Finite Group Databasebeta

← #24992201

Subgroups — #24992201

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#97×D43C211yesmaximal, characteristic
2#19142906C211yesmaximal, characteristic
3#19134358C211yesmaximal, characteristic
4C2×#14582640C211yesmaximal, characteristic, complemented
5C2×#14582640C211yesmaximal, characteristic, complemented
6#19132476C211yesmaximal, characteristic, complemented
7C43×#1295C211yesmaximal, characteristic, complemented
8C22×C8×D43—21no—
9C2×#13063317C2211yescharacteristic
10C2×C42×D43C2211yescharacteristic
11C2×(C2×D43)⋊C8—21no—
12C2×#13063236C2211yescharacteristic
13C2×#13063236C2211yescharacteristic
14C2×#13063235—21no—
15#97×D43—22no—
16#97×D43—22no—
17#14582798C411yescharacteristic
18#14582798C411yescharacteristic
19#14582784—21no—
20#14582784—21no—
21#14582773—21no—
22#14582773—21no—
23#14582756C411yescharacteristic
24#14582756C411yescharacteristic
25#14582653—21no—
26#14582640—22no—
27#14582640—22no—
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#382C2211yescharacteristic
31C22×C4×D43C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C2×C8×D43—24no—
37C2×C8×D43—24no—
38C2×C8×D43—24no—
39#13063317—21no—
40#13063317—21no—
41#13063317—21no—
42#13063317—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×C4×Dic43C2×C411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C42×D43—21no—
55C42×D43—21no—
56C42×D43—21no—
57C42×D43—21no—
58(C2×D43)⋊C8—24no—
59#13063236—21no—
60#13063236—21no—
61#13063236—21no—
62#13063236D412yes—
63#13063235—24no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C42×C43C2311yescharacteristic
73#97×C43—21no—
74#97×C43—21no—
75#97×C43—21no—
76#97×C43D412yes—
77#95×C43—21no—
78#95×C43—21no—
79C23×D43C22⋊C411yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—22no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—22no—
98C2×C4×D43—22no—
99C2×C4×D43—22no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114(C2×D43)⋊C4—42no—
115(C2×D43)⋊C4—42no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—42no—
121C4⋊Dic43—42no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126C4×Dic43—21no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C8×D43—216no—
139C23×C43C2×C22⋊C411yescharacteristic
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43#10112yes—
145C22×D43#10412yes—
146C22×D43#10412yes—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
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×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43#10412yes—
180C4×D43—24no—
181C4×D43—24no—
182C4×D43—42no—
183C4×D43—42no—
184C4×D43—42no—
185C4×D43—42no—
186C8×C43—24no—
187C8×C43—42no—
188C43⋊C8—24no—
189C43⋊C8—42no—
190#9121—431nomaximal, Sylow
191C22×C43#38611yescharacteristic
192C22×C43C2×#10111yescharacteristic
193C22×C43#41311yescharacteristic
194C22×C43C2×#10411yescharacteristic
195C22×C43C2×#10411yescharacteristic
196C22×C43C2×#10411yescharacteristic
197C22×C43#42111yescharacteristic
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—22no—
202C2×D43—22no—
203C2×D43—22no—
204C2×D43#33014yescomplemented
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43—81no—
213Dic43—22no—
214Dic43—41no—
215Dic43—41no—
216Dic43—81no—
217Dic43—81no—
218C22×#97—431no—
219#2851—431no—
220#1749—431no—
221C2×#330—431no—
222C2×#330—431no—
223#1295—431no—
224#1295D4311yescharacteristic, complemented
225C2×C43C2×#33011yescharacteristic
226C2×C43#152411yescharacteristic
227C2×C43#153111yescharacteristic
228C2×C43#153211yescharacteristic
229C2×C43#187111yescharacteristic
230C2×C43#189611yescharacteristic
231C2×C43#190111yescharacteristic
232D43—24no—
233C23×C8—861no—
234C2×#125—431no—
235C22×C42—431no—
236C2×C22⋊C8—861no—
