Finite Group Databasebeta

← #13168335

Subgroups — #13168335

Order 1728.

1138 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊#6296C211yesmaximal, characteristic, complemented
2#11723455C211yesmaximal, characteristic, complemented
3#11723426C211yesmaximal, characteristic
4#11723399C211yesmaximal, characteristic, complemented
5C3×C4×D3×Dic3C211yesmaximal, characteristic
6C3×#63856C211yesmaximal, characteristic
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723014C212yesmaximal, complemented
9#11722978C212yesmaximal
10#11722944C212yesmaximal, complemented
11#11722913C212yesmaximal
12#10595367—31nomaximal
13#10594808—31nomaximal
14#10593873—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6296C2212yes—
19C2×C3×D3×Dic3C2211yescharacteristic
20C2×C3×D3×Dic3C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88807C2212yes—
27#88807C2212yes—
28#88807C2212yes—
29#88806C2212yes—
30(C2×D3)⋊(C3⋊Dic3)C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×#3724C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×Dic32C2211yescharacteristic
36C3×Dic32C2212yes—
37C3×Dic32C2211yescharacteristic
38#64153—31no—
39#64133—31no—
40C4×#634—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#924—31no—
44C2×C3×C4×Dic3—31no—
45C3×C42×D3—31no—
46C3×C4×Dic6—31no—
47#63964—32no—
48#63955—32no—
49#63919—31no—
50#63918—31no—
51#63918—31no—
52C4×#627—32no—
53#63899—32no—
54#63877—32no—
55C4×D3×Dic3D311yescharacteristic
56#63867—32no—
57#63867—32no—
58#63866—31no—
59#63866—31no—
60#63866—61no—
61#63857—31no—
62#63857—31no—
63#63857—61no—
64#63856D311yescharacteristic
65#63855—32no—
66#63851—32no—
67#63847—32no—
68#63844—31no—
69#63844—31no—
70#63844—61no—
71Dic3×Dic6D311yescharacteristic, complemented
72#63837—32no—
73#63837—32no—
74C22×C32×D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77#6308—22no—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×Dic6—22no—
88#6296—24no—
89C3×D3×Dic3—22no—
90C3×D3×Dic3Q814yescomplemented
91#5622—91no—
92#5578—91no—
93#5470—91no—
94C2×C32×Q8—31no—
95C22×C32×C4—31no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—31no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—61no—
102C2×#634—121no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2×D311yescharacteristic
112C2×C3×Dic6C2×D311yescharacteristic
113C2×#627—32no—
114C2×#627—32no—
115C2×#627—32no—
116C2×D3×Dic3C2×D311yescharacteristic
117C2×D3×Dic3C2×D311yescharacteristic
118C32×C42—31no—
119#3757—32no—
120C4⋊(C3⋊Dic3)C2×D311yescharacteristic
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122#3750—32no—
123#3750—32no—
124#3750—32no—
125#3750—32no—
126C4×C3⋊Dic3—32no—
127C4×C3⋊Dic3C2×D311yescharacteristic
128C3×#217—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—61no—
136C3×C4⋊Dic3—61no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—61no—
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—32no—
153#3724—32no—
154#3724—32no—
155#3724—62no—
156#3724C2×D312yes—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—62no—
166Dic3⋊Dic3—62no—
167Dic3⋊Dic3—62no—
168Dic3⋊Dic3C2×D312yes—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—62no—
172(C2×D3)⋊Dic3C2×D312yes—
173Dic32—32no—
174Dic32—32no—
175Dic32—62no—
176Dic32C2×D311yescharacteristic
177Dic32C2×D312yes—
178Dic32C2×D311yescharacteristic
179C22×C33C2411yescharacteristic
180C2×C32×D3—21no—
181C2×C32×D3—21no—
182C2×C32×D3C2×Q812yes—
183C33×C4#4112yes—
184C3⋊(C3⋊Dic3)—22no—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3C2×Q812yes—
188C3×C3⋊Dic3#4112yes—
189C32×Dic3—21no—
190C32×Dic3—22no—
191C32×Dic3—21no—
192C32×Dic3C2×Q812yes—
193C3×C22⋊Q8—91no—
194C3×C4×Q8—91no—
195C2×C3×C42—91no—
196#946—31no—
197Q8×Dic3—31no—
198#944—91no—
199#944—91no—
200#944—181no—
201#926—92no—
202#924—31no—
203#924—92no—
204#924—91no—
205#924—91no—
206#924—181no—
207C2×C4×Dic3—31no—
208#897—91no—
209#896—92no—
210#889—92no—
211#889—92no—
212#888—91no—
213#888—91no—
214#887—92no—
215#887—91no—
216#878—92no—
217#877—92no—
218#872—92no—
219C42×D3—31no—
220#870—92no—
221#869—91no—
222#869—91no—
223C4×Dic6—31no—
224C4×Dic6—92no—
225C4×Dic6—92no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C4×Dic6—181no—
229C23×C32—31no—
230C22×C3×D3—21no—
231C22×C3×D3C22×D311yescharacteristic
232C22×C3×D3C22×D311yescharacteristic
