Finite Group Databasebeta

← C2×#10593899 #11902617

Subgroups — C2×#10593899 #11902617

Order 1152.

3405 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64084C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
6C2×#63909C211yesmaximal, characteristic, complemented
7C2×#63895C212yesmaximal, complemented
8C2×#63886C212yesmaximal, complemented
9C2×#63880C212yesmaximal, complemented
10C2×#63857C211yesmaximal, characteristic, complemented
11C2×#63852C212yesmaximal, complemented
12#10593899C2116yesmaximal, direct product factor
13C2×#5576—31nomaximal
14C2×#5552—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2212yes—
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×#624C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3799—28no—
27C2×#3799C2218yescomplemented
28C2×D3×Dic6—28no—
29C2×D3×Dic6C2218yescomplemented
30C2×C32×C42C2211yescharacteristic
31C2×#3752C2212yes—
32C2×#3752C2212yes—
33#64084C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2212yes—
40C3×C4×D12C2218yescomplemented
41C3×C4×Dic6C2218yescomplemented
42C2×Dic3⋊Dic3C2212yes—
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63909C2218yescomplemented
46#63895C22116yescomplemented
47#63886C22116yescomplemented
48#63880C22116yescomplemented
49#63857C2218yescomplemented
50#63852C22116yescomplemented
51C22×#239—31no—
52C22×D3×Q8—31no—
53C22×#235—31no—
54C23×Dic6—31no—
55C2×C3×C4×Q8—31no—
56C2×C3×C4×D4—31no—
57C2×#939—32no—
58C2×#930—31no—
59C2×#924—31no—
60#5576—316no—
61#5552—316no—
62C2×#897—31no—
63C2×#897—32no—
64C2×#896—32no—
65C2×#895—32no—
66C2×#895—31no—
67C2×#885—32no—
68C2×#67⋊C4—32no—
69C2×#875—31no—
70C2×#875—31no—
71C2×#875—32no—
72C2×#875—61no—
73C2×C4×D12—32no—
74C2×C4×D12D311yescharacteristic, complemented
75C2×C4×Dic6D311yescharacteristic, complemented
76C23×C3⋊D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2312yes—
83C2×C4⋊(C3⋊D3)—24no—
84C2×C4⋊(C3⋊D3)C2314yes—
85C2×#634—24no—
86C2×#634C2314yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C2×C3×D12—24no—
92C2×C3×D12C2314yes—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3C2314yes—
96C2×C3×C4×D3C2314yes—
97C2×C3×Dic6D418yescomplemented
98C2×C3×Dic6C2314yes—
99C2×#627—28no—
100C2×#627C2318yes—
101C2×#626—28no—
102C2×#626—28no—
103C2×#626C2318yes—
104C2×#626C2318yes—
105C2×#624—28no—
106C2×#624C2318yes—
107C2×D3×Dic3—28no—
108C2×D3×Dic3C2318yes—
109#3799—232no—
110D3×Dic6—232no—
111C32×C42C2314yes—
112#3752C2318yes—
113#3752C2318yes—
114C3×(C2×D3)⋊C4C2314yes—
115C3×(C2×D3)⋊C4C2314yes—
116C3×C4⋊Dic3C2314yes—
117C3×C4⋊Dic3C2314yes—
118C3×Dic3⋊C4C2318yes—
119C3×C4×Dic3C2318yes—
120Dic3⋊Dic3C2318yes—
121#3722C2318yes—
122(C2×D3)⋊Dic3C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×D4—31no—
126C23×C3×C4—31no—
127C23×C3×C4—31no—
128C22×#67—32no—
129C22×#67—32no—
130C23×Dic3—32no—
131C2×#239—38no—
132C2×#239—68no—
133C2×D3×Q8—38no—
134C2×D3×Q8—68no—
135C2×#235—38no—
136C2×#235—68no—
