Finite Group Databasebeta

← #11803593

Subgroups — #11803593

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×#63855C211yesmaximal, characteristic, complemented
4#10592920C211yesmaximal, characteristic, complemented
5#10591718C212yesmaximal, complemented
6#10591710C212yesmaximal, complemented
7#10591707C212yesmaximal, complemented
8#10591702C212yesmaximal, complemented
9#10591357C211yesmaximal, characteristic, complemented
10#10591313C211yesmaximal, characteristic, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#82633—31nomaximal
13#82396—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C2×#3757C2212yes—
19C2×#3757C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C3×#938C418yescomplemented
25C3×D4×Dic3—24no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2212yes—
36#63855—24no—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#121—31no—
41C2×C3×C4×D4—31no—
42C2×#938D311yescharacteristic
43C2×D4×Dic3D311yescharacteristic, complemented
44C2×#926—31no—
45C2×#872—31no—
46#5221—31no—
47#5221—31no—
48#5221—32no—
49#5221—61no—
50#5220—32no—
51#5213—32no—
52#5212—31no—
53#5210—32no—
54#4987—31no—
55#4984—31no—
56Dic3×C4⋊C4—31no—
57#4972—31no—
58#4957—32no—
59#4951—32no—
60#4950—32no—
61#4945—32no—
62C4×C4⋊Dic3—31no—
63C24×C32C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×D4—22no—
66C2×C32×D4—22no—
67C2×C32×D4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C3×#67—42no—
73C2×C3×#67—42no—
74C2×C3×#67C2×C418yescomplemented
75C22×C3×Dic3—24no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3C2×C414yescomplemented
86#3757—42no—
87#3757—42no—
88C4⋊(C3⋊Dic3)—22no—
89C4×C3⋊Dic3—22no—
90C3×#217—24no—
91C3×#217C2×C418yescomplemented
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3C2×C414yescomplemented
94C3×C4×Dic3D414yescomplemented
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—42no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—42no—
101Dic32—42no—
102#2324—91noSylow
103C22×C3×D4—21no—
104C22×C3×D4—32no—
105C22×C3×D4C2×D311yescharacteristic
106C22×C3×D4C2×D311yescharacteristic
107C23×C3×C4—31no—
108C23×C3×C4—32no—
109C22×#67C2×D312yes—
110C23×Dic3C2×D312yes—
111C22×C4×D3C2×D311yescharacteristic
112C3×#121—38no—
113C3×C4×D4—64no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—31no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—62no—
127C2×#217—62no—
128C2×#217C2×D312yes—
129C2×#217C2×D312yes—
130#938Dic318yescomplemented
131D4×Dic3—24no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—32no—
135#926—64no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—32no—
141C2×C4⋊Dic3—61no—
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—32no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3C2×D311yescharacteristic
153#872—64no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32C22×C414yes—
167C23×C32C2411yescharacteristic
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3—21no—
174C22×C3×D3C22×C412yes—
175C32×D4—28no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4#4112yes—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C3×#67—48no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—48no—
201C2×C3×Dic3C22×C414yes—
202C2×C3×Dic3C22×C412yes—
203C2×C3×Dic3C2×D412yes—
204C2×C3×Dic3C2×D412yes—
205C3×C4×D3—28no—
206C2×#121—31no—
207C2×C4×D4—31no—
208C2×#117—91no—
209#390—92no—
210#390—91no—
211#389—91no—
212#388—92no—
213#386—92no—
214#385—92no—
215#380—91no—
216C4×C4⋊C4—91no—
217C24×C3—22no—
218C24×C3—31no—
219C24×C3C22×D312yes—
220C24×C3C22×D312yes—
221C23×D3C22×D311yescharacteristic
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—24no—
227C2×C3×D4—38no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—122no—
231C2×C3×D4—122no—
232C2×C3×D4C4×D314yes—
233C2×C3×D4C2×Dic314yes—
234C22×C3×C4—21no—
235C22×C3×C4—32no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—34no—
240C22×C3×C4—32no—
241C22×C3×C4—64no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4—122no—
245C22×C3×C4—122no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—42no—
249C2×#67—42no—
250C2×#67C2×Dic318yescomplemented
251C22×Dic3—24no—