233C32×Q8—62no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—31no—
238C2×C32×C4—31no—
239C2×C32×C4—31no—
240C2×C32×C4—32no—
241C2×C32×C4—41no—
242C2×C32×C4—62no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C3⋊Dic3—32no—
247C2×C3⋊Dic3—32no—
248C2×C3⋊Dic3—32no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—62no—
251C2×C3⋊Dic3—62no—
252C2×C3⋊Dic3—122no—
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D312yes—
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257#634—62no—
258#634—64no—
259#634—62no—
260#634—62no—
261#634—122no—
262#634—122no—
263#634—124no—
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—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—34no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C3×C4×D3—22no—
291C3×C4×D3—22no—
292C3×C4×D3—34no—
293C3×C4×D3—42no—
294C3×C4×D3—62no—
295C3×Dic6—22no—
296C3×Dic6—22no—
297C3×Dic6—42no—
298#627—64no—
299#627—64no—
300#627—64no—
301D3×Dic3—22no—
302D3×Dic3Dic614yescomplemented
303#533—271noSylow
304C2×C33C22×Q811yescharacteristic
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C32×D3—22no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×Q8—61no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3D3211yescharacteristic
321C2×Dic6—92no—
322C2×Dic6—92no—
323C2×Dic6—92no—
324C2×Dic6—91no—
325C2×Dic6—91no—
326C2×Dic6—91no—
327C2×Dic6—181no—
328C2×Dic6—181no—
329C2×Dic6—181no—
330C2×Dic6—361no—
331C2×Dic6D3211yescharacteristic
332C3×C4⋊C4—92no—
333C3×C4⋊C4—92no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—91no—
336C3×C22⋊C4—92no—
337C3×C42—31no—
338C3×C42—31no—
339C3×C42—61no—
340C3×C42—91no—
341C3×C42—92no—
342C3×C42—91no—
343C3×C42—91no—
344#217—32no—
345#217—92no—
346#217—92no—
347#217—182no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—92no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—32no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—92no—
358C4⋊Dic3—92no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
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—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—182no—
376Dic3⋊C4—182no—
377Dic3⋊C4—182no—
378Dic3⋊C4—182no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—32no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—32no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—182no—
392C4×Dic3D3211yescharacteristic
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—32no—
397C22×C32—41no—
398C22×C32—61no—
399C22×C32—61no—
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3C2×Dic612yes—
411C2×C3×D3D3×Q812yes—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—32no—
416C32×C4—42no—
417C32×C4—61no—
418C32×C4—62no—
419C32×C4—61no—
420C32×C4#23512yes—
421C32×C4#23512yes—
422C32×C4#23712yes—
423C3⋊Dic3—22no—
424C3⋊Dic3—22no—
425C3⋊Dic3—62no—
426C3⋊Dic3—64no—
427C3⋊Dic3—62no—
428C3⋊Dic3—62no—
429C3⋊Dic3—122no—
430C3⋊Dic3—122no—
431C3⋊Dic3—124no—
432C3⋊Dic3C2×Dic612yes—
433C3⋊Dic3#23512yes—
434C3×Dic3—21no—
435C3×Dic3—22no—
436C3×Dic3—21no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—22no—
441C3×Dic3—32no—
442C3×Dic3—32no—
443C3×Dic3—32no—
444C3×Dic3—32no—
445C3×Dic3—42no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—62no—
454C3×Dic3—122no—
455C3×Dic3—122no—
456C3×Dic3C2×Dic612yes—
457C3×Dic3D3×Q812yes—
458C4⋊Q8—271no—
459C4⋊Q8—271no—
460#125—272no—
461C22⋊Q8—91no—
462C22⋊Q8—272no—
463C22⋊Q8—271no—
464C4×Q8—91no—
465C4×Q8—271no—
466C4×Q8—272no—
467#117—272no—
468C2×C42—91no—
469C33#53311yescharacteristic, complemented, Sylow
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—61no—
473C22×D3C2×D3211yescharacteristic
474C3×Q8—62no—
475C3×Q8—62no—
476C3×Q8—122no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—32no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—32no—
488C2×C3×C4—41no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—94no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—92no—
499C2×C3×C4—92no—
500C2×C3×C4—122no—
501C2×C3×C4—182no—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—34no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—92no—
520C2×Dic3—92no—
521C2×Dic3—92no—
522C2×Dic3—182no—
523C2×Dic3—182no—
524C2×Dic3—182no—
525C2×Dic3—362no—
526C2×Dic3C2×D3211yescharacteristic
