Finite Group Databasebeta

← #11878732

Subgroups — #11878732

Order 1152.

916 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591517C212yesmaximal, complemented
6#10591490C212yesmaximal, complemented
7#10590603C212yesmaximal, complemented
8#10590560C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10#10590363C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#83317—31nomaximal
13#80432—31nomaximal
14C2×C3×#235—21no—
15C2×D3×Dic6C2212yes—
16C32×C4×D4C2211yescharacteristic
17C2×#3754C2212yes—
18#64078C2211yescharacteristic
19C3×#940C2211yescharacteristic
20C3×#938C2211yescharacteristic
21C2×C3×#214C2212yes—
22C3×C4×#67—21no—
23C3×#895C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#885—21no—
26C3×#884—21no—
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30#63918—21no—
31#63918—21no—
32D3×C4⋊Dic3—21no—
33D3×C4⋊Dic3—21no—
34#63866C2212yes—
35C2×#3716C2212yes—
36C2×#3715C2212yes—
37#63637C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#810C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63567C2212yes—
42#63565C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#532—31no—
46D3×C4⋊Q8—31no—
47#5548D311yescharacteristic
48C2×#869—31no—
49C3×#461—31no—
50#5175—32no—
51#5170—32no—
52#5093—32no—
53#5083—31no—
54#5076—32no—
55#5040—32no—
56#5040—32no—
57#5019—31no—
58#5019—31no—
59#5019—31no—
60#5019—31no—
61#5019—61no—
62#5019D311yescharacteristic, complemented
63#4925—31no—
64#4841—31no—
65#4833—31no—
66#4806—32no—
67#4792—32no—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C2×#634C2312yes—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C3×#235—44no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C2×C3×Dic6C2312yes—
83C2×#627—22no—
84C2×D3×Dic3—22no—
85D3×Dic6—42no—
86D3×Dic6—42no—
87C32×C4⋊C4C2311yescharacteristic
88C32×C22⋊C4—21no—
89C32×C42C2311yescharacteristic
90#3754—42no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)—21no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#217—21no—
95C3×#214—42no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×Dic3⋊C4—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—22no—
107Dic3⋊Dic3—22no—
108#3716—42no—
109#3715—42no—
110#3206—91noSylow
111C2×C3×#41—61no—
112C2×D3×Q8—32no—
113C2×#235—21no—
114C22×Dic6—32no—
115C2×C3×SD16—32no—
116C3×C4⋊Q8—31no—
117C3×C4⋊Q8—31no—
118C3×#127—31no—
119C3×#124—61no—
120C3×#121—31no—
121C3×#121—31no—
122C3×#121—61no—
123C3×C4×D4—21no—
124C3×C4×D4—31no—
125C3×C4×D4—61no—
126C3×C4×D4C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128C2×C3×C42—31no—
129#944—32no—
130C2×#215—32no—
131#940C2×D311yescharacteristic
132#938C2×D311yescharacteristic
133C2×#214—32no—
134C2×#214—32no—
135C2×#214—32no—
136C2×#214—32no—
137C2×#214—62no—
138C2×#214C2×D312yes—
139C4×#67—21no—
140C2×C4⋊Dic3—61no—
141C2×C4⋊Dic3—61no—
142C2×#204—32no—
143#895C2×D311yescharacteristic
144D3×C4⋊C4—61no—
145D3×C4⋊C4—61no—
146#888—61no—
147#888—61no—
148#888C2×D311yescharacteristic
149#885—21no—
150#884—21no—
151C4×D12C2×D311yescharacteristic
