Finite Group Databasebeta

← C2×#10591007 #11857644

Subgroups — C2×#10591007 #11857644

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4C2×#63650C211yesmaximal, characteristic, complemented
5C2×C3×#824C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8#10591007C218yesmaximal, direct product factor
9C2×#5132—31nomaximal
10C2×#4751—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626C412yes—
15C22×#624C412yes—
16C2×#3799—21no—
17C2×#3799—22no—
18C2×#3799—21no—
19C2×#3799—21no—
20C2×#3799—21no—
21C2×#3799—22no—
22C2×#3799C414yes—
23C2×#3799C2214yes—
24C2×C32×M16C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C3×D3×M16—22no—
29C3×D3×M16C2214yescomplemented
30C2×C3×ΓL(1,𝔽25)—21no—
31C2×C3×D3×C8—21no—
32C2×#3711—21no—
33D3×#208—22no—
34D3×#208C2214yescomplemented
35C2×D3×C3⋊C8—21no—
36#63650C2214yescomplemented
37C3×#824C2214yescomplemented
38#63560C2214yescomplemented
39#63559C2214yescomplemented
40C22×#239—31no—
41C22×#235—31no—
42C22×C3×M16—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45C2×D3×M16D311yescharacteristic, complemented
46C2×C3×#101—31no—
47C2×#836—31no—
48C2×#824—31no—
49C2×#824D311yescharacteristic, complemented
50#5132—38no—
51C2×#823—31no—
52C2×#823—31no—
53C2×#823—31no—
54C2×#823—31no—
55C2×#823—61no—
56#4751—38no—
57C23×C3⋊D3C2×C412yes—
58C23×C3×D3C2×C411yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)C2×C412yes—
65C2×C4⋊(C3⋊D3)C2312yes—
66C22×C3×Dic3C2×C412yes—
67C22×C3×Dic3C2×C411yescharacteristic
68C2×C3×C4×D3C2×C412yes—
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3D412yes—
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D412yes—
75C2×C3×C4×D3C2312yes—
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×#624—24no—
87C2×#624—22no—
88C2×#624—22no—
89C2×#624C2×C418yes—
90#3799—24no—
91#3799—24no—
92#3799—24no—
93#3799—24no—
94#3799—24no—
95#3799—24no—
96#3799—24no—
97#3799—24no—
98C32×M16—21no—
99C32×M16C2312yes—
100C2×C32×C8—21no—
101#3748—21no—
102#3748C2312yes—
103C2×C3⋊(C3⋊C8)—21no—
104C3×#208—21no—
105C3×#208—21no—
106C3×#208C2312yes—
107C3×#208C2312yes—
108C2×C3×C3⋊C8—21no—
109C2×C3×C3⋊C8—21no—
110C3×ΓL(1,𝔽25)—24no—
111C3×D3×C8—24no—
112#3711—24no—
113D3×C3⋊C8—24no—
114C2×#413—91noSylow
115C22×C3×Q8—31no—
116C23×C3×C4—31no—
117C22×#67—32no—
118C2×#239—34no—
119C2×#239—34no—
120C2×#239—61no—
121C2×#239—61no—
122C2×#239—62no—
123C2×#239—61no—
124C2×#239—61no—
125C2×#239—62no—
126C2×#235—34no—
127C2×#235—34no—
128C2×#235—61no—
129C2×#235—61no—
130C2×#235—62no—
131C2×#235—61no—
132C2×#235—61no—
133C2×#235—62no—
134C22×D12—32no—
135C22×D12—31no—
136C22×D12—31no—
137C22×D12—61no—
138C22×C4×D3—32no—
139C22×C4×D3—32no—
140C22×C4×D3C2×D311yescharacteristic
141C22×Dic6C2×D311yescharacteristic
142C2×C3×M16—21no—
143C2×C3×M16—31no—
144C2×C3×M16—31no—
145C2×C3×M16—34no—
146C2×C3×M16—61no—
147C2×C3×M16—62no—
148C2×C3×M16C2×D311yescharacteristic
149C2×C3×M16C2×D311yescharacteristic
