Finite Group Databasebeta

← #11788141

Subgroups — #11788141

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×C3×#821C211yesmaximal, characteristic, complemented
4#10591325C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70203—31nomaximal
9#68885—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—21no—
13C22×C32×C8C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×#3743—22no—
16C2×#3743—22no—
17C2×#3743—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×#3722—21no—
22C2×(C2×D3)⋊Dic3—21no—
23#63916—22no—
24#63916C414yescomplemented
25C3×#821—22no—
26#63579—21no—
27#63562—22no—
28C2×#938—31no—
29C22×ΓL(1,𝔽25)—31no—
30C22×ΓL(1,𝔽25)—31no—
31C22×ΓL(1,𝔽25)—61no—
32C2×#895—31no—
33C2×C3×#102—31no—
34C2×#832—31no—
35C2×#821D311yescharacteristic, complemented
36#4987—31no—
37#4987—31no—
38C2×#809—31no—
39C3×#340—31no—
40#4551D311yescharacteristic, complemented
41#4529—31no—
42#4529—31no—
43C23×C3⋊D3D411yescharacteristic
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3C2×C412yes—
52C2×C4×C3⋊D3D412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×#626—24no—
63C2×#626—42no—
64C2×#626—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8D412yescomplemented
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)D412yescomplemented
71#3743—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2×C412yes—
78#3722—42no—
79(C2×D3)⋊Dic3—24no—
80#1895—91noSylow
81C22×C3×D4—31no—
82C22×#67—61no—
83C22×D12—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×#217—61no—
95#938—34no—
96#938—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C2×ΓL(1,𝔽25)—62no—
107C2×ΓL(1,𝔽25)—62no—
108C2×ΓL(1,𝔽25)—62no—
109C2×ΓL(1,𝔽25)—62no—
110C2×ΓL(1,𝔽25)—64no—
111C2×ΓL(1,𝔽25)—64no—
112C2×ΓL(1,𝔽25)—64no—
113C2×ΓL(1,𝔽25)—62no—
114C2×ΓL(1,𝔽25)—62no—
115#895—34no—
116#895—62no—
117C3×#102—62no—
118#832—62no—
119C3⋊#95—61no—
120C3⋊#95—61no—
121#821—22no—
122#809—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3C22⋊C412yes—
131C22×C3×D3—22no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3C22⋊C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—41no—
163C3×D12—41no—
164#626—48no—
165C32×C8—22no—
166C3⋊(C3⋊C8)—22no—
167C22×M16—91no—
168C2×#121—91no—
169C2×#102—31no—
170C2×#102—91no—
171#380—91no—
172#340—31no—
173#340—91no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—31no—
177C23×D3—31no—
178C23×D3—61no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—64no—
192C2×#67—122no—
193C2×#67—122no—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—61no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—64no—
206C2×D12—122no—
207C2×D12—122no—
208C2×D12C4×D312yes—
209C2×C4×D3—32no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—22no—
234C2×C3×C8D1212yescomplemented
235C2×C3×C8#6712yescomplemented
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242#217—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—122no—
245(C2×D3)⋊C4—122no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3C4×D312yes—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261ΓL(1,𝔽25)—616no—
262ΓL(1,𝔽25)—68no—
263ΓL(1,𝔽25)—68no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32AGL(1,ℤ/8)11yescharacteristic
268C22×C32AGL(1,ℤ/8)11yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32#13711yescharacteristic
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C2×C3×D3—81no—
284C2×C3×D3—81no—
285C32×C4C4×D411yescharacteristic
286C32×C4C4×D411yescharacteristic
287C32×C4#12011yescharacteristic
288C32×C4#12311yescharacteristic
289C3⋊Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—81no—
292C3×Dic3—81no—
293C22×D4—31no—
294C22×D4—181no—
295C23×C4—91no—
296C2×M16—182no—
297C2×M16—182no—
298C2×M16—182no—
299C22×C8—91no—
300C22×C8D3211yescharacteristic
301#121—94no—
302#121—182no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C22⋊C4—181no—
307C2×C22⋊C4—181no—
308#102—62no—
309#102—182no—
310#95—181no—
311C23×C3—21no—
312C23×C3—62no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3D3×D411yescharacteristic
320C23×C3D3×D411yescharacteristic
321C22×D3—22no—
322C22×D3—32no—
323C22×D3—32no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—121no—
352C3×D4—121no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—62no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4C2×C4×D311yescharacteristic
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4#23511yescharacteristic
372C2×C3×C4#23511yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4#23711yescharacteristic
378C2×C3×C4#23911yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380#67—128no—
381C2×Dic3—22no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399D12—22no—
400D12—22no—
401D12—41no—
402D12—41no—
403D12—128no—
404C4×D3—64no—
405C4×D3—64no—
406C4×D3—64no—
407C4×D3—64no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—62no—
415C4×D3—62no—
416C3×C8—24no—
417C3×C8—22no—
418C3×C8—22no—
419C3⋊C8—64no—
420C3⋊C8—62no—
421C3⋊C8—62no—
422C2×C32#38611yescharacteristic