152C42×D3C2×D311yescharacteristic
153#869—32no—
154#869—31no—
155#869—31no—
156#869—61no—
157#869—61no—
158#869—61no—
159#869C2×D311yescharacteristic
160C3×C4⋊C8—31no—
161C3×#103—32no—
162#835—32no—
163#830—32no—
164(C2×D3)⋊C8—32no—
165#816—32no—
166C8×Dic3—32no—
167#810—32no—
168#810—32no—
169#810—32no—
170#810—32no—
171#810—62no—
172#810C2×D312yes—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—31no—
175C4⋊(C3⋊C8)—61no—
176C4⋊(C3⋊C8)C2×D311yescharacteristic
177C4×C3⋊C8—32no—
178C23×C32—21no—
179C22×C3×D3—21no—
180C22×C3×D3C2×D411yescharacteristic
181C32×D4—21no—
182C32×D4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—22no—
189#634—22no—
190#634—22no—
191C3×#67—42no—
192C3×#67—42no—
193C3×#67—42no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—21no—
200C3×D12—21no—
201C3×D12—42no—
202C3×C4×D3—21no—
203C3×C4×D3—21no—
204C3×C4×D3—22no—
205C3×C4×D3—42no—
206C3×C4×D3SD1614yescomplemented
207C3×Dic6—22no—
208C3×Dic6—22no—
209C3×Dic6—42no—
210#627—44no—
211D3×Dic3—44no—
212C3⋊(C3⋊C8)—22no—
213C3×C3⋊C8—22no—
214#532—31no—
215C2×C4⋊Q8—91no—
216#492—92no—
217#487—92no—
218#461—31no—
219#461—91no—
220#461—91no—
221#461—91no—
222#448—92no—
223#448—92no—
224#431—91no—
225C3×#41—124no—
226C2×C3×Q8—32no—
227C2×C3×Q8—61no—
228C2×C3×D4—21no—
229C2×C3×D4—31no—
230C2×C3×D4—61no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C2×C3×D4—61no—
234C2×C3×D4C22×D311yescharacteristic
235C2×C3×D4C22×D311yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—41no—
242C22×C3×C4—61no—
243C2×#67—21no—
244C2×#67—21no—
245C2×#67—21no—
246C22×Dic3—62no—
247D3×Q8—122no—
248D3×Q8—122no—
249#235—44no—
250C2×D12—21no—
251C2×D12C22×D311yescharacteristic
252C2×C4×D3—21no—
253C2×C4×D3—62no—
254C2×C4×D3#6711yescharacteristic
255C2×C4×D3#6711yescharacteristic
256C2×C4×D3C22×D311yescharacteristic
257C2×Dic6—21no—
258C2×Dic6—32no—
259C2×Dic6—32no—
260C2×Dic6—62no—
261C2×Dic6—62no—
262C2×Dic6—62no—
263C2×Dic6—122no—
264C2×Dic6—122no—
265C2×Dic6C22×D312yes—
266C3×SD16—122no—
267C2×C3×C8—32no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4C22×D311yescharacteristic
274C3×C4⋊C4C22×D311yescharacteristic
275C3×C22⋊C4—21no—
276C3×C22⋊C4—21no—
277C3×C22⋊C4—41no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—21no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42C22×D311yescharacteristic
286C3×C42C22×D311yescharacteristic
287#217—21no—
288#215—122no—
289#214—42no—
290#214—122no—
291#214—122no—
292#214—122no—
293#214—122no—
294#214—124no—
295(C2×D3)⋊C4—21no—
296(C2×D3)⋊C4—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—62no—
300C4⋊Dic3—62no—
301C4⋊Dic3—61no—
302C4⋊Dic3—61no—
303C4⋊Dic3—61no—
304C4⋊Dic3—61no—
305C4⋊Dic3—121no—
306C4⋊Dic3—121no—
307C4⋊Dic3C22×D311yescharacteristic
308Dic3⋊C4—21no—
309Dic3⋊C4—62no—
310Dic3⋊C4—62no—
311C4×Dic3#6711yescharacteristic
312C4×Dic3#6711yescharacteristic
313C4×Dic3C22×D311yescharacteristic
314C2×C3⋊C8—32no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8C22×D312yes—