252C22×Dic3—31no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—42no—
259C22×Dic3—42no—
260C22×Dic3—61no—
261C22×Dic3—61no—
262C22×Dic3—62no—
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D311yescharacteristic
268C2×C4×D3—22no—
269C2×C4×D3—22no—
270C2×C4×D3C2×Dic314yescomplemented
271C3×C4⋊C4—34no—
272C3×C4⋊C4—62no—
273C3×C22⋊C4—38no—
274C3×C22⋊C4—64no—
275C3×C42—34no—
276#217—24no—
277#217—62no—
278#217—62no—
279#217—122no—
280#217—122no—
281#217—122no—
282#217—122no—
283#217—122no—
284#217—124no—
285#217—124no—
286#217C2×Dic318yescomplemented
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—122no—
290C4⋊Dic3—22no—
291C4⋊Dic3—62no—
292C4⋊Dic3—62no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295C4⋊Dic3—122no—
296C4⋊Dic3—122no—
297C4⋊Dic3C2×Dic314yescomplemented
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300Dic3⋊C4—122no—
301C4×Dic3—62no—
302C4×Dic3—62no—
303C4×Dic3—122no—
304C4×Dic3—122no—
305C4×Dic3—122no—
306C4×Dic3#6714yescomplemented
307C22×C32—24no—
308C22×C32—24no—
309C22×C32—24no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32C23×C411yescharacteristic
315C22×C32C22×D411yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C32H(5,𝔽2)11yescharacteristic
319C22×C32H(5,𝔽2)11yescharacteristic
320C22×C322−1+411yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4C4×D414yes—
329C3⋊Dic3—41no—
330C3⋊Dic3—41no—
331C3⋊Dic3—42no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C22×D4—32no—
338C22×D4D3211yescharacteristic
339C23×C4—31no—
340C23×C4—32no—
341#121—38no—
342C4×D4—64no—
343#117—184no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—91no—
348C2×C4⋊C4—91no—
349C2×C4⋊C4—92no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4—91no—
354C2×C22⋊C4—92no—
355C2×C22⋊C4—92no—
356C2×C22⋊C4—92no—
357C2×C42—31no—
358C2×C42—91no—
359C2×C42—92no—
360#95—92no—
361#95—92no—
362#95—92no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—21no—
376C23×C3—24no—
377C23×C3—32no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—61no—
390C23×C3C2×C4×D314yes—
391C23×C3C22×Dic314yes—
392C23×C3C23×D311yescharacteristic
393C23×C3C23×D311yescharacteristic
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3C22×Dic312yes—
401C3×D4—28no—
402C3×D4—28no—
403C3×D4—48no—
404C3×D4—128no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—32no—
409C2×C3×C4—34no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—68no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—128no—
425C2×C3×C4C2×C4×D312yes—
426C2×C3×C4#23512yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4#23712yes—
429C2×C3×C4C22×Dic312yes—
430C2×C3×C4C2×#6712yes—
431#67—48no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—48no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—61no—
448C2×Dic3—61no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—121no—
465C2×Dic3—121no—
466C2×Dic3—121no—
467C2×Dic3—121no—
468C2×Dic3—122no—
469C2×Dic3—122no—
470C2×Dic3—122no—
471C2×Dic3C22×Dic314yes—
472C2×Dic3C22×Dic312yes—
473C2×Dic3C2×#6712yes—
474C2×Dic3C2×#6712yes—
475C4×D3—28no—
476C2×C32—44no—
477C2×C32C2×C4×D411yescharacteristic
478C2×C32#51811yescharacteristic
479C2×C32#52011yescharacteristic
480C2×C32#53511yescharacteristic
481C2×C32#53711yescharacteristic
482C2×C32#54011yescharacteristic
483C2×C32#54211yescharacteristic
484C3×D3—42no—
485C24—31no—
486C24C2×D3212yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—38no—
490C2×D4—122no—
491C2×D4—122no—
492C2×D4D3×Dic314yes—
493C22×C4—31no—
494C22×C4—32no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—34no—
498C22×C4—32no—
499C22×C4—64no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—91no—
503C22×C4—92no—
504C22×C4—91no—
505C22×C4—122no—
506C22×C4—122no—
507C22×C4C2×D3211yescharacteristic
508C4⋊C4—34no—
509C4⋊C4—62no—
510C4⋊C4—182no—
511C4⋊C4—182no—
512C4⋊C4—182no—
513C4⋊C4—362no—
514C22⋊C4—38no—
515C22⋊C4—64no—
516C22⋊C4—182no—
517C22⋊C4—182no—
518C22⋊C4—362no—
519C22⋊C4—362no—
520C22⋊C4—362no—
521C42—34no—
522C42—182no—
523C42—362no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—62no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—82no—
