Finite Group Databasebeta

← C2×#10594830 #11902612

Subgroups — C2×#10594830 #11902612

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63959C212yesmaximal, complemented
6C2×#63958C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63904C212yesmaximal, complemented
9C2×#63863C211yesmaximal, characteristic, complemented
10C2×#63851C212yesmaximal, complemented
11#10594830C2116yesmaximal, direct product factor
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5831—31nomaximal
14C2×#5633—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C2×C3×#235—28no—
20C2×C3×#235C2218yescomplemented
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2212yes—
26C22×#626C2212yes—
27C22×#624C2212yes—
28C2×#3797—28no—
29C2×#3797C2218yescomplemented
30C2×#3757C2211yescharacteristic
31C4×#638C2218yescomplemented
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C3×#217C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#924C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43#63959C22116yescomplemented
44#63958C22116yescomplemented
45C2×Dic32C2212yes—
46#63916C2218yescomplemented
47#63904C22116yescomplemented
48#63863C2218yescomplemented
49#63851C22116yescomplemented
50#63843C2218yescomplemented
51C22×C3×#41—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56#5831—316no—
57C2×#947—31no—
58C2×Q8×Dic3—31no—
59C2×#938—32no—
60C2×#938—31no—
61C2×#936—31no—
62C2×#936—32no—
63C2×C4×#67—31no—
64C2×C4×#67—31no—
65C2×C4×#67—32no—
66C2×C4×#67—61no—
67C2×#924—32no—
68C2×#924D311yescharacteristic, complemented
69#5633—316no—
70C2×#896—32no—
71C2×#895—31no—
72C2×#893—32no—
73C2×#887—31no—
74C2×#885—32no—
75C2×#884—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C2×#638—24no—
84C2×#638C2314yes—
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C2×C4×C3⋊D3—24no—
89C2×C4×C3⋊D3C2314yes—
90C2×C3×#67—28no—
91C2×C3×#67C2318yes—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C3×#235—232no—
96C2×C3×D12—24no—
97C2×C3×D12C2314yes—
98C2×C3×C4×D3—28no—
99C2×C3×C4×D3C2318yes—
100C2×C3×Dic6—24no—
101C2×C3×Dic6D418yescomplemented
102C2×C3×Dic6C2314yes—
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×#626—28no—
107C2×#626C2318yes—
108C2×#624—28no—
109C2×#624C2318yes—
110#3797—232no—
111#3757C2314yes—
112#3752C2314yes—
113#3750C2314yes—
114C4×C3⋊Dic3C2314yes—
115C3×#217C2318yes—
116C3×C4⋊Dic3C2314yes—
117C3×Dic3⋊C4C2318yes—
118Dic3⋊Dic3C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×Q8—31no—
128C22×C3×D4—32no—
129C22×C3×D4—31no—
130C23×C3×C4—21no—
131C23×C3×C4—32no—
132C23×C3×C4C2×D311yescharacteristic
133C23×C3×C4C2×D311yescharacteristic
134C22×#67—31no—
135C22×#67—31no—
136C22×#67—32no—
137C22×#67—61no—
138C22×#67C2×D312yes—
139C2×D3×Q8—38no—
140C2×D3×Q8—38no—
141C2×D3×Q8—68no—
142C2×D3×Q8—68no—
143C2×#235—28no—
144C2×#235C2×D318yescomplemented
145C22×D12—32no—
146C22×D12C2×D311yescharacteristic
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—61no—
152C22×C4×D3C2×D312yes—
153C22×Dic6—32no—
154C22×Dic6—32no—
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D311yescharacteristic
157C3×C22⋊Q8—38no—
158C2×C3×C4⋊C4—32no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—32no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—32no—
164C2×#217—32no—
165C2×#217—32no—
166C2×#217—61no—
167C2×#217C2×D312yes—
168#947—38no—
169Q8×Dic3—38no—
170#938—316no—
171#938—38no—
172#936—38no—
173#936—316no—
174C4×#67—38no—
175C4×#67—38no—
176C4×#67—316no—
177C4×#67—68no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—61no—
184C2×C4⋊Dic3—32no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186#924—316no—