150C22×C3×C8—61no—
151C2×#208—31no—
152C2×#208—31no—
153C2×#208—34no—
154C2×#208—61no—
155C2×#208—61no—
156C2×#208—62no—
157C2×#208C2×D311yescharacteristic
158C2×#208C2×D311yescharacteristic
159C22×C3⋊C8—61no—
160D3×M16—22no—
161D3×M16—34no—
162D3×M16—62no—
163D3×M16C2×D314yescomplemented
164C2×ΓL(1,𝔽25)—21no—
165C2×ΓL(1,𝔽25)—61no—
166C2×D3×C8—21no—
167C2×D3×C8—61no—
168C3×#101—34no—
169#836—34no—
170#824—34no—
171#824C2×D314yescomplemented
172#823—34no—
173#823—34no—
174#823—34no—
175#823—34no—
176#823—64no—
177C23×C32C22×C411yescharacteristic
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—44no—
181C22×C3⋊D3C22×C414yes—
182C22×C3×D3—42no—
183C22×C3×D3C22⋊C411yescharacteristic
184C22×C3×D3C22⋊C411yescharacteristic
185C22×C3×D3C22⋊C412yes—
186C22×C3×D3C22×C412yes—
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C4⋊(C3⋊D3)—22no—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3C22⋊C412yes—
200C2×C3×Dic3C22⋊C411yescharacteristic
201C2×C3×Dic3C22⋊C411yescharacteristic
202C2×C3×Dic3C22×C414yes—
203C2×C3×Dic3C22×C412yes—
204C3×C4×D3C22⋊C412yes—
205C3×C4×D3C22⋊C412yes—
206C3×C4×D3C22⋊C412yes—
207C3×C4×D3C22⋊C412yes—
208C3×C4×D3C2×D412yes—
209C3×C4×D3C2×D412yes—
210C3×C4×D3C2×D412yes—
211C3×C4×D3C2×D412yes—
212C3×Dic6—22no—
213C3×Dic6—22no—
214C3×Dic6—22no—
215C3×Dic6—22no—
216#626—28no—
217#626—28no—
218#624—28no—
219#624—28no—
220C32×C8—22no—
221C3⋊(C3⋊C8)—22no—
222C3×C3⋊C8—22no—
223C3×C3⋊C8—22no—
224C22×#41—91no—
225C22×M16—31no—
226C22×M16—91no—
227#413—98no—
228C2×#101—31no—
229C2×#101—91no—
230C2×#100—91no—
231C2×#100—91no—
232C24×C3—31no—
233C23×D3—32no—
234C23×D3—32no—
235C23×D3—62no—
236C23×D3C4×D311yescharacteristic
237C2×C3×Q8—32no—
238C2×C3×Q8—32no—
239C2×C3×Q8—61no—
240C2×C3×Q8—61no—
241C2×C3×Q8—61no—
242C2×C3×Q8—61no—
243C22×C3×C4—21no—
244C22×C3×C4—31no—
245C22×C3×C4—32no—
246C22×C3×C4—31no—
247C22×C3×C4—32no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—32no—
251C22×C3×C4—31no—
252C22×C3×C4—32no—
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×Dic3C4×D312yes—
261C22×Dic3C4×D311yescharacteristic
262#239—64no—
263#239—64no—
264#239—64no—
265#239—64no—
266#239—64no—
267#239—64no—
268#239—64no—
269#239—64no—
270#235—64no—
271#235—64no—
272#235—64no—
273#235—64no—
274#235—64no—
275#235—64no—
276#235—64no—
277#235—64no—
278C2×D12—38no—
279C2×D12—32no—
280C2×D12—32no—
281C2×D12—32no—
282C2×D12—32no—
283C2×D12—62no—
284C2×D12—62no—
285C2×D12—62no—
286C2×D12—62no—
287C2×D12—64no—
288C2×D12—61no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12—61no—
292C2×D12—61no—
293C2×D12—61no—
294C2×D12—61no—
295C2×D12—61no—
296C2×D12—121no—
297C2×D12—121no—
298C2×D12—121no—
299C2×D12—121no—
300C2×C4×D3—38no—
301C2×C4×D3—38no—
302C2×C4×D3—64no—
303C2×C4×D3—62no—
304C2×C4×D3—62no—
305C2×C4×D3—64no—
306C2×C4×D3—62no—
307C2×C4×D3—62no—
308C2×C4×D3C4×D312yes—
309C2×C4×D3D1211yescharacteristic
310C2×C4×D3D1211yescharacteristic
