145826382
C2×C43×#3292
#968943