Finite Group Databasebeta

← C2×#10595237 #11902606

Subgroups — C2×#10595237 #11902606

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×#64147C211yesmaximal, characteristic, complemented
4C2×C3×#936C211yesmaximal, characteristic, complemented
5C2×#63964C212yesmaximal, complemented
6C2×#63959C212yesmaximal, complemented
7C2×#63958C212yesmaximal, complemented
8C2×#63952C212yesmaximal, complemented
9#10595237C2116yesmaximal, direct product factor
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5831—31nomaximal
14C2×#5677—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C2×C3×#237—28no—
21C2×C3×#237C2218yescomplemented
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2212yes—
26C22×#626C2211yescharacteristic
27C22×#624C2212yes—
28C2×#3797—28no—
29C2×#3797C2218yescomplemented
30C2×#3757C2212yes—
31#64147C2218yescomplemented
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×C3×#217C2212yes—
34C2×C3×#217C2212yes—
35C3×#936C2218yescomplemented
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2211yescharacteristic
40#63964C22116yescomplemented
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44#63959C22116yescomplemented
45#63958C22116yescomplemented
46C2×Dic32C2212yes—
47#63952C22116yescomplemented
48C4×#626C2218yescomplemented
49#63856C2218yescomplemented
50Dic3×Dic6C2218yescomplemented
51C22×C3×#41—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C22×#237D311yescharacteristic, complemented
55C2×C3×#124—31no—
56#5831—316no—
57C2×#946—31no—
58C2×Q8×Dic3—31no—
59C2×#938—31no—
60C2×#938—31no—
61C2×#938—32no—
62C2×#938—61no—
63C2×#936—32no—
64C2×#936D311yescharacteristic, complemented
65C2×C4×#67—32no—
66C2×C4×#67—31no—
67C2×#924—31no—
68C2×#924—32no—
69#5677—316no—
70C2×#885—32no—
71C2×#884—32no—
72C2×#67⋊C4—32no—
73C2×#878—32no—
74C2×C4×D12—31no—
75C2×C4×Dic6—31no—
76C24×C32C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C2×C32×D4—24no—
80C2×C32×D4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C2×#638—28no—
83C2×#638C2318yes—
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2312yes—
86C2×C4×C3⋊D3—24no—
87C2×C4×C3⋊D3C2314yes—
88C2×C3×#67—28no—
89C2×C3×#67C2318yes—
90C22×C3×Dic3—28no—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2318yes—
96C22×C3×Dic3C2312yes—
97C3×#237—232no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3C2314yes—
100C2×C3×Dic6—24no—
101C2×C3×Dic6D418yescomplemented
102C2×C3×Dic6C2314yes—
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×#626—24no—
107C2×#626C2314yes—
108C2×#624—28no—
109C2×#624C2318yes—
110#3797—232no—
111#3757C2318yes—
112C4⋊(C3⋊Dic3)C2314yes—
113C3×#217C2318yes—
114C3×#217C2318yes—
115C3×C4×Dic3C2314yes—
116#3724C2318yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2314yes—
119#3722C2314yes—
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2314yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×Q8—31no—
128C22×C3×D4—21no—
129C22×C3×D4—32no—
130C22×C3×D4C2×D311yescharacteristic
131C22×C3×D4C2×D311yescharacteristic
132C23×C3×C4—32no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—31no—
137C22×#67—62no—
138C22×#67C2×D312yes—
139C23×Dic3C2×D312yes—
140C2×D3×Q8—38no—
141C2×D3×Q8—38no—
142C2×D3×Q8—68no—
143C2×D3×Q8—68no—
144C2×#237—28no—
145C2×#237C2×D318yescomplemented
146C22×D12—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—61no—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—32no—
154C22×Dic6—32no—
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D311yescharacteristic
157C3×#124—38no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C42—31no—
161C2×#217—32no—
162C2×#217—32no—
163C2×#217—32no—
164C2×#217—31no—
165C2×#217—62no—
166C2×#217C2×D312yes—
167C2×#217C2×D312yes—