137C22×D12—32no—
138C22×D12—32no—
139C22×D12—31no—
140C22×D12—31no—
141C22×D12—61no—
142C22×D12C2×D311yescharacteristic
143C22×C4×D3—32no—
144C22×C4×D3—32no—
145C22×C4×D3—32no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C4×D3C2×D311yescharacteristic
148C22×Dic6—31no—
149C22×Dic6—31no—
150C22×Dic6—32no—
151C22×Dic6—32no—
152C22×Dic6—38no—
153C22×Dic6—61no—
154C22×Dic6—68no—
155C22×Dic6C2×D311yescharacteristic
156C3×C4×Q8—38no—
157C3×C4×D4—38no—
158C2×C3×C4⋊C4—32no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C42—21no—
164C2×C3×C42—32no—
165C2×C3×C42C2×D311yescharacteristic
166C2×C3×C42C2×D311yescharacteristic
167C2×#217—32no—
168#939—316no—
169#930—38no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—62no—
178C2×(C2×D3)⋊C4—62no—
179C2×(C2×D3)⋊C4C2×D311yescharacteristic
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×C4⋊Dic3—32no—
182C2×C4⋊Dic3C2×D311yescharacteristic
183C2×C4⋊Dic3C2×D311yescharacteristic
184#924—38no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4C2×D312yes—
187C2×C4×Dic3C2×D312yes—
188#897—38no—
189#897—316no—
190#896—316no—
191#895—316no—
192#895—38no—
193#885—316no—
194#67⋊C4—316no—
195#875—38no—
196#875—38no—
197#875—316no—
198#875—68no—
199C4×D12—316no—
200C4×D12C2×D318yescomplemented
201C4×Dic6C2×D318yescomplemented
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—24no—
206C22×C3⋊D3C2414yes—
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3#4114yescomplemented
213C22×C3×D3C2412yes—
214C22×C3×D3C2412yes—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2412yes—
220C2×C32×C4C2412yes—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3C2414yes—
223C4⋊(C3⋊D3)—28no—
224#634—28no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—24no—
228C2×C3×Dic3C2×D418yes—
229C2×C3×Dic3C2414yes—
230C2×C3×Dic3C2412yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2414yes—
233C3×D12—28no—
234C3×C4×D3—28no—
235C3×C4×D3—28no—
236C3×Dic6C2×D4116yescomplemented
237#627—216no—
238#626—216no—
239#626—216no—
240#624—216no—
241D3×Dic3—216no—
242C22×#41—91no—
243C23×Q8—91no—
244#548—916no—
245C2×#124—92no—
246C2×#124—91no—
247C2×C22⋊Q8—92no—
248C2×C22⋊Q8—91no—
249C2×#121—91no—
250C2×#121—92no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—92no—
254C24×C3—31no—
255C24×C3—31no—
256C23×D3—32no—
257C23×D3—32no—
258C23×D3—62no—
259C23×D3C22×D311yescharacteristic
260C23×D3C22×D311yescharacteristic
261C2×C3×Q8—38no—
262C2×C3×Q8—34no—
263C2×C3×D4—34no—
264C2×C3×D4—64no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—32no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—31no—
272C22×C3×C4—34no—
273C22×C3×C4—34no—
274C22×C3×C4—64no—
275C22×C3×C4—64no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—38no—
283C2×#67—38no—
284C2×#67—68no—
285C2×#67—68no—
286C22×Dic3—32no—
287C22×Dic3—32no—
288C22×Dic3—38no—
289C22×Dic3—62no—
290C22×Dic3—68no—
291C22×Dic3C22×D312yes—
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D312yes—
