Finite Group Databasebeta

← C2×#10591010 #11857645

Subgroups — C2×#10591010 #11857645

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C2×C3×#823C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7C2×#63558C211yesmaximal, characteristic, complemented
8#10591010C218yesmaximal, direct product factor
9C2×#4751—31nomaximal
10C2×#4745—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626C412yes—
15C22×D3×Dic3C412yes—
16C2×#3796—21no—
17C2×#3796—22no—
18C2×#3796—21no—
19C2×#3796—21no—
20C2×#3796—21no—
21C2×#3796—22no—
22C2×#3796C414yes—
23C2×#3796C2214yes—
24C2×C32×M16C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26M16×C3⋊D3—22no—
27M16×C3⋊D3C2214yescomplemented
28C2×#3743—21no—
29C2×C8×C3⋊D3—21no—
30C2×C3×#208C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C2×#3712—21no—
33#63818—22no—
34#63818C2214yescomplemented
35C2×#3710—21no—
36C3×#824C2214yescomplemented
37C3×#823C2214yescomplemented
38#63560C2214yescomplemented
39#63558C2214yescomplemented
40C22×#239—31no—
41C22×#237—31no—
42C2×D3×M16—31no—
43C2×D3×M16—31no—
44C2×D3×M16—31no—
45C2×D3×M16—31no—
46C2×D3×M16—61no—
47C2×C3×#101—31no—
48C2×C3×#100—31no—
49C2×#836—31no—
50C2×#833—31no—
51C2×#824—31no—
52C2×#824D311yescharacteristic, complemented
53C2×#823—31no—
54C2×#823D311yescharacteristic, complemented
55#4751—38no—
56#4745—38no—
57C23×C3⋊D3C2×C411yescharacteristic
58C23×C3×D3C2×C412yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2×C411yescharacteristic
61C2×C4×C3⋊D3C2×C412yes—
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3D412yes—
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D412yes—
68C2×C4×C3⋊D3C2312yes—
69C22×C3×Dic3C2×C412yes—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2×C412yes—
75C2×C3×D12C2312yes—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2×C412yes—
81C2×C3×Dic6C2312yes—
82C2×#626—22no—
83C2×#626—22no—
84C2×#626—24no—
85C2×#626C2×C418yes—
86C2×D3×Dic3—24no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—22no—
89C2×D3×Dic3C2×C418yes—
90#3796—24no—
91#3796—24no—
92#3796—24no—
93#3796—24no—
94#3796—24no—
95#3796—24no—
96#3796—24no—
97#3796—24no—
98C32×M16—21no—
99C32×M16C2312yes—
100C2×C32×C8—21no—
101#3748—21no—
102#3748C2312yes—
103C2×C3⋊(C3⋊C8)—21no—
104#3743—24no—
105C8×C3⋊D3—24no—
106C3×#208—21no—
107C3×#208—21no—
108C3×#208C2312yes—
109C3×#208C2312yes—
110C2×C3×C3⋊C8—21no—
111C2×C3×C3⋊C8—21no—
112#3712—24no—
113#3710—24no—
114C2×#413—91noSylow
115C22×C3×Q8—31no—
116C22×C3×D4—31no—
117C22×#67—32no—
118C23×Dic3—32no—
119C2×#239—34no—
120C2×#239—34no—
121C2×#239—61no—
122C2×#239—61no—
123C2×#239—61no—
124C2×#239—61no—
125C2×#239—62no—
126C2×#239—62no—
127C2×#237—34no—
128C2×#237—34no—
129C2×#237—61no—
130C2×#237—61no—
131C2×#237—61no—
132C2×#237—61no—
133C2×#237—62no—
134C2×#237—62no—
135C22×D12—32no—
136C22×D12C2×D311yescharacteristic
137C22×C4×D3—31no—
138C22×C4×D3—31no—
139C22×C4×D3—32no—
140C22×C4×D3—61no—
141C22×Dic6C2×D311yescharacteristic
142C2×C3×M16—21no—
143C2×C3×M16—31no—
144C2×C3×M16—31no—
