Finite Group Databasebeta

← #13169372

Subgroups — #13169372

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723667C211yesmaximal, characteristic
2#11723534C211yesmaximal, characteristic, complemented
3#11723454C211yesmaximal, characteristic, complemented
4#11723404C211yesmaximal, characteristic
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×C4×#624C211yesmaximal, characteristic
7C3×#63869C211yesmaximal, characteristic, complemented
8#11722972C212yesmaximal
9#11722970C212yesmaximal
10#11722943C212yesmaximal, complemented
11#11722940C212yesmaximal, complemented
12#10594448—31nomaximal
13#10593874—31nomaximal
14#10593859—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×#6293C2212yes—
17C2×C3×#627C2212yes—
18C2×C3×#624C2211yescharacteristic
19C2×C3×#624C2211yescharacteristic
20C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88814C2212yes—
27#88813C2212yes—
28#88807C2212yes—
29#88806C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38#64101—31no—
39#64079—31no—
40#64078—31no—
41C3×#890—31no—
42C3×#888—31no—
43C3×C42×D3—31no—
44C3×C42×D3—31no—
45C3×#870—31no—
46C3×#869—31no—
47#63918—31no—
48#63918—31no—
49#63918—61no—
50#63918D311yescharacteristic, complemented
51#63895—32no—
52#63888—32no—
53C4×#624D311yescharacteristic
54#63869—31no—
55#63869—31no—
56#63869—61no—
57#63869D311yescharacteristic, complemented
58#63857—32no—
59#63856—32no—
60#63851—32no—
61#63851—32no—
62#63849—31no—
63#63844—32no—
64#63843—32no—
65Dic3×Dic6—32no—
66#63841—31no—
67#63841—31no—
68#63841—31no—
69#63841—31no—
70#63841—61no—
71#63838—32no—
72#63837—32no—
73#63837—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C3×C4×C3⋊D3Q814yescomplemented
81C2×C32×Dic3C2311yescharacteristic
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86#6293—24no—
87C3×#627—24no—
88C3×#624—22no—
89C3×#624—22no—
90#5728—91no—
91#5688—91no—
92#5470—91no—
93C2×C4×C3⋊D3C2×D311yescharacteristic
94C2×#634—32no—
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—31no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—61no—
102C2×C3×Dic6—32no—
103C2×C3×Dic6—32no—
104C2×#627—32no—
105C2×#627—32no—
106C2×#627—62no—
107C2×#627C2×D312yes—
108C2×#624C2×D311yescharacteristic
109C2×#624C2×D311yescharacteristic
110C32×C4⋊C4—31no—
111C32×C42—31no—
112C32×C42—31no—
113#3752—32no—
114C4⋊(C3⋊Dic3)—31no—
115C4⋊(C3⋊Dic3)—31no—
116C4⋊(C3⋊Dic3)—31no—
117C4⋊(C3⋊Dic3)—32no—
118C4⋊(C3⋊Dic3)—61no—
119C4⋊(C3⋊Dic3)—61no—
120C4⋊(C3⋊Dic3)—61no—
121C4⋊(C3⋊Dic3)—121no—
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124#3750—32no—
125#3750—32no—
126C4×C3⋊Dic3—32no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3—31no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—61no—
135C3×C4⋊Dic3—61no—
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×C4×Dic3—21no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3C2×D311yescharacteristic
149C3×C4×Dic3C2×D311yescharacteristic
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—32no—
153#3724—32no—
154#3724—62no—
155#3724C2×D312yes—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3C2×D312yes—
163Dic3⋊Dic3C2×D312yes—
164#3722—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—62no—
170Dic32—32no—
