Finite Group Databasebeta

← #13168459

Subgroups — #13168459

Order 1728.

1100 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
1#11723677C211yesmaximal, characteristic
2#11723443C211yesmaximal, characteristic, complemented
3#11723439C211yesmaximal, characteristic
4#11723406C211yesmaximal, characteristic, complemented
5C3×C4×#627C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic
7C3×#63844C211yesmaximal, characteristic, complemented
8#11723027C212yesmaximal, complemented
9#11723023C212yesmaximal, complemented
10#11722970C212yesmaximal, complemented
11#11722915C212yesmaximal, complemented
12#10594335—31nomaximal
13#10593879—31nomaximal
14#10593850—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C3×#627C2211yescharacteristic
19C2×C3×#624C2212yes—
20C3×C4×C3⋊Dic3C2211yescharacteristic
21C32×C4⋊Dic3C2211yescharacteristic
22C32×C4×Dic3C2211yescharacteristic
23C32×C4×Dic3C2211yescharacteristic
24#88814C2212yes—
25#88814C2212yes—
26#88806C2212yes—
27Dic3⋊(C3⋊Dic3)C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29#88803C2212yes—
30#88803C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×#3724C2211yescharacteristic
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38#64096—31no—
39#64084—31no—
40#64078—31no—
41C3×#893—31no—
42C3×#887—31no—
43C3×C4×D12—31no—
44C3×C4×Dic6—31no—
45C3×C4×Dic6—31no—
46C3×C4×Dic6—31no—
47C4×#627D311yescharacteristic, complemented
48#63894D311yescharacteristic
49#63888—32no—
50#63868—32no—
51#63866—31no—
52#63866—31no—
53#63866—61no—
54#63864—31no—
55#63863—31no—
56#63862—32no—
57#63861—32no—
58#63861—32no—
59#63860—31no—
60#63860—31no—
61#63860—31no—
62#63860—61no—
63#63859—32no—
64#63856—32no—
65#63855—32no—
66#63851—32no—
67#63848—32no—
68#63844—31no—
69#63844—31no—
70#63844—61no—
71#63844D311yescharacteristic, complemented
72#63841—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77#6308—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4⋊(C3⋊D3)—22no—
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C3×#627—22no—
89C3×#624—24no—
90#5584—91no—
91#5568—91no—
92#5542—91no—
93C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
94C2×#634—31no—
95C2×#634—31no—
96C2×#634—31no—
97C2×#634—61no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—121no—
101C2×#634C2×D311yescharacteristic
102C2×C3×D12—31no—
103C2×C3×D12—31no—
104C2×C3×D12—61no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—32no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—61no—
112C2×#627C2×D311yescharacteristic
113C2×#624C2×D312yes—
114C32×C4⋊C4—31no—
115C32×C42—31no—
116C32×C42—31no—
117#3752—32no—
118#3752—32no—
119C4⋊(C3⋊Dic3)—32no—
120C4⋊(C3⋊Dic3)—32no—
121#3750—32no—
122C4×C3⋊Dic3—32no—
123C4×C3⋊Dic3C2×D311yescharacteristic
124C3×(C2×D3)⋊C4—32no—
125C3×(C2×D3)⋊C4—32no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—31no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3C2×D311yescharacteristic
130C3×C4⋊Dic3C2×D311yescharacteristic
131C3×Dic3⋊C4—32no—
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4—32no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—32no—
142C3×C4×Dic3—32no—
143C3×C4×Dic3—61no—
144C3×C4×Dic3C2×D311yescharacteristic
145C3×C4×Dic3C2×D311yescharacteristic
