Finite Group Databasebeta

← #11788343

Subgroups — #11788343

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63871C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic
3#10592825C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
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
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×Dic3⋊Dic3C412yes—
18C2×#3722C412yes—
19#63871—21no—
20#63871—21no—
21#63871—21no—
22#63871—21no—
23C2×#3712—21no—
24#63818—22no—
25#63818—22no—
26C2×#3710—21no—
27#63647—21no—
28#63647—21no—
29C3×#824—22no—
30#63560—22no—
31C2×#946—31no—
32C2×D3×M16—31no—
33C2×D3×M16—31no—
34C2×#897—31no—
35C2×C3×#101—31no—
36C2×#836—31no—
37C2×#824—31no—
38C2×#824D311yescharacteristic, complemented
39#5126—31no—
40#5126—31no—
41#5126—61no—
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×M16—21no—
67C2×C32×C8—21no—
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208D412yes—
76C3×#208D412yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79Dic3⋊Dic3—22no—
80Dic3⋊Dic3—22no—
81#3722—22no—
82#3722—22no—
83#3712—24no—
84#3710—24no—
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—62no—
114D3×M16—62no—
115C2×ΓL(1,𝔽25)—61no—
116C2×ΓL(1,𝔽25)—61no—
117C2×D3×C8—61no—
118C2×D3×C8—61no—
119#897—61no—
120#897—61no—
121#897—61no—
122#897—61no—
123C3×#101—62no—
124#836—62no—
125#824—22no—
126#824—62no—
127(C2×D3)⋊C8—61no—
128(C2×D3)⋊C8—61no—
129(C2×D3)⋊C8—61no—
130(C2×D3)⋊C8—61no—
131(C2×D3)⋊C8—62no—
132(C2×D3)⋊C8—62no—
133C23×C32C22×C411yescharacteristic
134C22×C3⋊D3—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—41no—
138C22×C3⋊D3C22⋊C411yescharacteristic
139C22×C3⋊D3C22⋊C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3C22⋊C411yescharacteristic
149C2×C3⋊Dic3C22⋊C411yescharacteristic
150C4×C3⋊D3—21no—
151C4×C3⋊D3—21no—
152C4×C3⋊D3—21no—
153C4×C3⋊D3—21no—
154C4×C3⋊D3—21no—
155C4×C3⋊D3—21no—
156C4×C3⋊D3—21no—
157C4×C3⋊D3—21no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C32×C8—41no—
168C3⋊(C3⋊C8)—41no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C22×M16—91no—
172C2×C22⋊Q8—91no—
173C2×#101—31no—
174C2×#101—91no—
175#407—91no—
176#343—31no—
177#343—91no—
178C23×D3—31no—
179C23×D3—31no—
180C23×D3—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C22×C3×C4—21no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—61no—
195C22×Dic3C4×D312yes—
196C22×Dic3C4×D312yes—
197C2×C4×D3—31no—
198C2×C4×D3—31no—
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—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—121no—
218C2×C4×D3—121no—
219C2×C4×D3—121no—
220C2×C4×D3—121no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C3×M16—21no—
228C3×M16—21no—
229C3×M16—21no—
230C3×M16—21no—
231C3×M16—32no—
232C3×M16—32no—
233C3×M16—41no—
234C3×M16—41no—
235C3×M16—61no—
236C3×M16—61no—
237C2×C3×C8—22no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—61no—
241C2×C3×C8—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254#208—21no—
255#208—21no—
256#208—61no—
257#208—61no—
258#208—61no—
259#208—61no—
260#208—121no—
261#208—121no—
262#208D1212yes—
263#208#6712yes—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269ΓL(1,𝔽25)—64no—
270ΓL(1,𝔽25)—64no—
271D3×C8—64no—
272D3×C8—64no—
273C22×C32—21no—
274C22×C32—21no—
275C22×C32C2×C22⋊C411yescharacteristic
276C22×C32C4×D411yescharacteristic
277C22×C32C4×D411yescharacteristic
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3#10112yescomplemented
286C32×C4#12011yescharacteristic
287C32×C4#12111yescharacteristic
288C32×C4#12111yescharacteristic
289C32×C4#12311yescharacteristic
290C3⋊Dic3—21no—
291C3⋊Dic3—21no—
292C3×Dic3—42no—
293C3×Dic3—42no—
294C22×Q8—31no—
295C23×C4—91no—
296C2×M16—31no—
297C2×M16—31no—
298C2×M16—91no—
299C2×M16—181no—
300C2×M16—182no—
301C2×M16—182no—
302C2×M16D3211yescharacteristic
303C22×C8—181no—
304C22⋊Q8—181no—
305C22⋊Q8—181no—
306C22⋊Q8—181no—
307C22⋊Q8—181no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—92no—
310C2×C22⋊C4—92no—
311#101—62no—
312#101—182no—
313C22⋊C8—181no—
314C22⋊C8—181no—
315C23×C3—21no—
316C23×C3C2×C4×D311yescharacteristic
317C23×C3C2×C4×D311yescharacteristic
318C22×D3—31no—
319C22×D3—31no—
320C22×D3—31no—
321C22×D3—31no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—122no—
336C3×Q8—121no—
337C3×Q8—121no—
338C3×Q8—121no—
339C3×Q8—121no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—122no—
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23911yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—31no—
368C2×Dic3—31no—
369C2×Dic3—31no—
370C2×Dic3—31no—
