Finite Group Databasebeta

← #24988250

Subgroups — #24988250

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063242C211yesmaximal, characteristic, complemented
2#19133197C212yesmaximal, complemented
3#19133038C212yesmaximal, complemented
4#19132936C211yesmaximal, characteristic, complemented
5C2×C43×#553C211yesmaximal, characteristic
6#14582956C2212yes—
7C2×#13063242—21no—
8C4×#10621877C2212yes—
9#14582668—21no—
10#14582641—24no—
11D4⋊(C43⋊C8)—24no—
12#14582623—21no—
13#14582623—21no—
14C43×#553—24no—
15C43×#553—24no—
16C2×#126×C43—21no—
17C2×#125×C43C2211yescharacteristic
18C2×#123×C43—21no—
19C2×#121×C43—21no—
20C2×#121×C43C411yescharacteristic
21C2×#121×C43C411yescharacteristic
22C2×C4×D4×C43—21no—
23C2×C4×D4×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C2×#117×C43C411yescharacteristic
26C22×C4⋊C4×C43C411yescharacteristic
27C2×#10621877—22no—
28C4⋊(C43⋊C8)—22no—
29#13063242—24no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32#13063236—22no—
33C4×C43⋊C8—22no—
34C22×D4×C43—21no—
35C22×D4×C43—21no—
36C22×D4×C43C2×C411yescharacteristic
37C22×D4×C43D411yescharacteristic
38C23×C4×C43—21no—
39C23×C4×C43—21no—
40C23×C4×C43C2×C411yescharacteristic
41C23×C4×C43C2×C411yescharacteristic
42#126×C43—28no—
43#125×C43—22no—
44#125×C43D414yes—
45#123×C43—28no—
46#121×C43—28no—
47#121×C43—22no—
48#121×C43—22no—
49#121×C43—22no—
50#121×C43—22no—
51C4×D4×C43—28no—
52C4×D4×C43—22no—
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C4×D4×C43D414yes—
56#117×C43—22no—
57#117×C43—22no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43C2×C411yescharacteristic
64C2×C4⋊C4×C43C2×C411yescharacteristic
65C2×C4⋊C4×C43C2×C411yescharacteristic
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C42×C43—21no—
74C2×C42×C43C2311yescharacteristic
75C24×C43—21no—
76C24×C43C22⋊C411yescharacteristic
77C24×C43C22⋊C411yescharacteristic
78C2×D4×C43—24no—
79C2×D4×C43—24no—
80C2×D4×C43—21no—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43—41no—
84C2×D4×C43—42no—
85C2×D4×C43—42no—
86C2×D4×C43—42no—
87C2×D4×C43—82no—
88C2×D4×C43C22⋊C412yes—
89C22×C4×C43—24no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—24no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—42no—
99C22×C4×C43—42no—
100C22×C4×C43—82no—
101C22×C4×C43—82no—
102C22×C4×C43C22⋊C411yescharacteristic
103C22×C4×C43C22⋊C411yescharacteristic
104C22×C4×C43C22×C411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C4⋊C4×C43—24no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—24no—
112C4⋊C4×C43—24no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43C22⋊C412yes—
115C4⋊C4×C43C22⋊C412yes—
116C4⋊C4×C43C22⋊C412yes—
117C22⋊C4×C43—24no—
118C22⋊C4×C43—24no—
119C22⋊C4×C43—24no—
120C22⋊C4×C43—24no—
121C22⋊C4×C43—22no—
122C22⋊C4×C43—22no—
123C42×C43—24no—
124C42×C43C2×D412yes—
125C42×C43C2×D412yes—
126#10621877—24no—
127#10621877—42no—
128C2×C43⋊C8—42no—
129C2×C43⋊C8—42no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—22no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—42no—
139C23×C43—42no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43#10412yes—
145C23×C43C2×C22⋊C411yescharacteristic
146D4×C43—24no—
147D4×C43—44no—
148D4×C43—42no—
149D4×C43—48no—
150D4×C43—84no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—22no—
154C2×C4×C43—21no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—21no—
158C2×C4×C43—22no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—84no—
171C2×C4×C43—84no—
172C2×C4×C43C2×C22⋊C411yescharacteristic
173C2×C4×C43C2×C22⋊C411yescharacteristic
174C2×C4×C43#12012yes—
175C2×C4×C43#12012yes—
176C43⋊C8—44no—
177C43⋊C8—82no—
178#8373—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—22no—
182C22×C43—42no—
183C22×C43—42no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—42no—
187C22×C43—41no—
188C22×C43—42no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—42no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43#37911yescharacteristic
197C22×C43C2×#10411yescharacteristic
198C22×C43#42111yescharacteristic
