Finite Group Databasebeta

← #11811916

Subgroups — #11811916

Order 1152.

1833 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×#64106C211yesmaximal, characteristic, complemented
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×#63860C211yesmaximal, characteristic, complemented
5C3×#4988C211yesmaximal, characteristic, complemented
6C3×#4973C211yesmaximal, characteristic, complemented
7#10591379C214yesmaximal, complemented
8#10591312C214yesmaximal, complemented
9C4×#3722C211yesmaximal, characteristic, complemented
10#76498—31nomaximal
11#76445—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626C2212yes—
17C22×D3×Dic3C2212yes—
18C2×#3796—24no—
19C2×#3796—24no—
20C2×#3796—24no—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2212yes—
24#64106—24no—
25C2×C3×(C2×D3)⋊C4C2214yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2214yes—
29C2×#3722C2212yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31#63866—24no—
32#63860—24no—
33C3×C3⋊#95C2214yes—
34#63579C2212yes—
35C22×#239—31no—
36C22×#237—31no—
37C2×#944—31no—
38C2×#936—31no—
39C2×#897—31no—
40C2×#897—31no—
41C2×#897—61no—
42C2×#875—31no—
43C2×#869—31no—
44C3×#391—31no—
45C3×#390—31no—
46#4988D311yescharacteristic, complemented
47#4973D311yescharacteristic, complemented
48#4961—34no—
49#4950—34no—
50C4×(C2×D3)⋊C4—31no—
51C4×(C2×D3)⋊C4—31no—
52#4672—34no—
53#4668—34no—
54C23×C3⋊D3C2311yescharacteristic
55C23×C3×D3C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3D414yes—
63C2×#634—22no—
64C2×#634—22no—
65C2×#634—22no—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12D414yes—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D414yes—
75C2×#626—24no—
76C2×#626—24no—
77C2×#626—24no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81#3796—232no—
82C32×C4⋊C4—22no—
83#3752—24no—
84C4⋊(C3⋊Dic3)—24no—
85C3×(C2×D3)⋊C4—28no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3—22no—
88Dic3⋊Dic3—28no—
89#3722—24no—
90(C2×D3)⋊Dic3—28no—
91#2432—91noSylow
92C22×C3×Q8—31no—
93C22×C3×D4—31no—
94C22×#67—32no—
95C23×Dic3—32no—
96C2×#239—64no—
97C2×#239—64no—
98C2×#239—64no—
99C2×#237—64no—
100C2×#237—64no—
101C2×#237—64no—
102C22×D12—32no—
103C22×D12C2×D311yescharacteristic
104C22×C4×D3—31no—
105C22×C4×D3—31no—
106C22×C4×D3—32no—
107C22×C4×D3—61no—
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—61no—
111C22×Dic6C2×D311yescharacteristic
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4—34no—
116C2×C3×C42—31no—
117C2×C3×C42—31no—
118C2×#217—34no—
119#944—64no—
120#936—64no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—62no—
127C2×(C2×D3)⋊C4C2×D314yes—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—34no—
131C2×C4⋊Dic3—62no—
132C2×Dic3⋊C4—34no—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×C4×Dic3C2×D311yescharacteristic
135#897—64no—
136#897—64no—
137#897—68no—
138#875—64no—
139#869—64no—
140C3×#95—34no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95C2×D314yes—
144C23×C32C2411yescharacteristic
145C22×C3⋊D3—22no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3C2×D412yes—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—24no—
153C22×C3×D3—24no—
154C22×C3×D3C2×D414yes—
155C2×C32×C4—22no—
156C2×C32×C4—24no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C2×D412yes—
166C4×C3⋊D3—28no—
167#634—44no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D414yes—
176C2×C3×Dic3#4114yescomplemented
177C3×D12—28no—
178C3×Dic6—28no—
179#626—216no—
180D3×Dic3—216no—
181C22×#41—91no—
182C2×C4⋊Q8—91no—
183C2×#124—91no—
184C2×C22⋊Q8—91no—
185#394—94no—
186#391—31no—
187#390—31no—
188#385—94no—
189C4×C22⋊C4—91no—