187#924C2×D318yescomplemented
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—61no—
192C2×Dic3⋊C4C2×D312yes—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—32no—
196C2×C4×Dic3—32no—
197C2×C4×Dic3—61no—
198#896—316no—
199#895—38no—
200#893—316no—
201#887—38no—
202#885—316no—
203#884—316no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3#4114yescomplemented
212C22×C3⋊D3C2412yes—
213C22×C3×D3—24no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3C2414yes—
217C2×C32×C4—22no—
218C2×C32×C4—28no—
219C2×C32×C4C2×D414yes—
220C2×C32×C4C2412yes—
221C2×C32×C4C2412yes—
222#638—28no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3C2412yes—
227C2×C3⋊Dic3C2412yes—
228C2×C3⋊Dic3C2412yes—
229C4×C3⋊D3—28no—
230C3×#67—216no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3C2×D418yes—
234C2×C3×Dic3C2414yes—
235C2×C3×Dic3C2414yes—
236C2×C3×Dic3C2414yes—
237C3×D12—28no—
238C3×C4×D3—216no—
239C3×Dic6—28no—
240C3×Dic6C2×D4116yescomplemented
241#627—216no—
242#626—216no—
243#624—216no—
244C22×#41—31no—
245C23×Q8—91no—
246#548—916no—
247C2×#124—92no—
248C2×#124—91no—
249C2×C22⋊Q8—31no—
250C2×C22⋊Q8—92no—
251C2×#121—92no—
252C2×#121—91no—
253C2×C4×Q8—91no—
254C2×C4×D4—92no—
255C2×C4×D4—91no—
256C24×C3—21no—
257C24×C3—32no—
258C24×C3C22×D311yescharacteristic
259C24×C3C22×D311yescharacteristic
260C23×D3—31no—
261C23×D3—31no—
262C23×D3—61no—
263C23×D3C22×D312yes—
264C3×#41—632no—
265C2×C3×Q8—38no—
266C2×C3×Q8—34no—
267C2×C3×Q8—34no—
268C2×C3×Q8—64no—
269C2×C3×D4—38no—
270C2×C3×D4—34no—
271C2×C3×D4—68no—
272C2×C3×D4—64no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—24no—
278C22×C3×C4—32no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—38no—
282C22×C3×C4—44no—
283C22×C3×C4—68no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C2×#67—28no—
291C2×#67—34no—
292C2×#67—34no—
293C2×#67—38no—
294C2×#67—64no—
295C2×#67—68no—
296C2×#67—64no—
297C2×#67—64no—
298C2×#67—68no—
299C2×#67C22×D318yes—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3C22×D312yes—
310C22×Dic3C22×D312yes—
311C22×Dic3C22×D312yes—
312D3×Q8—632no—
313D3×Q8—632no—
314#235—232no—
315C2×D12—24no—
316C2×D12—38no—
317C2×D12—68no—
318C2×D12C22×D314yes—
319C2×C4×D3—28no—
320C2×C4×D3—34no—
321C2×C4×D3—34no—
322C2×C4×D3—38no—
323C2×C4×D3—38no—
324C2×C4×D3—64no—
325C2×C4×D3—68no—
326C2×C4×D3—64no—
327C2×C4×D3—64no—
328C2×C4×D3—68no—
329C2×C4×D3—124no—
330C2×C4×D3C22×D318yes—
331C2×Dic6—24no—
332C2×Dic6—38no—
333C2×Dic6—38no—
334C2×Dic6—68no—
335C2×Dic6—68no—
336C2×Dic6#6718yescomplemented
337C2×Dic6C22×D314yes—
338C2×Dic6C22×D314yes—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—38no—
341C3×C22⋊C4—38no—
342#217—34no—
343#217—34no—
344#217—38no—
345#217—38no—
346#217—38no—
347#217—64no—
348#217C22×D318yes—
349(C2×D3)⋊C4—38no—
350(C2×D3)⋊C4—38no—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—64no—
355C4⋊Dic3—38no—
356C4⋊Dic3C22×D314yes—
357Dic3⋊C4—34no—
358Dic3⋊C4—34no—
359Dic3⋊C4—38no—
360Dic3⋊C4—64no—
361Dic3⋊C4C22×D318yes—
362C4×Dic3—34no—
363C4×Dic3—34no—
364C4×Dic3—38no—
365C4×Dic3—38no—
366C4×Dic3—64no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—44no—
371C22×C32C22×D412yes—
372C22×C32C2×#4112yes—
373C22×C322−1+412yes—
374C22×C32C2511yescharacteristic
375C2×C3⋊D3—28no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3C2×#4114yescomplemented
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3—24no—
382C2×C3×D3—48no—
383C32×C4—22no—
384C32×C4C22×D414yes—
385C3⋊Dic3—22no—
386C3⋊Dic3—22no—
387C3⋊Dic3—22no—
