Finite Group Databasebeta

← #24988285

Subgroups — #24988285

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134685C212yesmaximal, complemented
2#19134583C211yesmaximal, characteristic
3#19133167C212yesmaximal, complemented
4#19132913C211yesmaximal, characteristic
5C2×C43×#554C211yesmaximal, characteristic
6C2×#13063240—21no—
7C2×C22⋊(C43⋊C8)C2212yes—
8#14582759C2212yes—
9#14582666—21no—
10#14582661—24no—
11#14582636—24no—
12#14582625—21no—
13#14582623—21no—
14C43×#554—24no—
15C43×#554—24no—
16C2×C4⋊Q8×C43C411yescharacteristic, complemented
17C2×#125×C43—21no—
18C2×C22⋊Q8×C43—21no—
19C2×C22⋊Q8×C43—21no—
20C2×C22⋊Q8×C43C411yescharacteristic, complemented
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C4×Q8×C43C411yescharacteristic, complemented
23C2×C4×D4×C43—21no—
24C2×C4×D4×C43C2211yescharacteristic
25C22×C4⋊C4×C43C411yescharacteristic, complemented
26C22×C4⋊C4×C43C2211yescharacteristic
27C22×C43⋊C8—22no—
28C2×C4⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30#13063240—42no—
31C22⋊(C43⋊C8)—22no—
32C22⋊(C43⋊C8)—22no—
33C43⋊#95—22no—
34C22×Q8×C43—21no—
35C22×Q8×C43C2×C411yescharacteristic
36C22×D4×C43D411yescharacteristic
37C23×C4×C43—21no—
38C23×C4×C43—21no—
39C23×C4×C43C2×C411yescharacteristic
40C23×C4×C43C2311yescharacteristic
41C4⋊Q8×C43—22no—
42C4⋊Q8×C43—22no—
43#125×C43—28no—
44C22⋊Q8×C43—28no—
45C22⋊Q8×C43—28no—
46C22⋊Q8×C43—22no—
47C22⋊Q8×C43—22no—
48C22⋊Q8×C43—22no—
49C22⋊Q8×C43D414yes—
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C4×D4×C43—28no—
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43C2×C411yescharacteristic
65C2×C4⋊C4×C43C2×C411yescharacteristic
66C2×C4⋊C4×C43C2×C411yescharacteristic
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43D414yes—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2×C411yescharacteristic
75C24×C43C22⋊C411yescharacteristic
76C24×C43C2×D411yescharacteristic
77C2×Q8×C43—24no—
78C2×Q8×C43—21no—
79C2×Q8×C43—42no—
80C2×Q8×C43—82no—
81C2×Q8×C43C22⋊C412yes—
82C2×D4×C43—22no—
83C2×D4×C43—22no—
84C2×D4×C43SD1612yes—
85C2×D4×C43Q1612yes—
86C22×C4×C43—24no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—24no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43—82no—
97C22×C4×C43—82no—
98C22×C4×C43C22⋊C411yescharacteristic
99C22×C4×C43C22⋊C411yescharacteristic
100C22×C4×C43C22⋊C411yescharacteristic
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D412yes—
104C22×C4×C43C2×D412yes—
105C22×Dic43—42no—
106C4⋊C4×C43—24no—
107C4⋊C4×C43—24no—
108C4⋊C4×C43—24no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—24no—
114C4⋊C4×C43—24no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43C22⋊C412yes—
117C4⋊C4×C43C22⋊C412yes—
118C4⋊C4×C43C22⋊C412yes—
119C22⋊C4×C43—24no—
120C22⋊C4×C43—22no—
121C22⋊C4×C43—24no—
122C22⋊C4×C43—22no—
123C42×C43—24no—
124C42×C43—21no—
125C42×C43—21no—
126C22⋊Dic43—42no—
127C22⋊Dic43—42no—
128C4⋊Dic43—44no—
129C2×C43⋊C8—44no—
130C2×C43⋊C8—42no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43#10312yes—
138C23×C43C2×C22⋊C411yescharacteristic
139C23×C43#12012yes—
140C23×C43C2×SD1611yescharacteristic
141C23×C43C2×Q1611yescharacteristic
142C23×C43#13712yes—
143Q8×C43—42no—
144Q8×C43—42no—
145Q8×C43—84no—
146D4×C43—24no—
147D4×C43—24no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—24no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—21no—
154C2×C4×C43—22no—
155C2×C4×C43—21no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—84no—
169C2×C4×C43—84no—
170C2×C4×C43#10312yes—
171C2×C4×C43C2×C22⋊C411yescharacteristic
172C2×C4×C43C2×C22⋊C411yescharacteristic
173C2×C4×C43#12012yes—
174C2×Dic43—82no—
175C2×Dic43—82no—
176C2×Dic43—82no—
177C43⋊C8—82no—
178#8380—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—22no—
181C22×C43—21no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43#37911yescharacteristic
192C22×C43C2×#10311yescharacteristic
193C22×C43#41911yescharacteristic
194C22×C43#44812yes—
195C22×C43#45112yes—
196C4×C43—22no—
197C4×C43—21no—
198C4×C43—22no—
199C4×C43—42no—
200C4×C43—42no—
201C4×C43—42no—
202C4×C43—41no—
203C4×C43—41no—
204C4×C43—42no—
205C4×C43#41012yes—
206Dic43—162no—
207C2×#554D4311yescharacteristic
208#1824—432no—
209#1799—431no—
210#1520—432no—
211#1459—431no—
212C2×C43—22no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—22no—
