Finite Group Databasebeta

← #13178726

Subgroups — #13178726

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
1C3×#64156C211yesmaximal, characteristic
2C3×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#64153C211yesmaximal, characteristic, complemented
4C4×#6296C211yesmaximal, characteristic, complemented
5#11723692C212yesmaximal, complemented
6#11723691C211yesmaximal, characteristic
7#11723683C212yesmaximal, complemented
8#11723677C211yesmaximal, characteristic
9#11723676C212yesmaximal, complemented
10#11723675C212yesmaximal, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595389—31nomaximal
13#10595387—31nomaximal
14#10595384—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×#6296C2211yescharacteristic
19C2×#6294C2212yes—
20C3×#3752C2212yes—
21C3×#3752C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2212yes—
24C3×#3750C2212yes—
25C3×#3750C2212yes—
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C3×C4×C3⋊Dic3C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2212yes—
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88814C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88813C2212yes—
38#64156D311yescharacteristic
39Q8×C3⋊Dic3D311yescharacteristic, complemented
40#64153D311yescharacteristic, complemented
41C3×#947—31no—
42C3×#947—31no—
43C3×#947—61no—
44C3×Q8×Dic3—31no—
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—61no—
47C3×#944—31no—
48C3×#944—31no—
49C3×#944—61no—
50C4×#627—31no—
51C4×#627—31no—
52C4×#627—31no—
53#63899—32no—
54#63898—31no—
55#63895—32no—
56#63894—31no—
57#63893—32no—
58Dic3×D12—31no—
59#63878—32no—
60#63877—32no—
61#63868—32no—
62#63864—31no—
63#63863—31no—
64#63862—32no—
65#63861—32no—
66#63860—31no—
67#63859—32no—
68#63858—32no—
69#63848—32no—
70#63844—31no—
71#63843—31no—
72Dic3×Dic6—31no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C33×Q8—22no—
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C3×C4⋊(C3⋊D3)—22no—
87C3×#634—22no—
88#6296—22no—
89#6294—24no—
90#5732—91no—
91#5671—91no—
92#5568—91no—
93C2×C32×Q8—21no—
94C2×C32×Q8—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—41no—
97C2×C32×Q8C2×D311yescharacteristic
98C2×C32×Q8C2×D311yescharacteristic
99C2×C32×Q8C2×D311yescharacteristic
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×#634C2×D311yescharacteristic
102C2×C3×D12—31no—
103C2×C3×D12—31no—
104C2×C3×D12—61no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—61no—
108C2×#627—31no—
109C2×#627—31no—
110C2×#627—31no—
111C2×#624—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114#3752C2×D312yes—
115#3752C2×D312yes—
116C4⋊(C3⋊Dic3)C2×D311yescharacteristic
117C4⋊(C3⋊Dic3)C2×D312yes—
118#3750C2×D312yes—
119#3750C2×D312yes—
120C4×C3⋊Dic3C2×D311yescharacteristic
121C4×C3⋊Dic3C2×D312yes—
122C4×C3⋊Dic3C2×D311yescharacteristic
123C4×C3⋊Dic3C2×D311yescharacteristic
124C3×(C2×D3)⋊C4—32no—
125C3×(C2×D3)⋊C4—32no—
126C3×(C2×D3)⋊C4—32no—
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—62no—
129C3×(C2×D3)⋊C4—62no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—61no—
135C3×C4⋊Dic3—62no—
136C3×Dic3⋊C4—32no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—62no—
141C3×Dic3⋊C4—62no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—61no—
151C3×C4×Dic3—61no—
152C3×C4×Dic3—62no—
153C3×C4×Dic3—61no—
154#3724—32no—
155#3724—31no—
156#3724—31no—
157#3724—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166#3722—32no—
167#3722—32no—
168#3722—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C33×C4—22no—
183C33×C4#4112yes—
184C3×C3⋊Dic3—22no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3#4112yes—
192C3×C4⋊Q8—91no—
193C3×#124—91no—
194C3×C4×Q8—91no—
195#947—31no—
196#947—31no—
197#947—61no—
198#947—91no—
199Q8×Dic3—31no—
200Q8×Dic3—31no—
201Q8×Dic3—61no—
202Q8×Dic3—91no—
203#944—31no—
204#944—31no—
205#944—61no—
206#936—91no—
207D4×Dic3—91no—
208#898—92no—
209#898—92no—
210#898—92no—
211#897—92no—
212#896—92no—