145C2×C3×M16C2×D311yescharacteristic
146C2×C3×M16C2×D311yescharacteristic
147C2×#208—31no—
148C2×#208—31no—
149C2×#208—61no—
150C2×#208C2×D311yescharacteristic
151C2×#208C2×D311yescharacteristic
152D3×M16—34no—
153D3×M16—34no—
154D3×M16—34no—
155D3×M16—34no—
156D3×M16—64no—
157D3×M16—62no—
158D3×M16—62no—
159D3×M16—62no—
160D3×M16—62no—
161D3×M16—64no—
162C2×ΓL(1,𝔽25)—61no—
163C2×ΓL(1,𝔽25)—61no—
164C2×ΓL(1,𝔽25)—61no—
165C2×ΓL(1,𝔽25)—61no—
166C2×ΓL(1,𝔽25)—62no—
167C2×D3×C8—61no—
168C2×D3×C8—61no—
169C2×D3×C8—61no—
170C2×D3×C8—61no—
171C2×D3×C8—62no—
172C3×#101—34no—
173C3×#100—34no—
174#836—34no—
175#833—34no—
176#824—34no—
177#824C2×D314yescomplemented
178#823—34no—
179#823C2×D314yescomplemented
180C23×C32C22×C411yescharacteristic
181C22×C3⋊D3—42no—
182C22×C3⋊D3C22⋊C411yescharacteristic
183C22×C3⋊D3C22⋊C411yescharacteristic
184C22×C3⋊D3C22⋊C412yes—
185C22×C3⋊D3C22×C412yes—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—44no—
189C22×C3×D3C22×C414yes—
190C2×C32×C4C22×C411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2411yescharacteristic
196C2×C3⋊Dic3C22⋊C412yes—
197C2×C3⋊Dic3C22⋊C411yescharacteristic
198C2×C3⋊Dic3C22⋊C411yescharacteristic
199C2×C3⋊Dic3C22×C412yes—
200C4×C3⋊D3C22⋊C412yes—
201C4×C3⋊D3C22⋊C412yes—
202C4×C3⋊D3C22⋊C412yes—
203C4×C3⋊D3C22⋊C412yes—
204C4×C3⋊D3C2×D412yes—
205C4×C3⋊D3C2×D412yes—
206C4×C3⋊D3C2×D412yes—
207C4×C3⋊D3C2×D412yes—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3C22×C414yes—
211C3×D12—22no—
212C3×D12—22no—
213C3×D12—22no—
214C3×D12—22no—
215C3×Dic6—22no—
216C3×Dic6—22no—
217C3×Dic6—22no—
218C3×Dic6—22no—
219#626—28no—
220#626—28no—
221D3×Dic3—28no—
222D3×Dic3—28no—
223C32×C8—22no—
224C3⋊(C3⋊C8)—22no—
225C3×C3⋊C8—22no—
226C3×C3⋊C8—22no—
227C22×#41—91no—
228C22×M16—91no—
229C22×M16—91no—
230#413—98no—
231C2×#101—31no—
232C2×#101—91no—
233C2×#100—31no—
234C2×#100—91no—
235C24×C3—32no—
236C23×D3—31no—
237C23×D3—31no—
238C23×D3—61no—
239C23×D3C4×D312yes—
240C2×C3×Q8—32no—
241C2×C3×Q8—32no—
242C2×C3×Q8—61no—
243C2×C3×Q8—61no—
244C2×C3×Q8—61no—
245C2×C3×Q8—61no—
246C2×C3×D4—32no—
247C2×C3×D4—32no—
248C2×C3×D4—61no—
249C2×C3×D4—61no—
250C2×C3×D4—61no—
251C2×C3×D4—61no—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—38no—
257C2×#67—62no—
258C2×#67—62no—
259C2×#67—64no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—38no—
263C22×Dic3—61no—
264C22×Dic3—64no—
265C22×Dic3—62no—
266C22×Dic3—62no—
267C22×Dic3C4×D312yes—
268#239—64no—
269#239—64no—
270#239—64no—
271#239—64no—
272#239—64no—
273#239—64no—
274#239—64no—
275#239—64no—
276#237—64no—
277#237—64no—
278#237—64no—
279#237—64no—
280#237—64no—
281#237—64no—
282#237—64no—
283#237—64no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—38no—
289C2×D12—62no—
290C2×D12—62no—
291C2×D12—64no—
292C2×D12C4×D312yes—
293C2×D12C22×D312yes—
294C2×C4×D3—32no—
295C2×C4×D3—32no—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—32no—
305C2×C4×D3—32no—
306C2×C4×D3—32no—
307C2×C4×D3—32no—
308C2×C4×D3—32no—
309C2×C4×D3—32no—