295#239—632no—
296D3×Q8—632no—
297#235—632no—
298C2×D12—24no—
299C2×D12—38no—
300C2×D12—38no—
301C2×D12—34no—
302C2×D12—34no—
303C2×D12—64no—
304C2×D12—68no—
305C2×D12—68no—
306C2×D12—64no—
307C2×D12—64no—
308C2×D12—124no—
309C2×D12C22×D314yes—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—38no—
313C2×C4×D3—38no—
314C2×C4×D3—38no—
315C2×C4×D3—68no—
316C2×C4×D3—68no—
317C2×C4×D3—68no—
318C2×C4×D3C22×D314yes—
319C2×C4×D3C22×D314yes—
320C2×Dic6—34no—
321C2×Dic6—34no—
322C2×Dic6—38no—
323C2×Dic6—38no—
324C2×Dic6—64no—
325C2×Dic6—68no—
326C2×Dic6—64no—
327C2×Dic6—64no—
328C2×Dic6—68no—
329C2×Dic6—632no—
330C2×Dic6—124no—
331C2×Dic6D1218yescomplemented
332C2×Dic6C22×D314yes—
333C3×C4⋊C4—38no—
334C3×C4⋊C4—34no—
335C3×C4⋊C4—34no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4—34no—
338C3×C42—24no—
339C3×C42—38no—
340C3×C42C22×D314yes—
341C3×C42C22×D314yes—
342#217—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—38no—
348(C2×D3)⋊C4—38no—
349(C2×D3)⋊C4—38no—
350(C2×D3)⋊C4—68no—
351(C2×D3)⋊C4—68no—
352(C2×D3)⋊C4C22×D314yes—
353(C2×D3)⋊C4C22×D314yes—
354C4⋊Dic3—38no—
355C4⋊Dic3C22×D314yes—
356C4⋊Dic3C22×D314yes—
357Dic3⋊C4—38no—
358Dic3⋊C4C22×D318yes—
359C4×Dic3C22×D318yes—
360C22×C32C22×D412yes—
361C22×C32C2×#4112yes—
362C22×C322−1+412yes—
363C22×C32C2511yescharacteristic
364C2×C3⋊D3—24no—
365C2×C3⋊D3—24no—
366C2×C3⋊D3—24no—
367C2×C3⋊D3—48no—
368C2×C3×D3—28no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—44no—
375C2×C3×D3C2×#4114yescomplemented
376C32×C4—22no—
377C32×C4—22no—
378C32×C4C22×D414yes—
379C3⋊Dic3—24no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—24no—
383C3×Dic3C22×D418yes—
384C2×#41—98no—
385C2×#41—188no—
386C22×Q8—31no—
387C22×Q8—92no—
388C22×Q8—98no—
389C22×Q8—91no—
390C22×Q8—188no—
391C22×D4—31no—
392C22×D4—92no—
393C22×D4—92no—
394C22×D4—91no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—92no—
398C23×C4—92no—
399#124—916no—
400#124—98no—
401C22⋊Q8—916no—
402C22⋊Q8—98no—
403#121—98no—
404#121—916no—
405C4×Q8—38no—
406C4×D4—38no—
407C4×D4—916no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—92no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—92no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—92no—
417C2×C22⋊C4—92no—
418C2×C42—32no—
419C2×C42D3211yescharacteristic
420C23×C3—21no—
421C23×C3—34no—
422C23×C3—32no—
423C23×C3—32no—
424C23×C3—62no—
425C23×C3—62no—
426C23×C3—62no—
427C23×C3—62no—
428C23×C3—62no—
429C23×C3C23×D311yescharacteristic
430C23×C3C23×D311yescharacteristic
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—34no—
437C22×D3—34no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—124no—
446C22×D3—124no—
447C22×D3—124no—
448C22×D3#23514yescomplemented
449C22×D3C23×D312yes—
450C22×D3C23×D312yes—
451C3×Q8—316no—
452C3×D4—68no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
461C2×C3×C4—38no—
462C2×C3×C4—34no—
463C2×C3×C4—32no—
464C2×C3×C4—34no—