213#893—91no—
214#892—92no—
215#887—91no—
216#879—92no—
217#879—92no—
218#878—92no—
219#877—92no—
220#876—92no—
221#875—91no—
222C4×D12—91no—
223#872—92no—
224C4×Dic6—91no—
225C4×Dic6—91no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C22×C3⋊D3C22×D312yes—
229C22×C3×D3—32no—
230C22×C3×D3—32no—
231C22×C3×D3—62no—
232C32×Q8—22no—
233C32×Q8—24no—
234C32×Q8—22no—
235C32×Q8—22no—
236C32×Q8—42no—
237C32×Q8—42no—
238C32×Q8—44no—
239C2×C32×C4—22no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—22no—
244C2×C32×C4—22no—
245C2×C32×C4—41no—
246C2×C32×C4—42no—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D312yes—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D312yes—
255C2×C3⋊Dic3C22×D312yes—
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C4⋊(C3⋊D3)—22no—
262#634—22no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—62no—
287C3×D12—62no—
288C3×D12—62no—
289C3×D12—122no—
290C3×Dic6—62no—
291C3×Dic6—62no—
292C3×Dic6—122no—
293#627—62no—
294#627—62no—
295#627—62no—
296#624—64no—
297D3×Dic3—64no—
298D3×Dic3—64no—
299#556—271noSylow
300C2×C33C2×#4111yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C2×C332−1+411yescharacteristic
303C3×C3⋊D3—42no—
304C2×C3×Q8—21no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—41no—
308C2×C3×Q8—91no—
309C2×C3×Q8D3211yescharacteristic
310C2×C3×Q8D3211yescharacteristic
311C2×C3×Q8D3211yescharacteristic
312C2×C3×D4—91no—
313C22×Dic3—92no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×C4×D3—92no—
318C2×C4×D3—92no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C2×Dic6—91no—
323C2×Dic6—91no—
324C2×Dic6—91no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—92no—
327C3×C4⋊C4—92no—
328C3×C4⋊C4—92no—
329C3×C22⋊C4—92no—
330C3×C22⋊C4—92no—
331C3×C42—91no—
332C3×C42—91no—
333C3×C42—91no—
334C3×C42—92no—
335#217—92no—
336#217—92no—
337#217—92no—
338(C2×D3)⋊C4—32no—
339(C2×D3)⋊C4—32no—
340(C2×D3)⋊C4—32no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344(C2×D3)⋊C4—92no—
345(C2×D3)⋊C4—92no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—32no—
353C4⋊Dic3—32no—
354C4⋊Dic3—61no—
355C4⋊Dic3—62no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—92no—
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—92no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—92no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—32no—
381C4×Dic3—32no—
382C4×Dic3—61no—
383C4×Dic3—62no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—92no—
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—24no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—42no—
416C32×C4—42no—
417C32×C4—42no—
418C32×C4—44no—
419C32×C4#23512yes—
420C32×C4#23712yes—
421C32×C4#23712yes—
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—22no—
425C3⋊Dic3—22no—
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3#23912yes—
430C3×Dic3—32no—
431C3×Dic3—32no—
432C3×Dic3—62no—
433C3×Dic3—62no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—62no—
437C3×Dic3—62no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3—61no—
441C3×Dic3—61no—
442C3×Dic3—61no—
443C3×Dic3—61no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—122no—
450C3×Dic3—121no—
451C3×Dic3—121no—
452C3×Dic3—121no—
453C3×Dic3—122no—
454C4⋊Q8—91no—
455#126—272no—
456#126—272no—
457#124—91no—
458#124—271no—
459C22⋊Q8—272no—
460C4×Q8—91no—
461C4×Q8—271no—
462C4×Q8—271no—
463C4×D4—271no—
464#117—272no—
465C33#55611yescharacteristic, complemented, Sylow
466C23×C3—92no—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—62no—
470C3×Q8—24no—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C3×Q8—42no—
476C3×Q8—44no—
477C3×Q8—182no—
478C3×D4—182no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—42no—
486C2×C3×C4—41no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—92no—
490C2×C3×C4—92no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4C2×D3212yes—
496C2×C3×C4C2×D3212yes—
497C2×C3×C4C2×D3212yes—