146C3×C4×Dic3C2×D311yescharacteristic
147C3×C4×Dic3C2×D311yescharacteristic
148#3724—32no—
149#3724—32no—
150#3724—62no—
151#3724C2×D312yes—
152#3724C2×D311yescharacteristic
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—62no—
158Dic3⋊Dic3—62no—
159Dic3⋊Dic3C2×D311yescharacteristic
160Dic3⋊Dic3C2×D311yescharacteristic
161#3722—32no—
162#3722—32no—
163#3722C2×D312yes—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—62no—
173(C2×D3)⋊Dic3—62no—
174Dic32—32no—
175Dic32—32no—
176Dic32—62no—
177Dic32C2×D312yes—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C33×C4#4112yes—
183C3⋊(C3⋊Dic3)—22no—
184C3×C3⋊Dic3—21no—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—21no—
187C32×Dic3—22no—
188C32×Dic3—21no—
189C32×Dic3—21no—
190C32×Dic3—21no—
191C32×Dic3#4112yes—
192C3×C4×Q8—91no—
193C3×C4×Q8—91no—
194C3×C4×D4—91no—
195#947—91no—
196#946—92no—
197#944—91no—
198#936—91no—
199#936—91no—
200#926—92no—
201#924—92no—
202#898—92no—
203#898—92no—
204#898—92no—
205#896—92no—
206#893—31no—
207#892—92no—
208#887—31no—
209#887—91no—
210#887—91no—
211#887—181no—
212#879—92no—
213#879—92no—
214#876—92no—
215#875—91no—
216#875—91no—
217#875—91no—
218#875—181no—
219C4×D12—31no—
220#872—92no—
221#869—91no—
222#869—91no—
223#869—181no—
224C4×Dic6—31no—
225C4×Dic6—31no—
226C4×Dic6—31no—
227C4×Dic6—91no—
228C22×C3⋊D3C22×D312yes—
229C22×C3×D3—32no—
230C22×C3×D3—32no—
231C22×C3×D3—62no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—31no—
236C2×C32×C4—31no—
237C2×C32×C4—32no—
238C2×C32×C4—31no—
239C2×C32×C4—31no—
240C2×C32×C4—41no—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C3⋊Dic3—32no—
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—32no—
247C2×C3⋊Dic3—62no—
248C2×C3⋊Dic3—62no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—122no—
251C2×C3⋊Dic3C22×D312yes—
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C4⋊(C3⋊D3)—22no—
255#634—22no—
256#634—62no—
257#634—64no—
258#634—62no—
259#634—62no—
260#634—122no—
261#634—122no—
262#634—124no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3C22×D312yes—
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C3×D12—62no—
288C3×D12—62no—
289C3×D12—122no—
290C3×C4×D3—64no—
291C3×C4×D3—64no—
292C3×Dic6—62no—
293C3×Dic6—62no—
294C3×Dic6—62no—
295C3×Dic6—62no—
296C3×Dic6—122no—
297#627—22no—
298#624—24no—
299#556—271noSylow
300C2×C33C2×#4111yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C2×C332−1+411yescharacteristic
303C3×C3⋊D3—42no—
304C2×C3×Q8—91no—
305C2×C3×Q8—91no—
306C2×C3×D4—91no—
307C22×C3×C4—92no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×C4×D3—32no—
312C2×C4×D3—32no—
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—61no—
318C2×Dic6—91no—
319C2×Dic6—91no—
320C2×Dic6—91no—
321C2×Dic6—181no—
322C2×Dic6—181no—
323C2×Dic6—181no—
324C2×Dic6—361no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—92no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C22⋊C4—92no—
333C3×C42—31no—
334C3×C42—31no—
335C3×C42—31no—
336C3×C42—31no—
337C3×C42—61no—
338C3×C42—61no—
339C3×C42—92no—
340C3×C42—91no—
341#217—92no—
342#217—92no—
343#217—92no—
344#217—92no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—32no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—182no—