465C2×C3×C4—32no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—64no—
471C2×C3×C4—68no—
472C2×C3×C4—68no—
473C2×C3×C4C2×D1214yes—
474C2×C3×C4D3×D414yes—
475C2×C3×C4C23×D312yes—
476C2×C3×C4C23×D312yes—
477C2×C3×C4C23×D312yes—
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D312yes—
481#67—616no—
482#67—616no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—24no—
486C2×Dic3—34no—
487C2×Dic3—34no—
488C2×Dic3—64no—
489C2×Dic3—64no—
490C2×Dic3—64no—
491C2×Dic3—616no—
492C2×Dic3—124no—
493C2×Dic3C2×D1218yes—
494C2×Dic3C23×D314yes—
495C2×Dic3C23×D312yes—
496C2×Dic3C23×D312yes—
497C2×Dic3C23×D314yes—
498D12—28no—
499D12—616no—
500D12—616no—
501D12—68no—
502D12—68no—
503D12—128no—
504C4×D3—28no—
505C4×D3—28no—
506C4×D3—616no—
507C4×D3—616no—
508C4×D3—616no—
509Dic6—616no—
510Dic6—68no—
511Dic6—68no—
512Dic6—616no—
513Dic6—128no—
514Dic6C2×D12116yescomplemented
515C2×C32#54814yescomplemented
516C2×C32C23×D411yescharacteristic
517C2×C32C22×#4111yescharacteristic
518C2×C32C2×2−1+411yescharacteristic
519C3⋊D3—44no—
520C3×D3—24no—
521C3×D3—42no—
522C24—31no—
523C24—31no—
524C24—92no—
525#41—1832no—
526C2×Q8—34no—
527C2×Q8—38no—
528C2×Q8—98no—
529C2×Q8—94no—
530C2×Q8—188no—
531C2×Q8—1832no—
532C2×Q8—184no—
533C2×D4—34no—
534C2×D4—64no—
535C2×D4—98no—
536C2×D4—98no—
537C2×D4—94no—
538C2×D4—188no—
539C2×D4—188no—
540C2×D4—184no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—34no—
546C22×C4—34no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—98no—
550C22×C4—98no—
551C22×C4—92no—
552C22×C4—188no—
553C22×C4—188no—
554C22×C4C2×D3211yescharacteristic
555C22×C4C2×D3211yescharacteristic
556C22×C4C2×D3211yescharacteristic
557C4⋊C4—34no—
558C4⋊C4—38no—
559C4⋊C4—34no—
560C4⋊C4—98no—
561C22⋊C4—34no—
562C22⋊C4—34no—
563C22⋊C4—98no—
564C22⋊C4—98no—
565C22⋊C4—98no—
566C22⋊C4—98no—
567C42—38no—
568C42C2×D3214yes—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—21no—
573C22×C3—34no—
574C22×C3—62no—
575C22×C3—62no—
576C22×C3—68no—
577C22×C3—62no—
578C22×C3—62no—
579C22×C3—62no—
580C22×C3—124no—
581C22×C3C22×D1212yes—
582C22×C3C2×#23512yes—
583C22×C3C2×D3×D412yes—
584C22×C3#100712yes—
585C22×C3D3×#4112yes—
586C22×C3#101012yes—
587C22×C3C24×D311yescharacteristic
588C22×C3C24×D311yescharacteristic
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—28no—
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—22no—
595C2×D3—44no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—124no—
603C2×D3—124no—
604C2×D3—124no—
605C2×D3—128no—
606C2×D3—128no—
607C2×D3—248no—
608C2×D3C2×#23514yescomplemented
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—24no—
614C3×C4—38no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—64no—
620C3×C4C22×D1214yes—
621C3×C4C2×D3×D414yes—
622Dic3—22no—
623Dic3—22no—
624Dic3—24no—
625Dic3—64no—
626Dic3—64no—
627Dic3—124no—
628Dic3C22×D1218yes—
629C32C2×#54811yescharacteristic, complemented, Sylow
630C23—34no—
631C23—32no—