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—62no—
176Dic32C2×D311yescharacteristic
177Dic32C2×D311yescharacteristic
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3C2×Q812yes—
182C33×C4C2×Q812yes—
183C3⋊(C3⋊Dic3)—22no—
184C3×C3⋊Dic3—22no—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3C2×Q812yes—
187C32×Dic3—21no—
188C32×Dic3—21no—
189C32×Dic3—22no—
190C32×Dic3#4112yes—
191C32×Dic3#4112yes—
192C3×C4⋊Q8—91no—
193C3×#125—91no—
194C2×C3×C42—91no—
195#946—92no—
196Q8×Dic3—92no—
197#926—91no—
198#926—91no—
199#924—92no—
200#924—92no—
201#897—92no—
202#896—92no—
203#896—92no—
204#892—91no—
205#892—91no—
206#892—91no—
207#892—91no—
208#892—181no—
209#890—31no—
210#890—91no—
211#888—31no—
212#888—91no—
213#887—92no—
214#887—92no—
215#887—92no—
216C42×D3—31no—
217C42×D3—31no—
218#870—31no—
219#870—91no—
220#870—91no—
221#870—181no—
222#869—31no—
223#869—91no—
224#869—91no—
225#869—181no—
226C4×Dic6—92no—
227C4×Dic6—92no—
228C22×C3⋊D3C22×D311yescharacteristic
229C22×C3×D3—31no—
230C22×C3×D3—31no—
231C22×C3×D3—61no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—31no—
236C2×C32×C4—31no—
237C2×C32×C4—31no—
238C2×C32×C4—31no—
239C2×C32×C4—32no—
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×D312yes—
253C2×C3⋊Dic3C22×D311yescharacteristic
254C4×C3⋊D3Dic614yescomplemented
255#634—64no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—62no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3C22×D312yes—
271C2×C3×Dic3C22×D312yes—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C3×C4×D3—34no—
281C3×C4×D3—34no—
282C3×C4×D3—64no—
283C3×C4×D3—62no—
284C3×C4×D3—62no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×Dic6—64no—
288C3×Dic6—64no—
289#627—24no—
290#627—64no—
291#627—64no—
292#627—124no—
293#624—22no—
294#624—22no—
295#533—271noSylow
296C2×C33C22×Q811yescharacteristic
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C3×C3⋊D3—22no—
300C2×C3×Q8—92no—
301C22×C3×C4—91no—
302C22×C3×C4—91no—
303C22×C3×C4—91no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—61no—
311C2×Dic6—32no—
312C2×Dic6—32no—
313C2×Dic6—92no—
314C2×Dic6—92no—
315C2×Dic6—92no—
316C2×Dic6—182no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—92no—
321C3×C4⋊C4—92no—
322C3×C4⋊C4—92no—
323C3×C4⋊C4—91no—
324C3×C4⋊C4—91no—
325C3×C42—31no—
326C3×C42—31no—
327C3×C42—31no—
328C3×C42—31no—
329C3×C42—61no—
330C3×C42—61no—
331C3×C42—91no—
332C3×C42—91no—
333#217—92no—
334#217—92no—
335(C2×D3)⋊C4—92no—
336(C2×D3)⋊C4—92no—
337(C2×D3)⋊C4—92no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—182no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—32no—
345C4⋊Dic3—32no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—92no—
349C4⋊Dic3—92no—
350C4⋊Dic3—91no—
351C4⋊Dic3—91no—
352C4⋊Dic3—91no—
353C4⋊Dic3—92no—
354C4⋊Dic3—182no—
355C4⋊Dic3—181no—
356C4⋊Dic3—181no—
357C4⋊Dic3—181no—
358C4⋊Dic3—361no—
359C4⋊Dic3D3211yescharacteristic
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—92no—
365Dic3⋊C4—92no—
366Dic3⋊C4—92no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—182no—
371Dic3⋊C4—182no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—92no—
377C4×Dic3—92no—
378C4×Dic3—92no—
379C4×Dic3—92no—
380C4×Dic3—92no—
381C4×Dic3—92no—