190C24×C3—32no—
191C23×D3—31no—
192C23×D3—31no—
193C23×D3—61no—
194C23×D3C22×D312yes—
195C2×C3×Q8—34no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C2×C3×D4—34no—
199C2×C3×D4—62no—
200C2×C3×D4—62no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—64no—
211C2×#67—64no—
212C2×#67—64no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3—64no—
220C22×Dic3—64no—
221C22×Dic3—64no—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225#239—632no—
226#237—632no—
227C2×D12—22no—
228C2×D12—22no—
229C2×D12—64no—
230C2×D12—64no—
231C2×D12—64no—
232C2×D12D1214yes—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—122no—
244C2×C4×D3—122no—
245C2×Dic6—22no—
246C2×Dic6—22no—
247C2×Dic6—64no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—62no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—122no—
255C2×Dic6—122no—
256C2×Dic6D1214yes—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C22⋊C4—68no—
261C3×C42—62no—
262C3×C42—62no—
263#217—68no—
264(C2×D3)⋊C4—28no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—68no—
269(C2×D3)⋊C4—68no—
270(C2×D3)⋊C4—64no—
271C4⋊Dic3—64no—
272C4⋊Dic3—64no—
273C4⋊Dic3—68no—
274C4⋊Dic3—68no—
275Dic3⋊C4—68no—
276C4×Dic3—22no—
277C4×Dic3—22no—
278C22×C32C22×D411yescharacteristic
279C22×C32C22×D411yescharacteristic
280C22×C32C22×D411yescharacteristic
281C22×C32C2×#4112yes—
282C22×C322−1+412yes—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3×D3—24no—
289C2×C3×D3—28no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—44no—
293C32×C4—42no—
294C32×C4#12014yes—
295C3⋊Dic3—22no—
296C3⋊Dic3—42no—
297C3×Dic3—24no—
298C3×Dic3—24no—
299C3×Dic3—42no—
300C2×#41—184no—
301C2×#41—184no—
302C2×#41—184no—
303C22×Q8—31no—
304C22×Q8—91no—
305C22×D4—31no—
306C22×D4—92no—
307C23×C4—92no—
308C23×C4—91no—
309C4⋊Q8—184no—
310#124—184no—
311C22⋊Q8—184no—
312C2×C4⋊C4—94no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4D3211yescharacteristic
315C2×C22⋊C4—34no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—94no—
318C2×C22⋊C4—92no—
319C2×C42—31no—
320C2×C42—31no—
321#95—34no—
322#95—92no—
323C23×C3—21no—
324C23×C3—34no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3—64no—
328C23×C3—64no—
329C23×C3C23×D311yescharacteristic
330C23×C3C23×D311yescharacteristic
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—24no—
334C22×D3—24no—
335C22×D3—32no—
336C22×D3—32no—
337C22×D3—62no—
338C22×D3—64no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—122no—
350C22×D3C2×D1214yes—
351C3×Q8—68no—
352C3×D4—68no—
353C2×C3×C4—24no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—34no—
362C2×C3×C4—34no—
363C2×C3×C4—44no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4C2×D1212yes—
372C2×C3×C4C2×D1212yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4D3×D412yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D412yes—
377#67—616no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—62no—
388C2×Dic3—616no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—64no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3C2×D1214yes—
405C2×Dic3#23714yescomplemented
406D12—28no—
407D12—616no—
408C4×D3—616no—
409C4×D3—68no—
410C4×D3—68no—
411C4×D3—128no—
412Dic6—28no—
413Dic6—128no—
414Dic6—124no—
415Dic6—124no—
416C2×C32C2×#12011yescharacteristic
417C2×C32#53211yescharacteristic
418C2×C32#53611yescharacteristic
419C2×C32#54712yes—
420C2×C32#54812yes—
421C3⋊D3—42no—
422C3×D3—44no—
423C24—32no—
424C24—91no—
425#41—1832no—
426C2×Q8—34no—
427C2×Q8—62no—
428C2×Q8—62no—
429C2×Q8—182no—
430C2×Q8—182no—
431C2×Q8—182no—
432C2×D4—34no—
433C2×D4—62no—
434C2×D4—62no—
435C2×D4—184no—