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500C2×C3×C4C2×D3211yescharacteristic
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—62no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—62no—
525C2×Dic3—184no—
526D12—62no—
527D12—62no—
528D12—122no—
529C4×D3—184no—
530C4×D3—184no—
531Dic6—62no—
532Dic6—62no—
533Dic6—122no—
534Dic6—182no—
535Dic6—182no—
536Dic6—182no—
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×#23711yescharacteristic
551C2×C32C2×#23711yescharacteristic
552C2×C32C2×#23911yescharacteristic
553C2×C32#100711yescharacteristic
554C2×C32#100711yescharacteristic
555C2×C32D3×#4111yescharacteristic
556C2×C32D3×#4111yescharacteristic
557C2×C32#101011yescharacteristic
558C3⋊D3—42no—
559C3×D3—122no—
560C3×D3—122no—
561C3×D3—242no—
562C2×Q8—91no—
563C2×Q8—271no—
564C2×Q8#111311yescharacteristic
565C2×D4—91no—
566C22×C4—272no—
567C4⋊C4—92no—
568C4⋊C4—91no—
569C4⋊C4—92no—
570C4⋊C4—92no—
571C4⋊C4—271no—
572C4⋊C4—272no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C22⋊C4—92no—
576C22⋊C4—92no—
577C22⋊C4—272no—
578C22⋊C4—272no—
579C22⋊C4—272no—
580C42—92no—
581C42—91no—
582C42—91no—
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—24no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—44no—
614C3×C4—42no—
615C3×C4—92no—
616C3×C4—181no—
617C3×C4—181no—
618C3×C4—181no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4—182no—
622C3×C4—182no—
623C3×C4#380412yes—
624C3×C4#380412yes—
625C3×C4#380512yes—
626Dic3—32no—
627Dic3—32no—
628Dic3—62no—
629Dic3—62no—
630Dic3—62no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—61no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—62no—
640Dic3—61no—
641Dic3—61no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—121no—
647Dic3—122no—
648Dic3—121no—
649Dic3—121no—
650C32—21no—
651C32—21no—
652C32—21no—
653C32—41no—
654C32#556811yescharacteristic, complemented
655C32#567111yescharacteristic, complemented
656C32#573211yescharacteristic, complemented
657C23—92no—
658Q8—22no—
659Q8—182no—
660Q8—542no—
661D4—182no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—92no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—92no—
670C2×C4—544no—
671C2×C4C2×#111312yes—
672C2×C4C2×#111311yescharacteristic
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×C3#6431511yescharacteristic
687C2×C3#6431511yescharacteristic
688C2×C3#6431611yescharacteristic
689C2×C3D3×#23911yescharacteristic
690C2×C3D3×#23911yescharacteristic
691C2×C3#6431911yescharacteristic
692C2×C3C2×#380411yescharacteristic
693C2×C3C2×#380411yescharacteristic
694C2×C3C2×#380511yescharacteristic
695D3—122no—
696D3—122no—
697D3—242no—
698C22—182no—
699C22—182no—
700C22—182no—
701C22C22×#111311yescharacteristic
702C4—22no—
703C4—92no—
704C4—181no—
705C4—181no—
706C4—181no—
707C4—182no—
708C4—181no—
709C4—181no—
710C4—182no—
711C4#8904612yes—
712C3—21no—
713C3—21no—
714C3—21no—
715C3—41no—
716C3#1059538411yescharacteristic, complemented
717C3#1059538711yescharacteristic, complemented
718C3#1059538911yescharacteristic, complemented
719C2—362no—
720C2#1172462411yescharacteristic
721C2#1172462611yescharacteristic
722C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC2×Q8#1113
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×C3⋊Dic3C2semidirect
3. C3×#64153C2semidirect
4. C4×#6296C2semidirect
5. #11723692C2semidirect
7. #11723683C2semidirect
9. #11723676C2semidirect
10. #11723675C2semidirect
11. #11723668C2semidirect
39. Q8×C3⋊Dic3D3semidirect
40. #64153D3semidirect
465. C33#556semidirect
654. C32#5568semidirect
655. C32#5671semidirect
656. C32#5732semidirect
716. C3#10595384semidirect
717. C3#10595387semidirect
718. C3#10595389semidirect

Maximal subgroups

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

subgroupindex
C3×#641562
C3×Q8×C3⋊Dic32
C3×#641532
C4×#62962
#117236922
#117236912
#117236832
#117236772
#117236762
#117236752
#117236682
#105953893
#105953873
#105953843