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3C22×D418yes—
391C2×#41—38no—
392C2×#41—68no—
393C22×Q8—31no—
394C22×Q8—31no—
395C22×Q8—92no—
396C22×Q8—98no—
397C22×Q8—188no—
398C22×D4—32no—
399C22×D4—31no—
400C22×D4—92no—
401C22×D4—91no—
402C23×C4—32no—
403C23×C4—92no—
404C23×C4—91no—
405C23×C4D3211yescharacteristic
406#124—916no—
407#124—98no—
408C22⋊Q8—38no—
409C22⋊Q8—916no—
410#121—916no—
411#121—98no—
412C4×Q8—98no—
413C4×D4—916no—
414C4×D4—98no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—92no—
418C2×C4⋊C4—91no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—92no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—92no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C42—92no—
426C2×C42—91no—
427C23×C3—24no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—34no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—64no—
440C23×C3—64no—
441C23×C3—64no—
442C23×C3C23×D312yes—
443C23×C3C23×D312yes—
444C23×C3C23×D311yescharacteristic
445C23×C3C23×D311yescharacteristic
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—34no—
450C22×D3—34no—
451C22×D3—32no—
452C22×D3—32no—
453C22×D3—64no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—62no—
458C22×D3—62no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3C23×D314yes—
462C3×Q8—316no—
463C3×Q8—68no—
464C3×D4—616no—
465C3×D4—68no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—28no—
469C2×C3×C4—28no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—24no—
473C2×C3×C4—38no—
474C2×C3×C4—34no—
475C2×C3×C4—34no—
476C2×C3×C4—34no—
477C2×C3×C4—48no—
478C2×C3×C4—42no—
479C2×C3×C4—616no—
480C2×C3×C4—64no—
481C2×C3×C4—64no—
482C2×C3×C4D3×D414yes—
483C2×C3×C4C2×#6714yes—
484C2×C3×C4C23×D312yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487C2×C3×C4C23×D312yes—
488#67—216no—
489#67—616no—
490#67—68no—
491#67—68no—
492#67—616no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—32no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—64no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3C2×#6718yes—
514C2×Dic3C23×D314yes—
515C2×Dic3C23×D314yes—
516C2×Dic3C23×D314yes—
517D12—28no—
518D12—616no—
519C4×D3—216no—
520C4×D3—616no—
521C4×D3—68no—
522C4×D3—68no—
523C4×D3—616no—
524C4×D3—128no—
525Dic6—28no—
526Dic6—616no—
527Dic6—616no—
528Dic6C2×#67116yescomplemented
529C2×C32—42no—
530C2×C32#54814yescomplemented
531C2×C32C23×D411yescharacteristic
532C2×C32C22×#4111yescharacteristic
533C2×C32C2×2−1+411yescharacteristic
534C3⋊D3—24no—
535C3×D3—44no—
536C24—32no—
537C24—91no—
538C24C2×D3211yescharacteristic
539#41—632no—
540C2×Q8—34no—
541C2×Q8—34no—
542C2×Q8—38no—
543C2×Q8—64no—
544C2×Q8—98no—
545C2×Q8—188no—
546C2×Q8—1832no—
547C2×D4—38no—
548C2×D4—34no—
549C2×D4—68no—
550C2×D4—64no—
551C2×D4—98no—
552C2×D4—94no—
553C2×D4—188no—
554C2×D4—184no—
555C22×C4—24no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—38no—
560C22×C4—68no—
561C22×C4—98no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—91no—
565C22×C4—94no—
566C22×C4—188no—
567C22×C4—184no—
568C22×C4C2×D3214yes—
569C22×C4C2×D3211yescharacteristic
570C22×C4C2×D3211yescharacteristic
571C4⋊C4—38no—
572C4⋊C4—34no—
573C4⋊C4—98no—
574C4⋊C4—94no—
575C22⋊C4—38no—
576C22⋊C4—98no—
577C22⋊C4—98no—
578C22⋊C4—98no—
579C22⋊C4—94no—
580C22⋊C4—94no—
581C42—98no—
582C42—94no—
583C22×C3—24no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—48no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—128no—
603C22×C3C2×D3×D412yes—
604C22×C3#100712yes—
605C22×C3D3×#4112yes—
606C22×C3D3×#4112yes—
607C22×C3#101012yes—
608C22×C3C22×#6712yes—
609C22×C3C24×D311yescharacteristic
