Finite Group Databasebeta

← #13170792

Subgroups — #13170792

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88957C211yesmaximal, characteristic, complemented
2C2×#88949C211yesmaximal, characteristic
3#11723700C211yesmaximal, characteristic
4#11723502C212yesmaximal, complemented
5C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#63900C211yesmaximal, characteristic, complemented
7C3×#63895C212yesmaximal, complemented
8#11722983C212yesmaximal, complemented
9#11722970C212yesmaximal, complemented
10#11722911C211yesmaximal, characteristic, complemented
11#11722905C211yesmaximal, characteristic
12#10594631—31nomaximal
13D3×#896—32nomaximal
14C22×#1113C2211yescharacteristic
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×#6294C2211yescharacteristic
17C2×#6293C2212yescomplemented
18C2×Dic3×C3⋊D3C2212yes—
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×C3×#627C2212yescomplemented
22C2×C3×#624C2211yescharacteristic
23C2×C3×#624C2212yes—
24C2×C3×#624C2211yescharacteristic
25#88957—24no—
26#88949—24no—
27#88857C2211yescharacteristic, complemented
28C3×#3752C2212yes—
29C32×C4⋊Dic3C2212yescomplemented
30C32×Dic3⋊C4C2211yescharacteristic, complemented
31#88814C2212yes—
32#88806C2212yescomplemented
33#88806C2211yescharacteristic, complemented
34Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35#88803C2212yes—
36C3×#3724C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×#3722C2212yes—
39C2×C4×D32—32no—
40C2×C4×D32—31no—
41C2×#3797—31no—
42C2×D3×Dic6—32no—
43#64105—32no—
44C4⋊C4×C3⋊D3—31no—
45C3×#897—32no—
46C3×#896—32no—
47C3×D3×C4⋊C4—32no—
48#63921—31no—
49#63921—31no—
50D3×(C2×D3)⋊C4—32no—
51D3×(C2×D3)⋊C4—32no—
52#63900—31no—
53#63900D311yescharacteristic, complemented
54#63899—32no—
55#63899—32no—
56#63899—32no—
57#63899—62no—
58#63896—32no—
59#63895D312yescomplemented
60#63888—32no—
61D3×Dic3⋊C4—32no—
62D3×Dic3⋊C4—32no—
63D3×Dic3⋊C4—61no—
64#63865—32no—
65#63856—32no—
66#63851—32no—
67C22×C3×C3⋊D3C2312yes—
68C22×C3×C3⋊D3C2311yescharacteristic
69C2×#1113—22no—
70C2×#1113—22no—
71C2×#1113Q814yescomplemented
72C2×C33×C4C2311yescharacteristic
73C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3×C3⋊Dic3C2312yes—
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C3×C4×C3⋊D3—22no—
78C2×C32×Dic3C2312yes—
79C2×C32×Dic3C2312yes—
80C2×C32×Dic3C2311yescharacteristic
81C2×C32×Dic3C2311yescharacteristic
82#6294—22no—
83#6293—24no—
84Dic3×C3⋊D3—22no—
85Dic3×C3⋊D3—24no—
86Dic3×C3⋊D3D414yes—
87C3×#627—24no—
88C3×#624—22no—
89C3×#624—22no—
90C3×#624—24no—
91D3×C22⋊Q8—92no—
92C2×#896—91no—
93C22×D32—32no—
94C22×D32—31no—
95C2×C4×C3⋊D3—31no—
96C2×C4×C3⋊D3—32no—
97C2×C4×C3⋊D3—31no—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634—32no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—32no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—32no—
108C2×#627—32no—
109C2×#627—32no—
110C2×#627—62no—
111C2×#627C2×D312yescomplemented
112C2×#624—31no—
113C2×#624C2×D311yescharacteristic
114C2×#624C2×D312yes—
115C2×#624C2×D311yescharacteristic
116C2×D3×Dic3—32no—
117C2×D3×Dic3—32no—
