Finite Group Databasebeta

← #24988962

Subgroups — #24988962

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135428C211yesmaximal, characteristic, complemented
2#19133325C211yesmaximal, characteristic, complemented
3#19133317C211yesmaximal, characteristic, complemented
4#19133230C211yesmaximal, characteristic, complemented
5#19133107C211yesmaximal, characteristic, complemented
6#19133103C211yesmaximal, characteristic, complemented
7C43×#3548C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582923C2211yescharacteristic
11C2×#13063252—22no—
12#14582745C2211yescharacteristic
13#14582648—21no—
14#14582645—21no—
15#14582645—21no—
16#14582643—21no—
17#14582639—22no—
18#14582636—22no—
19#14582633—22no—
20C43×#562—22no—
21C43×#554—21no—
22C43×#554C412yescomplemented
23C43×#550—21no—
24C43×#550C412yescomplemented
25C43×#547—21no—
26C43×#547—21no—
27C43×#540—22no—
28C43×#537—22no—
29C43×#537—22no—
30C43×#533C2211yescharacteristic
31C43×#532C2211yescharacteristic
32C43×#532C2211yescharacteristic
33C2×#10621877—21no—
34C2×C4×Dic43—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39#13063252—44no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42#13063236—21no—
43#13063236—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C2×#41×C43—22no—
47C2×#41×C43—22no—
48C2×#41×C43—21no—
49C2×#41×C43D412yes—
50C4⋊Q8×C43C2×C411yescharacteristic
51C4⋊Q8×C43D411yescharacteristic
52C4⋊Q8×C43D411yescharacteristic
53C4⋊Q8×C43D411yescharacteristic
54#127×C43—22no—
55#127×C43C2×C411yescharacteristic
56#127×C43D411yescharacteristic
57#125×C43—22no—
58#125×C43—21no—
59#124×C43—21no—
60#124×C43D412yes—
61#123×C43—24no—
62#123×C43—24no—
63C22⋊Q8×C43—22no—
64C22⋊Q8×C43—24no—
65C22⋊Q8×C43—22no—
66C22⋊Q8×C43—24no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43D412yes—
69#121×C43—24no—
70#121×C43—24no—
71#121×C43—22no—
72#121×C43—24no—
73#121×C43—24no—
74#121×C43—21no—
75#121×C43—21no—
76#121×C43—21no—
77#121×C43—22no—
78#121×C43D412yes—
79C4×Q8×C43—21no—
80C4×Q8×C43C2×C412yes—
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83C4×D4×C43—21no—
84C4×D4×C43—21no—
85C4×D4×C43—21no—
86C4×D4×C43C2×C412yes—
87#117×C43—21no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—22no—
90C2×C42×C43C2311yescharacteristic
91#41×C43—42no—
92#41×C43—42no—
93#41×C43—82no—
94#41×C43—84no—
95#41×C43—82no—
96#41×C43—82no—
97C2×Q8×C43—21no—
98C2×Q8×C43—21no—
99C2×Q8×C43C22⋊C412yes—
100C2×Q8×C43C22⋊C412yes—
101C2×D4×C43—24no—
102C2×D4×C43—24no—
103C2×D4×C43—21no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43C22⋊C412yes—
110C2×D4×C43C22⋊C412yes—
111C22×C4×C43—24no—
112C22×C4×C43—24no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×Dic43—41no—
119C4⋊C4×C43—24no—
120C4⋊C4×C43—24no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43C22⋊C412yes—
130C4⋊C4×C43C22⋊C412yes—
131C22⋊C4×C43—24no—
132C22⋊C4×C43—24no—
133C22⋊C4×C43—22no—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—22no—
138C42×C43—22no—
139C42×C43C22×C411yescharacteristic
140C42×C43C2×D411yescharacteristic
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143C4×Dic43—22no—
144C4×Dic43—41no—
145#10621877—42no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149C23×C43—22no—
150C23×C43—22no—
151C23×C43#12011yescharacteristic
152Q8×C43—42no—
153Q8×C43—42no—
154Q8×C43—41no—
155Q8×C43—41no—
156Q8×C43—81no—
157D4×C43—42no—
158D4×C43—42no—
159D4×C43—42no—
160D4×C43—42no—
161D4×C43—41no—
162D4×C43—41no—
163D4×C43—81no—
164D4×C43—82no—
165D4×C43—82no—
166D4×C43—84no—
167D4×C43—84no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—22no—
173C2×C4×C43—22no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—44no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—84no—
180C2×C4×C43—84no—
181C2×C4×C43C2×C22⋊C411yescharacteristic
182C2×C4×C43C2×C22⋊C411yescharacteristic
183C2×C4×C43C2×C22⋊C411yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12011yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×Dic43—42no—
188C2×Dic43—81no—
189C2×Dic43—81no—
190C43⋊C8—81no—
191C43⋊C8—81no—
192C43⋊C8—81no—
193#8493—431nomaximal, Sylow
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—42no—
198C22×C43—42no—
199C22×C43—42no—
200C22×C43—42no—
201C22×C43—42no—
202C22×C43—42no—
203C22×C43#37911yescharacteristic
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—42no—
210C4×C43—42no—
211C4×C43—42no—
212C4×C43—42no—
