Finite Group Databasebeta

← #25012577

Subgroups — #25012577

Order 11008.

680 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063321C211yesmaximal, characteristic
2C2×#14582691C212yesmaximal
3#19134583C211yesmaximal, characteristic, complemented
4#19132719C212yesmaximal, complemented
5C43×#1799C211yesmaximal, characteristic, complemented
6C2×#13063321C2211yescharacteristic
7C2×C4×D172C411yescharacteristic, complemented
8C2×C4×C22⋊D43—21no—
9C2×C4×C22⋊D43—21no—
10C2×#13063240C2212yes—
11#14582802C2211yescharacteristic
12#14582800C411yescharacteristic, complemented
13#14582799—21no—
14#14582799—21no—
15#14582768C411yescharacteristic, complemented
16#14582759—21no—
17C42×Dic43C411yescharacteristic, complemented
18#14582691—24no—
19#14582666—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C2×#99×C43C2212yes—
22C43×#380—21no—
23C43×#342—21no—
24C22×D172C2×C411yescharacteristic
25C22×C22⋊D43—21no—
26C22×C22⋊D43—21no—
27C22×C4×D43—21no—
28#13063321—21no—
29#13063321—21no—
30#13063321D412yes—
31#13063321Q812yes—
32C4×D172—41no—
33C4×D172—41no—
34C4×C22⋊D43—44no—
35C4×C22⋊D43—44no—
36C2×C4⋊Dic43—41no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—22no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×C4×Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43C2×C411yescharacteristic
50#13063240—22no—
51#13063240—22no—
52C43⋊#95—41no—
53C22×D4×C43C2311yescharacteristic
54C23×C4×C43D411yescharacteristic
55C23×C4×C43D411yescharacteristic
56C4×D4×C43—41no—
57C4×D4×C43—41no—
58C2×C4⋊C4×C43—41no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43—22no—
61C2×C22⋊C4×C43D411yescharacteristic
62C2×C22⋊C4×C43D411yescharacteristic
63C2×C42×C43C2×C411yescharacteristic
64#99×C43—22no—
65#99×C43—22no—
66#95×C43—41no—
67C24×C43C2×D411yescharacteristic
68C24×C43C2×D411yescharacteristic
69C23×D43—21no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43C2×D411yescharacteristic
73C2×D4×C43C2×Q811yescharacteristic
74C2×D4×C43#4111yescharacteristic
75C2×D4×C43#4111yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—42no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22×C411yescharacteristic
88C2×C22⋊D43—22no—
89C2×C22⋊D43—22no—
90C2×C22⋊D43—22no—
91C2×C22⋊D43—22no—
92C2×C22⋊D43—42no—
93C2×C22⋊D43—42no—
94C2×C22⋊D43—42no—
95C2×C22⋊D43—42no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—42no—
100C2×D172—21no—
101C2×D172—41no—
102C2×D172—41no—
103C2×D172C4⋊C412yescomplemented
104C2×C4×D43—42no—
105C2×C4×D43—42no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—82no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—42no—
113C22⋊C4×C43—42no—
114C42×C43—21no—
115C42×C43—21no—
116C22⋊Dic43—42no—
117C22⋊Dic43—42no—
118C22⋊Dic43—42no—
119C22⋊Dic43—42no—
120(C2×D43)⋊C4—42no—
121(C2×D43)⋊C4—42no—
122(C2×D43)⋊C4—42no—
123C4⋊Dic43—41no—
124C4⋊Dic43—82no—
125Dic43⋊C4—42no—
126Dic43⋊C4—42no—
127C4×Dic43—24no—
128C4×Dic43—21no—
129C4×Dic43—42no—
130C4×Dic43—41no—
131C4×Dic43C4⋊C412yescomplemented
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43C2×C22⋊C411yescharacteristic
141C23×C43#12111yescharacteristic