168#946—38no—
169Q8×Dic3—38no—
170#938—38no—
171#938—38no—
172#938—316no—
173#938—68no—
174#936—316no—
175#936C2×D318yescomplemented
176C4×#67—316no—
177C4×#67—38no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3—61no—
187#924—38no—
188#924—316no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—32no—
193C2×C4×Dic3—32no—
194C2×C4×Dic3—32no—
195C2×C4×Dic3C2×D311yescharacteristic
196#885—316no—
197#884—316no—
198#67⋊C4—316no—
199#878—316no—
200C4×D12—38no—
201C4×Dic6—38no—
202C23×C32—24no—
203C23×C32—24no—
204C23×C32—24no—
205C23×C32C2414yes—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3#4114yescomplemented
210C22×C3⋊D3C2412yes—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3C2412yes—
215C32×D4—28no—
216C2×C32×C4C2×D414yes—
217C2×C32×C4C2412yes—
218#638—216no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—24no—
221C2×C3⋊Dic3C2414yes—
222C2×C3⋊Dic3C2412yes—
223C4×C3⋊D3—28no—
224C3×#67—216no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—216no—
230C2×C3×Dic3C2×D418yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2414yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2412yes—
235C2×C3×Dic3C2414yes—
236C3×C4×D3—28no—
237C3×Dic6—28no—
238C3×Dic6C2×D4116yescomplemented
239#627—216no—
240#626—28no—
241#624—216no—
242C22×#41—31no—
243C23×Q8—91no—
244#548—916no—
245C2×#124—31no—
246C2×#124—92no—
247C2×C22⋊Q8—92no—
248C2×C22⋊Q8—91no—
249C2×#121—92no—
250C2×#121—91no—
251C2×C4×Q8—91no—
252C2×C4×D4—91no—
253C2×C4×D4—92no—
254C24×C3—22no—
255C24×C3—31no—
256C24×C3C22×D312yes—
257C24×C3C22×D312yes—
258C23×D3—31no—
259C23×D3—31no—
260C23×D3—61no—
261C23×D3C22×D311yescharacteristic
262C3×#41—632no—
263C2×C3×Q8—38no—
264C2×C3×Q8—34no—
265C2×C3×Q8—34no—
266C2×C3×Q8—64no—
267C2×C3×D4—24no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—38no—
271C2×C3×D4—44no—
272C2×C3×D4—68no—
273C2×C3×D4C22×D314yes—
274C2×C3×D4C22×D314yes—
275C22×C3×C4—21no—
276C22×C3×C4—32no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—32no—
281C22×C3×C4—38no—
282C22×C3×C4—34no—
283C22×C3×C4—68no—
284C22×C3×C4—64no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C2×#67—28no—
288C2×#67—38no—
289C2×#67—38no—
290C2×#67—34no—
291C2×#67—68no—
292C2×#67—64no—
293C2×#67—68no—
294C2×#67—68no—
295C2×#67—128no—
296C2×#67C22×D318yes—
297C22×Dic3—28no—
298C22×Dic3—32no—
299C22×Dic3—32no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—62no—
303C22×Dic3—61no—
304C22×Dic3C22×D318yes—
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D312yes—
309C22×Dic3C22×D312yes—
310D3×Q8—632no—
311D3×Q8—632no—
312#237—232no—
313C2×D12—34no—
314C2×D12—64no—
315C2×C4×D3—24no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—38no—
319C2×C4×D3—38no—
320C2×C4×D3—64no—
321C2×C4×D3—68no—
322C2×C4×D3—64no—
323C2×C4×D3—64no—
324C2×C4×D3—68no—
325C2×C4×D3—124no—
326C2×C4×D3C22×D314yes—
327C2×Dic6—24no—
328C2×Dic6—38no—
329C2×Dic6—38no—
330C2×Dic6—68no—
331C2×Dic6—68no—
332C2×Dic6#6718yescomplemented
333C2×Dic6C22×D314yes—
334C2×Dic6C22×D314yes—
335C3×C22⋊C4—38no—
336C3×C22⋊C4—38no—
337C3×C42—34no—
338#217—38no—
339#217—38no—
340#217—38no—
341#217—34no—
342#217—68no—
343#217C22×D318yes—
344#217C22×D318yes—
345(C2×D3)⋊C4—34no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—34no—
349C4⋊Dic3—34no—
350C4⋊Dic3—34no—
351C4⋊Dic3—34no—
352C4⋊Dic3—38no—
353C4⋊Dic3—64no—
354Dic3⋊C4—38no—
355Dic3⋊C4—38no—
356Dic3⋊C4—34no—
357Dic3⋊C4—38no—
358C4×Dic3—38no—
359C4×Dic3—38no—
360C4×Dic3C22×D314yes—
361C22×C32—24no—
362C22×C32—24no—
363C22×C32—24no—
364C22×C32—48no—
365C22×C32C22×D412yes—
366C22×C32C2×#4112yes—
367C22×C322−1+412yes—
368C22×C32C2511yescharacteristic
369C2×C3⋊D3—28no—
370C2×C3⋊D3—22no—