311C2×C4×D3D1212yes—
312C2×C4×D3#6711yescharacteristic
313C2×C4×D3#6711yescharacteristic
314C2×C4×D3#6712yes—
315C2×C4×D3C22×D312yes—
316C2×Dic6—21no—
317C2×Dic6—21no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6C4×D312yes—
321C2×Dic6C22×D312yes—
322C3×M16—21no—
323C3×M16—21no—
324C3×M16—22no—
325C3×M16—32no—
326C3×M16—32no—
327C3×M16—41no—
328C3×M16—64no—
329C3×M16—61no—
330C3×M16—61no—
331C3×M16C22×D312yes—
332C3×M16C22×D312yes—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—41no—
336C2×C3×C8—64no—
337C2×C3×C8—61no—
338C2×C3×C8—61no—
339#208—21no—
340#208—21no—
341#208—32no—
342#208—32no—
343#208—62no—
344#208—64no—
345#208—61no—
346#208—61no—
347#208—121no—
348#208C22×D312yes—
349#208C22×D312yes—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—64no—
353C2×C3⋊C8—61no—
354C2×C3⋊C8—61no—
355C2×C3⋊C8—121no—
356ΓL(1,𝔽25)—24no—
357ΓL(1,𝔽25)—64no—
358D3×C8—24no—
359D3×C8—64no—
360C22×C32—22no—
361C22×C32C2×C22⋊C411yescharacteristic
362C22×C32C2×C22⋊C411yescharacteristic
363C22×C32C23×C411yescharacteristic
364C2×C3⋊D3—24no—
365C2×C3⋊D3—44no—
366C2×C3⋊D3—44no—
367C2×C3⋊D3—44no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—42no—
371C2×C3×D3—42no—
372C2×C3×D3C2×C22⋊C412yes—
373C2×C3×D3C2×C22⋊C412yes—
374C32×C4C2×C22⋊C411yescharacteristic
375C32×C4C2×C22⋊C411yescharacteristic
376C32×C4C22×D411yescharacteristic
377C32×C4C22×D411yescharacteristic
378C3×Dic3—24no—
379C3×Dic3C2×C22⋊C412yes—
380C3×Dic3C2×C22⋊C412yes—
381C2×#41—94no—
382C2×#41—94no—
383C2×#41—181no—
384C2×#41—182no—
385C2×#41—181no—
386C2×#41—181no—
387C2×#41—182no—
388C2×#41—181no—
389C22×Q8—31no—
390C22×D4—92no—
391C22×D4—91no—
392C23×C4—31no—
393C23×C4—92no—
394C2×M16—31no—
395C2×M16—31no—
396C2×M16—34no—
397C2×M16—61no—
398C2×M16—62no—
399C2×M16—94no—
400C2×M16—91no—
401C2×M16—181no—
402C2×M16—182no—
403C2×M16D3211yescharacteristic
404C22×C8—61no—
405C22×C8—181no—
406#101—34no—
407#101—94no—
408#100—94no—
409#100—94no—
410C23×C3—21no—
411C23×C3—31no—
412C23×C3—31no—
413C23×C3—32no—
414C23×C3—32no—
415C23×C3—122no—
416C23×C3C2×C4×D311yescharacteristic
417C23×C3C2×C4×D311yescharacteristic
418C22×D3—34no—
419C22×D3—34no—
420C22×D3—42no—
421C22×D3—64no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—122no—
427C22×D3—122no—
428C22×D3—124no—
429C22×D3—124no—
430C22×D3—244no—
431C22×D3(C2×D3)⋊C411yescharacteristic
432C22×D3(C2×D3)⋊C411yescharacteristic
433C22×D3(C2×D3)⋊C412yes—
434C22×D3C2×C4×D312yes—
435C3×Q8—62no—
436C3×Q8—62no—
437C3×Q8—62no—
438C3×Q8—62no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—32no—
446C2×C3×C4—31no—
447C2×C3×C4—31no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—32no—
456C2×C3×C4—32no—
457C2×C3×C4—34no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4C2×C4×D311yescharacteristic
461C2×C3×C4C2×C4×D311yescharacteristic
462C2×C3×C4C2×D1211yescharacteristic
463C2×C3×C4C2×D1211yescharacteristic
464C2×C3×C4D3×D411yescharacteristic
