Finite Group Databasebeta

← #26268056

Subgroups — #26268056

Order 12032.

812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689533C211yesmaximal, characteristic, complemented
2C2×#15689420C211yesmaximal, characteristic
3#20248337C211yesmaximal, characteristic
4#20244864C211yesmaximal, characteristic, complemented
5#20244859C211yesmaximal, characteristic, complemented
6#20244773C211yesmaximal, characteristic
7#20244759C211yesmaximal, characteristic
8#20244336C211yesmaximal, characteristic, complemented
9#20244151C211yesmaximal, characteristic, complemented
10#20244146C211yesmaximal, characteristic, complemented
11#20244112C211yesmaximal, characteristic, complemented
12#20244015C211yesmaximal, characteristic
13#20244008C211yesmaximal, characteristic
14#20243216C211yesmaximal, characteristic
15C47×#2370C211yesmaximal, characteristic, complemented
16C2×#13094024C2211yescharacteristic
17C2×#13094004—21no—
18C2×#13094004—21no—
19C2×C4×D188C2211yescharacteristic
20#15689533—24no—
21#15689420—24no—
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×#13093955C2211yescharacteristic
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36#15689060—21no—
37#15689060—21no—
38#15689025C2211yescharacteristic
39#15689025C2211yescharacteristic
40#15688993C2211yescharacteristic
41#15688993C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×#125×C47C2211yescharacteristic
51C47×#389—21no—
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#387—21no—
55C47×#387—21no—
56C4×C4⋊C4×C47—21no—
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C22×Dic94—21no—
62C22×D188C2311yescharacteristic
63C22×C4×D47—21no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094024—22no—
69#13094024—22no—
70#13094004—44no—
71#13094004—44no—
72C4×D188—22no—
73C4×D188—22no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87#13093957—22no—
88#13093957—22no—
89#13093957—22no—
90#13093955—22no—
91#13093955—22no—
92#13093955—22no—
93C4⋊(C47⋊C8)—22no—
94C4⋊(C47⋊C8)—22no—
95C4⋊(C47⋊C8)—22no—
96#13093944—22no—
97#13093944—22no—
98#13093944—22no—
99#13093944Q814yescomplemented
100#13093935—22no—
101#125×C47—22no—
102#125×C47D414yes—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47D411yescharacteristic
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C42×C47—21no—
114C2×C42×C47—21no—
115C2×C42×C47—21no—
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47D411yescharacteristic
125#95×C47D411yescharacteristic
126C23×D47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2411yescharacteristic
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188C2×Q812yes—
147C2×C4×D47—42no—
148C2×C4×D47—42no—
149C2×C4×D47—42no—
150C2×Dic94—42no—
151C2×Dic94—42no—
152C2×Dic94—42no—
153C4⋊C4×C47—24no—
154C4⋊C4×C47—24no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—22no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—42no—
163C4⋊C4×C47—81no—
164C4⋊C4×C47C2×D412yes—
165C4⋊C4×C47C2×D412yes—
166C4⋊C4×C47C2×Q812yes—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—42no—
172C42×C47—81no—
173C42×C47—81no—
174C42×C47C2×D412yes—
175C42×C47#4112yes—
176(C2×D47)⋊C4—42no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—42no—
179(C2×D47)⋊C4—42no—
180(C2×D47)⋊C4—42no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—42no—
188C4⋊Dic47—42no—
189C4⋊Dic47—42no—
190C4⋊Dic47—42no—
191C4⋊Dic47—42no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8C2×Q812yes—
203C2×C47⋊C8#4112yes—
204C23×C47C22×D411yescharacteristic
205C22×D47—22no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—41no—
211C22×D47—41no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47#12112yes—
239C2×C4×C47#12112yes—
240C2×C4×C47AGL(1,ℤ/8)12yes—
241C2×C4×C47AGL(1,ℤ/8)12yes—
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×Q811yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C472−1+411yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257D188—22no—
258D188—22no—
259D188—41no—
260D188—41no—
261C4×D47—84no—
262Dic94—84no—
263C47⋊C8—22no—
264C47⋊C8—22no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267#25465—471nomaximal, Sylow
268C22×C47C2×#12111yescharacteristic
269C22×C47#54711yescharacteristic
270C22×C47D4×Q811yescharacteristic
271C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C47#57711yescharacteristic
274C22×C47#57811yescharacteristic
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—81no—
279C2×D47—81no—
280C2×D47—81no—
281C2×D47—81no—
282C4×C47—22no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—42no—
289C4×C47—42no—
290C4×C47—42no—
291C4×C47—81no—
292C4×C47#53311yescharacteristic
293C4×C47#54111yescharacteristic
294C4×C47#54811yescharacteristic
295C4×C47D4×Q811yescharacteristic
296Dic47—81no—
297Dic47—81no—
298Dic47—81no—
299C2×#501—471no—
300C2×#478—471no—
301#2542—471no—
302#2370D4711yescharacteristic, complemented
303#2084—471no—
304#2083—471no—
305#2067—471no—
306#2065—471no—
307#1987—471no—
308#1948—471no—
309#1947—471no—
310#1940—471no—
311#1926—471no—
312#1925—471no—
313#1762—471no—
314C2×C47#242911yescharacteristic