371C2×C3⋊D3—22no—
372C2×C3⋊D3C2×#4114yescomplemented
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—44no—
377C32×C4C22×D414yes—
378C3⋊Dic3—22no—
379C3⋊Dic3—24no—
380C3×Dic3—24no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3C22×D418yes—
385C2×#41—38no—
386C2×#41—68no—
387C22×Q8—31no—
388C22×Q8—31no—
389C22×Q8—92no—
390C22×Q8—98no—
391C22×Q8—188no—
392C22×D4—32no—
393C22×D4—91no—
394C22×D4—92no—
395C22×D4D3211yescharacteristic
396C23×C4—32no—
397C23×C4—31no—
398C23×C4—92no—
399C23×C4—91no—
400#124—38no—
401#124—916no—
402C22⋊Q8—916no—
403C22⋊Q8—98no—
404#121—916no—
405#121—98no—
406C4×Q8—98no—
407C4×D4—98no—
408C4×D4—916no—
409C2×C4⋊C4—92no—
410C2×C4⋊C4—91no—
411C2×C4⋊C4—92no—
412C2×C4⋊C4—91no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—91no—
416C2×C22⋊C4—91no—
417C2×C22⋊C4—92no—
418C2×C22⋊C4—92no—
419C2×C42—31no—
420C2×C42—92no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—21no—
429C23×C3—32no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—62no—
436C23×C3C23×D314yes—
437C23×C3C23×D314yes—
438C23×C3C23×D311yescharacteristic
439C23×C3C23×D311yescharacteristic
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—34no—
444C22×D3—34no—
445C22×D3—32no—
446C22×D3—32no—
447C22×D3—64no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—122no—
454C22×D3—122no—
455C22×D3C23×D312yes—
456C3×Q8—316no—
457C3×Q8—68no—
458C3×D4—28no—
459C3×D4—28no—
460C3×D4—48no—
461C3×D4—616no—
462C2×C3×C4—22no—
463C2×C3×C4—24no—
464C2×C3×C4—38no—
465C2×C3×C4—34no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—34no—
470C2×C3×C4—616no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—64no—
475C2×C3×C4—68no—
476C2×C3×C4D3×D414yes—
477C2×C3×C4C2×#6714yes—
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D312yes—
480#67—216no—
481#67—68no—
482#67—616no—
483#67—616no—
484#67—1216no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—216no—
490C2×Dic3—34no—
491C2×Dic3—34no—
492C2×Dic3—32no—
493C2×Dic3—32no—
494C2×Dic3—64no—
495C2×Dic3—62no—
496C2×Dic3—62no—
497C2×Dic3—64no—
498C2×Dic3—64no—
499C2×Dic3—62no—
500C2×Dic3—122no—
501C2×Dic3—124no—
502C2×Dic3C2×#6718yes—
503C2×Dic3C23×D312yes—
504C2×Dic3C23×D312yes—
505C2×Dic3C23×D312yes—
506C2×Dic3C23×D314yes—
507C2×Dic3C23×D314yes—
508D12—68no—
509C4×D3—28no—
510C4×D3—616no—
511C4×D3—68no—
512C4×D3—68no—
513C4×D3—616no—
514C4×D3—128no—
515Dic6—28no—
516Dic6—616no—
517Dic6—616no—
518Dic6C2×#67116yescomplemented
519C2×C32—44no—
520C2×C32#54814yescomplemented
521C2×C32C23×D411yescharacteristic
522C2×C32C22×#4111yescharacteristic
523C2×C32C2×2−1+411yescharacteristic
524C3⋊D3—24no—
525C3×D3—42no—
526C24—31no—
527C24—91no—
528C24C2×D3212yes—
529#41—632no—
530C2×Q8—34no—
531C2×Q8—34no—
532C2×Q8—38no—
533C2×Q8—64no—
534C2×Q8—98no—
535C2×Q8—188no—
536C2×Q8—1832no—
537C2×D4—24no—
538C2×D4—38no—
539C2×D4—68no—
540C2×D4—94no—
541C2×D4—98no—
542C2×D4—184no—
543C2×D4—188no—
544C2×D4C2×D3214yes—
545C22×C4—32no—
546C22×C4—38no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—32no—
550C22×C4—31no—
551C22×C4—34no—
552C22×C4—68no—
553C22×C4—64no—
554C22×C4—98no—
555C22×C4—92no—
556C22×C4—91no—
557C22×C4—94no—
558C22×C4—188no—
559C22×C4—184no—
560C22×C4C2×D3211yescharacteristic
561C4⋊C4—98no—
562C4⋊C4—94no—
563C4⋊C4—98no—
564C4⋊C4—94no—
565C22⋊C4—38no—
566C22⋊C4—38no—
567C22⋊C4—94no—
568C22⋊C4—94no—
569C22⋊C4—98no—
570C22⋊C4—98no—
571C42—34no—
572C42—98no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—24no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—21no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—48no—
587C22×C3—48no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—88no—
592C22×C3—124no—
593C22×C3C2×D3×D412yes—