142C23×C43#12111yescharacteristic
143C23×C43C22⋊Q811yescharacteristic
144C23×C43C22⋊Q811yescharacteristic
145C22×D43—22no—
146C22×D43—41no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152D4×C43—41no—
153D4×C43—41no—
154D4×C43—41no—
155D4×C43—41no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—22no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43—82no—
170C2×C4×C43—82no—
171C2×C4×C43—82no—
172C2×C4×C43#9911yescharacteristic
173C2×C4×C43#9911yescharacteristic
174C2×C4×C43C2×C4⋊C411yescharacteristic
175C2×C4×C43#11711yescharacteristic
176C22⋊D43—44no—
177C22⋊D43—44no—
178C22⋊D43—44no—
179C22⋊D43—44no—
180C2×Dic43—22no—
181C2×Dic43—22no—
182C2×Dic43—22no—
183C2×Dic43—22no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—82no—
190C2×Dic43—82no—
191C2×Dic43—82no—
192D172—42no—
193D172—42no—
194C4×D43—82no—
195C4×D43—82no—
196#12797—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43—81no—
212C22×C43—81no—
213C22×C43#38011yescharacteristic
214C22×C43C2×#9911yescharacteristic
215C22×C43#41011yescharacteristic
216C2×D43—42no—
217C2×D43—42no—
218C2×D43—42no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—41no—
227C4×C43—41no—
228C4×C43—41no—
229C4×C43—162no—
230C4×C43#35312yescomplemented
231Dic43—24no—
232Dic43—42no—
233Dic43—81no—
234Dic43—162no—
235C4×#127—431no—
236C2×#353—432no—
237#1799—431no—
238#1799D4311yescharacteristic, complemented
239#1393—432no—
240C2×C43—21no—
241C2×C43—21no—
242C2×C43—41no—
243C2×C43—41no—
244C2×C43—41no—
245C2×C43—41no—
246C2×C43#179911yescharacteristic
247C2×C43C2×#35311yescharacteristic
248C2×C43#212611yescharacteristic
249D43—82no—
250C2×#127—431no—
251C2×C4×D4—431no—
252C2×C4×D4—861no—
253C2×C4×D4—861no—
254C2×C4×D4C2×D4311yescharacteristic
255C2×#99—432no—
256C2×#99C2×D4312yes—
257#390—431no—
258#390—431no—
259#390—861no—
260#390—861no—
261#384—431no—
262#380—21no—
263#380—861no—
264C43—431no—
265#353—864no—
266#342—21no—
267#342—861no—
268C43#1279711yescharacteristic, complemented, Sylow
269C22×D4—431no—
270C22×D4—861no—
271C22×D4—861no—
272C22×D4C22×D4311yescharacteristic
273C23×C4—861no—
274C23×C4D17211yescharacteristic
275C23×C4C22⋊D4311yescharacteristic
276#127—432no—
277#127—432no—
278#127—861no—
279#127—861no—
280C4×D4—41no—
281C4×D4—41no—
282C4×D4—1721no—
283C4×D4—1721no—
284C4×D4—1724no—
285C4×D4—1724no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—431no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—1721no—
291C2×C4⋊C4C4×D4311yescharacteristic
292C2×C22⋊C4—22no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4—861no—
296C2×C22⋊C4—861no—
297C2×C22⋊C4—861no—
298C2×C22⋊C4—862no—
299C2×C22⋊C4D17211yescharacteristic
300C2×C22⋊C4C22⋊D4311yescharacteristic
301C2×C42—431no—
302C2×C42—431no—
303C2×C42—861no—
304C2×C42—861no—
305C2×C42C4×D4311yescharacteristic
306#99—22no—
307#99—22no—
308#99—862no—
309#99—862no—
310#95—41no—
311#95—1721no—
312C24—861no—
313C24C2×D17211yescharacteristic
314C24C2×C22⋊D4311yescharacteristic
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—432no—
318C2×D4—862no—
319C2×D4—862no—
320C2×D4—862no—
321C2×D4—862no—
