Finite Group Databasebeta

← #11788346

Subgroups — #11788346

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×C3×#824C211yesmaximal, characteristic, complemented
4C2×#63560C211yesmaximal, characteristic, complemented
5#10591074C211yesmaximal, characteristic
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70115—31nomaximal
9#68993—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14M16×C3⋊D3—22no—
15M16×C3⋊D3—22no—
16C2×#3743—21no—
17C2×C8×C3⋊D3—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×Dic3⋊Dic3C412yes—
22C2×#3722C412yes—
23#63871—21no—
24#63871—21no—
25#63871—21no—
26#63871—21no—
27C3×#824—22no—
28#63560—22no—
29#63557—21no—
30#63557—21no—
31C2×#946—31no—
32C2×D3×M16—31no—
33C2×D3×M16—31no—
34C2×D3×M16—61no—
35C2×#897—31no—
36C2×C3×#101—31no—
37C2×#836—31no—
38C2×#824—31no—
39C2×#824D311yescharacteristic, complemented
40#5126—31no—
41#5126—31no—
42C3×#343—31no—
43#4554—31no—
44#4554D311yescharacteristic, complemented
45#4530—31no—
46C23×C3⋊D3C2×C411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C22×C3×Dic3C2×C412yes—
58C22×C3×Dic3C2×C412yes—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C32×M16—21no—
66C32×M16D412yes—
67C2×C32×C8—21no—
68#3748—21no—
69#3748D412yes—
70C2×C3⋊(C3⋊C8)—21no—
71#3743—24no—
72C8×C3⋊D3—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81Dic3⋊Dic3—22no—
82Dic3⋊Dic3—22no—
83#3722—22no—
84#3722—22no—
85#1901—91noSylow
86C22×C3×Q8—31no—
87C22×C4×D3—31no—
88C22×C4×D3—31no—
89C22×C4×D3—61no—
90C22×Dic6C2×D311yescharacteristic
91C2×C3×M16—21no—
92C2×C3×M16—31no—
93C2×C3×M16—31no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×C4⋊C4—31no—
97#946—61no—
98#946—61no—
99#946—61no—
100#946—61no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×C4⋊Dic3—32no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—32no—
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111D3×M16—62no—
112D3×M16—62no—
113D3×M16—64no—
114D3×M16—64no—
115D3×M16—62no—
116D3×M16—62no—
117C2×ΓL(1,𝔽25)—61no—
118C2×ΓL(1,𝔽25)—61no—
119C2×ΓL(1,𝔽25)—62no—
120C2×D3×C8—61no—
121C2×D3×C8—61no—
122C2×D3×C8—62no—
123#897—61no—
124#897—61no—
125#897—61no—
126#897—61no—
127C3×#101—62no—
128#836—62no—
129#824—22no—
130#824—62no—
131(C2×D3)⋊C8—61no—
132(C2×D3)⋊C8—61no—
133(C2×D3)⋊C8—61no—
134(C2×D3)⋊C8—61no—
135C23×C32C22×C411yescharacteristic
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—41no—
140C22×C3⋊D3C22⋊C411yescharacteristic
141C22×C3⋊D3C22⋊C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3C22⋊C411yescharacteristic
151C2×C3⋊Dic3C22⋊C411yescharacteristic
152C4×C3⋊D3—21no—
153C4×C3⋊D3—21no—
154C4×C3⋊D3—21no—
155C4×C3⋊D3—21no—
156C4×C3⋊D3—21no—
157C4×C3⋊D3—21no—
158C4×C3⋊D3—21no—
159C4×C3⋊D3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—42no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C3×Dic6—41no—
168C3×Dic6—41no—
169C32×C8—22no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8—41no—
172C3×C3⋊C8—41no—
173C22×M16—91no—
174C2×C22⋊Q8—91no—
175C2×#101—31no—
176C2×#101—91no—
177#407—91no—
178#343—31no—
179#343—91no—
180C23×D3—31no—
181C23×D3—31no—
182C23×D3—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—61no—
197C22×Dic3C4×D312yes—
198C22×Dic3C4×D312yes—
199C2×C4×D3—31no—
200C2×C4×D3—31no—
201C2×C4×D3—31no—
202C2×C4×D3—31no—