318#204—122no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32C22×D411yescharacteristic
323C2×C3×D3—21no—
324C2×C3×D3—21no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3C2×SD1612yes—
329C32×C4—21no—
330C32×C4—41no—
331C32×C4C2×SD1612yes—
332C32×C4H(5,𝔽2)11yescharacteristic
333C32×C4H(5,𝔽2)11yescharacteristic
334C3⋊Dic3—42no—
335C3×Dic3—21no—
336C3×Dic3—42no—
337C3×Dic3—41no—
338C3×Dic3C2×SD1612yes—
339C3×Dic3#13712yes—
340C2×#41—61no—
341C22×Q8—92no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×SD16—92no—
345C2×SD16—92no—
346C4⋊Q8—31no—
347C4⋊Q8—31no—
348C4⋊Q8—92no—
349C4⋊Q8—91no—
350C4⋊Q8—181no—
351C4⋊Q8—181no—
352#127—31no—
353#124—61no—
354#121—31no—
355#121—31no—
356#121—61no—
357C4×D4—31no—
358C4×D4—61no—
359C4×D4D3211yescharacteristic
360C2×C4⋊C4—181no—
361C2×C4⋊C4—181no—
362C2×C42—31no—
363C4⋊C8—31no—
364C4⋊C8—91no—
365#103—32no—
366#103—92no—
367#103—92no—
368#103—92no—
369C22⋊C8—92no—
370C4×C8—92no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—31no—
374C23×C3—41no—
375C23×C3—61no—
376C22×D3—21no—
377C22×D3C2×#6711yescharacteristic
378C3×Q8—62no—
379C3×Q8—62no—
380C3×Q8—122no—
381C3×D4—22no—
382C3×D4—21no—
383C3×D4—21no—
384C3×D4—21no—
385C3×D4—21no—
386C3×D4—41no—
387C3×D4—61no—
388C3×D4—61no—
389C3×D4—122no—
390C3×D4—122no—
391C3×D4—122no—
392C3×D4—122no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—34no—
401C2×C3×C4—31no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—62no—
410C2×C3×C4—82no—
411C2×C3×C4—122no—
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—42no—
419#67—42no—
420#67—42no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3C2×#6711yescharacteristic
428C2×Dic3C2×#6711yescharacteristic
429C2×Dic3C2×#6711yescharacteristic
430D12—21no—
431D12—21no—
432D12—42no—
433C4×D3—21no—
434C4×D3—21no—
435C4×D3—22no—
436C4×D3—42no—
437C4×D3—124no—
438C4×D3#21414yescomplemented
439Dic6—22no—
440Dic6—22no—
441Dic6—42no—
442Dic6—62no—
443Dic6—62no—
444Dic6—62no—
445Dic6—62no—
446Dic6—122no—
447Dic6—122no—
448Dic6—124no—
449Dic6—124no—
450C3×C8—62no—
451C3⋊C8—22no—
452C3⋊C8—62no—
453C3⋊C8—62no—
454C3⋊C8—122no—
455C2×C32—81no—
456C2×C32#53511yescharacteristic
457C2×C32C22×SD1611yescharacteristic
458C2×C32C2×#13711yescharacteristic
459C3×D3—22no—
460C3×D3—81no—
461#41—124no—
462C2×Q8—32no—
463C2×Q8—61no—
464C2×Q8—92no—
465C2×Q8—182no—
466C2×Q8—362no—
467C2×Q8—362no—
468C2×D4—31no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—61no—
473C2×D4C2×D3211yescharacteristic
474C22×C4—21no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—61no—
479C22×C4—182no—
480SD16—122no—
481SD16—362no—
482SD16—362no—
483SD16—362no—
484C2×C8—32no—
485C2×C8—92no—
486C4⋊C4—31no—
487C4⋊C4—61no—
488C4⋊C4—61no—
489C4⋊C4—61no—
490C4⋊C4—182no—
491C4⋊C4—182no—
492C4⋊C4—181no—
493C4⋊C4—181no—
494C4⋊C4C2×D3211yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—61no—
497C22⋊C4—61no—
498C22⋊C4—61no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42C2×D3211yescharacteristic
503C22×C3—21no—
504C22×C3—32no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—61no—