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4C2×#6711yescharacteristic
469C2×C3×C4C2×#6711yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472#67—68no—
473#67—68no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3(C2×D3)⋊C412yes—
477C2×Dic3(C2×D3)⋊C411yescharacteristic
478C2×Dic3(C2×D3)⋊C411yescharacteristic
479C2×Dic3C2×C4×D314yes—
480C2×Dic3C2×C4×D312yes—
481D12—68no—
482D12—68no—
483D12—62no—
484D12—62no—
485D12—62no—
486D12—62no—
487D12—62no—
488D12—62no—
489D12—62no—
490D12—62no—
491D12—122no—
492D12—122no—
493D12—122no—
494D12—122no—
495C4×D3—68no—
496C4×D3—68no—
497C4×D3—68no—
498C4×D3—68no—
499C4×D3(C2×D3)⋊C412yes—
500C4×D3(C2×D3)⋊C412yes—
501C4×D3(C2×D3)⋊C412yes—
502C4×D3(C2×D3)⋊C412yes—
503C4×D3C2×D1212yes—
504C4×D3C2×D1212yes—
505C4×D3C2×#6712yes—
506C4×D3C2×#6712yes—
507Dic6—22no—
508Dic6—22no—
509Dic6—22no—
510Dic6—22no—
511C3×C8—22no—
512C3×C8—22no—
513C3×C8—42no—
514C3×C8—62no—
515C3×C8—62no—
516C3⋊C8—22no—
517C3⋊C8—22no—
518C3⋊C8—62no—
519C3⋊C8—62no—
520C3⋊C8—122no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32#41312yescomplemented
524C2×C32C22×C22⋊C411yescharacteristic
525C3⋊D3—44no—
526C3×D3—22no—
527C3×D3—22no—
528C24—31no—
529C24—92no—
530#41—184no—
531#41—184no—
532#41—184no—
533#41—184no—
534#41—184no—
535#41—184no—
536#41—184no—
537#41—184no—
538C2×Q8—32no—
539C2×Q8—32no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×D4—98no—
545C2×D4—92no—
546C2×D4—92no—
547C2×D4—184no—
548C2×D4—182no—
549C2×D4—182no—
550C2×D4—181no—
551C2×D4—181no—
552C2×D4—181no—
553C2×D4—181no—
554C22×C4—31no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—31no—
558C22×C4—32no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—32no—
562C22×C4—31no—
563C22×C4—32no—
564C22×C4—98no—
565C22×C4—184no—
566C22×C4—182no—
567C22×C4—182no—
568C22×C4C2×D3211yescharacteristic
569M16—21no—
570M16—32no—
571M16—32no—
572M16—64no—
573M16—61no—
574M16—61no—
575M16—92no—
576M16—184no—
577M16—181no—
578M16C2×D3212yes—
579C2×C8—21no—
580C2×C8—64no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—184no—
584C2×C8—181no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—32no—
591C22×C3—32no—
592C22×C3—42no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—122no—
596C22×C3—122no—
597C22×C3D3×C22⋊C411yescharacteristic
598C22×C3D3×C22⋊C411yescharacteristic
599C22×C3C2×(C2×D3)⋊C411yescharacteristic
600C22×C3C2×(C2×D3)⋊C411yescharacteristic
601C22×C3C22×C4×D311yescharacteristic
602C22×C3C22×C4×D311yescharacteristic
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—124no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C2×D3—124no—
615C2×D3—124no—
616C2×D3—244no—
617C2×D3—244no—
618C2×D3—244no—
619C2×D3C2×(C2×D3)⋊C412yes—
620C2×D3C2×(C2×D3)⋊C412yes—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—32no—
626C3×C4—32no—
627C3×C4—64no—
628C3×C4D3×C22⋊C411yescharacteristic
629C3×C4D3×C22⋊C411yescharacteristic