371C2×Dic3—42no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C4×D3—61no—
381C4×D3—61no—
382C4×D3—61no—
383C4×D3—61no—
384C4×D3—61no—
385C4×D3—61no—
386C4×D3—61no—
387C4×D3—61no—
388C4×D3—61no—
389C4×D3—61no—
390C4×D3—61no—
391C4×D3—61no—
392C4×D3—61no—
393C4×D3—61no—
394C4×D3—61no—
395C4×D3—61no—
396C4×D3—121no—
397C4×D3—121no—
398C4×D3—121no—
399C4×D3—121no—
400C4×D3—121no—
401C4×D3—121no—
402C4×D3—121no—
403C4×D3—121no—
404Dic6—41no—
405Dic6—41no—
406Dic6—41no—
407Dic6—41no—
408C3×C8—42no—
409C3×C8—41no—
410C3×C8—41no—
411C3×C8—62no—
412C3×C8—62no—
413C3⋊C8—22no—
414C3⋊C8—22no—
415C3⋊C8—122no—
416C3⋊C8—121no—
417C3⋊C8—121no—
418C2×C32—21no—
419C2×C32—21no—
420C2×C32#38611yescharacteristic
421C2×C32C2×#10111yescharacteristic
422C2×C32#41311yescharacteristic
423C3⋊D3—22no—
424C3⋊D3—41no—
425C24—91no—
426C2×Q8—61no—
427C2×Q8—61no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C22×C4—32no—
433C22×C4—32no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—181no—
440C22×C4—181no—
441C22×C4—181no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444M16—21no—
445M16—21no—
446M16—32no—
447M16—32no—
448M16—61no—
449M16—61no—
450M16—184no—
451M16—181no—
452M16—181no—
453C2×C8—21no—
454C2×C8—61no—
455C2×C8—61no—
456C2×C8—184no—
457C2×C8—181no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C22⋊C4—182no—
463C22⋊C4—182no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3C4×D1211yescharacteristic
474C22×C3D3×C22⋊C411yescharacteristic
475C22×C3D3×C22⋊C411yescharacteristic
476C22×C3#67⋊C411yescharacteristic
477C22×C3#89311yescharacteristic
478C22×C3C4×#6711yescharacteristic
479C2×D3—32no—
480C2×D3—32no—
481C2×D3—62no—
482C2×D3—61no—
483C2×D3—61no—
484C2×D3—61no—
485C2×D3—61no—
486C2×D3—62no—
487C2×D3—61no—
488C2×D3—61no—
489C2×D3—61no—
490C2×D3—61no—
491C2×D3—61no—
492C2×D3—61no—
493C2×D3—121no—
494C2×D3—121no—
495C2×D3—121no—
496C2×D3—121no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—124no—
502C2×D3—124no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—122no—
508C3×C4—122no—
509C3×C4#88211yescharacteristic
510C3×C4#88311yescharacteristic
511C3×C4#88411yescharacteristic
512C3×C4#88411yescharacteristic
513C3×C4#89411yescharacteristic
514C3×C4#89511yescharacteristic
515C3×C4#93711yescharacteristic
516C3×C4#93811yescharacteristic
517Dic3—42no—
518Dic3—42no—
519Dic3—61no—
520Dic3—61no—
521Dic3—61no—
522Dic3—61no—
523Dic3—121no—
524Dic3—121no—
525C32#190111yescharacteristic, complemented, Sylow
526C23—91no—
527C23—91no—
528C23—182no—
529C23—181no—
530C23—181no—
531C23—361no—
532C23C4×D3211yescharacteristic
533Q8—121no—
534Q8—121no—
535Q8—121no—
536Q8—121no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—91no—
542C2×C4—91no—
543C2×C4—122no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4#379911yescharacteristic
555C2×C4D3×D1211yescharacteristic
556C2×C4#380211yescharacteristic
557C2×C4#380411yescharacteristic
558C2×C4D3×#6711yescharacteristic
559C2×C4#381111yescharacteristic
560C8—41no—
561C8—62no—
562C8—62no—
563C8—361no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—41no—
572C2×C3—41no—
573C2×C3#466511yescharacteristic
574C2×C3#474511yescharacteristic
575C2×C3D3×#10111yescharacteristic
576C2×C3D3×#10111yescharacteristic
577C2×C3#475111yescharacteristic
578C2×C3#495611yescharacteristic
579D3—62no—
580D3—62no—
581D3—122no—
582D3—122no—
583D3—121no—
584D3—121no—
585C22—21no—
586C22—21no—
587C22—92no—
588C22—181no—
589C22—181no—
590C22—181no—
591C22—181no—
592C22—181no—
593C22—362no—
594C22—362no—
595C22#6388011yescharacteristic
596C22#6390411yescharacteristic
597C22#6392111yescharacteristic
598C4—122no—
599C4—122no—
600C4—181no—
601C4—181no—
602C4#6385411yescharacteristic
603C4#6391011yescharacteristic
604C4#6392211yescharacteristic
605C4#6395811yescharacteristic
606C3—21no—
607C3#6899311yescharacteristic, complemented
608C3#7011511yescharacteristic, complemented
609C2—21no—
610C2—21no—
611C2—182no—
612C2—361no—
613C2#1059100311yescharacteristic
614C2#1059101011yescharacteristic
615C2#1059127511yescharacteristic
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
4. C2×C3×#824C2semidirect
5. C2×#63560C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
38. C2×#824D3semidirect
44. #4554D3semidirect
285. C2×C3⋊D3#101semidirect
525. C32#1901semidirect
607. C3#68993semidirect
608. C3#70115semidirect

Maximal subgroups

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

subgroupindex
C2×#638712
C2×#638182
#105928252
C2×C3×#8242
C2×#635602
C3×#45542
#105891672
#701153
#689933