199C4×C43—22no—
200C4×C43—21no—
201C4×C43—22no—
202C4×C43—42no—
203C4×C43—42no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43—42no—
207C4×C43#41312yes—
208C2×#553D4311yescharacteristic
209C4×#100—431no—
210#1528—432no—
211#1490—432no—
212#1466—431no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—42no—
216C2×C43—81no—
217C2×C43—82no—
218C2×C43#178511yescharacteristic
219C2×C43#178911yescharacteristic
220C2×C43#179511yescharacteristic
221#553—24no—
222#553—24no—
223C2×#126—21no—
224C2×#125C2×D4311yescharacteristic
225C2×#123—21no—
226C2×#121—21no—
227C2×#121Dic4311yescharacteristic
228C2×#121Dic4311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2×D4311yescharacteristic
231C2×C4×D4C2×D4311yescharacteristic
232C2×#117Dic4311yescharacteristic
233C22×C4⋊C4Dic4311yescharacteristic
234#432—432no—
235C2×#100—861no—
236C4×M16—432no—
237#343—861no—
238#330—864no—
239D4⋊C8—864no—
240#323—861no—
241#323—861no—
242C43#837311yescharacteristic, complemented, Sylow
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C2×Dic4311yescharacteristic
246C22×D4C22⋊D4311yescharacteristic
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C2×Dic4311yescharacteristic
250C23×C4C2×Dic4311yescharacteristic
251C2×M16—862no—
252#126—28no—
253#125—22no—
254#125C22⋊D4314yes—
255#123—28no—
256#121—28no—
257#121—22no—
258#121—22no—
259#121—22no—
260#121—22no—
261C4×D4—28no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4C22⋊D4314yes—
266#117—22no—
267#117—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4C2×Dic4311yescharacteristic
274C2×C4⋊C4C2×Dic4311yescharacteristic
275C2×C4⋊C4C2×Dic4311yescharacteristic
276C2×C4⋊C4C22⋊D4311yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4C22⋊D4311yescharacteristic
282C2×C22⋊C4C22⋊D4311yescharacteristic
283C2×C42—21no—
284C2×C42C22×D4311yescharacteristic
285C4⋊C8—862no—
286#100—864no—
287C22⋊C8—862no—
288#97—862no—
289#97—862no—
290C4×C8—862no—
291C24—21no—
292C24C22⋊Dic4311yescharacteristic
293C24C22⋊Dic4311yescharacteristic
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—82no—
304C2×D4C22⋊Dic4312yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4C22⋊Dic4311yescharacteristic
319C22×C4C22⋊Dic4311yescharacteristic
320C22×C4C22×Dic4311yescharacteristic
321C22×C4C2×C22⋊D4311yescharacteristic
322C22×C4C2×C22⋊D4311yescharacteristic
323M16—864no—
324M16—1722no—
325C2×C8—1722no—
326C2×C8—1722no—
327C4⋊C4—24no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4C22⋊Dic4312yes—
335C4⋊C4C22⋊Dic4312yes—
336C4⋊C4C22⋊Dic4312yes—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C42—24no—
344C42C2×C22⋊D4312yes—
345C42C2×C22⋊D4312yes—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23#1306325212yes—
361C23C2×C22⋊Dic4311yescharacteristic
362D4—24no—
363D4—44no—
364D4—42no—
365D4—48no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—84no—
387C2×C4—84no—
388C2×C4C2×C22⋊Dic4311yescharacteristic
389C2×C4C2×C22⋊Dic4311yescharacteristic
390C2×C4#1306329412yes—
391C2×C4#1306329412yes—
392C8—3442no—
393C8—1724no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—41no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22#1458275511yescharacteristic
412C22C2×#1306325211yescharacteristic
413C22#1458291611yescharacteristic
414C4—21no—
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—42no—
420C4—42no—
421C4—42no—
422C4#1458288312yes—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—82no—
427C2—81no—
428C2#1913452311yescharacteristic
429C2#1913453911yescharacteristic
430C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC2×C43×#553C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenterC2×#553D43
hypocenterC43#8373
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C4×#13063242C2semidirect
2. #19133197C2semidirect
3. #19133038C2semidirect
4. #19132936C2semidirect
242. C43#8373semidirect

Maximal subgroups

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

subgroupindex
C4×#130632422
#191331972
#191330382
#191329362
C2×C43×#5532
#837343