203C2×C4×D3—31no—
204C2×C4×D3—31no—
205C2×C4×D3—31no—
206C2×C4×D3—31no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C3×M16—22no—
230C3×M16—21no—
231C3×M16—21no—
232C3×M16—22no—
233C3×M16—61no—
234C3×M16—61no—
235C3×M16—61no—
236C3×M16—61no—
237C3×M16D1212yes—
238C3×M16#6712yes—
239C2×C3×C8—22no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—61no—
243C2×C3×C8—61no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256#208—21no—
257#208—21no—
258#208—21no—
259#208—21no—
260#208—32no—
261#208—32no—
262#208—62no—
263#208—62no—
264#208—61no—
265#208—61no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271ΓL(1,𝔽25)—68no—
272ΓL(1,𝔽25)—64no—
273ΓL(1,𝔽25)—64no—
274D3×C8—68no—
275D3×C8—64no—
276D3×C8—64no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C2×C22⋊C411yescharacteristic
280C22×C32C4×D411yescharacteristic
281C22×C32C4×D411yescharacteristic
282C2×C3⋊D3—21no—
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—42no—
289C2×C3⋊D3#10112yescomplemented
290C32×C4#12011yescharacteristic
291C32×C4#12111yescharacteristic
292C32×C4#12111yescharacteristic
293C32×C4#12311yescharacteristic
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C22×Q8—31no—
299C23×C4—91no—
300C2×M16—31no—
301C2×M16—31no—
302C2×M16—91no—
303C2×M16—181no—
304C2×M16—182no—
305C2×M16—182no—
306C2×M16D3211yescharacteristic
307C22×C8—181no—
308C22⋊Q8—181no—
309C22⋊Q8—181no—
310C22⋊Q8—181no—
311C22⋊Q8—181no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—92no—
314C2×C22⋊C4—92no—
315#101—62no—
316#101—182no—
317C22⋊C8—181no—
318C22⋊C8—181no—
319C23×C3—21no—
320C23×C3C2×C4×D311yescharacteristic
321C23×C3C2×C4×D311yescharacteristic
322C22×D3—31no—
323C22×D3—31no—
324C22×D3—31no—
325C22×D3—31no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—122no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—122no—
340C3×Q8—121no—
341C3×Q8—121no—
342C3×Q8—121no—
343C3×Q8—121no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—122no—
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4#23911yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—31no—
372C2×Dic3—31no—
373C2×Dic3—31no—
374C2×Dic3—31no—
375C2×Dic3—42no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C4×D3—62no—
385C4×D3—62no—
386C4×D3—62no—
387C4×D3—62no—
388C4×D3—62no—
389C4×D3—62no—
390C4×D3—62no—
391C4×D3—62no—
392C4×D3—61no—
393C4×D3—61no—
394C4×D3—61no—
395C4×D3—61no—
396C4×D3—61no—
397C4×D3—61no—
398C4×D3—61no—
399C4×D3—61no—
400C4×D3—61no—
401C4×D3—61no—
402C4×D3—61no—
403C4×D3—61no—
404C4×D3—61no—
405C4×D3—61no—
406C4×D3—61no—
407C4×D3—61no—
408Dic6—41no—
409Dic6—41no—
410Dic6—41no—
411Dic6—41no—
412C3×C8—24no—
413C3×C8—22no—
414C3×C8—22no—
415C3×C8—121no—
416C3×C8—121no—
417C3⋊C8—41no—
418C3⋊C8—41no—
419C3⋊C8—64no—
420C3⋊C8—62no—
421C3⋊C8—62no—
422C2×C32—21no—
423C2×C32—21no—
424C2×C32#38611yescharacteristic
425C2×C32C2×#10111yescharacteristic
426C2×C32#41311yescharacteristic
427C3⋊D3—22no—
428C3⋊D3—41no—
429C24—91no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—61no—
433C2×Q8—61no—
434C2×Q8—61no—
435C2×Q8—61no—
436C22×C4—32no—
437C22×C4—32no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—181no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—181no—
447C22×C4C2×D3211yescharacteristic
448M16—21no—
449M16—61no—
450M16—61no—