436C2×D4—184no—
437C2×D4—184no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—91no—
442C22×C4—94no—
443C22×C4—92no—
444C22×C4—184no—
445C22×C4—184no—
446C22×C4—184no—
447C22×C4—182no—
448C22×C4—182no—
449C22×C4C2×D3212yes—
450C22×C4C2×D3211yescharacteristic
451C4⋊C4—22no—
452C4⋊C4—184no—
453C4⋊C4—188no—
454C22⋊C4—68no—
455C22⋊C4—184no—
456C22⋊C4—184no—
457C22⋊C4—188no—
458C42—62no—
459C42—62no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—64no—
466C22×C3—68no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—124no—
470C22×C3C22×D1211yescharacteristic
471C22×C3C22×D1211yescharacteristic
472C22×C3C2×D3×D411yescharacteristic
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C2×D3×D411yescharacteristic
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C2×#23712yes—
477C22×C3#100712yes—
478C22×C3D3×#4112yes—
479C22×C3#101012yes—
480C2×D3—24no—
481C2×D3—28no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3—44no—
485C2×D3—64no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C3×C4—24no—
501C3×C4—44no—
502C3×C4—42no—
503C3×C4—42no—
504C3×C4—64no—
505C3×C4—64no—
506C3×C4—122no—
507C3×C4#88214yes—
508C3×C4#88214yes—
509Dic3—24no—
510Dic3—24no—
511Dic3—42no—
512Dic3—62no—
513Dic3—62no—
514Dic3—122no—
515Dic3—124no—
516Dic3—122no—
517Dic3—122no—
518C32#243211yescharacteristic, complemented, Sylow
519C23—34no—
520C23—62no—
521C23—64no—
522C23—64no—
523C23—62no—
524C23—92no—
525C23—181no—
526C23—181no—
527C23—182no—
528C23—182no—
529C23C22×D3211yescharacteristic
530Q8—68no—
531Q8—364no—
532D4—68no—
533D4—1816no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—34no—
537C2×C4—34no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—92no—
546C2×C4—1816no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—188no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—182no—
553C2×C4D3×D1212yes—
554C2×C4D3×D1212yes—
555C2×C4#381112yes—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—22no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—124no—
562C2×C3C2×#88211yescharacteristic
563C2×C3C2×#88211yescharacteristic
564C2×C3#555512yes—
565C2×C3#557612yes—
566C2×C3#559812yes—
567C2×C3#563112yes—
568C2×C3#566811yescharacteristic
569C2×C3#567511yescharacteristic
570C2×C3#571611yescharacteristic
571C2×C3#572411yescharacteristic
572D3—44no—
573D3—124no—
574D3—122no—
575D3—122no—
576C22—68no—
577C22—64no—
578C22—122no—
579C22—124no—
580C22—122no—
581C22—182no—
582C22—182no—
583C22—182no—
584C22—362no—
585C22—362no—
586C22C2×D3×D1211yescharacteristic
587C22C2×D3×D1211yescharacteristic
588C22D3×#23712yes—
589C22#6431512yes—
590C22C2×#381111yescharacteristic
591C4—42no—
592C4—64no—
593C4—64no—
594C4—122no—
595C4—182no—
596C4—362no—
597C4#6392314yes—
598C3—21no—
599C3#7644511yescharacteristic, complemented
600C3#7649811yescharacteristic, complemented
601C2—124no—
602C2—362no—
603C2#1059438112yes—
604C2#1059438212yes—
605C2C2×#6392311yescharacteristic
606C2#1059516711yescharacteristic
607C2#1059536411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#3796C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64106C2semidirect
3. C2×#63866C2semidirect
4. C2×#63860C2semidirect
5. C3×#4988C2semidirect
6. C3×#4973C2semidirect
7. #10591379C2semidirect
8. #10591312C2semidirect
9. C4×#3722C2semidirect
46. #4988D3semidirect
47. #4973D3semidirect
176. C2×C3×Dic3#41semidirect
405. C2×Dic3#237semidirect
518. C32#2432semidirect
599. C3#76445semidirect
600. C3#76498semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#641062
C2×#638662
C2×#638602
C3×#49882
C3×#49732
#105913792
#105913122
C4×#37222
#764983
#764453