118C2×D3×Dic3—32no—
119C2×D3×Dic3—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—61no—
122C2×D3×Dic3—61no—
123C2×D3×Dic3—62no—
124C4×D32—68no—
125C4×D32—64no—
126#3797—64no—
127D3×Dic6—68no—
128C32×C4⋊C4—32no—
129C32×C4⋊C4—31no—
130#3752—32no—
131#3752C2×D312yes—
132C4⋊(C3⋊Dic3)—31no—
133#3750—31no—
134#3750—32no—
135#3750—31no—
136#3750—32no—
137#3750—61no—
138#3750—62no—
139#3750—121no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—62no—
145C3×C4⋊Dic3—22no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3C2×D312yescomplemented
148C3×C4⋊Dic3C2×D312yescomplemented
149C3×Dic3⋊C4—21no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4C2×D312yescomplemented
154#3724—32no—
155#3724—32no—
156#3724—32no—
157#3724—61no—
158#3724—62no—
159#3724C2×D312yescomplemented
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—61no—
162Dic3⋊Dic3C2×D312yescomplemented
163#3722—32no—
164#3722C2×D312yes—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—62no—
170C22×C33C2411yescharacteristic
171C2×C3×C3⋊D3—22no—
172C2×C3×C3⋊D3—22no—
173C2×C3×C3⋊D3C2×D412yes—
174C2×C3×C3⋊D3C2×Q812yes—
175C2×C3×C3⋊D3C2×Q814yescomplemented
176C2×C3×C3⋊D3#4112yes—
177#1113—28no—
178C33×C4—21no—
179C3⋊(C3⋊Dic3)—21no—
180C3⋊(C3⋊Dic3)C2×D412yes—
181C3×C3⋊Dic3—22no—
182C3×C3⋊Dic3—21no—
183C32×Dic3—22no—
184C32×Dic3—22no—
185C32×Dic3—21no—
186C32×Dic3C2×D412yes—
187C2×D3×Q8—92no—
188C22×C4×D3—91no—
189C22×C4×D3—92no—
190C22×Dic6—91no—
191C3×C22⋊Q8—92no—
192C2×C3×C4⋊C4—91no—
193#946—92no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196#924—92no—
197C2×Dic3⋊C4—91no—
198C2×Dic3⋊C4—91no—
199#897—32no—
200#896—32no—
201#896—92no—
202#896—92no—
203#896—92no—
204#896—92no—
205#896—92no—
206#896—182no—
207D3×C4⋊C4—32no—
208D3×C4⋊C4—92no—
209D3×C4⋊C4—92no—
210D3×C4⋊C4—181no—
211D3×C22⋊C4—92no—
212D3×C22⋊C4—92no—
213#878—92no—
214#878—92no—
215C22×C3⋊D3C22×D312yes—
216C22×C3⋊D3C22×D311yescharacteristic
217C22×C3×D3—32no—
218C22×C3×D3—32no—
219C22×C3×D3—32no—
220C22×C3×D3—61no—
221C22×C3×D3—62no—
222C2×D32—34no—
223C2×D32—38no—
224C2×D32—64no—
225C2×D32—64no—
226C2×D32—62no—
227C2×D32—62no—
228C2×C32×C4—21no—
229C2×C32×C4—22no—
230C2×C32×C4—31no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—31no—
234C2×C32×C4—41no—
235C2×C32×C4C22×D312yes—
236C2×C32×C4C22×D311yescharacteristic
237C2×C3⋊Dic3—32no—
238C2×C3⋊Dic3—31no—
239C2×C3⋊Dic3—31no—
240C2×C3⋊Dic3—32no—
241C2×C3⋊Dic3—61no—
242C2×C3⋊Dic3—62no—
243C2×C3⋊Dic3—62no—
244C2×C3⋊Dic3—61no—
245C2×C3⋊Dic3—121no—
246C2×C3⋊Dic3—121no—
247C2×C3⋊Dic3C22×D311yescharacteristic
248C2×C3⋊Dic3C22×D312yes—
249C4×C3⋊D3—22no—
250C4×C3⋊D3—34no—
251C4×C3⋊D3—64no—
252C4×C3⋊D3—62no—
253#634—64no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—61no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3C22×D312yes—
264C2×C3×Dic3C22×D312yes—
265C2×C3×Dic3C22×D312yes—
266C2×C3×Dic3C22×D312yes—
267C2×C3×Dic3C22×D312yes—
268C2×C3×Dic3C22×D312yes—
269C3×C4×D3—64no—
270C3×C4×D3—64no—
271C3×C4×D3—64no—
272C3×C4×D3—64no—
273C3×C4×D3—64no—
274C3×C4×D3—122no—
275C3×Dic6—64no—