356(C2×D3)⋊C4—182no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—182no—
364C4⋊Dic3—182no—
365C4⋊Dic3D3211yescharacteristic
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—182no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—32no—
381C4×Dic3—32no—
382C4×Dic3—61no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C4×Dic3—92no—
386C4×Dic3—182no—
387C4×Dic3D3211yescharacteristic
388C4×Dic3D3211yescharacteristic
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—41no—
393C22×C32C23×D311yescharacteristic
394C22×C32C23×D311yescharacteristic
395C22×C32C23×D311yescharacteristic
396C2×C3⋊D3—22no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—122no—
406C2×C3×D3—122no—
407C2×C3×D3—122no—
408C32×C4—22no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—32no—
412C32×C4—42no—
413C32×C4—61no—
414C32×C4—62no—
415C32×C4—61no—
416C32×C4—61no—
417C32×C4#23512yes—
418C32×C4#23512yes—
419C32×C4#23912yes—
420C3⋊Dic3—21no—
421C3⋊Dic3—21no—
422C3⋊Dic3—22no—
423C3⋊Dic3—62no—
424C3⋊Dic3—64no—
425C3⋊Dic3—62no—
426C3⋊Dic3—62no—
427C3⋊Dic3—122no—
428C3⋊Dic3—122no—
429C3⋊Dic3—124no—
430C3×Dic3—22no—
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—22no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—22no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—42no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—62no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—122no—
451C3×Dic3—121no—
452C3×Dic3#23512yes—
453C3×Dic3#23712yes—
454C4⋊Q8—271no—
455#126—272no—
456#126—272no—
457#124—271no—
458#124—271no—
459C22⋊Q8—272no—
460C4×Q8—91no—
461C4×Q8—91no—
462C4×Q8—271no—
463C4×D4—91no—
464#117—272no—
465C33#55611yescharacteristic, complemented, Sylow
466C23×C3—92no—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—62no—
470C3×Q8—182no—
471C3×Q8—182no—
472C3×D4—182no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—91no—
493C2×C3×C4—92no—
494C2×C3×C4—91no—
495C2×C3×C4—184no—
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—62no—
508C2×Dic3—92no—
509C2×Dic3—92no—
510C2×Dic3—92no—
511C2×Dic3—182no—
512C2×Dic3—182no—
513C2×Dic3—182no—
514C2×Dic3—362no—
515C2×Dic3C2×D3211yescharacteristic
516C2×Dic3C2×D3212yes—
517C2×Dic3C2×D3211yescharacteristic
518C2×Dic3C2×D3211yescharacteristic
519C2×Dic3C2×D3211yescharacteristic
520D12—62no—
521D12—62no—
522D12—122no—
523C4×D3—64no—
524C4×D3—64no—
525Dic6—62no—
526Dic6—62no—
527Dic6—62no—
528Dic6—62no—
529Dic6—122no—
530Dic6—184no—
531Dic6—182no—
532Dic6—182no—
533Dic6—182no—
534Dic6—362no—
535Dic6—362no—
536Dic6—364no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—41no—
547C2×C32—41no—
548C2×C32—41no—
549C2×C32C2×#23511yescharacteristic
550C2×C32C2×#23511yescharacteristic
551C2×C32C2×#23511yescharacteristic
552C2×C32C2×#23711yescharacteristic
553C2×C32C2×#23911yescharacteristic
554C2×C32#100711yescharacteristic
555C2×C32D3×#4111yescharacteristic
556C2×C32#101011yescharacteristic
557C2×C32#101011yescharacteristic
558C3⋊D3—42no—
559C3×D3—122no—
560C3×D3—122no—
561C3×D3—242no—
562C2×Q8—91no—
563C2×Q8—91no—
564C2×Q8—271no—
565C2×D4—91no—
566C22×C4—92no—
567C4⋊C4—31no—
568C4⋊C4—91no—
569C4⋊C4—92no—
570C4⋊C4—91no—
571C4⋊C4—91no—
572C4⋊C4—272no—
573C4⋊C4—272no—
