Finite Group Databasebeta

← #11788311

Subgroups — #11788311

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic, complemented
4C2×#63558C211yesmaximal, characteristic, complemented
5#10591074C211yesmaximal, 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
15M16×C3⋊D3—22no—
16M16×C3⋊D3—22no—
17C2×#3743—21no—
18C2×C8×C3⋊D3—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×(C2×D3)⋊Dic3C412yes—
23#63916—21no—
24#63916—21no—
25#63916—21no—
26#63916—21no—
27C3×#823—22no—
28#63558—22no—
29#63557—21no—
30#63557—21no—
31C2×#938—31no—
32C2×D3×M16—31no—
33C2×D3×M16—31no—
34C2×D3×M16—61no—
35C2×#895—31no—
36C2×C3×#100—31no—
37C2×#833—31no—
38C2×#823—31no—
39C2×#823D311yescharacteristic, complemented
40#5126—31no—
41#5126—31no—
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×M16D412yescomplemented
70C2×C32×C8—21no—
71#3748—21no—
72#3748D412yescomplemented
73C2×C3⋊(C3⋊C8)—21no—
74#3743—24no—
75C8×C3⋊D3—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C3×#208—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84(C2×D3)⋊Dic3—22no—
85(C2×D3)⋊Dic3—22no—
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—64no—
115D3×M16—64no—
116D3×M16—62no—
117D3×M16—62no—
118C2×ΓL(1,𝔽25)—61no—
119C2×ΓL(1,𝔽25)—61no—
120C2×ΓL(1,𝔽25)—62no—
121C2×D3×C8—61no—
122C2×D3×C8—61no—
123C2×D3×C8—62no—
124#895—61no—
125#895—61no—
126#895—61no—
127#895—61no—
128C3×#100—62no—
129#833—62no—
130#823—22no—
131#823—62no—
132(C2×D3)⋊C8—61no—
133(C2×D3)⋊C8—61no—
134(C2×D3)⋊C8—61no—
135(C2×D3)⋊C8—61no—
136C23×C32C22×C411yescharacteristic
137C22×C3⋊D3—21no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—41no—
141C22×C3⋊D3C22⋊C411yescharacteristic
142C22×C3⋊D3C22⋊C411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—42no—
147C22×C3×D3—42no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C32×C4#4111yescharacteristic
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3C22⋊C411yescharacteristic
157C2×C3⋊Dic3C22⋊C411yescharacteristic
158C4×C3⋊D3—21no—
159C4×C3⋊D3—21no—
160C4×C3⋊D3—21no—
161C4×C3⋊D3—21no—
162C4×C3⋊D3—21no—
163C4×C3⋊D3—21no—
164C4×C3⋊D3—21no—
165C4×C3⋊D3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C3×D12—41no—
169C3×D12—41no—
170C3×D12—41no—
171C3×D12—41no—
172#626—44no—
173#626—44no—
174C32×C8—22no—
175C3⋊(C3⋊C8)—22no—
176C3×C3⋊C8—41no—
177C3×C3⋊C8—41no—
178C22×M16—91no—
179C2×#121—91no—
180C2×#100—31no—
181C2×#100—91no—
182#407—91no—
183#343—31no—
184#343—91no—
185C24×C3—32no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C23×D3C4×D312yes—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C22×C3×C4—21no—
197C22×C3×C4—32no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—124no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—61no—
206C22×Dic3C4×D312yes—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—124no—
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—31no—
223C2×C4×D3—31no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C3×M16—22no—
241C3×M16—21no—
242C3×M16—21no—
243C3×M16—22no—
244C3×M16—61no—
245C3×M16—61no—
246C3×M16—61no—
247C3×M16—61no—
248C3×M16D1212yescomplemented
249C3×M16#6712yescomplemented
250C2×C3×C8—22no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—61no—
254C2×C3×C8—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257#217—62no—
258#217—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263#208—21no—
264#208—21no—
265#208—21no—
266#208—21no—
267#208—32no—