423C2×C32#41711yescharacteristic
424C2×C32#41811yescharacteristic
425C2×C32#46811yescharacteristic
426C2×C32#46811yescharacteristic
427C2×C32#46911yescharacteristic
428C2×C32#46911yescharacteristic
429C3⋊D3—42no—
430C3×D3—82no—
431C24—61no—
432C24—91no—
433C2×D4—32no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—184no—
440C2×D4—362no—
441C2×D4—362no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—91no—
446C22×C4—92no—
447C22×C4—92no—
448C22×C4—181no—
449C22×C4—181no—
450C22×C4—181no—
451C22×C4—181no—
452C22×C4C2×D3211yescharacteristic
453M16—188no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—92no—
457C2×C8—181no—
458C2×C8—181no—
459C2×C8#62612yescomplemented
460C4⋊C4—32no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C22⋊C4—184no—
467C22⋊C4—362no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—241no—
479C22×C3—241no—
480C22×C3—241no—
481C22×C3—241no—
482C22×C3D3×C22⋊C411yescharacteristic
483C22×C3D3×C22⋊C411yescharacteristic
484C22×C3#88411yescharacteristic
485C22×C3#88411yescharacteristic
486C22×C3#89511yescharacteristic
487C22×C3#91111yescharacteristic
488C22×C3#91111yescharacteristic
489C22×C3#91111yescharacteristic
490C22×C3#91411yescharacteristic
491C22×C3#91411yescharacteristic
492C22×C3#91411yescharacteristic
493C22×C3#91511yescharacteristic
494C22×C3#91811yescharacteristic
495C22×C3#93811yescharacteristic
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—64no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—81no—
507C2×D3—81no—
508C2×D3—81no—
509C2×D3—81no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—122no—
529C3×C4—241no—
530C3×C4—241no—
531C3×C4C4×D1211yescharacteristic
532C3×C4#67⋊C411yescharacteristic
533C3×C4#88211yescharacteristic
534C3×C4#88311yescharacteristic
535C3×C4#89311yescharacteristic
536C3×C4#89411yescharacteristic
537C3×C4C4×#6711yescharacteristic
538C3×C4#93711yescharacteristic
539Dic3—42no—
540Dic3—64no—
541Dic3—62no—
542Dic3—62no—
543Dic3—81no—
544Dic3—81no—
545C32#189511yescharacteristic, complemented, Sylow
546C23—62no—
547C23—92no—
548C23—121no—
549C23—121no—
550C23—121no—
551C23—121no—
552C23—121no—
553C23—121no—
554C23—181no—
555C23—181no—
556C23—181no—
557C23—181no—
558C23—181no—
559C23—181no—
560C23#380211yescharacteristic
561D4—62no—
562D4—62no—
563D4—121no—
564D4—121no—
565D4—368no—
566C2×C4—62no—
567C2×C4—92no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—121no—
575C2×C4—121no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—182no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4#379611yescharacteristic
583C2×C4#379811yescharacteristic
584C2×C4C4×D3211yescharacteristic
585C2×C4C2×#62611yescharacteristic
586C2×C4#381111yescharacteristic
587C2×C4#381111yescharacteristic
588C8—22no—
589C8—182no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—242no—
598C2×C3#466511yescharacteristic
599C2×C3#477011yescharacteristic
600C2×C3#477011yescharacteristic
601C2×C3#477111yescharacteristic
602C2×C3#478011yescharacteristic
603C2×C3#478211yescharacteristic
604C2×C3#478211yescharacteristic
605C2×C3#480311yescharacteristic
606C2×C3#481211yescharacteristic
607C2×C3#486511yescharacteristic
608C2×C3#488611yescharacteristic
609C2×C3#495611yescharacteristic
610C2×C3#515911yescharacteristic
611C2×C3#517411yescharacteristic
612D3—82no—
613D3—124no—
614D3—122no—
615D3—122no—
616C22—122no—
617C22—122no—
618C22—122no—
619C22—182no—
620C22—182no—
621C22—182no—
622C22—241no—
623C22—241no—
624C22—241no—
625C22—241no—
626C22—361no—
627C22—361no—
628C22—361no—
629C22—361no—
630C22#6379811yescharacteristic
631C22#6379811yescharacteristic
632C22#6379811yescharacteristic
633C22#6381111yescharacteristic
634C22#6391211yescharacteristic
635C22#6391611yescharacteristic
636C22#6392111yescharacteristic
637C4—122no—
638C4—182no—
639C4—241no—
640C4—241no—
641C4#6385311yescharacteristic
642C4#6388111yescharacteristic
643C4C4×#62611yescharacteristic
644C4#6398111yescharacteristic
645C3—21no—
646C3#6888511yescharacteristic, complemented
647C3#7020311yescharacteristic, complemented
648C2—242no—
649C2—362no—
650C2#1059084011yescharacteristic
651C2#1059084211yescharacteristic
652C2#1059084511yescharacteristic
653C2#1059084611yescharacteristic
654C2#1059094111yescharacteristic
655C2#1059095711yescharacteristic
656C2#1059138711yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1895
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3743C2semidirect
3. C2×C3×#821C2semidirect
4. #10591325C2semidirect
5. C2×#63562C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
24. #63916C4semidirect
35. C2×#821D3semidirect
40. #4551D3semidirect
67. C2×C32×C8D4semidirect
70. C2×C3⋊(C3⋊C8)D4semidirect
234. C2×C3×C8D12semidirect
235. C2×C3×C8#67semidirect
459. C2×C8#626semidirect
545. C32#1895semidirect
646. C3#68885semidirect
647. C3#70203semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#639162
C2×C3×#8212
#105913252
C2×#635622
C3×#45512
#105891632
#702033
#688853