213C4×C43#45311yescharacteristic
214C4×C43#45511yescharacteristic
215Dic43—82no—
216#3548D4311yescharacteristic
217#1963—431no—
218#1559—431no—
219#1557—431no—
220#1536—431no—
221#1506—431no—
222#1505—431no—
223C2×C43—41no—
224C2×C43—82no—
225C2×C43—82no—
226C2×C43#179211yescharacteristic
227C2×C43#179511yescharacteristic
228C2×C43#179611yescharacteristic
229#562—22no—
230#554—21no—
231#554Dic4312yescomplemented
232#550—21no—
233#550Dic4312yescomplemented
234#547—21no—
235#547—21no—
236#540—22no—
237#537—22no—
238#537—22no—
239#533C2×D4311yescharacteristic
240#532C2×D4311yescharacteristic
241#532C2×D4311yescharacteristic
242#432—431no—
243#432—431no—
244#423—431no—
245C2×#104—862no—
246#376—431no—
247#333—861no—
248#332—861no—
249#332—861no—
250#331—861no—
251#329—862no—
252#328—862no—
253#327—862no—
254C43#849311yescharacteristic, complemented, Sylow
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—21no—
258C2×#41C22⋊D4312yes—
259C2×M16—861no—
260C4⋊Q8C2×Dic4311yescharacteristic
261C4⋊Q8C22⋊D4311yescharacteristic
262C4⋊Q8C22⋊D4311yescharacteristic
263C4⋊Q8C22⋊D4311yescharacteristic
264#127—22no—
265#127C2×Dic4311yescharacteristic
266#127C22⋊D4311yescharacteristic
267#125—22no—
268#125—21no—
269#124—21no—
270#124C22⋊D4312yes—
271#123—24no—
272#123—24no—
273C22⋊Q8—22no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277C22⋊Q8—21no—
278C22⋊Q8C22⋊D4312yes—
279#121—24no—
280#121—24no—
281#121—22no—
282#121—24no—
283#121—24no—
284#121—21no—
285#121—21no—
286#121—21no—
287#121—22no—
288#121C22⋊D4312yes—
289C4×Q8—21no—
290C4×Q8C2×Dic4312yes—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4C2×Dic4312yes—
297#117—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C42—861no—
301C2×C42C22×D4311yescharacteristic
302C4⋊C8—861no—
303C4⋊C8—861no—
304C4⋊C8—861no—
305C4⋊C8—861no—
306#104—1724no—
307C22⋊C8—861no—
308C22⋊C8—861no—
309#97—861no—
310#97—861no—
311#95—861no—
312#95—861no—
313#41—42no—
314#41—42no—
315#41—82no—
316#41—84no—
317#41—82no—
318#41—82no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8C22⋊Dic4312yes—
322C2×Q8C22⋊Dic4312yes—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4C22⋊Dic4312yes—
332C2×D4C22⋊Dic4312yes—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—1721no—
338C22×C4C2×C22⋊D4311yescharacteristic
339C22×C4C2×C22⋊D4311yescharacteristic
340C22×C4C2×C22⋊D4311yescharacteristic
341M16—1722no—
342C2×C8—1721no—
343C2×C8—1721no—
344C2×C8—1721no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4C22⋊Dic4312yes—
356C4⋊C4C22⋊Dic4312yes—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C42—22no—
365C42—862no—
366C42—1721no—
367C42C22×Dic4311yescharacteristic
368C42C2×C22⋊D4311yescharacteristic
369C42C2×C22⋊D4311yescharacteristic
370C42C2×C22⋊D4311yescharacteristic
371C23—22no—
372C23—22no—
373C23#1306329411yescharacteristic
374Q8—42no—
375Q8—42no—
376Q8—41no—
377Q8—41no—
378Q8—81no—
379D4—42no—
380D4—42no—
381D4—42no—
382D4—42no—
383D4—41no—
384D4—41no—
385D4—81no—
386D4—82no—
387D4—82no—
388D4—84no—
389D4—84no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—84no—
402C2×C4—84no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—1722no—
406C2×C4C2×C22⋊Dic4311yescharacteristic
407C2×C4C2×C22⋊Dic4311yescharacteristic
408C2×C4C2×C22⋊Dic4311yescharacteristic
409C2×C4#1306329411yescharacteristic
410C2×C4#1306329411yescharacteristic
411C2×C4#1306329411yescharacteristic
412C8—3441no—
413C8—3441no—
414C8—3441no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22#1458275511yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—3442no—
435C4#1458306711yescharacteristic
436C4#1458307711yescharacteristic
437C2—41no—
438C2—82no—
439C2—82no—
440C2#1913454911yescharacteristic
441C2#1913456511yescharacteristic
442C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3548C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3548D43
hypocenterC43#8493
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #19135428C2semidirect
2. #19133325C2semidirect
3. #19133317C2semidirect
4. #19133230C2semidirect
5. #19133107C2semidirect
6. #19133103C2semidirect
22. C43×#554C4semidirect
24. C43×#550C4semidirect
231. #554Dic43semidirect
233. #550Dic43semidirect
254. C43#8493semidirect

Maximal subgroups

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

subgroupindex
#191354282
#191333252
#191333172
#191332302
#191331072
#191331032
C43×#35482
#849343