630C3×C4C2×(C2×D3)⋊C411yescharacteristic
631C3×C4C2×(C2×D3)⋊C411yescharacteristic
632C3×C4C22×D1211yescharacteristic
633C3×C4C2×D3×D411yescharacteristic
634C3×C4C2×D3×D411yescharacteristic
635C3×C4C22×#6711yescharacteristic
636Dic3—24no—
637Dic3C2×(C2×D3)⋊C412yes—
638Dic3C2×(C2×D3)⋊C412yes—
639C32C2×#41311yescharacteristic, complemented, Sylow
640C23—31no—
641C23—31no—
642C23—32no—
643C23—32no—
644C23—94no—
645C23—122no—
646C23—182no—
647C23—182no—
648C23—364no—
649C23C4×D3211yescharacteristic
650Q8—62no—
651Q8—62no—
652Q8—62no—
653Q8—62no—
654D4—188no—
655D4—188no—
656D4—182no—
657D4—182no—
658D4—182no—
659D4—182no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—34no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—188no—
676C2×C4—188no—
677C2×C4C4×D3211yescharacteristic
678C2×C4D3×D1211yescharacteristic
679C2×C4D3×D1211yescharacteristic
680C2×C4D3×#6711yescharacteristic
681C2×C4D3×#6711yescharacteristic
682C2×C4C22×D3211yescharacteristic
683C8—22no—
684C8—62no—
685C8—62no—
686C8—182no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—22no—
692C2×C3—21no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—62no—
696C2×C3—62no—
697C2×C3#475112yescomplemented
698C2×C3#513212yescomplemented
699C2×C3C2×D3×C22⋊C411yescharacteristic
700C2×C3C22×(C2×D3)⋊C411yescharacteristic
701D3—22no—
702D3—22no—
703D3—124no—
704D3—124no—
705D3—244no—
706C22—22no—
707C22—32no—
708C22—32no—
709C22—62no—
710C22—62no—
711C22—122no—
712C22—122no—
713C22—184no—
714C22—364no—
715C22—364no—
716C22—364no—
717C22D3×(C2×D3)⋊C411yescharacteristic
718C22D3×(C2×D3)⋊C411yescharacteristic
719C22C2×C4×D3211yescharacteristic
720C4—32no—
721C4—32no—
722C4—64no—
723C4D3×(C2×D3)⋊C411yescharacteristic
724C4D3×(C2×D3)⋊C411yescharacteristic
725C4C2×D3×D1211yescharacteristic
726C4C2×D3×#6711yescharacteristic
727C3—21no—
728C3C2×#475111yescharacteristic, complemented
729C3C2×#513211yescharacteristic, complemented
730C2—21no—
731C2—21no—
732C2—62no—
733C2—62no—
734C2—364no—
735C2#1059100712yesdirect product factor
736C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3799C2
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×C3×D3×M16C2semidirect
3. C2×D3×#208C2semidirect
4. C2×#63650C2semidirect
5. C2×C3×#824C2semidirect
6. C2×#63560C2semidirect
7. C2×#63559C2semidirect
8. #10591007C2direct (N × H)
29. C3×D3×M16C22semidirect
34. D3×#208C22semidirect
36. #63650C22semidirect
37. C3×#824C22semidirect
38. #63560C22semidirect
39. #63559C22semidirect
45. C2×D3×M16D3semidirect
49. C2×#824D3semidirect
163. D3×M16C2×D3semidirect
171. #824C2×D3semidirect
523. C2×C32#413semidirect
639. C32C2×#413semidirect
697. C2×C3#4751semidirect
698. C2×C3#5132semidirect
728. C3C2×#4751semidirect
729. C3C2×#5132semidirect
735. C2#10591007direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×D3×M162
C2×D3×#2082
C2×#636502
C2×C3×#8242
C2×#635602
C2×#635592
#105910072
C2×#51323
C2×#47513