513C22×C3—61no—
514C22×C3—81no—
515C22×C3—81no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—121no—
519C22×C3C2×D3×D411yescharacteristic
520C22×C3C22×#6711yescharacteristic
521C2×D3—21no—
522C2×D3—21no—
523C2×D3—41no—
524C2×D3—41no—
525C2×D3—41no—
526C2×D3C2×#21412yes—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—32no—
533C3×C4—32no—
534C3×C4—41no—
535C3×C4—41no—
536C3×C4—41no—
537C3×C4—61no—
538C3×C4—81no—
539C3×C4—121no—
540C3×C4—122no—
541C3×C4D3×SD1612yes—
542C3×C4C2×#21412yes—
543C3×C4#100411yescharacteristic
544C3×C4#100911yescharacteristic
545C3×C4#100911yescharacteristic
546C3×C4#100911yescharacteristic
547Dic3—21no—
548Dic3—41no—
549Dic3—42no—
550Dic3—122no—
551Dic3—122no—
552Dic3—242no—
553Dic3C2×#21412yes—
554Dic3#95112yes—
555C32#320611yescharacteristic, complemented, Sylow
556C23—21no—
557C23—31no—
558C23—61no—
559Q8—62no—
560Q8—62no—
561Q8—122no—
562Q8—182no—
563Q8—182no—
564Q8—364no—
565D4—21no—
566D4—21no—
567D4—61no—
568D4—61no—
569D4—122no—
570D4—122no—
571D4—122no—
572D4—122no—
573C2×C4—21no—
574C2×C4—31no—
575C2×C4—31no—
576C2×C4—34no—
577C2×C4—31no—
578C2×C4—42no—
579C2×C4—62no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—61no—
583C2×C4—62no—
584C2×C4—122no—
585C2×C4—182no—
586C2×C4—364no—
587C2×C4D3×#6711yescharacteristic
588C2×C4D3×#6711yescharacteristic
589C2×C4C22×D3211yescharacteristic
590C8—62no—
591C8—182no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—62no—
596C2×C3—82no—
597C2×C3—81no—
598C2×C3—81no—
599C2×C3—241no—
600C2×C3#560711yescharacteristic
601C2×C3C2×D3×SD1611yescharacteristic
602C2×C3D3×#13711yescharacteristic
603C2×C3C22×#21411yescharacteristic
604C2×C3C2×#95111yescharacteristic
605C2×C3#583011yescharacteristic
606D3—22no—
607D3—81no—
608C22—32no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—61no—
613C22—61no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22C2×D3×#6711yescharacteristic
618C4—21no—
619C4—32no—
620C4—32no—
621C4—41no—
622C4—61no—
623C4—121no—
624C4—122no—
625C4—362no—
626C4D3×#21412yes—
627C4#6430711yescharacteristic
628C4#6430811yescharacteristic
629C3—21no—
630C3#8043211yescharacteristic, complemented
631C3#8331711yescharacteristic, complemented
632C2—62no—
633C2—81no—
634C2—241no—
635C2#1059506411yescharacteristic
636C2C2×D3×#21411yescharacteristic
637C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5548C2
hypercenterC4×D4D32
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. D3×#869C2semidirect
3. #10592718C2semidirect
4. C3×#5019C2semidirect
5. #10591517C2semidirect
6. #10591490C2semidirect
7. #10590603C2semidirect
8. #10590560C2semidirect
9. #10590365C2semidirect
10. #10590363C2semidirect
11. #10590248C2semidirect
62. #5019D3semidirect
206. C3×C4×D3SD16semidirect
438. C4×D3#214semidirect
555. C32#3206semidirect
630. C3#80432semidirect
631. C3#83317semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
D3×#8692
#105927182
C3×#50192
#105915172
#105914902
#105906032
#105905602
#105903652
#105903632
#105902482
#833173
#804323