276C3×Dic6—64no—
277#627—24no—
278#627—64no—
279#627—64no—
280#627—124no—
281#624—22no—
282#624—22no—
283#624—24no—
284#624—62no—
285D3×Dic3—38no—
286D3×Dic3—64no—
287D3×Dic3—64no—
288D3×Dic3—64no—
289D3×Dic3—64no—
290D3×Dic3—64no—
291D3×Dic3—124no—
292D3×Dic3—122no—
293C2×C22⋊Q8—271noSylow
294C2×C33C22×D411yescharacteristic
295C2×C33C22×Q811yescharacteristic
296C2×C33C2×#4111yescharacteristic
297C3×C3⋊D3—24no—
298C3×C3⋊D3C22⋊Q814yescomplemented
299C23×D3—92no—
300C23×D3—91no—
301C2×C3×Q8—92no—
302C22×C3×C4—91no—
303C22×C3×C4—92no—
304C22×C3×C4—91no—
305C22×C3×C4—91no—
306C22×Dic3—91no—
307C22×Dic3—91no—
308C22×Dic3—92no—
309C22×Dic3—91no—
310D3×Q8—188no—
311C2×C4×D3—32no—
312C2×C4×D3—32no—
313C2×C4×D3—32no—
314C2×C4×D3—32no—
315C2×C4×D3—32no—
316C2×C4×D3—61no—
317C2×C4×D3—92no—
318C2×C4×D3—92no—
319C2×C4×D3—92no—
320C2×C4×D3—92no—
321C2×C4×D3—92no—
322C2×C4×D3—181no—
323C2×C4×D3—181no—
324C2×C4×D3—182no—
325C2×C4×D3—188no—
326C2×C4×D3—184no—
327C2×Dic6—32no—
328C2×Dic6—32no—
329C2×Dic6—92no—
330C2×Dic6—92no—
331C2×Dic6—92no—
332C2×Dic6—182no—
333C2×Dic6—184no—
334C3×C4⋊C4—32no—
335C3×C4⋊C4—32no—
336C3×C4⋊C4—32no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—62no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4—92no—
341C3×C22⋊C4—92no—
342C3×C22⋊C4—92no—
343#217—92no—
344#217—92no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—32no—
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—182no—
355C4⋊Dic3—32no—
356C4⋊Dic3—92no—
357C4⋊Dic3—181no—
358C4⋊Dic3D3212yescomplemented
359Dic3⋊C4—32no—
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—92no—
363Dic3⋊C4—92no—
364Dic3⋊C4—92no—
365Dic3⋊C4—92no—
366Dic3⋊C4—91no—
367Dic3⋊C4—92no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—181no—
371Dic3⋊C4—182no—
372Dic3⋊C4—181no—
373Dic3⋊C4—182no—
374Dic3⋊C4—361no—
375Dic3⋊C4D3211yescharacteristic, complemented
376C22×C32—21no—
377C22×C32—22no—
378C22×C32—41no—
379C22×C32C23×D311yescharacteristic
380C22×C32C23×D312yes—
381C2×C3⋊D3—22no—
382C2×C3⋊D3—22no—
383C2×C3⋊D3#23512yes—
384C2×C3⋊D3D3×D412yes—
385C2×C3⋊D3D3×Q812yes—
386C2×C3⋊D3D3×Q814yescomplemented
387C2×C3×D3—34no—
388C2×C3×D3—34no—
389C2×C3×D3—34no—
390C2×C3×D3—34no—
391C2×C3×D3—34no—
392C2×C3×D3—62no—
393C2×C3×D3—62no—
394C2×C3×D3—62no—
395C2×C3×D3—64no—
396C2×C3×D3—62no—
397C2×C3×D3—62no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—122no—
401C2×C3×D3—122no—
402D32—616no—
403D32—68no—
404C32×C4—21no—
405C32×C4—22no—
406C32×C4—32no—
407C32×C4—41no—
408C32×C4—42no—
409C32×C4—61no—
410C32×C4—62no—
411C32×C4—62no—
412C32×C4—81no—
413C3⋊Dic3—21no—
414C3⋊Dic3—22no—
415C3⋊Dic3—34no—
416C3⋊Dic3—32no—
417C3⋊Dic3—62no—
418C3⋊Dic3—64no—
419C3⋊Dic3—61no—
420C3⋊Dic3—62no—
421C3⋊Dic3—122no—
422C3⋊Dic3—121no—
423C3⋊Dic3—122no—
424C3⋊Dic3—241no—
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—22no—
431C3×Dic3—42no—
432C3×Dic3—41no—
433C3×Dic3—42no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—62no—
437C3×Dic3—122no—
438C3×Dic3—121no—
439C3×Dic3D3×D414yes—
440C22×Q8—271no—
441C23×C4—271no—
442C22⋊Q8—92no—