268#208—32no—
269#208—62no—
270#208—62no—
271#208—61no—
272#208—61no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278ΓL(1,𝔽25)—68no—
279ΓL(1,𝔽25)—64no—
280ΓL(1,𝔽25)—64no—
281D3×C8—68no—
282D3×C8—64no—
283D3×C8—64no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32C2×C22⋊C411yescharacteristic
287C22×C32C4×D411yescharacteristic
288C22×C32C4×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—42no—
296C2×C3⋊D3#10012yescomplemented
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3—82no—
301C2×C3×D3—82no—
302C32×C4#12011yescharacteristic
303C32×C4#12111yescharacteristic
304C32×C4#12111yescharacteristic
305C32×C4#12311yescharacteristic
306C3⋊Dic3—21no—
307C3⋊Dic3—21no—
308C3×Dic3—42no—
309C22×D4—31no—
310C22×D4—92no—
311C23×C4—91no—
312C2×M16—31no—
313C2×M16—31no—
314C2×M16—91no—
315C2×M16—181no—
316C2×M16—182no—
317C2×M16—182no—
318C2×M16D3211yescharacteristic
319C22×C8—181no—
320#121—181no—
321#121—181no—
322#121—181no—
323#121—181no—
324C2×C4⋊C4—31no—
325C2×C22⋊C4—92no—
326#100—62no—
327#100—182no—
328C22⋊C8—181no—
329C22⋊C8—181no—
330C23×C3—21no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—122no—
335C23×C3—122no—
336C23×C3C2×C4×D311yescharacteristic
337C23×C3C2×C4×D311yescharacteristic
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—31no—
342C22×D3—31no—
343C22×D3—31no—
344C22×D3—31no—
345C22×D3—42no—
346C22×D3—42no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—122no—
358C22×D3—121no—
359C22×D3—121no—
360C22×D3—122no—
361C3×D4—121no—
362C3×D4—121no—
363C3×D4—121no—
364C3×D4—121no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—62no—
372C2×C3×C4—122no—
373C2×C3×C4C2×D1211yescharacteristic
374C2×C3×C4#23511yescharacteristic
375C2×C3×C4#23511yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4#23711yescharacteristic
383C2×C3×C4#23911yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385#67—124no—
386#67—124no—
387C2×Dic3—22no—
388C2×Dic3—31no—
389C2×Dic3—31no—
390C2×Dic3—31no—
391C2×Dic3—31no—
392C2×Dic3—42no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401D12—41no—
402D12—41no—
403D12—41no—
404D12—41no—
405D12—124no—
406D12—124no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—62no—
415C4×D3—61no—
416C4×D3—61no—
417C4×D3—61no—
418C4×D3—61no—
419C4×D3—61no—
420C4×D3—61no—
421C4×D3—61no—
422C4×D3—61no—
423C4×D3—61no—
424C4×D3—61no—
425C4×D3—61no—
426C4×D3—61no—
427C4×D3—61no—
428C4×D3—61no—
429C4×D3—61no—
430C4×D3—61no—
431C3×C8—24no—
432C3×C8—22no—
433C3×C8—22no—
434C3×C8—121no—
435C3×C8—121no—
436C3⋊C8—41no—
437C3⋊C8—41no—
438C3⋊C8—64no—
439C3⋊C8—62no—
440C3⋊C8—62no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32#38611yescharacteristic
444C2×C32C2×#10011yescharacteristic
445C2×C32#41311yescharacteristic
446C3⋊D3—22no—
447C3⋊D3—41no—
448C3×D3—82no—
449C24—32no—
450C24—91no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—61no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—182no—
458C2×D4—182no—
459C2×D4—364no—
460C22×C4—32no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4—181no—
470C22×C4C2×D3211yescharacteristic
471M16—21no—
472M16—61no—
473M16—61no—
474M16—61no—
475M16—61no—
476M16—92no—
477M16—184no—
478M16—181no—
479M16#62612yescomplemented
480C2×C8—21no—
481C2×C8—61no—
482C2×C8—61no—
483C2×C8—184no—
484C2×C8—181no—
485C4⋊C4—61no—
486C4⋊C4—61no—
487C22⋊C4—182no—
488C22⋊C4—182no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—242no—
