Finite Group Databasebeta

← #24988395

Subgroups — #24988395

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135536C211yesmaximal, characteristic, complemented
2C4×#13063244C211yesmaximal, characteristic, complemented
3#19133183C212yesmaximal, complemented
4#19133008C212yesmaximal, complemented
5C43×#3461C211yesmaximal, characteristic
6C2×C4⋊(C43⋊C8)C2211yescharacteristic
7C2×#13063244—21no—
8C4×#10621877C2212yes—
9C2×#13063236C2211yescharacteristic
10#14582668—21no—
11#14582654—21no—
12#14582654—21no—
13#14582641—22no—
14#14582639—22no—
15Q8⋊(C43⋊C8)—22no—
16D4⋊(C43⋊C8)—22no—
17C43×#544C411yescharacteristic
18C43×#542—22no—
19C43×#541—22no—
20C43×#539—21no—
21C43×#539C412yes—
22C43×#537C411yescharacteristic
23C43×#536—21no—
24C43×#533—22no—
25C43×#529—22no—
26C43×#529—21no—
27C43×#529C2212yes—
28C4×#41×C43—21no—
29C2×C4×Q8×C43C2211yescharacteristic
30C2×#10621877—22no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33C4⋊(C43⋊C8)—22no—
34#13063244—24no—
35#13063236—22no—
36#13063236—22no—
37C4×C43⋊C8—22no—
38C2×#41×C43—21no—
39C22×Q8×C43D411yescharacteristic
40C4⋊Q8×C43—22no—
41C4⋊Q8×C43—22no—
42#126×C43—22no—
43#126×C43—22no—
44#126×C43—22no—
45#126×C43—22no—
46#125×C43—21no—
47#125×C43—22no—
48#125×C43—22no—
49#125×C43—22no—
50#125×C43D412yes—
51#124×C43—22no—
52#124×C43—21no—
53#124×C43D412yes—
54#123×C43—22no—
55#123×C43—22no—
56#123×C43—22no—
57#123×C43—22no—
58C22⋊Q8×C43—22no—
59C22⋊Q8×C43—22no—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43C2×C412yes—
65#121×C43—22no—
66#121×C43—21no—
67#121×C43C2×C412yes—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—22no—
72C4×Q8×C43—22no—
73C4×Q8×C43D412yes—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C4×D4×C43D412yes—
80#117×C43—22no—
81#117×C43—22no—
82#117×C43—21no—
83#117×C43—22no—
84C2×C4⋊C4×C43C2×C411yescharacteristic
85C2×C4⋊C4×C43C2×C411yescharacteristic
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C42×C43—22no—
88C2×C42×C43D411yescharacteristic
89C2×C42×C43D411yescharacteristic
90C2×C42×C43C2311yescharacteristic
91#41×C43—42no—
92#41×C43—42no—
93C2×Q8×C43—21no—
94C2×Q8×C43—21no—
95C2×Q8×C43—22no—
96C2×Q8×C43—22no—
97C2×Q8×C43—41no—
98C2×Q8×C43C22⋊C412yes—
99C2×D4×C43—21no—
100C2×D4×C43—21no—
101C2×D4×C43—22no—
102C2×D4×C43C22⋊C412yes—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43C22⋊C411yescharacteristic
107C22×C4×C43C22⋊C411yescharacteristic
108C22×C4×C43C22⋊C411yescharacteristic
109C22×C4×C43C22⋊C411yescharacteristic
110C22×C4×C43C22×C411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C4⋊C4×C43—21no—
114C4⋊C4×C43—22no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43C22⋊C412yes—
129C4⋊C4×C43C22⋊C412yes—
130C22⋊C4×C43—22no—
131C22⋊C4×C43—22no—
132C22⋊C4×C43—22no—
133C22⋊C4×C43—22no—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C42×C43—22no—
140C42×C43—22no—
141C42×C43—21no—
142C42×C43—22no—
143C42×C43—21no—
144C42×C43—21no—
145C42×C43—21no—
146C42×C43C2×D412yes—
147C42×C43C2×D412yes—
148#10621877—24no—
149#10621877—42no—
150C2×C43⋊C8—22no—
151C2×C43⋊C8—41no—
152C2×C43⋊C8—42no—
153C2×C43⋊C8—41no—
154C2×C43⋊C8—42no—
155C2×C43⋊C8—41no—
156C23×C43—22no—
157C23×C43C2×C22⋊C411yescharacteristic
158Q8×C43—44no—
159Q8×C43—42no—
160Q8×C43—42no—
161Q8×C43—81no—
162D4×C43—42no—
163D4×C43—42no—
164D4×C43—42no—
165D4×C43—42no—
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—21no—
174C2×C4×C43—22no—
175C2×C4×C43—22no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—22no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—41no—
182C2×C4×C43—44no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—82no—
188C2×C4×C43#10412yes—
189C2×C4×C43C2×C22⋊C412yes—
190C2×C4×C43#12011yescharacteristic
191C2×C4×C43#12012yes—
192C2×C4×C43#12011yescharacteristic
193C43⋊C8—42no—
194C43⋊C8—44no—
195C43⋊C8—81no—
196#8402—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—42no—
200C22×C43—42no—
201C22×C43—42no—
202C22×C43#37911yescharacteristic
203C22×C43C2×#10411yescharacteristic
204C22×C43#42111yescharacteristic
205C4×C43—21no—
206C4×C43—22no—
207C4×C43—22no—
208C4×C43—22no—
209C4×C43—42no—
210C4×C43—41no—
211C4×C43—42no—
212C4×C43—41no—