382C4×Dic3—182no—
383C4×Dic3D3211yescharacteristic
384C4×Dic3D3211yescharacteristic
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—41no—
389C22×C32C23×D311yescharacteristic
390C22×C32C23×D311yescharacteristic
391C22×C32C23×D311yescharacteristic
392C2×C3⋊D3—21no—
393C2×C3⋊D3—21no—
394C2×C3⋊D3C2×Dic612yes—
395C2×C3×D3—32no—
396C2×C3×D3—32no—
397C2×C3×D3—62no—
398C2×C3×D3—61no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
401C2×C3×D3—61no—
402C2×C3×D3—121no—
403C2×C3×D3—121no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—32no—
408C32×C4—32no—
409C32×C4—42no—
410C32×C4—62no—
411C32×C4—61no—
412C32×C4—61no—
413C32×C4C2×Dic612yes—
414C32×C4D3×Q812yes—
415C32×C4D3×Q812yes—
416C3⋊Dic3—22no—
417C3⋊Dic3—22no—
418C3⋊Dic3—62no—
419C3⋊Dic3—62no—
420C3⋊Dic3—62no—
421C3⋊Dic3—122no—
422C3⋊Dic3—122no—
423C3⋊Dic3—122no—
424C3⋊Dic3—242no—
425C3⋊Dic3C2×Dic612yes—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—32no—
435C3×Dic3—32no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—42no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—122no—
445C3×Dic3—122no—
446C3×Dic3#23512yes—
447C3×Dic3#23512yes—
448C3×Dic3#23712yes—
449C3×Dic3#23912yes—
450C4⋊Q8—91no—
451C4⋊Q8—271no—
452#125—91no—
453#125—271no—
454C22⋊Q8—272no—
455C22⋊Q8—272no—
456C4×Q8—272no—
457C4×Q8—272no—
458#117—271no—
459#117—271no—
460C2×C42—91no—
461C33#53311yescharacteristic, complemented, Sylow
462C23×C3—91no—
463C22×D3—31no—
464C22×D3—31no—
465C22×D3—61no—
466C3×Q8—184no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—62no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—91no—
487C2×C3×C4—94no—
488C2×C3×C4—92no—
489C2×C3×C4—92no—
490C2×C3×C4—182no—
491C2×C3×C4—182no—
492C2×C3×C4C2×D3211yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—32no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—61no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—92no—
505C2×Dic3—92no—
506C2×Dic3—92no—
507C2×Dic3—182no—
508C2×Dic3—182no—
509C2×Dic3—182no—
510C2×Dic3—362no—
511C2×Dic3C2×D3211yescharacteristic
512C2×Dic3C2×D3211yescharacteristic
513C2×Dic3C2×D3212yes—
514C2×Dic3C2×D3211yescharacteristic
515C2×Dic3C2×D3211yescharacteristic
516C4×D3—34no—
517C4×D3—34no—
518C4×D3—64no—
519C4×D3—62no—
520C4×D3—62no—
521C4×D3—62no—
522C4×D3—62no—
523Dic6—64no—
524Dic6—64no—
525Dic6—184no—
526Dic6—184no—
527Dic6—184no—
528Dic6—364no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32C22×Dic611yescharacteristic
542C2×C32C2×#23511yescharacteristic
543C2×C32C2×#23511yescharacteristic
544C2×C32C2×#23711yescharacteristic
545C2×C32C2×D3×Q811yescharacteristic
546C2×C32C2×D3×Q811yescharacteristic
547C2×C32C2×#23911yescharacteristic
548C2×C32D3×#4111yescharacteristic
549C2×C32D3×#4111yescharacteristic
550C3⋊D3—22no—
551C3×D3—62no—
552C3×D3—62no—
553C3×D3—122no—
554C2×Q8—92no—
555C2×Q8—272no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—91no—
559C4⋊C4—31no—
560C4⋊C4—92no—
561C4⋊C4—92no—
562C4⋊C4—92no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—272no—
566C4⋊C4—272no—
567C4⋊C4—272no—
568C4⋊C4—271no—
569C22⋊C4—272no—
570C22⋊C4—272no—
571C42—31no—
572C42—31no—
573C42—91no—
574C42—91no—
575C42—272no—
576C42—272no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—41no—
