Finite Group Databasebeta

← #11808777

Subgroups — #11808777

Order 1152.

1704 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×C4×#634C211yesmaximal, characteristic, complemented
3C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
4C4×#3757C211yesmaximal, characteristic, complemented
5#10592660C211yesmaximal, characteristic
6#10592658C211yesmaximal, characteristic
7#10592651C211yesmaximal, characteristic, complemented
8#10592646C211yesmaximal, characteristic, complemented
9C4×#3752C211yesmaximal, characteristic, complemented
10C4×#3752C211yesmaximal, characteristic, complemented
11#10592631C211yesmaximal, characteristic, complemented
12#10592374C211yesmaximal, characteristic, complemented
13#10592372C211yesmaximal, characteristic, complemented
14#10592359C211yesmaximal, characteristic, complemented
15#10592357C211yesmaximal, characteristic, complemented
16#73481—34nomaximal
17C23×C32×C4C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C4×#638—24no—
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C4×#634—24no—
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C2×C4×#67—34no—
55C2×C4×Dic6—34no—
56C3×C4×C22⋊C4D314yescomplemented
57C4×#217—34no—
58#4961—34no—
59#4959—34no—
60#4952—34no—
61#4947—34no—
62C4×(C2×D3)⋊C4—34no—
63C4×(C2×D3)⋊C4—34no—
64#4932—34no—
65#4675—34no—
66#4673—34no—
67#4660—34no—
68#4658—34no—
69C24×C32C2311yescharacteristic
70C23×C3⋊D3C2311yescharacteristic
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638—22no—
81C2×#638—22no—
82C2×#638—22no—
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C2×C4×C3⋊D3—22no—
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—22no—
93C2×#634—22no—
94C2×#634—22no—
95C2×#634—22no—
96C32×C22⋊C4—22no—
97C32×C22⋊C4—22no—
98C32×C42—22no—
99C32×C42—22no—
100#3757—22no—
101#3757—22no—
102#3757—22no—
103#3752—22no—
104#3752—22no—
105#3752—22no—
106#3752—22no—
107#3752—22no—
108C4⋊(C3⋊Dic3)—22no—
109#3750—22no—
110#3750—22no—
111#3750—22no—
112C4×C3⋊Dic3—22no—
113C4×C3⋊Dic3—22no—
114C4×C3⋊Dic3D414yes—
115#2398—91noSylow
116C23×C3×C4C2×D314yes—
117C22×#67—34no—
118C22×C4×D3—34no—
119C22×Dic6—34no—
120C2×C3×C22⋊C4C2×D314yes—
121C2×C3×C22⋊C4C2×D314yes—
122C2×C3×C42C2×D314yes—
123C2×C3×C42C2×D314yes—
124C2×#217—34no—
125C2×#217—34no—
126C2×#217—34no—
127C4×#67—616no—
128C2×(C2×D3)⋊C4—34no—
129C2×(C2×D3)⋊C4—34no—
130C2×(C2×D3)⋊C4—34no—
131C2×(C2×D3)⋊C4—34no—
132C2×(C2×D3)⋊C4—34no—
133C2×C4⋊Dic3—34no—
134C2×Dic3⋊C4—34no—
135C2×Dic3⋊C4—34no—
136C2×Dic3⋊C4—34no—
137C2×C4×Dic3—34no—
138C2×C4×Dic3—34no—
139C2×C4×Dic3—34no—
140C4×Dic6—616no—
141C3×#95C2×D314yes—
142C3×#95C2×D314yes—
143C3⋊#95—34no—
144C3⋊#95—34no—
145C3⋊#95—34no—
146C3⋊#95—34no—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C3⋊#95—34no—
152C3⋊#95—34no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32—21no—
159C23×C32#4112yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3#4112yes—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—44no—
183C2×C32×C4C2×D412yes—
184C2×C32×C4#4112yes—
185C2×C32×C4#4112yes—
186C2×C32×C4#4112yes—
187#638—28no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C2×D412yes—
207C2×C3⋊Dic3C2×D412yes—
208C2×C3⋊Dic3#4112yes—
209C4×C3⋊D3—44no—
210#634—28no—
211C2×C4×Q8—91no—
212C2×C4×D4—91no—