574C4⋊C4—272no—
575C22⋊C4—92no—
576C22⋊C4—272no—
577C22⋊C4—272no—
578C22⋊C4—272no—
579C22⋊C4—272no—
580C42—31no—
581C42—31no—
582C42—92no—
583C42—91no—
584C42—272no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—41no—
589C22×C3—182no—
590C22×C3—182no—
591C22×C3—182no—
592C22×C3C22×D3211yescharacteristic
593C22×C3C22×D3211yescharacteristic
594C22×C3C22×D3211yescharacteristic
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—122no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—32no—
608C3×C4—32no—
609C3×C4—42no—
610C3×C4—62no—
611C3×C4—62no—
612C3×C4—61no—
613C3×C4—62no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—62no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—122no—
621C3×C4—121no—
622C3×C4—121no—
623C3×C4—182no—
624C3×C4—181no—
625C3×C4—181no—
626C3×C4#379812yes—
627C3×C4#379912yes—
628C3×C4#379912yes—
629Dic3—21no—
630Dic3—21no—
631Dic3—21no—
632Dic3—22no—
633Dic3—62no—
634Dic3—61no—
635Dic3—61no—
636Dic3—61no—
637Dic3—62no—
638Dic3—62no—
639Dic3—61no—
640Dic3—122no—
641Dic3—121no—
642Dic3—184no—
643Dic3—182no—
644Dic3—182no—
645Dic3—182no—
646Dic3—362no—
647Dic3—362no—
648Dic3—364no—
649Dic3#379512yes—
650C32—21no—
651C32—21no—
652C32—21no—
653C32—41no—
654C32#554211yescharacteristic, complemented
655C32#556811yescharacteristic, complemented
656C32#558411yescharacteristic, complemented
657C23—92no—
658Q8—182no—
659Q8—182no—
660Q8—542no—
661D4—182no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—32no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—92no—
670C2×C4—184no—
671C2×C4—272no—
672C2×C4D3311yescharacteristic
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—362no—
686C2×C3C2×#379511yescharacteristic
687C2×C3#6429711yescharacteristic
688C2×C3#6429811yescharacteristic
689C2×C3C2×#379811yescharacteristic
690C2×C3C2×#379911yescharacteristic
691C2×C3C2×#379911yescharacteristic
692C2×C3D3×#23511yescharacteristic
693C2×C3D3×#23711yescharacteristic
694C2×C3#6431511yescharacteristic
695D3—122no—
696D3—122no—
697D3—242no—
698C22—182no—
699C22—182no—
700C22—182no—
701C22C2×D3311yescharacteristic
702C4—32no—
703C4—62no—
704C4—61no—
705C4—61no—
706C4—61no—
707C4—181no—
708C4—181no—
709C4—182no—
710C4—542no—
711C4#8896512yes—
712C3—21no—
713C3—21no—
714C3—21no—
715C3—41no—
716C3#1059385011yescharacteristic, complemented
717C3#1059387911yescharacteristic, complemented
718C3#1059433511yescharacteristic, complemented
719C2—362no—
720C2D3×#379511yescharacteristic
721C2#1172439611yescharacteristic
722C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723443C2semidirect
4. #11723406C2semidirect
5. C3×C4×#627C2semidirect
7. C3×#63844C2semidirect
8. #11723027C2semidirect
9. #11723023C2semidirect
10. #11722970C2semidirect
11. #11722915C2semidirect
47. C4×#627D3semidirect
71. #63844D3semidirect
465. C33#556semidirect
654. C32#5542semidirect
655. C32#5568semidirect
656. C32#5584semidirect
716. C3#10593850semidirect
717. C3#10593879semidirect
718. C3#10594335semidirect

Maximal subgroups

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

subgroupindex
#117236772
#117234432
#117234392
#117234062
C3×C4×#6272
C3×#638942
C3×#638442
#117230272
#117230232
#117229702
#117229152
#105943353
#105938793
#105938503