527C2×Dic3C2×D3211yescharacteristic
528C2×Dic3C2×D3212yes—
529C2×Dic3C2×D3211yescharacteristic
530C4×D3—22no—
531C4×D3—34no—
532C4×D3—62no—
533Dic6—22no—
534Dic6—184no—
535Dic6—184no—
536Dic6—184no—
537Dic6—184no—
538Dic6—182no—
539Dic6—182no—
540Dic6—182no—
541Dic6—362no—
542Dic6—362no—
543Dic6—364no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—41no—
554C2×C32—41no—
555C2×C32—41no—
556C2×C32—62no—
557C2×C32C22×Dic611yescharacteristic
558C2×C32C2×#23511yescharacteristic
559C2×C32C2×#23511yescharacteristic
560C2×C32C2×#23511yescharacteristic
561C2×C32C2×#23711yescharacteristic
562C2×C32C2×D3×Q811yescharacteristic
563C2×C32C2×D3×Q811yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C3×D3—22no—
567C3×D3—22no—
568C3×D3—42no—
569C2×Q8—31no—
570C2×Q8—272no—
571C2×Q8—271no—
572C22×C4—31no—
573C22×C4—91no—
574C22×C4—91no—
575C4⋊C4—92no—
576C4⋊C4—92no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—272no—
580C4⋊C4—272no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C22⋊C4—92no—
585C22⋊C4—272no—
586C42—31no—
587C42—91no—
588C42—91no—
589C42—92no—
590C42—91no—
591C42—272no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—32no—
596C22×C3—32no—
597C22×C3—41no—
598C22×C3—62no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C22×D3211yescharacteristic
606C22×C3C22×D3211yescharacteristic
607C22×C3C22×D3211yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3D3×Dic612yes—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—32no—
615C3×C4—32no—
616C3×C4—42no—
617C3×C4—62no—
618C3×C4—61no—
619C3×C4—62no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—61no—
623C3×C4—62no—
624C3×C4—92no—
625C3×C4—92no—
626C3×C4—121no—
627C3×C4—122no—
628C3×C4—121no—
629C3×C4—182no—
630C3×C4—182no—
631C3×C4#379812yes—
632C3×C4#380412yes—
633C3×C4#380412yes—
634Dic3—21no—
635Dic3—22no—
636Dic3—21no—
637Dic3—32no—
638Dic3—32no—
639Dic3—32no—
640Dic3—32no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—62no—
647Dic3—122no—
648Dic3—122no—
649Dic3—184no—
650Dic3—182no—
651Dic3—182no—
652Dic3—182no—
653Dic3—362no—
654Dic3—362no—
655Dic3—364no—
656Dic3D3×Dic612yes—
657C32—21no—
658C32—21no—
659C32—21no—
660C32—41no—
661C32#547011yescharacteristic, complemented
662C32#557811yescharacteristic, complemented
663C32#562211yescharacteristic, complemented
664C23—31no—
665Q8—62no—
666Q8—544no—
667Q8—542no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—32no—
672C2×C4—62no—
673C2×C4—94no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—92no—
677C2×C4—92no—
678C2×C4—182no—
679C2×C4—272no—
680C2×C4D3311yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—41no—
693C2×C3—62no—
694C2×C3—62no—
695C2×C3—122no—
696C2×C3C2×D3×Dic611yescharacteristic
697C2×C3C2×D3×Dic611yescharacteristic
698C2×C3C2×#379811yescharacteristic
699C2×C3D3×#23511yescharacteristic
700C2×C3D3×#23511yescharacteristic
701C2×C3D32×Q811yescharacteristic
702C2×C3#6431911yescharacteristic
703C2×C3C2×#380411yescharacteristic
704C2×C3C2×#380411yescharacteristic
705D3—22no—
706C22—32no—
707C22—61no—
708C22—61no—
709C22C2×D3311yescharacteristic
710C4—32no—
711C4—61no—
712C4—61no—
713C4—62no—
714C4—92no—
715C4—92no—
716C4—182no—
717C4—182no—
718C4—542no—
719C4#8895912yes—
720C3—21no—
721C3—21no—
722C3—21no—
723C3—41no—
724C3#1059387311yescharacteristic, complemented
725C3#1059480811yescharacteristic, complemented
726C3#1059536711yescharacteristic, complemented
727C2—62no—
728C2D32×Dic611yescharacteristic
729C2#1172438911yescharacteristic
730C2C2×#8895911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×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
1. C4⋊#6296C2semidirect
2. #11723455C2semidirect
4. #11723399C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723014C2semidirect
10. #11722944C2semidirect
71. Dic3×Dic6D3semidirect
90. C3×D3×Dic3Q8semidirect
302. D3×Dic3Dic6semidirect
469. C33#533semidirect
661. C32#5470semidirect
662. C32#5578semidirect
663. C32#5622semidirect
724. C3#10593873semidirect
725. C3#10594808semidirect
726. C3#10595367semidirect

Maximal subgroups

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

subgroupindex
C4⋊#62962
#117234552
#117234262
#117233992
C3×C4×D3×Dic32
C3×#638562
C3×Dic3×Dic62
#117230142
#117229782
#117229442
#117229132
#105953673
#105948083
#105938733