610C22×C3C24×D311yescharacteristic
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—34no—
615C2×D3—34no—
616C2×D3—48no—
617C2×D3—64no—
618C2×D3—68no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—68no—
624C2×D3—122no—
625C2×D3—128no—
626C2×D3—122no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—24no—
630C3×C4—38no—
631C3×C4—42no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4C2×D3×D414yes—
635C3×C4C22×#6714yes—
636Dic3—24no—
637Dic3—24no—
638Dic3—64no—
639Dic3—62no—
640Dic3—62no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—122no—
647Dic3C22×#6718yes—
648C32C2×#54811yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—34no—
653C23—64no—
654C23—64no—
655C23—64no—
656C23—94no—
657C23—92no—
658C23—182no—
659C23—182no—
660C23C22×D3212yes—
661C23C22×D3211yescharacteristic
662Q8—316no—
663Q8—68no—
664Q8—1816no—
665D4—616no—
666D4—68no—
667D4—1816no—
668D4—188no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—38no—
672C2×C4—34no—
673C2×C4—34no—
674C2×C4—34no—
675C2×C4—616no—
676C2×C4—64no—
677C2×C4—64no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—1816no—
682C2×C4—182no—
683C2×C4—182no—
684C2×C4—182no—
685C2×C4—188no—
686C2×C4D3×#6714yes—
687C2×C4C22×D3212yes—
688C2×C4C22×D3212yes—
689C2×C3—24no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—44no—
694C2×C3—42no—
695C2×C3—42no—
696C2×C3—124no—
697C2×C3#563314yescomplemented
698C2×C3#583114yescomplemented
699C2×C3C22×D3×D411yescharacteristic
700C2×C3C2×#100711yescharacteristic
701C2×C3C2×D3×#4111yescharacteristic
702C2×C3C2×D3×#4111yescharacteristic
703C2×C3C2×#101011yescharacteristic
704C2×C3C23×#6711yescharacteristic
705D3—44no—
706D3—64no—
707D3—64no—
708D3—124no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—64no—
714C22—64no—
715C22—64no—
716C22—94no—
717C22—128no—
718C22—188no—
719C22—182no—
720C22—182no—
721C22#6429712yes—
722C22#6430612yes—
723C22C2×D3×#6712yes—
724C22C23×D3211yescharacteristic
725C4—22no—
726C4—38no—
727C4—64no—
728C4—64no—
729C4—182no—
730C4—182no—
731C4—182no—
732C4C2×D3×#6714yes—
733C3—21no—
734C3C2×#563311yescharacteristic, complemented
735C3C2×#583111yescharacteristic, complemented
736C2—42no—
737C2—124no—
738C2—184no—
739C2#1059483014yesdirect product factor
740C2C2×#6429711yescharacteristic
741C2C2×#6430611yescharacteristic
742C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×#3797C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63959C2semidirect
6. C2×#63958C2semidirect
7. C2×#63916C2semidirect
8. C2×#63904C2semidirect
9. C2×#63863C2semidirect
10. C2×#63851C2semidirect
11. #10594830C2direct (N × H)
12. C2×#63843C2semidirect
20. C2×C3×#235C22semidirect
29. C2×#3797C22semidirect
31. C4×#638C22semidirect
37. C3×#924C22semidirect
43. #63959C22semidirect
44. #63958C22semidirect
46. #63916C22semidirect
47. #63904C22semidirect
48. #63863C22semidirect
49. #63851C22semidirect
50. #63843C22semidirect
54. C22×#235D3semidirect
68. C2×#924D3semidirect
101. C2×C3×Dic6D4semidirect
144. C2×#235C2×D3semidirect
187. #924C2×D3semidirect
211. C22×C3⋊D3#41semidirect
240. C3×Dic6C2×D4semidirect
336. C2×Dic6#67semidirect
378. C2×C3⋊D3C2×#41semidirect
528. Dic6C2×#67semidirect
530. C2×C32#548semidirect
648. C32C2×#548semidirect
697. C2×C3#5633semidirect
698. C2×C3#5831semidirect
734. C3C2×#5633semidirect
735. C3C2×#5831semidirect
739. C2#10594830direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37972
C2×C4×#6382
C2×C3×#9242
C2×#639592
C2×#639582
C2×#639162
C2×#639042
C2×#638632
C2×#638512
#105948302
C2×#638432
C2×#58313
C2×#56333