Finite Group Databasebeta

← #11788308

Subgroups — #11788308

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic, complemented
3#10592825C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70081—31nomaximal
9#68992—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626C412yes—
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×(C2×D3)⋊Dic3C412yes—
19#63916—21no—
20#63916—21no—
21#63916—21no—
22#63916—21no—
23C2×#3712—21no—
24#63818—22no—
25#63818—22no—
26C2×#3710—21no—
27#63647—21no—
28#63647—21no—
29C3×#823—22no—
30#63558—22no—
31C2×#938—31no—
32C2×D3×M16—31no—
33C2×D3×M16—31no—
34C2×#895—31no—
35C2×C3×#100—31no—
36C2×#833—31no—
37C2×#823—31no—
38C2×#823D311yescharacteristic, 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
47C23×C3×D3C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C22×C3×Dic3C2×C412yes—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×#626—22no—
66C2×#626—22no—
67C2×#626—44no—
68C32×M16—21no—
69C32×M16—21no—
70C2×C32×C8—21no—
71#3748—21no—
72#3748—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208D412yescomplemented
79C3×#208D412yescomplemented
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82(C2×D3)⋊Dic3—22no—
83(C2×D3)⋊Dic3—22no—
84#3712—24no—
85#3710—24no—
86#1900—91noSylow
87C22×C3×D4—31no—
88C22×#67—32no—
89C22×D12—32no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—31no—
92C22×C4×D3—31no—
93C22×C4×D3—61no—
94C2×C3×M16—21no—
95C2×C3×M16—31no—
96C2×C3×M16—31no—
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×C4⋊C4—31no—
100C2×#217—32no—
101#938—61no—
102#938—61no—
103#938—61no—
104#938—61no—
105C2×(C2×D3)⋊C4—32no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110C2×#208C2×D311yescharacteristic
111C2×#208C2×D311yescharacteristic
112D3×M16—62no—
113D3×M16—62no—
114D3×M16—62no—
115D3×M16—62no—
116C2×ΓL(1,𝔽25)—61no—
117C2×ΓL(1,𝔽25)—61no—
118C2×D3×C8—61no—
119C2×D3×C8—61no—
120#895—61no—
121#895—61no—
122#895—61no—
123#895—61no—
124C3×#100—62no—
125#833—62no—
126#823—22no—
127#823—62no—
128(C2×D3)⋊C8—61no—
129(C2×D3)⋊C8—61no—
130(C2×D3)⋊C8—61no—
131(C2×D3)⋊C8—61no—
132(C2×D3)⋊C8—62no—
133(C2×D3)⋊C8—62no—
134C23×C32C22×C411yescharacteristic
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—41no—
139C22×C3⋊D3C22⋊C411yescharacteristic
140C22×C3⋊D3C22⋊C411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3C22⋊C411yescharacteristic
155C2×C3⋊Dic3C22⋊C411yescharacteristic
156C4×C3⋊D3—21no—
157C4×C3⋊D3—21no—
158C4×C3⋊D3—21no—
159C4×C3⋊D3—21no—
160C4×C3⋊D3—21no—
161C4×C3⋊D3—21no—
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C3×D12—41no—
167C3×D12—41no—
168C3×D12—41no—
169C3×D12—41no—
170#626—44no—
171#626—44no—
172C32×C8—41no—
173C3⋊(C3⋊C8)—41no—
174C3×C3⋊C8—22no—
175C3×C3⋊C8—22no—
176C22×M16—91no—
177C2×#121—91no—
178C2×#100—31no—
179C2×#100—91no—
180#407—91no—
181#343—31no—
182#343—91no—
183C24×C3—32no—
184C23×D3—31no—
185C23×D3—31no—
186C23×D3—61no—
187C23×D3C4×D312yes—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—32no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—124no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—61no—
204C22×Dic3C4×D312yes—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—124no—
214C2×C4×D3—31no—
215C2×C4×D3—31no—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—31no—
219C2×C4×D3—31no—
220C2×C4×D3—31no—
221C2×C4×D3—31no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—121no—
235C2×C4×D3—121no—
236C2×C4×D3—121no—
237C2×C4×D3—121no—
238C3×M16—21no—
239C3×M16—21no—
240C3×M16—21no—
241C3×M16—21no—
242C3×M16—32no—
243C3×M16—32no—
244C3×M16—41no—
245C3×M16—41no—
246C3×M16—61no—
247C3×M16—61no—