310C2×C4×D3—38no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—62no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—62no—
319C2×C4×D3—64no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×Dic6—21no—
323C2×Dic6—21no—
324C2×Dic6—21no—
325C2×Dic6—21no—
326C2×Dic6C4×D312yes—
327C2×Dic6C22×D312yes—
328C3×M16—22no—
329C3×M16—21no—
330C3×M16—21no—
331C3×M16—22no—
332C3×M16—32no—
333C3×M16—32no—
334C3×M16—61no—
335C3×M16—61no—
336C3×M16C22×D312yes—
337C3×M16C22×D312yes—
338C2×C3×C8—22no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—61no—
342C2×C3×C8—61no—
343#208—21no—
344#208—21no—
345#208—32no—
346#208—32no—
347#208—62no—
348#208—62no—
349#208—61no—
350#208—61no—
351#208C22×D312yes—
352#208C22×D312yes—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—62no—
356C2×C3⋊C8—61no—
357C2×C3⋊C8—61no—
358ΓL(1,𝔽25)—64no—
359ΓL(1,𝔽25)—64no—
360ΓL(1,𝔽25)—64no—
361ΓL(1,𝔽25)—64no—
362ΓL(1,𝔽25)—68no—
363D3×C8—64no—
364D3×C8—64no—
365D3×C8—64no—
366D3×C8—64no—
367D3×C8—68no—
368C22×C32—22no—
369C22×C32C2×C22⋊C411yescharacteristic
370C22×C32C2×C22⋊C411yescharacteristic
371C22×C32C23×C411yescharacteristic
372C2×C3⋊D3—22no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—42no—
375C2×C3⋊D3—42no—
376C2×C3⋊D3C2×C22⋊C412yes—
377C2×C3⋊D3C2×C22⋊C412yes—
378C2×C3×D3—24no—
379C2×C3×D3—44no—
380C2×C3×D3—44no—
381C2×C3×D3—44no—
382C32×C4C2×C22⋊C411yescharacteristic
383C32×C4C2×C22⋊C411yescharacteristic
384C32×C4C22×D411yescharacteristic
385C32×C4C22×D411yescharacteristic
386C3⋊Dic3C2×C22⋊C412yes—
387C3⋊Dic3C2×C22⋊C412yes—
388C3×Dic3—24no—
389C2×#41—94no—
390C2×#41—94no—
391C2×#41—181no—
392C2×#41—182no—
393C2×#41—181no—
394C2×#41—181no—
395C2×#41—182no—
396C2×#41—181no—
397C22×Q8—31no—
398C22×D4—31no—
399C22×D4—92no—
400C23×C4—92no—
401C23×C4—91no—
402C2×M16—31no—
403C2×M16—31no—
404C2×M16—94no—
405C2×M16—91no—
406C2×M16—94no—
407C2×M16—181no—
408C2×M16—181no—
409C2×M16—182no—
410C2×M16—182no—
411C2×M16D3211yescharacteristic
412C22×C8—181no—
413C22×C8—181no—
414#101—34no—
415#101—94no—
416#100—34no—
417#100—94no—
418C23×C3—21no—
419C23×C3—34no—
420C23×C3—62no—
421C23×C3—62no—
422C23×C3—124no—
423C23×C3C2×C4×D311yescharacteristic
424C23×C3C2×C4×D311yescharacteristic
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—31no—
428C22×D3—31no—
429C22×D3—31no—
430C22×D3—31no—
431C22×D3—32no—
432C22×D3—32no—
433C22×D3—32no—
434C22×D3—32no—
435C22×D3—44no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—62no—
439C22×D3—62no—
440C22×D3—122no—
441C22×D3—122no—
442C22×D3—124no—
443C22×D3C2×C4×D314yes—
444C3×Q8—62no—
445C3×Q8—62no—
446C3×Q8—62no—
447C3×Q8—62no—
448C3×D4—62no—
449C3×D4—62no—
450C3×D4—62no—
451C3×D4—62no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—34no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4C2×C4×D311yescharacteristic
462C2×C3×C4C2×C4×D311yescharacteristic
463C2×C3×C4D3×D411yescharacteristic
464C2×C3×C4D3×D411yescharacteristic
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4D3×D411yescharacteristic