216C2×C43—42no—
217C2×C43#178211yescharacteristic
218C2×C43#178711yescharacteristic
219C2×C43#179511yescharacteristic
220#554—24no—
221#554—24no—
222C2×C4⋊Q8Dic4311yescharacteristic, complemented
223C2×#125—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8Dic4311yescharacteristic, complemented
227C2×C22⋊Q8C2×D4311yescharacteristic
228C2×C4×Q8Dic4311yescharacteristic, complemented
229C2×C4×D4—21no—
230C2×C4×D4C2×D4311yescharacteristic
231C22×C4⋊C4Dic4311yescharacteristic, complemented
232C22×C4⋊C4C2×D4311yescharacteristic
233C2×#99—861no—
234C2×C22⋊C8—432no—
235#380—432no—
236#342—861no—
237#340—864no—
238#328—864no—
239#324—861no—
240#323—861no—
241C43#838011yescharacteristic, complemented, Sylow
242C22×Q8—21no—
243C22×Q8C2×Dic4311yescharacteristic
244C22×D4C22⋊D4311yescharacteristic
245C23×C4—21no—
246C23×C4—21no—
247C23×C4C2×Dic4311yescharacteristic
248C23×C4C22×D4311yescharacteristic
249C22×C8—862no—
250C4⋊Q8—22no—
251C4⋊Q8—22no—
252#125—28no—
253C22⋊Q8—28no—
254C22⋊Q8—28no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8C22⋊D4314yes—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×D4—28no—
262C4×D4—22no—
263C4×D4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—862no—
274C2×C4⋊C4C2×Dic4311yescharacteristic
275C2×C4⋊C4C2×Dic4311yescharacteristic
276C2×C4⋊C4C2×Dic4311yescharacteristic
277C2×C4⋊C4C22⋊D4311yescharacteristic
278C2×C4⋊C4C22⋊D4314yes—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—862no—
282C2×C22⋊C4C22⋊D4311yescharacteristic
283C2×C22⋊C4C22⋊D4311yescharacteristic
284C2×C42—21no—
285C2×C42C2×Dic4311yescharacteristic
286#99—1722no—
287C22⋊C8—862no—
288C22⋊C8—862no—
289#95—862no—
290C24C22⋊Dic4311yescharacteristic
291C24C2×C22⋊D4311yescharacteristic
292C2×Q8—24no—
293C2×Q8—21no—
294C2×Q8—42no—
295C2×Q8—82no—
296C2×Q8C22⋊Dic4312yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4#1062188412yes—
300C2×D4#1062188512yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—82no—
312C22×C4—82no—
313C22×C4—1722no—
314C22×C4C22⋊Dic4311yescharacteristic
315C22×C4C22⋊Dic4311yescharacteristic
316C22×C4C22⋊Dic4311yescharacteristic
317C22×C4C22×Dic4311yescharacteristic
318C22×C4C2×C22⋊D4312yes—
319C22×C4C2×C22⋊D4312yes—
320C22×C4C2×C22⋊D4311yescharacteristic
321C2×C8—1724no—
322C2×C8—1722no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—1724no—
334C4⋊C4C22⋊Dic4312yes—
335C4⋊C4C22⋊Dic4312yes—
336C4⋊C4C22⋊Dic4312yes—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—1722no—
342C22⋊C4—1722no—
343C42—24no—
344C42—21no—
345C42—21no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#1306324912yes—
353C23C2×C22⋊Dic4311yescharacteristic
354C23#1306329412yes—
355C23C2×#1062188411yescharacteristic
356C23C2×#1062188511yescharacteristic
357C23#1306335612yes—
358Q8—42no—
359Q8—42no—
360Q8—84no—
361D4—24no—
362D4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—84no—
384C2×C4—84no—
385C2×C4—3442no—
386C2×C4—3442no—
387C2×C4—3442no—
388C2×C4#1306324912yes—
389C2×C4C2×C22⋊Dic4311yescharacteristic
390C2×C4C2×C22⋊Dic4311yescharacteristic
391C2×C4#1306329412yes—
392C8—3442no—
393C22—21no—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22#1458275511yescharacteristic
406C22C2×#1306324911yescharacteristic
407C22#1458290811yescharacteristic
408C22#1458303812yes—
409C22#1458305512yes—
410C4—22no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—42no—
418C4—41no—
419C4—6882no—
420C4#1458287312yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—42no—
426C2#1913451311yescharacteristic
427C2#1913453011yescharacteristic
428C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#554C2
socleC22×C43#379
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenterC2×#554D43
hypocenterC43#8380
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19134685C2semidirect
3. #19133167C2semidirect
16. C2×C4⋊Q8×C43C4semidirect
20. C2×C22⋊Q8×C43C4semidirect
22. C2×C4×Q8×C43C4semidirect
25. C22×C4⋊C4×C43C4semidirect
222. C2×C4⋊Q8Dic43semidirect
226. C2×C22⋊Q8Dic43semidirect
228. C2×C4×Q8Dic43semidirect
231. C22×C4⋊C4Dic43semidirect
241. C43#8380semidirect

Maximal subgroups

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

subgroupindex
#191346852
#191345832
#191331672
#191329132
C2×C43×#5542
#838043