213#400—91no—
214#400—91no—
215#397—91no—
216#397—91no—
217#394—91no—
218#394—91no—
219#393—91no—
220#393—91no—
221C4×C22⋊C4—91no—
222C4×C22⋊C4—91no—
223C4×C22⋊C4—91no—
224C4×C22⋊C4C3⋊D311yescharacteristic, complemented
225#376—91no—
226C24×C3C22×D314yes—
227C23×D3—34no—
228C22×C3×C4—28no—
229C22×C3×C4—28no—
230C22×C3×C4—28no—
231C22×C3×C4C22×D314yes—
232C22×C3×C4C22×D314yes—
233C22×C3×C4C22×D314yes—
234C22×C3×C4C22×D314yes—
235C22×C3×C4C22×D314yes—
236C22×C3×C4C22×D314yes—
237C2×#67—68no—
238C2×#67—68no—
239C2×#67—68no—
240C22×Dic3—34no—
241C22×Dic3—34no—
242C22×Dic3—34no—
243C22×Dic3—34no—
244C22×Dic3—34no—
245C22×Dic3—34no—
246C22×Dic3—34no—
247C2×C4×D3—68no—
248C2×C4×D3—68no—
249C2×C4×D3—68no—
250C2×Dic6—68no—
251C2×Dic6—68no—
252C2×Dic6—68no—
253C3×C22⋊C4—28no—
254C3×C22⋊C4—28no—
255C3×C42—28no—
256C3×C42—28no—
257#217—68no—
258#217—68no—
259#217—68no—
260(C2×D3)⋊C4—68no—
261(C2×D3)⋊C4—68no—
262(C2×D3)⋊C4—68no—
263(C2×D3)⋊C4—68no—
264(C2×D3)⋊C4—68no—
265C4⋊Dic3—68no—
266Dic3⋊C4—68no—
267Dic3⋊C4—68no—
268Dic3⋊C4—68no—
269C4×Dic3—316no—
270C4×Dic3—68no—
271C4×Dic3—68no—
272C22×C32—22no—
273C22×C32—22no—
274C22×C32—22no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32C22×D411yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32C2×#4111yescharacteristic
284C22×C32C2×#4111yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—41no—
293C32×C4—22no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4#12414yes—
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C3⋊Dic3—41no—
306C22×Q8—91no—
307C22×D4—91no—
308C23×C4—91no—
309C23×C4C2×C3⋊D311yescharacteristic
310C4×Q8—184no—
311C4×D4—184no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4C2×C3⋊D311yescharacteristic
325C2×C22⋊C4C2×C3⋊D311yescharacteristic
326C2×C42—91no—
327C2×C42—91no—
328C2×C42—91no—
329C2×C42C2×C3⋊D311yescharacteristic
330C2×C42C2×C3⋊D311yescharacteristic
331#95—91no—
332#95—91no—
333#95—91no—
334#95—91no—
335#95—91no—
336#95—91no—
337#95—91no—
338#95—91no—
339#95—91no—
340#95—91no—
341#95C2×C3⋊D311yescharacteristic
342#95C2×C3⋊D311yescharacteristic
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3#23518yes—
350C23×C3C23×D314yes—
351C22×D3—38no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—64no—
356C22×D3—64no—
357C22×D3—64no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—416no—
373C2×C3×C4#23518yes—
374C2×C3×C4#23518yes—
375C2×C3×C4D3×D418yes—
376C2×C3×C4#23718yes—
377#67—632no—
378C2×Dic3—38no—
379C2×Dic3—38no—
380C2×Dic3—38no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—64no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—64no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—64no—
399C4×D3—1216no—
400Dic6—632no—
401C2×C32—42no—
402C2×C32#52511yescharacteristic
403C2×C32#52511yescharacteristic
404C2×C32C2×#12411yescharacteristic
405C2×C32#52911yescharacteristic
406C2×C32#52911yescharacteristic
407C2×C32#52911yescharacteristic
408C2×C32#52911yescharacteristic
409C3⋊D3—42no—
410C24—91no—
411C24C22×C3⋊D311yescharacteristic
412C2×Q8—182no—
413C2×Q8—182no—
414C2×Q8—182no—
415C2×D4—182no—
416C2×D4—182no—
417C2×D4—182no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—182no—
431C22×C4C22×C3⋊D311yescharacteristic
432C22×C4C22×C3⋊D311yescharacteristic