594C22×C3D3×#4112yes—
595C22×C3D3×#4112yes—
596C22×C3#101012yes—
597C22×C3#101012yes—
598C22×C3C22×#6712yes—
599C22×C3C24×D311yescharacteristic
600C22×C3C24×D311yescharacteristic
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—34no—
605C2×D3—34no—
606C2×D3—44no—
607C2×D3—64no—
608C2×D3—68no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—68no—
614C2×D3—122no—
615C2×D3—122no—
616C2×D3—128no—
617C3×C4—24no—
618C3×C4—38no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—64no—
623C3×C4C2×D3×D414yes—
624C3×C4C22×#6714yes—
625Dic3—24no—
626Dic3—22no—
627Dic3—22no—
628Dic3—22no—
629Dic3—62no—
630Dic3—64no—
631Dic3—64no—
632Dic3—62no—
633Dic3—122no—
634Dic3—124no—
635Dic3C22×#6718yes—
636C32C2×#54811yescharacteristic, complemented, Sylow
637C23—24no—
638C23—24no—
639C23—24no—
640C23—32no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—94no—
645C23—92no—
646C23—182no—
647C23—182no—
648C23C22×D3214yes—
649C23C22×D3211yescharacteristic
650Q8—316no—
651Q8—68no—
652Q8—1816no—
653D4—28no—
654D4—616no—
655D4—188no—
656D4—1816no—
657C2×C4—38no—
658C2×C4—34no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—616no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—64no—
668C2×C4—68no—
669C2×C4—94no—
670C2×C4—92no—
671C2×C4—1816no—
672C2×C4—184no—
673C2×C4—182no—
674C2×C4—188no—
675C2×C4D3×#6714yes—
676C2×C4C22×D3212yes—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—24no—
681C2×C3—44no—
682C2×C3—44no—
683C2×C3—84no—
684C2×C3—122no—
685C2×C3#567714yescomplemented
686C2×C3#583114yescomplemented
687C2×C3C22×D3×D411yescharacteristic
688C2×C3C2×D3×#4111yescharacteristic
689C2×C3C2×D3×#4111yescharacteristic
690C2×C3C2×#101011yescharacteristic
691C2×C3C2×#101011yescharacteristic
692C2×C3C23×#6711yescharacteristic
693D3—42no—
694D3—64no—
695D3—64no—
696D3—124no—
697C22—24no—
698C22—24no—
699C22—24no—
700C22—48no—
701C22—62no—
702C22—62no—
703C22—62no—
704C22—94no—
705C22—124no—
706C22—182no—
707C22—182no—
708C22—188no—
709C22#6430912yes—
710C22#6431212yes—
711C22C2×D3×#6712yes—
712C22C23×D3211yescharacteristic
713C4—38no—
714C4—62no—
715C4—62no—
716C4—62no—
717C4—64no—
718C4—184no—
719C4—182no—
720C4C2×D3×#6714yes—
721C3—21no—
722C3C2×#567711yescharacteristic, complemented
723C3C2×#583111yescharacteristic, complemented
724C2—44no—
725C2—122no—
726C2—184no—
727C2#1059523714yesdirect product factor
728C2C2×#6430911yescharacteristic
729C2C2×#6431211yescharacteristic
730C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×#3797C2semidirect
3. C2×#64147C2semidirect
4. C2×C3×#936C2semidirect
5. C2×#63964C2semidirect
6. C2×#63959C2semidirect
7. C2×#63958C2semidirect
8. C2×#63952C2semidirect
9. #10595237C2direct (N × H)
10. C2×C4×#626C2semidirect
11. C2×#63856C2semidirect
12. C2×Dic3×Dic6C2semidirect
21. C2×C3×#237C22semidirect
29. C2×#3797C22semidirect
31. #64147C22semidirect
35. C3×#936C22semidirect
40. #63964C22semidirect
44. #63959C22semidirect
45. #63958C22semidirect
47. #63952C22semidirect
48. C4×#626C22semidirect
49. #63856C22semidirect
50. Dic3×Dic6C22semidirect
54. C22×#237D3semidirect
64. C2×#936D3semidirect
101. C2×C3×Dic6D4semidirect
145. C2×#237C2×D3semidirect
175. #936C2×D3semidirect
209. C22×C3⋊D3#41semidirect
238. C3×Dic6C2×D4semidirect
332. C2×Dic6#67semidirect
372. C2×C3⋊D3C2×#41semidirect
518. Dic6C2×#67semidirect
520. C2×C32#548semidirect
636. C32C2×#548semidirect
685. C2×C3#5677semidirect
686. C2×C3#5831semidirect
722. C3C2×#5677semidirect
723. C3C2×#5831semidirect
727. C2#10595237direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×#37972
C2×#641472
C2×C3×#9362
C2×#639642
C2×#639592
C2×#639582
C2×#639522
#105952372
C2×C4×#6262
C2×#638562
C2×Dic3×Dic62
C2×#58313
C2×#56773