237C2×#97—431no—
238C2×#97—431no—
239C2×#97—862no—
240C2×#97—861no—
241C2×#97—862no—
242C2×#97C2×D4311yescharacteristic
243C2×#97C2×D4311yescharacteristic
244#389—431no—
245#389—431no—
246#387—861no—
247#387—861no—
248#385—861no—
249#385—861no—
250#382C2×D4311yescharacteristic
251#380—431no—
252#380—431no—
253#336—861no—
254#330—862no—
255#330—862no—
256C43#912111yescharacteristic, complemented, Sylow
257C23×C4—431no—
258C23×C4—431no—
259C23×C4—431no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—864no—
263C22×C8—864no—
264C22×C8—864no—
265C22×C8—861no—
266C22×C8—861no—
267#125—861no—
268#125—861no—
269#125—861no—
270#125—861no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4—431no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4C4×D4311yescharacteristic
278C2×C4⋊C4C4×D4311yescharacteristic
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C42—431no—
282C2×C42—431no—
283C2×C42—431no—
284C2×C42—861no—
285C2×C42—861no—
286C2×C42—861no—
287C2×C42—861no—
288C2×C42C22×D4311yescharacteristic
289C22⋊C8—864no—
290#97—21no—
291#97—21no—
292#97—21no—
293#97—432no—
294#97—864no—
295#97—861no—
296#97—861no—
297#97—861no—
298#97D17212yes—
299#95—21no—
300#95—21no—
301#95—861no—
302#95—861no—
303#95—861no—
304#95—861no—
305C24—431no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—431no—
311C22×C4—862no—
312C22×C4—862no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—1721no—
324C22×C4—1721no—
325C22×C4C2×C4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—8616no—
335C2×C8—862no—
336C2×C8—862no—
337C2×C8—862no—
338C2×C8—862no—
339C2×C8—1721no—
340C2×C8—1721no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—1722no—
348C4⋊C4—1722no—
349C4⋊C4—1721no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C4⋊C4—1721no—
353C22⋊C4—1722no—
354C22⋊C4—1722no—
355C42—861no—
356C42—861no—
357C42—861no—
358C42—861no—
359C42—861no—
360C42—861no—
361C42C2×D17211yescharacteristic
362C42#1062189811yescharacteristic
363C42D4×D4311yescharacteristic
364C42#1062190211yescharacteristic
365C23—432no—
366C23—432no—
367C23—432no—
368C23—861no—
369C23—861no—
370C23—861no—
371C23—861no—
372C23C22⋊C4×D4311yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—432no—
386C2×C4—864no—
387C2×C4—864no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4#1306328711yescharacteristic
407C2×C4C4×D17211yescharacteristic
408C2×C4#1306329511yescharacteristic
409C2×C4#1306329811yescharacteristic
410C2×C4#1306330011yescharacteristic
411C2×C4#1306331011yescharacteristic
412C8—24no—
413C8—42no—
414C8—864no—
415C8—1722no—
416C22—434no—
417C22—862no—
418C22—862no—
419C22—862no—
420C22—862no—
421C22—862no—
422C22—862no—
423C22#1458277711yescharacteristic
424C22#101×D4311yescharacteristic
425C22#1458288011yescharacteristic
426C22#104×D4311yescharacteristic
427C22#104×D4311yescharacteristic
428C22#104×D4311yescharacteristic
429C22#1458291411yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—862no—
439C4—3441no—
440C4—3441no—
441C4—1721no—
442C4—1721no—
443C2—864no—
444C2#330×D4311yescharacteristic
445C2#1913318011yescharacteristic
446C2#1913320811yescharacteristic
447C2#1913321211yescharacteristic
448C2#1913489611yescharacteristic
449C2#1913503711yescharacteristic
450C2#1913506211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#9121
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. C2×#14582640C2semidirect
5. C2×#14582640C2semidirect
6. #19132476C2semidirect
7. C43×#1295C2semidirect
204. C2×D43#330semidirect
224. #1295D43semidirect
256. C43#9121semidirect

Maximal subgroups

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

subgroupindex
C2×#97×D432
#191429062
#191343582
C2×#145826402
#191324762
C43×#12952
#912143