632C23—32no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—94no—
639C23—184no—
640C23—184no—
641C23—184no—
642C23C22×D3211yescharacteristic
643Q8—316no—
644Q8—1816no—
645Q8—188no—
646D4—68no—
647D4—1816no—
648D4—1816no—
649D4—188no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—38no—
653C2×C4—34no—
654C2×C4—34no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—64no—
660C2×C4—68no—
661C2×C4—68no—
662C2×C4—94no—
663C2×C4—1816no—
664C2×C4—1816no—
665C2×C4—184no—
666C2×C4D3×D1214yes—
667C2×C4C22×D3212yes—
668C2×C4C22×D3212yes—
669C2×C4C22×D3212yes—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—24no—
674C2×C3—64no—
675C2×C3—122no—
676C2×C3#555214yescomplemented
677C2×C3#557614yescomplemented
678C2×C3C23×D1211yescharacteristic
679C2×C3C22×#23511yescharacteristic
680C2×C3C22×D3×D411yescharacteristic
681C2×C3C2×#100711yescharacteristic
682C2×C3C2×D3×#4111yescharacteristic
683C2×C3C2×#101011yescharacteristic
684D3—24no—
685D3—42no—
686D3—124no—
687D3—124no—
688D3—244no—
689C22—34no—
690C22—62no—
691C22—62no—
692C22—68no—
693C22—62no—
694C22—62no—
695C22—62no—
696C22—124no—
697C22—184no—
698C22—184no—
699C22—184no—
700C22—368no—
701C22#6429712yes—
702C22C2×D3×D1212yes—
703C22D3×#23512yes—
704C22C23×D3211yescharacteristic
705C4—22no—
706C4—22no—
707C4—38no—
708C4—62no—
709C4—62no—
710C4—64no—
711C4—184no—
712C4C2×D3×D1214yes—
713C3—21no—
714C3C2×#555211yescharacteristic, complemented
715C3C2×#557611yescharacteristic, complemented
716C2—64no—
717C2—122no—
718C2—364no—
719C2#1059389914yesdirect product factor
720C2C2×#6429711yescharacteristic
721C2C22×D3×D1211yescharacteristic
722C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64084C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×C3×C4×Dic6C2semidirect
6. C2×#63909C2semidirect
7. C2×#63895C2semidirect
8. C2×#63886C2semidirect
9. C2×#63880C2semidirect
10. C2×#63857C2semidirect
11. C2×#63852C2semidirect
12. #10593899C2direct (N × H)
27. C2×#3799C22semidirect
29. C2×D3×Dic6C22semidirect
33. #64084C22semidirect
40. C3×C4×D12C22semidirect
41. C3×C4×Dic6C22semidirect
45. #63909C22semidirect
46. #63895C22semidirect
47. #63886C22semidirect
48. #63880C22semidirect
49. #63857C22semidirect
50. #63852C22semidirect
74. C2×C4×D12D3semidirect
75. C2×C4×Dic6D3semidirect
97. C2×C3×Dic6D4semidirect
200. C4×D12C2×D3semidirect
201. C4×Dic6C2×D3semidirect
212. C22×C3×D3#41semidirect
236. C3×Dic6C2×D4semidirect
331. C2×Dic6D12semidirect
375. C2×C3×D3C2×#41semidirect
448. C22×D3#235semidirect
514. Dic6C2×D12semidirect
515. C2×C32#548semidirect
608. C2×D3C2×#235semidirect
629. C32C2×#548semidirect
676. C2×C3#5552semidirect
677. C2×C3#5576semidirect
714. C3C2×#5552semidirect
715. C3C2×#5576semidirect
719. C2#10593899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×D3×Dic62
C2×#640842
C2×C3×C4×D122
C2×C3×C4×Dic62
C2×#639092
C2×#638952
C2×#638862
C2×#638802
C2×#638572
C2×#638522
#105938992
C2×#55763
C2×#55523