443C22⋊Q8—272no—
444C22⋊Q8—272no—
445C22⋊Q8—272no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—271no—
448C2×C4⋊C4—271no—
449C2×C22⋊C4—271no—
450C2×C22⋊C4—271no—
451C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
452C23×C3—91no—
453C23×C3—92no—
454C22×D3—32no—
455C22×D3—32no—
456C22×D3—32no—
457C22×D3—61no—
458C22×D3—62no—
459C22×D3—98no—
460C22×D3—94no—
461C22×D3—184no—
462C22×D3—184no—
463C22×D3—182no—
464C22×D3—182no—
465C3×Q8—184no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
473C2×C3×C4—32no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—91no—
480C2×C3×C4—92no—
481C2×C3×C4—182no—
482C2×C3×C4—184no—
483C2×C3×C4—182no—
484C2×C3×C4—182no—
485C2×C3×C4C2×D3211yescharacteristic
486C2×C3×C4C2×D3212yes—
487C2×Dic3—32no—
488C2×Dic3—32no—
489C2×Dic3—32no—
490C2×Dic3—61no—
491C2×Dic3—62no—
492C2×Dic3—91no—
493C2×Dic3—92no—
494C2×Dic3—94no—
495C2×Dic3—91no—
496C2×Dic3—92no—
497C2×Dic3—181no—
498C2×Dic3—182no—
499C2×Dic3—182no—
500C2×Dic3—181no—
501C2×Dic3—184no—
502C2×Dic3—182no—
503C2×Dic3—182no—
504C2×Dic3—361no—
505C2×Dic3—361no—
506C2×Dic3C2×D3211yescharacteristic
507C2×Dic3C2×D3212yes—
508C2×Dic3C2×D3212yes—
509C2×Dic3C2×D3211yescharacteristic
510C4×D3—64no—
511C4×D3—64no—
512C4×D3—64no—
513C4×D3—64no—
514C4×D3—64no—
515C4×D3—98no—
516C4×D3—122no—
517C4×D3—184no—
518C4×D3—184no—
519C4×D3—184no—
520C4×D3—184no—
521C4×D3—184no—
522C4×D3—364no—
523C4×D3—362no—
524Dic6—64no—
525Dic6—64no—
526Dic6—184no—
527Dic6—184no—
528Dic6—184no—
529Dic6—364no—
530C2×C32—21no—
531C2×C32—22no—
532C2×C32—22no—
533C2×C32—21no—
534C2×C32—22no—
535C2×C32—21no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32C2×#23511yescharacteristic
540C2×C32C2×D3×D412yes—
541C2×C32C2×D3×D411yescharacteristic
542C2×C32C2×D3×Q811yescharacteristic
543C2×C32C2×D3×Q812yes—
544C2×C32D3×#4112yes—
545C3⋊D3—24no—
546C3⋊D3#89614yescomplemented
547C3×D3—38no—
548C3×D3—64no—
549C3×D3—64no—
550C3×D3—64no—
551C3×D3—124no—
552C24—271no—
553C2×Q8—92no—
554C2×Q8—272no—
555C2×Q8—544no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—92no—
559C22×C4—91no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—272no—
563C22×C4—271no—
564C22×C4—544no—
565C4⋊C4—32no—
566C4⋊C4—31no—
567C4⋊C4—92no—
568C4⋊C4—92no—
569C4⋊C4—271no—
570C4⋊C4—272no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C22⋊C4—92no—
574C22⋊C4—92no—
575C22⋊C4—272no—
576C22⋊C4—272no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—41no—
580C22×C3—92no—
581C22×C3—92no—
582C22×C3—92no—
583C22×C3—94no—
584C22×C3—182no—
585C22×C3—182no—
586C22×C3C22×D3211yescharacteristic
587C22×C3C22×D3212yes—
588C2×D3—34no—
589C2×D3—34no—
590C2×D3—34no—
591C2×D3—34no—
592C2×D3—34no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—64no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—1816no—
604C2×D3—188no—
605C3×C4—22no—
606C3×C4—21no—
607C3×C4—34no—
608C3×C4—41no—
609C3×C4—42no—
610C3×C4—62no—
611C3×C4—62no—
612C3×C4—62no—
613C3×C4—62no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—81no—
617C3×C4—122no—
618C3×C4—122no—
619C3×C4—121no—
620C3×C4—182no—