470C2×C3×C4D3×D411yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473#67—68no—
474#67—68no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—32no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—32no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—62no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—62no—
489C2×Dic3—68no—
490C2×Dic3—68no—
491C2×Dic3C2×C4×D314yes—
492D12—22no—
493D12—22no—
494D12—22no—
495D12—22no—
496D12—68no—
497D12—68no—
498C4×D3—32no—
499C4×D3—32no—
500C4×D3—32no—
501C4×D3—32no—
502C4×D3—32no—
503C4×D3—32no—
504C4×D3—32no—
505C4×D3—32no—
506C4×D3—32no—
507C4×D3—32no—
508C4×D3—32no—
509C4×D3—32no—
510C4×D3—32no—
511C4×D3—32no—
512C4×D3—32no—
513C4×D3—32no—
514C4×D3—62no—
515C4×D3—62no—
516C4×D3—62no—
517C4×D3—62no—
518C4×D3—62no—
519C4×D3—62no—
520C4×D3—62no—
521C4×D3—62no—
522C4×D3—68no—
523C4×D3—68no—
524Dic6—22no—
525Dic6—22no—
526Dic6—22no—
527Dic6—22no—
528C3×C8—24no—
529C3×C8—22no—
530C3×C8—22no—
531C3×C8—62no—
532C3×C8—62no—
533C3⋊C8—22no—
534C3⋊C8—22no—
535C3⋊C8—64no—
536C3⋊C8—62no—
537C3⋊C8—62no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32#41312yescomplemented
541C2×C32C22×C22⋊C411yescharacteristic
542C3⋊D3—22no—
543C3⋊D3—22no—
544C3×D3—44no—
545C24—32no—
546C24—91no—
547#41—184no—
548#41—184no—
549#41—184no—
550#41—184no—
551#41—184no—
552#41—184no—
553#41—184no—
554#41—184no—
555C2×Q8—32no—
556C2×Q8—32no—
557C2×Q8—61no—
558C2×Q8—61no—
559C2×Q8—61no—
560C2×Q8—61no—
561C2×D4—32no—
562C2×D4—32no—
563C2×D4—61no—
564C2×D4—61no—
565C2×D4—61no—
566C2×D4—61no—
567C2×D4—98no—
568C2×D4—184no—
569C2×D4—182no—
570C2×D4—182no—
571C22×C4—32no—
572C22×C4—98no—
573C22×C4—91no—
574C22×C4—92no—
575C22×C4—92no—
576C22×C4—91no—
577C22×C4—92no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—92no—
581C22×C4—91no—
582C22×C4—184no—
583C22×C4—182no—
584C22×C4—182no—
585C22×C4C2×D3211yescharacteristic
586M16—21no—
587M16—32no—
588M16—32no—
589M16—61no—
590M16—61no—
591M16—92no—
592M16—184no—
593M16—184no—
594M16—181no—
595M16C2×D3212yes—
596C2×C8—21no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—184no—
600C2×C8—184no—
601C2×C8—181no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—64no—
609C22×C3—124no—
610C22×C3—124no—
611C22×C3—124no—
612C22×C3D3×C22⋊C411yescharacteristic
613C22×C3D3×C22⋊C411yescharacteristic
614C22×C3D3×C22⋊C411yescharacteristic
615C22×C3D3×C22⋊C411yescharacteristic
616C22×C3C22×C4×D311yescharacteristic
617C22×C3C22×C4×D311yescharacteristic
618C2×D3—24no—
619C2×D3—32no—
620C2×D3—32no—
621C2×D3—32no—
622C2×D3—32no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—64no—
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—122no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—122no—
637C2×D3—122no—
638C2×D3—124no—
639C2×D3—124no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—64no—
645C3×C4D3×C22⋊C411yescharacteristic
646C3×C4D3×C22⋊C411yescharacteristic
647C3×C4D3×C22⋊C411yescharacteristic
648C3×C4D3×C22⋊C411yescharacteristic