451M16—61no—
452M16—61no—
453M16—92no—
454M16—184no—
455M16—181no—
456M16#62612yes—
457C2×C8—21no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8—184no—
461C2×C8—181no—
462C4⋊C4—61no—
463C4⋊C4—61no—
464C4⋊C4—182no—
465C4⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3C4×D1211yescharacteristic
478C22×C3D3×C22⋊C411yescharacteristic
479C22×C3D3×C22⋊C411yescharacteristic
480C22×C3#67⋊C411yescharacteristic
481C22×C3#89311yescharacteristic
482C22×C3C4×#6711yescharacteristic
483C2×D3—32no—
484C2×D3—32no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—61no—
489C2×D3—61no—
490C2×D3—61no—
491C2×D3—61no—
492C2×D3—62no—
493C2×D3—61no—
494C2×D3—61no—
495C2×D3—61no—
496C2×D3—61no—
497C2×D3—61no—
498C2×D3—61no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—124no—
506C2×D3—124no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—122no—
512C3×C4—122no—
513C3×C4#88211yescharacteristic
514C3×C4#88311yescharacteristic
515C3×C4#88411yescharacteristic
516C3×C4#88411yescharacteristic
517C3×C4#89411yescharacteristic
518C3×C4#89511yescharacteristic
519C3×C4#93711yescharacteristic
520C3×C4#93811yescharacteristic
521Dic3—42no—
522Dic3—42no—
523Dic3—62no—
524Dic3—62no—
525Dic3—61no—
526Dic3—61no—
527Dic3—61no—
528Dic3—61no—
529C32#190111yescharacteristic, complemented, Sylow
530C23—91no—
531C23—91no—
532C23—182no—
533C23—181no—
534C23—181no—
535C23—361no—
536C23C4×D3211yescharacteristic
537Q8—121no—
538Q8—121no—
539Q8—121no—
540Q8—121no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—91no—
546C2×C4—91no—
547C2×C4—122no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4#379611yescharacteristic
559C2×C4#379811yescharacteristic
560C2×C4#380211yescharacteristic
561C2×C4C2×#62611yescharacteristic
562C2×C4#381111yescharacteristic
563C2×C4#381111yescharacteristic
564C8—22no—
565C8—121no—
566C8—121no—
567C8—182no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—41no—
576C2×C3—41no—
577C2×C3#466511yescharacteristic
578C2×C3#474511yescharacteristic
579C2×C3D3×#10111yescharacteristic
580C2×C3D3×#10111yescharacteristic
581C2×C3#475111yescharacteristic
582C2×C3#495611yescharacteristic
583D3—64no—
584D3—62no—
585D3—62no—
586D3—122no—
587D3—121no—
588D3—121no—
589C22—21no—
590C22—21no—
591C22—92no—
592C22—181no—
593C22—181no—
594C22—181no—
595C22—181no—
596C22—181no—
597C22—362no—
598C22—362no—
599C22#6388111yescharacteristic
600C22C4×#62611yescharacteristic
601C22#6392111yescharacteristic
602C4—122no—
603C4—122no—
604C4—181no—
605C4—181no—
606C4#6385311yescharacteristic
607C4#6391211yescharacteristic
608C4#6391611yescharacteristic
609C4#6398111yescharacteristic
610C3—21no—
611C3#6899311yescharacteristic, complemented
612C3#7011511yescharacteristic, complemented
613C2—21no—
614C2—21no—
615C2—182no—
616C2—361no—
617C2#1059100311yescharacteristic
618C2#1059101011yescharacteristic
619C2#1059138711yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C3×#824C2semidirect
4. C2×#63560C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
39. C2×#824D3semidirect
44. #4554D3semidirect
289. C2×C3⋊D3#101semidirect
529. C32#1901semidirect
611. C3#68993semidirect
612. C3#70115semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
C2×#638712
C2×C3×#8242
C2×#635602
#105910742
C3×#45542
#105891672
#701153
#689933