621C3×C4—181no—
622Dic3—22no—
623Dic3—22no—
624Dic3—21no—
625Dic3—62no—
626Dic3—62no—
627Dic3—62no—
628Dic3—92no—
629Dic3—94no—
630Dic3—122no—
631Dic3—121no—
632Dic3—184no—
633Dic3—182no—
634Dic3—182no—
635Dic3—181no—
636Dic3—362no—
637Dic3—361no—
638Dic3—362no—
639Dic3—721no—
640Dic3#380212yes—
641C32—22no—
642C32—21no—
643C32—41no—
644C32C2×#89611yescharacteristic, complemented
645C32D3×C22⋊Q812yescomplemented
646C23—91no—
647C23—92no—
648C23—274no—
649C23—542no—
650C23—542no—
651Q8—184no—
652Q8—544no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—92no—
658C2×C4—91no—
659C2×C4—182no—
660C2×C4—184no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4—274no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—544no—
667C2×C4—542no—
668C2×C4—542no—
669C2×C4D3311yescharacteristic
670C2×C3—21no—
671C2×C3—22no—
672C2×C3—22no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—22no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—94no—
680C2×C3—184no—
681C2×C3C2×#380211yescharacteristic
682C2×C3D3×#23512yes—
683C2×C3D32×D412yes—
684C2×C3#6431211yescharacteristic
685C2×C3D32×Q812yes—
686C2×C3D32×Q811yescharacteristic
687D3—38no—
688D3—64no—
689D3—64no—
690D3—64no—
691D3—124no—
692C22—92no—
693C22—92no—
694C22—92no—
695C22—94no—
696C22—182no—
697C22—182no—
698C22—548no—
699C22C2×D3311yescharacteristic
700C4—21no—
701C4—32no—
702C4—62no—
703C4—62no—
704C4—61no—
705C4—182no—
706C4—181no—
707C4—272no—
708C4—541no—
709C3—21no—
710C3—22no—
711C3—41no—
712C3D3×#89612yescomplemented
713C3#1059463111yescharacteristic, complemented
714C2—94no—
715C2—184no—
716C2#1172437811yescharacteristic
717C2D3×#380211yescharacteristic
718C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×#1113C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88957C2semidirect
4. #11723502C2semidirect
5. C3⋊D3×Dic3⋊C4C2semidirect
6. C3×#63900C2semidirect
7. C3×#63895C2semidirect
8. #11722983C2semidirect
9. #11722970C2semidirect
10. #11722911C2semidirect
17. C2×#6293C22semidirect
21. C2×C3×#627C22semidirect
27. #88857C22semidirect
29. C32×C4⋊Dic3C22semidirect
30. C32×Dic3⋊C4C22semidirect
32. #88806C22semidirect
33. #88806C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
36. C3×#3724C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
53. #63900D3semidirect
59. #63895D3semidirect
71. C2×#1113Q8semidirect
111. C2×#627C2×D3semidirect
147. C3×C4⋊Dic3C2×D3semidirect
148. C3×C4⋊Dic3C2×D3semidirect
153. C3×Dic3⋊C4C2×D3semidirect
159. #3724C2×D3semidirect
162. Dic3⋊Dic3C2×D3semidirect
175. C2×C3×C3⋊D3C2×Q8semidirect
298. C3×C3⋊D3C22⋊Q8semidirect
358. C4⋊Dic3D32semidirect
375. Dic3⋊C4D32semidirect
386. C2×C3⋊D3D3×Q8semidirect
451. C33C2×C22⋊Q8semidirect
546. C3⋊D3#896semidirect
644. C32C2×#896semidirect
645. C32D3×C22⋊Q8semidirect
712. C3D3×#896semidirect
713. C3#10594631semidirect

Maximal subgroups

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

subgroupindex
C2×#889572
C2×#889492
#117237002
#117235022
C3⋊D3×Dic3⋊C42
C3×#639002
C3×#638952
#117229832
#117229702
#117229112
#117229052
#105946313
D3×#8963