248C2×C3×C8—22no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—61no—
252C2×C3×C8—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255#217—62no—
256#217—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261#208—21no—
262#208—21no—
263#208—61no—
264#208—61no—
265#208—61no—
266#208—61no—
267#208—121no—
268#208—121no—
269#208D1212yescomplemented
270#208#6712yescomplemented
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276ΓL(1,𝔽25)—64no—
277ΓL(1,𝔽25)—64no—
278D3×C8—64no—
279D3×C8—64no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32C2×C22⋊C411yescharacteristic
283C22×C32C4×D411yescharacteristic
284C22×C32C4×D411yescharacteristic
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3—21no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3#10012yescomplemented
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—42no—
296C2×C3×D3—82no—
297C2×C3×D3—82no—
298C32×C4#12011yescharacteristic
299C32×C4#12111yescharacteristic
300C32×C4#12111yescharacteristic
301C32×C4#12311yescharacteristic
302C3⋊Dic3—21no—
303C3⋊Dic3—21no—
304C3×Dic3—42no—
305C22×D4—31no—
306C22×D4—92no—
307C23×C4—91no—
308C2×M16—31no—
309C2×M16—31no—
310C2×M16—91no—
311C2×M16—181no—
312C2×M16—182no—
313C2×M16—182no—
314C2×M16D3211yescharacteristic
315C22×C8—181no—
316#121—181no—
317#121—181no—
318#121—181no—
319#121—181no—
320C2×C4⋊C4—31no—
321C2×C22⋊C4—92no—
322#100—62no—
323#100—182no—
324C22⋊C8—181no—
325C22⋊C8—181no—
326C23×C3—21no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—122no—
331C23×C3—122no—
332C23×C3C2×C4×D311yescharacteristic
333C23×C3C2×C4×D311yescharacteristic
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—31no—
338C22×D3—31no—
339C22×D3—31no—
340C22×D3—31no—
341C22×D3—42no—
342C22×D3—42no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—122no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C22×D3—122no—
357C3×D4—121no—
358C3×D4—121no—
359C3×D4—121no—
360C3×D4—121no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—62no—
368C2×C3×C4—122no—
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4#23511yescharacteristic
371C2×C3×C4#23511yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4#23711yescharacteristic
379C2×C3×C4#23911yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381#67—124no—
382#67—124no—
383C2×Dic3—22no—
384C2×Dic3—31no—
385C2×Dic3—31no—
386C2×Dic3—31no—
387C2×Dic3—31no—
388C2×Dic3—42no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397D12—41no—
398D12—41no—
399D12—41no—
400D12—41no—
401D12—124no—
402D12—124no—
403C4×D3—61no—
404C4×D3—61no—
405C4×D3—61no—
406C4×D3—61no—
407C4×D3—61no—
408C4×D3—61no—
409C4×D3—61no—
410C4×D3—61no—
411C4×D3—61no—
412C4×D3—61no—
413C4×D3—61no—
414C4×D3—61no—
415C4×D3—61no—
416C4×D3—61no—
417C4×D3—61no—
418C4×D3—61no—
419C4×D3—121no—
420C4×D3—121no—
421C4×D3—121no—
422C4×D3—121no—
423C4×D3—121no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C3×C8—42no—
428C3×C8—41no—
429C3×C8—41no—
430C3×C8—62no—
431C3×C8—62no—
432C3⋊C8—22no—
433C3⋊C8—22no—
434C3⋊C8—122no—
435C3⋊C8—121no—
436C3⋊C8—121no—
437C2×C32—21no—
438C2×C32—21no—
439C2×C32#38611yescharacteristic
440C2×C32C2×#10011yescharacteristic
441C2×C32#41311yescharacteristic
442C3⋊D3—22no—
443C3⋊D3—41no—
444C3×D3—82no—
445C24—32no—
446C24—91no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—182no—
454C2×D4—182no—
455C2×D4—364no—
456C22×C4—32no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4C2×D3211yescharacteristic
467M16—21no—
468M16—21no—
469M16—32no—
470M16—32no—
471M16—61no—
472M16—61no—
473M16—184no—
474M16—181no—
475M16—181no—
476C2×C8—21no—
477C2×C8—61no—
478C2×C8—61no—
479C2×C8—184no—
480C2×C8—181no—
481C4⋊C4—61no—
482C4⋊C4—61no—