581C22×C3—92no—
582C22×C3—181no—
583C22×C3—181no—
584C22×C3C22×D3211yescharacteristic
585C22×C3C22×D3211yescharacteristic
586C22×C3C22×D3211yescharacteristic
587C2×D3—32no—
588C2×D3—32no—
589C2×D3—62no—
590C2×D3—61no—
591C2×D3—61no—
592C2×D3—61no—
593C2×D3—61no—
594C2×D3—121no—
595C2×D3—121no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—32no—
600C3×C4—32no—
601C3×C4—32no—
602C3×C4—32no—
603C3×C4—42no—
604C3×C4—62no—
605C3×C4—62no—
606C3×C4—62no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—62no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—92no—
613C3×C4—121no—
614C3×C4—122no—
615C3×C4—121no—
616C3×C4—182no—
617C3×C4—182no—
618C3×C4D3×Dic612yes—
619C3×C4D3×Dic612yes—
620C3×C4#379712yes—
621Dic3—21no—
622Dic3—21no—
623Dic3—22no—
624Dic3—32no—
625Dic3—32no—
626Dic3—62no—
627Dic3—62no—
628Dic3—62no—
629Dic3—62no—
630Dic3—62no—
631Dic3—122no—
632Dic3—122no—
633Dic3—182no—
634Dic3—182no—
635Dic3—182no—
636Dic3—362no—
637Dic3—362no—
638Dic3—362no—
639Dic3—722no—
640Dic3#379512yes—
641Dic3#379912yes—
642C32—21no—
643C32—21no—
644C32—21no—
645C32—41no—
646C32#547011yescharacteristic, complemented
647C32#568811yescharacteristic, complemented
648C32#572811yescharacteristic, complemented
649C23—91no—
650Q8—184no—
651Q8—544no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—32no—
657C2×C4—91no—
658C2×C4—94no—
659C2×C4—92no—
660C2×C4—92no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4—272no—
664C2×C4D3311yescharacteristic
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—41no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—182no—
678C2×C3C2×D3×Dic611yescharacteristic
679C2×C3C2×D3×Dic611yescharacteristic
680C2×C3C2×#379511yescharacteristic
681C2×C3C2×#379711yescharacteristic
682C2×C3C2×#379911yescharacteristic
683C2×C3D3×#23511yescharacteristic
684C2×C3D3×#23511yescharacteristic
685C2×C3D3×#23711yescharacteristic
686C2×C3D3×#23911yescharacteristic
687D3—62no—
688D3—62no—
689D3—122no—
690C22—92no—
691C22—181no—
692C22—181no—
693C22C2×D3311yescharacteristic
694C4—32no—
695C4—32no—
696C4—61no—
697C4—62no—
698C4—61no—
699C4—92no—
700C4—182no—
701C4—182no—
702C4—542no—
703C4#8895712yes—
704C3—21no—
705C3—21no—
706C3—21no—
707C3—41no—
708C3#1059385911yescharacteristic, complemented
709C3#1059387411yescharacteristic, complemented
710C3#1059444811yescharacteristic, complemented
711C2—182no—
712C2D3×#379511yescharacteristic
713C2D3×#379911yescharacteristic
714C2C2×#8895711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723534C2semidirect
3. #11723454C2semidirect
5. C3×#63918C2semidirect
7. C3×#63869C2semidirect
10. #11722943C2semidirect
11. #11722940C2semidirect
50. #63918D3semidirect
57. #63869D3semidirect
80. C3×C4×C3⋊D3Q8semidirect
254. C4×C3⋊D3Dic6semidirect
461. C33#533semidirect
646. C32#5470semidirect
647. C32#5688semidirect
648. C32#5728semidirect
708. C3#10593859semidirect
709. C3#10593874semidirect
710. C3#10594448semidirect

Maximal subgroups

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

subgroupindex
#117236672
#117235342
#117234542
#117234042
C3×#639182
C3×C4×#6242
C3×#638692
#117229722
#117229702
#117229432
#117229402
#105944483
#105938743
#105938593