433C22×C4C22×C3⋊D311yescharacteristic
434C22×C4C22×C3⋊D311yescharacteristic
435C22×C4C22×C3⋊D311yescharacteristic
436C22×C4C22×C3⋊D311yescharacteristic
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—182no—
440C4⋊C4—182no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—182no—
444C22⋊C4—182no—
445C22⋊C4—182no—
446C22⋊C4—182no—
447C22⋊C4—182no—
448C22⋊C4—182no—
449C22⋊C4—182no—
450C22⋊C4—182no—
451C42—22no—
452C42—22no—
453C42—94no—
454C42—182no—
455C42—182no—
456C22×C3—28no—
457C22×C3—28no—
458C22×C3—28no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3C2×#23514yes—
464C22×C3C2×#23514yes—
465C22×C3C2×#23514yes—
466C22×C3C2×D3×D414yes—
467C22×C3C2×#23714yes—
468C22×C3D3×#4114yes—
469C22×C3D3×#4114yes—
470C2×D3—68no—
471C2×D3—68no—
472C2×D3—68no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—124no—
476C2×D3—124no—
477C3×C4—28no—
478C3×C4—44no—
479C3×C4—44no—
480C3×C4—44no—
481C3×C4—44no—
482C3×C4#885116yes—
483Dic3—68no—
484Dic3—68no—
485Dic3—68no—
486Dic3—124no—
487Dic3—124no—
488Dic3—124no—
489Dic3—124no—
490C32#239811yescharacteristic, complemented, Sylow
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—92no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23—181no—
502C23—181no—
503C23—181no—
504C23#382812yes—
505C23C23×C3⋊D311yescharacteristic
506Q8—188no—
507D4—188no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—364no—
545C2×C4#382812yes—
546C2×C4#382812yes—
547C2×C4D4×C3⋊D312yes—
548C2×C4#383012yes—
549C2×C3—48no—
550C2×C3#547914yes—
551C2×C3C2×#88514yes—
552C2×C3#552814yes—
553C2×C3#553814yes—
554C2×C3#554714yes—
555C2×C3#554714yes—
556C2×C3#555714yes—
557D3—128no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—182no—
566C22—182no—
567C22—182no—
568C22—361no—
569C22—361no—
570C22—361no—
571C22—361no—
572C22C2×#382811yescharacteristic
573C22C2×#382811yescharacteristic
574C22C2×#382811yescharacteristic
575C22C2×D4×C3⋊D311yescharacteristic
576C22C2×#383011yescharacteristic
577C22#41×C3⋊D311yescharacteristic
578C22#41×C3⋊D311yescharacteristic
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—182no—
585C4—182no—
586C4—182no—
587C4—361no—
588C4—361no—
589C4—361no—
590C4—361no—
591C4#6409414yes—
592C3#7348114yescomplemented
593C2—42no—
594C2—362no—
595C2#1059595011yescharacteristic
596C2C2×#6409411yescharacteristic
597C2#1059599911yescharacteristic
598C2#1059600911yescharacteristic
599C2#1059601811yescharacteristic
600C2#1059601811yescharacteristic
601C2#1059602811yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC32×C4×C22⋊C4C2
prime radicalC22×#638C22
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#634C2semidirect
3. C32×C4×C22⋊C4C2semidirect
4. C4×#3757C2semidirect
7. #10592651C2semidirect
8. #10592646C2semidirect
9. C4×#3752C2semidirect
10. C4×#3752C2semidirect
11. #10592631C2semidirect
12. #10592374C2semidirect
13. #10592372C2semidirect
14. #10592359C2semidirect
15. #10592357C2semidirect
56. C3×C4×C22⋊C4D3semidirect
224. C4×C22⋊C4C3⋊D3semidirect
490. C32#2398semidirect
592. C3#73481semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C4×#6342
C32×C4×C22⋊C42
C4×#37572
#105926602
#105926582
#105926512
#105926462
C4×#37522
#105926312
#105923742
#105923722
#105923592
#105923572
#734813