213C4×C43—41no—
214C4×C43—42no—
215C4×C43#45411yescharacteristic
216C4×C43#45611yescharacteristic
217#3461D4311yescharacteristic
218#1985—431no—
219C4×#101—431no—
220#1524—432no—
221#1483—432no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—82no—
225C2×C43#178911yescharacteristic
226C2×C43#179111yescharacteristic
227C2×C43#179311yescharacteristic
228#544Dic4311yescharacteristic
229#542—22no—
230#541—22no—
231#539—21no—
232#539Dic4312yes—
233#537Dic4311yescharacteristic
234#536—21no—
235#533—22no—
236#529—22no—
237#529—21no—
238#529C2×D4312yes—
239C4×#41—21no—
240C2×C4×Q8C2×D4311yescharacteristic
241C2×C4⋊C8—431no—
242C2×#101—861no—
243C4×M16—432no—
244C2×#97—431no—
245#343—861no—
246#336—861no—
247#336—861no—
248#330—862no—
249#329—862no—
250Q8⋊C8—862no—
251D4⋊C8—862no—
252C43#840211yescharacteristic, complemented, Sylow
253C2×#41—21no—
254C22×Q8C22⋊D4311yescharacteristic
255C2×M16—862no—
256C22×C8—861no—
257C22×C8—861no—
258C4⋊Q8—22no—
259C4⋊Q8—22no—
260#126—22no—
261#126—22no—
262#126—22no—
263#126—22no—
264#125—21no—
265#125—22no—
266#125—22no—
267#125—22no—
268#125C22⋊D4312yes—
269#124—22no—
270#124—21no—
271#124C22⋊D4312yes—
272#123—22no—
273#123—22no—
274#123—22no—
275#123—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—21no—
281C22⋊Q8—22no—
282C22⋊Q8C2×Dic4312yes—
283#121—22no—
284#121—21no—
285#121C2×Dic4312yes—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×Q8C22⋊D4312yes—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4C22⋊D4312yes—
298#117—22no—
299#117—22no—
300#117—21no—
301#117—22no—
302C2×C4⋊C4C2×Dic4311yescharacteristic
303C2×C4⋊C4C2×Dic4311yescharacteristic
304C2×C4⋊C4C22⋊D4311yescharacteristic
305C2×C42—22no—
306C2×C42C22⋊D4311yescharacteristic
307C2×C42C22⋊D4311yescharacteristic
308C2×C42C22×D4311yescharacteristic
309C4⋊C8—862no—
310#101—864no—
311#97—862no—
312#97—862no—
313C4×C8—862no—
314#41—42no—
315#41—42no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—41no—
321C2×Q8C22⋊Dic4312yes—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—21no—
325C2×D4C22⋊Dic4312yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4C22⋊Dic4311yescharacteristic
330C22×C4C22⋊Dic4311yescharacteristic
331C22×C4C22⋊Dic4311yescharacteristic
332C22×C4C22⋊Dic4311yescharacteristic
333C22×C4C22×Dic4311yescharacteristic
334C22×C4C2×C22⋊D4311yescharacteristic
335C22×C4C2×C22⋊D4311yescharacteristic
336M16—864no—
337M16—1722no—
338C2×C8—862no—
339C2×C8—1722no—
340C2×C8—1721no—
341C2×C8—1721no—
342C2×C8—1722no—
343C2×C8—1721no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4C22⋊Dic4312yes—
360C4⋊C4C22⋊Dic4312yes—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C42—22no—
371C42—22no—
372C42—21no—
373C42—21no—
374C42—21no—
375C42—22no—
376C42—21no—
377C42C2×C22⋊D4312yes—
378C42C2×C22⋊D4312yes—
379C23—22no—
380C23C2×C22⋊Dic4311yescharacteristic
381Q8—44no—
382Q8—42no—
383Q8—42no—
384Q8—81no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—81no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—82no—
411C2×C4#1306325212yes—
412C2×C4C2×C22⋊Dic4312yes—
413C2×C4#1306329411yescharacteristic
414C2×C4#1306329412yes—
415C2×C4#1306329411yescharacteristic
416C8—3441no—
417C8—1722no—
418C8—1724no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22#1458275511yescharacteristic
425C22C2×#1306325211yescharacteristic
426C22#1458291611yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—21no—
431C4—41no—
432C4—42no—
433C4—41no—
434C4—41no—
435C4—42no—
436C4—42no—
437C4#1458307211yescharacteristic
438C4#1458308211yescharacteristic
439C2—21no—
440C2—21no—
441C2—82no—
442C2#1913453911yescharacteristic
443C2#1913454611yescharacteristic
444C2#1913455411yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3461C2
socleC22×C43#379
prime radicalC43×#537C4
cosocleC2×C42×C43C23
hypercenter#3461D43
hypocenterC43#8402
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #19135536C2semidirect
2. C4×#13063244C2semidirect
3. #19133183C2semidirect
4. #19133008C2semidirect
252. C43#8402semidirect

Maximal subgroups

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

subgroupindex
#191355362
C4×#130632442
#191331832
#191330082
C43×#34612
#840243