502C22×C3—242no—
503C22×C3C4×D1211yescharacteristic
504C22×C3D3×C22⋊C411yescharacteristic
505C22×C3D3×C22⋊C411yescharacteristic
506C22×C3#67⋊C411yescharacteristic
507C22×C3#89311yescharacteristic
508C22×C3C4×#6711yescharacteristic
509C2×D3—32no—
510C2×D3—32no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—62no—
517C2×D3—61no—
518C2×D3—61no—
519C2×D3—61no—
520C2×D3—61no—
521C2×D3—62no—
522C2×D3—61no—
523C2×D3—61no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—61no—
528C2×D3—82no—
529C2×D3—82no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—124no—
537C2×D3—124no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—122no—
543C3×C4#88211yescharacteristic
544C3×C4#88311yescharacteristic
545C3×C4#88411yescharacteristic
546C3×C4#88411yescharacteristic
547C3×C4#89411yescharacteristic
548C3×C4#89511yescharacteristic
549C3×C4#93711yescharacteristic
550C3×C4#93811yescharacteristic
551Dic3—42no—
552Dic3—62no—
553Dic3—62no—
554Dic3—61no—
555Dic3—61no—
556Dic3—61no—
557Dic3—61no—
558C32#190011yescharacteristic, complemented, Sylow
559C23—62no—
560C23—62no—
561C23—62no—
562C23—91no—
563C23—91no—
564C23—122no—
565C23—122no—
566C23—182no—
567C23—181no—
568C23—181no—
569C23—361no—
570C23C4×D3211yescharacteristic
571D4—121no—
572D4—121no—
573D4—121no—
574D4—121no—
575D4—364no—
576D4—364no—
577C2×C4—62no—
578C2×C4—91no—
579C2×C4—91no—
580C2×C4—122no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4#379611yescharacteristic
592C2×C4#379811yescharacteristic
593C2×C4#380211yescharacteristic
594C2×C4C2×#62611yescharacteristic
595C2×C4#381111yescharacteristic
596C2×C4#381111yescharacteristic
597C8—22no—
598C8—121no—
599C8—121no—
600C8—182no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—41no—
609C2×C3—41no—
610C2×C3—242no—
611C2×C3#466511yescharacteristic
612C2×C3D3×#10011yescharacteristic
613C2×C3D3×#10011yescharacteristic
614C2×C3#474511yescharacteristic
615C2×C3#475111yescharacteristic
616C2×C3#495611yescharacteristic
617D3—64no—
618D3—62no—
619D3—62no—
620D3—82no—
621D3—122no—
622D3—121no—
623D3—121no—
624C22—21no—
625C22—21no—
626C22—92no—
627C22—122no—
628C22—122no—
629C22—122no—
630C22—181no—
631C22—181no—
632C22—181no—
633C22—181no—
634C22—181no—
635C22—242no—
636C22—242no—
637C22—362no—
638C22—362no—
639C22#6388111yescharacteristic
640C22C4×#62611yescharacteristic
641C22#6392111yescharacteristic
642C4—122no—
643C4—181no—
644C4—181no—
645C4#6385311yescharacteristic
646C4#6391211yescharacteristic
647C4#6391611yescharacteristic
648C4#6398111yescharacteristic
649C3—21no—
650C3#6899211yescharacteristic, complemented
651C3#7008111yescharacteristic, complemented
652C2—21no—
653C2—21no—
654C2—182no—
655C2—242no—
656C2—361no—
657C2#1059100111yescharacteristic
658C2#1059101011yescharacteristic
659C2#1059138711yescharacteristic
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
1. C2×M16×C3⋊D3C2semidirect
3. C2×C3×#823C2semidirect
4. C2×#63558C2semidirect
5. #10591074C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
39. C2×#823D3semidirect
44. #4554D3semidirect
69. C32×M16D4semidirect
72. #3748D4semidirect
248. C3×M16D12semidirect
249. C3×M16#67semidirect
296. C2×C3⋊D3#100semidirect
479. M16#626semidirect
558. C32#1900semidirect
650. C3#68992semidirect
651. C3#70081semidirect

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×#639162
C2×C3×#8232
C2×#635582
#105910742
C3×#45542
#105891672
#700813
#689923