483C22⋊C4—182no—
484C22⋊C4—182no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3—122no—
497C22×C3—242no—
498C22×C3—242no—
499C22×C3C4×D1211yescharacteristic
500C22×C3D3×C22⋊C411yescharacteristic
501C22×C3D3×C22⋊C411yescharacteristic
502C22×C3#67⋊C411yescharacteristic
503C22×C3#89311yescharacteristic
504C22×C3C4×#6711yescharacteristic
505C2×D3—32no—
506C2×D3—32no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—62no—
511C2×D3—61no—
512C2×D3—61no—
513C2×D3—61no—
514C2×D3—61no—
515C2×D3—62no—
516C2×D3—61no—
517C2×D3—61no—
518C2×D3—61no—
519C2×D3—61no—
520C2×D3—61no—
521C2×D3—61no—
522C2×D3—82no—
523C2×D3—82no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—124no—
533C2×D3—124no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—122no—
539C3×C4#88211yescharacteristic
540C3×C4#88311yescharacteristic
541C3×C4#88411yescharacteristic
542C3×C4#88411yescharacteristic
543C3×C4#89411yescharacteristic
544C3×C4#89511yescharacteristic
545C3×C4#93711yescharacteristic
546C3×C4#93811yescharacteristic
547Dic3—42no—
548Dic3—61no—
549Dic3—61no—
550Dic3—61no—
551Dic3—61no—
552Dic3—121no—
553Dic3—121no—
554C32#190011yescharacteristic, complemented, Sylow
555C23—62no—
556C23—62no—
557C23—62no—
558C23—91no—
559C23—91no—
560C23—122no—
561C23—122no—
562C23—182no—
563C23—181no—
564C23—181no—
565C23—361no—
566C23C4×D3211yescharacteristic
567D4—121no—
568D4—121no—
569D4—121no—
570D4—121no—
571D4—364no—
572D4—364no—
573C2×C4—62no—
574C2×C4—91no—
575C2×C4—91no—
576C2×C4—122no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4#379911yescharacteristic
588C2×C4D3×D1211yescharacteristic
589C2×C4#380211yescharacteristic
590C2×C4#380411yescharacteristic
591C2×C4D3×#6711yescharacteristic
592C2×C4#381111yescharacteristic
593C8—41no—
594C8—62no—
595C8—62no—
596C8—361no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—41no—
605C2×C3—41no—
606C2×C3—242no—
607C2×C3#466511yescharacteristic
608C2×C3D3×#10011yescharacteristic
609C2×C3D3×#10011yescharacteristic
610C2×C3#474511yescharacteristic
611C2×C3#475111yescharacteristic
612C2×C3#495611yescharacteristic
613D3—62no—
614D3—62no—
615D3—82no—
616D3—122no—
617D3—122no—
618D3—121no—
619D3—121no—
620C22—21no—
621C22—21no—
622C22—92no—
623C22—122no—
624C22—122no—
625C22—122no—
626C22—181no—
627C22—181no—
628C22—181no—
629C22—181no—
630C22—181no—
631C22—242no—
632C22—242no—
633C22—362no—
634C22—362no—
635C22#6388011yescharacteristic
636C22#6390411yescharacteristic
637C22#6392111yescharacteristic
638C4—122no—
639C4—181no—
640C4—181no—
641C4#6385411yescharacteristic
642C4#6391011yescharacteristic
643C4#6392211yescharacteristic
644C4#6395811yescharacteristic
645C3—21no—
646C3#6899211yescharacteristic, complemented
647C3#7008111yescharacteristic, complemented
648C2—21no—
649C2—21no—
650C2—182no—
651C2—242no—
652C2—361no—
653C2#1059100111yescharacteristic
654C2#1059101011yescharacteristic
655C2#1059127511yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#63916C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1900
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
2. C2×#63818C2semidirect
3. #10592825C2semidirect
4. C2×C3×#823C2semidirect
5. C2×#63558C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
38. C2×#823D3semidirect
44. #4554D3semidirect
78. C3×#208D4semidirect
79. C3×#208D4semidirect
269. #208D12semidirect
270. #208#67semidirect
292. C2×C3⋊D3#100semidirect
554. C32#1900semidirect
646. C3#68992semidirect
647. C3#70081semidirect

Maximal subgroups

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

subgroupindex
C2×#639162
C2×#638182
#105928252
C2×C3×#8232
C2×#635582
C3×#45542
#105891672
#700813
#689923