322C2×D4—861no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1722no—
326C2×D4—1722no—
327C2×D4—1722no—
328C2×D4—1722no—
329C2×D4D4×D4311yescharacteristic
330C2×D4#1062190011yescharacteristic
331C2×D4Q8×D4311yescharacteristic
332C2×D4#1062190211yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—1722no—
344C22×C4—1722no—
345C22×C4—1722no—
346C22×C4—1721no—
347C22×C4—1721no—
348C22×C4(C2×D43)⋊C411yescharacteristic
349C22×C4(C2×D43)⋊C411yescharacteristic
350C22×C4(C2×D43)⋊C411yescharacteristic
351C22×C4(C2×D43)⋊C411yescharacteristic
352C22×C4C2×C4×D4311yescharacteristic
353C4⋊C4—41no—
354C4⋊C4—82no—
355C4⋊C4—3442no—
356C4⋊C4—1721no—
357C4⋊C4—1722no—
358C4⋊C4—1722no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—1722no—
364C22⋊C4—1722no—
365C22⋊C4—1722no—
366C22⋊C4—1722no—
367C22⋊C4—1722no—
368C22⋊C4—1722no—
369C22⋊C4—1722no—
370C42—21no—
371C42—21no—
372C42—432no—
373C42—864no—
374C42—861no—
375C42—1721no—
376C42—1722no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—862no—
386C23—1721no—
387C23—1721no—
388C23—1721no—
389C23—1721no—
390C23—1721no—
391C23—1721no—
392C23C2×(C2×D43)⋊C411yescharacteristic
393C23#1306329611yescharacteristic
394C23#1306330011yescharacteristic
395C23#1306330111yescharacteristic
396C23#1306330511yescharacteristic
397D4—41no—
398D4—41no—
399D4—41no—
400D4—41no—
401D4—1722no—
402D4—1722no—
403D4—1724no—
404D4—1724no—
405D4—1724no—
406D4—1724no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—862no—
424C2×C4—862no—
425C2×C4—862no—
426C2×C4—862no—
427C2×C4—3442no—
428C2×C4—3442no—
429C2×C4—3442no—
430C2×C4—3442no—
431C2×C4—3442no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4#1306323911yescharacteristic
438C2×C4#1306323911yescharacteristic
439C2×C4C4⋊C4×D4311yescharacteristic
440C2×C4#1306328311yescharacteristic
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—81no—
456C22—81no—
457C22—3441no—
458C22—3441no—
459C22—3441no—
460C22—3441no—
461C22—1722no—
462C22—1722no—
463C22—1722no—
464C22#1458275611yescharacteristic
465C22C2×#1306323911yescharacteristic
466C22#1458287211yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—162no—
474C4—864no—
475C4—3441no—
476C4—1722no—
477C4—6882no—
478C4#1458269112yescomplemented
479C2—21no—
480C2—21no—
481C2—41no—
482C2—41no—
483C2—41no—
484C2—41no—
485C2—3442no—
486C2#1913458011yescharacteristic
487C2C2×#1458269111yescharacteristic
488C2#1913625811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radicalC2×#13063321C22
cosocleC22×D4×C43C23
hypercenter#1799D43
hypocenterC43#12797
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #19134583C2semidirect
4. #19132719C2semidirect
5. C43×#1799C2semidirect
7. C2×C4×D172C4semidirect
12. #14582800C4semidirect
15. #14582768C4semidirect
17. C42×Dic43C4semidirect
103. C2×D172C4⋊C4semidirect
131. C4×Dic43C4⋊C4semidirect
230. C4×C43#353semidirect
238. #1799D43semidirect
268. C43#12797semidirect
478. C4#14582691semidirect

Maximal subgroups

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

subgroupindex
C4×#130633212
C2×#145826912
#191345832
#191327192
C43×#17992
#1279743