552C22×C3—82no—
553C22×C3—82no—
554C22×C3—82no—
555C22×C3—121no—
556C22×C3—121no—
557C22×C3—121no—
558C22×C3—121no—
559C22×C3C22×C4×D311yescharacteristic
560C22×C3C2×#23511yescharacteristic
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C2×#23711yescharacteristic
563C22×C3#100411yescharacteristic
564C22×C3#100411yescharacteristic
565C22×C3#100411yescharacteristic
566C22×C3#100411yescharacteristic
567C22×C3#100911yescharacteristic
568C22×C3#100911yescharacteristic
569C22×C3#101011yescharacteristic
570C22×C3#101011yescharacteristic
571C22×C3C23×Dic311yescharacteristic
572C22×C3C22×#6711yescharacteristic
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C2×D3—41no—
580C3×C4—24no—
581C3×C4—62no—
582C3×C4—64no—
583C3×C4—62no—
584C3×C4—62no—
585C3×C4—122no—
586C3×C4C4×#6714yes—
587C3×C4D4×Dic314yes—
588Dic3—22no—
589Dic3—24no—
590Dic3—22no—
591Dic3—22no—
592Dic3—42no—
593Dic3—122no—
594Dic3—122no—
595Dic3—121no—
596Dic3—122no—
597Dic3—121no—
598Dic3—121no—
599Dic3—121no—
600Dic3—122no—
601Dic3—242no—
602C32#232411yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—32no—
610C23—61no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23C2×D3×Dic314yes—
617C23C22×D3211yescharacteristic
618D4—28no—
619D4—128no—
620C2×C4—32no—
621C2×C4—34no—
622C2×C4—32no—
623C2×C4—32no—
624C2×C4—61no—
625C2×C4—62no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—62no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—68no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—128no—
637C2×C4—181no—
638C2×C4—181no—
639C2×C4—182no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—182no—
643C2×C4—182no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4C2×D3×Dic312yes—
647C2×C4#380412yes—
648C2×C4D3×#6712yes—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—44no—
657C2×C3—44no—
658C2×C3—84no—
659C2×C3—122no—
660C2×C3#554511yescharacteristic
661C2×C3#554611yescharacteristic
662C2×C3#556111yescharacteristic
663C2×C3#556211yescharacteristic
664C2×C3#560311yescharacteristic
665C2×C3#560711yescharacteristic
666C2×C3#560811yescharacteristic
667C2×C3#561911yescharacteristic
668C2×C3C2×C4×#6711yescharacteristic
669C2×C3C2×D4×Dic311yescharacteristic
670C2×C3#579811yescharacteristic
671C2×C3#580511yescharacteristic
672C2×C3#582711yescharacteristic
673C2×C3#583311yescharacteristic
674D3—42no—
675C22—24no—
676C22—24no—
677C22—24no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—62no—
683C22—62no—
684C22—62no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22—121no—
689C22#6430911yescharacteristic
690C22#6431311yescharacteristic
691C22#6431411yescharacteristic
692C22#6431411yescharacteristic
693C22C22×D3×Dic311yescharacteristic
694C22C2×#380411yescharacteristic
695C22C2×D3×#6711yescharacteristic
696C4—64no—
697C4—62no—
698C4—62no—
699C4—62no—
700C4—122no—
701C4—362no—
702C4—361no—
703C4—361no—
704C4Dic3×#6714yes—
705C3—21no—
706C3#8239611yescharacteristic, complemented
707C3#8263311yescharacteristic, complemented
708C2—44no—
709C2—122no—
710C2#1059512411yescharacteristic
711C2#1059512511yescharacteristic
712C2#1059521511yescharacteristic
713C2#1059522211yescharacteristic
714C2#1059523111yescharacteristic
715C2#1059523211yescharacteristic
716C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×#63855C2semidirect
4. #10592920C2semidirect
5. #10591718C2semidirect
6. #10591710C2semidirect
7. #10591707C2semidirect
8. #10591702C2semidirect
9. #10591357C2semidirect
10. #10591313C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
24. C3×#938C4semidirect
43. C2×D4×Dic3D3semidirect
74. C2×C3×#67C2×C4semidirect
85. C2×C3×C4×D3C2×C4semidirect
91. C3×#217C2×C4semidirect
93. C3×C4⋊Dic3C2×C4semidirect
94. C3×C4×Dic3D4semidirect
130. #938Dic3semidirect
250. C2×#67C2×Dic3semidirect
270. C2×C4×D3C2×Dic3semidirect
286. #217C2×Dic3semidirect
297. C4⋊Dic3C2×Dic3semidirect
306. C4×Dic3#67semidirect
602. C32#2324semidirect
706. C3#82396semidirect
707. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C3×D4×Dic32
C2×#638552
#105929202
#105917182
#105917102
#105917072
#105917022
#105913572
#105913132
Dic3×C4⋊Dic32
#826333
#823963