649C3×C4C2×D3×D411yescharacteristic
650C3×C4C2×D3×D411yescharacteristic
651C3×C4C2×D3×D411yescharacteristic
652C3×C4C2×D3×D411yescharacteristic
653Dic3—24no—
654Dic3—32no—
655Dic3—32no—
656Dic3—32no—
657Dic3—32no—
658Dic3—62no—
659Dic3—62no—
660C32C2×#41311yescharacteristic, complemented, Sylow
661C23—34no—
662C23—62no—
663C23—62no—
664C23—91no—
665C23—91no—
666C23—92no—
667C23—92no—
668C23—124no—
669C23—362no—
670C23C4×D3211yescharacteristic
671Q8—62no—
672Q8—62no—
673Q8—62no—
674Q8—62no—
675D4—62no—
676D4—62no—
677D4—62no—
678D4—62no—
679D4—188no—
680D4—188no—
681C2×C4—34no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—92no—
685C2×C4—92no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—92no—
689C2×C4—92no—
690C2×C4—92no—
691C2×C4—92no—
692C2×C4—92no—
693C2×C4—92no—
694C2×C4—92no—
695C2×C4—92no—
696C2×C4—188no—
697C2×C4—188no—
698C2×C4C4×D3211yescharacteristic
699C2×C4#380211yescharacteristic
700C2×C4#380211yescharacteristic
701C2×C4#381111yescharacteristic
702C2×C4#381111yescharacteristic
703C2×C4C22×D3211yescharacteristic
704C8—22no—
705C8—62no—
706C8—62no—
707C8—182no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—41no—
715C2×C3—41no—
716C2×C3—124no—
717C2×C3#474512yescomplemented
718C2×C3#475112yescomplemented
719C2×C3C2×D3×C22⋊C411yescharacteristic
720C2×C3C2×D3×C22⋊C411yescharacteristic
721D3—44no—
722D3—64no—
723D3—62no—
724D3—62no—
725D3—62no—
726D3—62no—
727D3—122no—
728C22—22no—
729C22—64no—
730C22—92no—
731C22—92no—
732C22—124no—
733C22—124no—
734C22—124no—
735C22—182no—
736C22—182no—
737C22—362no—
738C22—362no—
739C22#6392111yescharacteristic
740C22#6392111yescharacteristic
741C22C2×C4×D3211yescharacteristic
742C4—64no—
743C4—92no—
744C4—92no—
745C4#6392111yescharacteristic
746C4#6392111yescharacteristic
747C4C2×#380211yescharacteristic
748C4C2×#381111yescharacteristic
749C3—21no—
750C3C2×#474511yescharacteristic, complemented
751C3C2×#475111yescharacteristic, complemented
752C2—21no—
753C2—21no—
754C2—124no—
755C2—182no—
756C2—182no—
757C2#1059101012yesdirect product factor
758C2C2×#6392111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3796C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#413
LCSG ▷ C22×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×M16×C3⋊D3C2semidirect
3. C2×#63818C2semidirect
4. C2×C3×#824C2semidirect
5. C2×C3×#823C2semidirect
6. C2×#63560C2semidirect
7. C2×#63558C2semidirect
8. #10591010C2direct (N × H)
27. M16×C3⋊D3C22semidirect
34. #63818C22semidirect
36. C3×#824C22semidirect
37. C3×#823C22semidirect
38. #63560C22semidirect
39. #63558C22semidirect
52. C2×#824D3semidirect
54. C2×#823D3semidirect
177. #824C2×D3semidirect
179. #823C2×D3semidirect
540. C2×C32#413semidirect
660. C32C2×#413semidirect
717. C2×C3#4745semidirect
718. C2×C3#4751semidirect
750. C3C2×#4745semidirect
751. C3C2×#4751semidirect
757. C2#10591010direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×M16×C3⋊D32
C2×#638182
C2×C3×#8242
C2×C3×#8232
C2×#635602
C2×#635582
#105910102
C2×#47513
C2×#47453