315C2×C47#303811yescharacteristic
316C2×C47#304611yescharacteristic
317C2×C47#334311yescharacteristic
318C2×C47#334511yescharacteristic
319C2×C47#338411yescharacteristic
320C2×C47#338611yescharacteristic
321D47—82no—
322C2×C4⋊Q8—471no—
323C2×#125C2×D4711yescharacteristic
324C2×C22⋊Q8—941no—
325C2×C22⋊Q8—941no—
326C2×C4×D4—471no—
327#501—944no—
328#478—944no—
329C2×#107—471no—
330C2×#107—471no—
331C2×#107—471no—
332C2×#106—471no—
333C2×#106—471no—
334C2×#106—471no—
335C2×C4⋊C8—471no—
336C2×C4⋊C8—471no—
337C2×C4⋊C8—471no—
338C2×#102—471no—
339C2×#102—471no—
340C2×#102—471no—
341C2×#102—471no—
342C2×#97—471no—
343#399—941no—
344#399—941no—
345#390—471no—
346#390—471no—
347#389—21no—
348#389C2×D4711yescharacteristic
349#389C2×D4711yescharacteristic
350#387—21no—
351#387—21no—
352#384—471no—
353#384—471no—
354C4×C4⋊C4—21no—
355C4×C4⋊C4C2×D4711yescharacteristic
356C4×C4⋊C4C2×D4711yescharacteristic
357C4×C4⋊C4C2×D4711yescharacteristic
358C4×C4⋊C4C2×D4711yescharacteristic
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#336—471no—
366#336—471no—
367C47#2546511yescharacteristic, complemented, Sylow
368C22×Q8—941no—
369C22×D4—471no—
370C23×C4—941no—
371C22×C8—471no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375C4⋊Q8—942no—
376C4⋊Q8—942no—
377#125—22no—
378#125D18814yes—
379C22⋊Q8—1884no—
380C22⋊Q8—1884no—
381C4×D4—942no—
382C4×D4—942no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4C22⋊D4711yescharacteristic
396C2×C4⋊C4C22⋊D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C4⋊C4C22×D4711yescharacteristic
400C2×C4⋊C4C22×D4711yescharacteristic
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C22⋊C4—941no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42C22×D4711yescharacteristic
410C2×C42C22×D4711yescharacteristic
411C2×C42C22×D4711yescharacteristic
412#107—942no—
413#107—942no—
414#107—942no—
415#106—942no—
416#106—942no—
417#106—942no—
418C4⋊C8—942no—
419C4⋊C8—942no—
420C4⋊C8—942no—
421#102—474no—
422#102—942no—
423#102—942no—
424#102—942no—
425#97—942no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95C22⋊D4711yescharacteristic
432#95C22⋊D4711yescharacteristic
433C24—941no—
434C2×Q8—1882no—
435C2×Q8—1882no—
436C2×Q8—1882no—
437C2×D4—472no—
438C2×D4—941no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—1882no—
451C22×C4—1882no—
452C22×C4—1882no—
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460C2×C8—472no—
461C2×C8—472no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—1882no—
490C4⋊C4—1882no—
491C4⋊C4—1882no—
492C4⋊C4—1882no—
493C4⋊C4—1882no—
494C4⋊C4C2×D18812yes—
495C4⋊C4C2×D18812yes—
496C4⋊C4Q8×D4712yes—
497C22⋊C4—1882no—
498C22⋊C4—1882no—
499C22⋊C4—1882no—
500C22⋊C4—1882no—
501C22⋊C4—1882no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—81no—
508C42—81no—
509C42C2×D18812yes—
510C42#1062535012yes—
511C23—942no—
512C23—1881no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23—1881no—
518C23C22×C22⋊D4711yescharacteristic
519Q8—3764no—
520D4—942no—
521D4—942no—
522D4—1881no—
523D4—1881no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—3764no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4#1309399812yes—
561C2×C4#1309399812yes—
562C2×C4#1309404912yes—
563C2×C4#1309404912yes—
564C2×C4C22×D18811yescharacteristic
565C2×C4C2×Q8×D4711yescharacteristic
566C2×C4#41×D4711yescharacteristic
567C2×C4C2×#1062535011yescharacteristic
568C2×C4#1309407111yescharacteristic
569C2×C4#1309407211yescharacteristic
570C8—942no—
571C8—942no—
572C8—1881no—
573C8—1881no—
574C22—3761no—
575C22—3761no—
576C22—3761no—
577C22—3761no—
578C22—1882no—
579C22—1882no—
580C22—1882no—
581C22C2×#1309399811yescharacteristic
582C22#1568977211yescharacteristic
583C22Q8×C22⋊D4711yescharacteristic
584C22C2×#1309404911yescharacteristic
585C22C2×#1309404911yescharacteristic
586C22#1568993411yescharacteristic
587C22#1568993811yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—3761no—
599C4—3761no—
600C4—3761no—
601C4#1568967711yescharacteristic
602C4#1568973111yescharacteristic
603C4#1568978511yescharacteristic
604C4Q8×D18811yescharacteristic
605C2—3762no—
606C2#2024698111yescharacteristic
607C2#2025286811yescharacteristic
608C2#2025293811yescharacteristic
609C2#2025582811yescharacteristic
610C2#2025585211yescharacteristic
611C2#2025628711yescharacteristic
612C2#2025630511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2370C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2370D47
hypocenterC47#25465
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
1. C2×#15689533C2semidirect
4. #20244864C2semidirect
5. #20244859C2semidirect
8. #20244336C2semidirect
9. #20244151C2semidirect
10. #20244146C2semidirect
11. #20244112C2semidirect
15. C47×#2370C2semidirect
99. #13093944Q8semidirect
302. #2370D47semidirect
367. C47#25465semidirect

Maximal subgroups

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

subgroupindex
C2×#156895332
C2×#156894202
#202483372
#202448642
#202448592
#202447732
#202447592
#202443362
#202441512
#202441462
#202441122
#202440152
#202440082
#202432162
C47×#23702
#2546547