Finite Group Databasebeta

← #13178142

Subgroups — #13178142

Order 1728.

1054 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×#64081C211yesmaximal, characteristic
2C3×#64079C211yesmaximal, characteristic, complemented
3C3×#64078C211yesmaximal, characteristic, complemented
4C4⋊#6296C211yesmaximal, characteristic, complemented
5#11723692C212yesmaximal
6#11723689C211yesmaximal, characteristic
7#11723688C212yesmaximal
8#11723680C211yesmaximal, characteristic, complemented
9#11723669C212yesmaximal, complemented
10#11723667C211yesmaximal, characteristic
11#11723666C212yesmaximal, complemented
12#10593959—31nomaximal
13#10593954—31nomaximal
14#10593855—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2212yes—
17C2×#6296C2212yes—
18C2×#6294C2212yes—
19C33×C42C2211yescharacteristic
20C3×#3752C2211yescharacteristic
21C3×#3752C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2212yes—
28C3×#3750C2212yes—
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32#88815C2212yes—
33#88815C2212yes—
34#88815C2212yes—
35#88815C2212yes—
36#88814C2212yes—
37#88813C2212yes—
38#64081D311yescharacteristic
39#64079D311yescharacteristic, complemented
40#64078D311yescharacteristic, complemented
41C3×#872—31no—
42C3×#872—31no—
43C3×#872—61no—
44C3×#870—31no—
45C3×#870—31no—
46C3×#870—61no—
47C3×#869—31no—
48C3×#869—31no—
49C3×#869—61no—
50#63919—31no—
51#63918—31no—
52#63918—31no—
53#63900—31no—
54#63899—32no—
55#63896—32no—
56#63895—32no—
57#63893—32no—
58D3×C4⋊Dic3—31no—
59D3×C4⋊Dic3—31no—
60#63888—32no—
61#63887—32no—
62#63872—31no—
63#63869—31no—
64#63869—31no—
65#63849—31no—
66#63847—32no—
67#63846—32no—
68#63845—32no—
69#63841—31no—
70#63841—31no—
71#63840—32no—
72#63839—32no—
73#63839—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4×C3⋊D3Q814yescomplemented
86C3×#634—42no—
87#6296—42no—
88#6294—42no—
89#5729—91no—
90#5689—91no—
91#5519—91no—
92C2×C4×C3⋊D3C2×D311yescharacteristic
93C2×#634C2×D312yes—
94C2×C3×C4×D3—31no—
95C2×C3×C4×D3—31no—
96C2×C3×C4×D3—61no—
97C2×C3×Dic6—32no—
98C2×C3×Dic6—32no—
99C2×C3×Dic6—62no—
100C2×#627—32no—
101C2×#627—32no—
102C2×#627—32no—
103C2×#624—32no—
104C2×D3×Dic3—32no—
105C2×D3×Dic3—32no—
106C32×C42—21no—
107C32×C42—21no—
108C32×C42—21no—
109C32×C42—41no—
110C32×C42C2×D311yescharacteristic
111C32×C42C2×D311yescharacteristic
112C32×C42C2×D311yescharacteristic
113#3752C2×D311yescharacteristic
114#3752C2×D311yescharacteristic
115C4⋊(C3⋊Dic3)C2×D311yescharacteristic
116C4⋊(C3⋊Dic3)C2×D312yes—
117C4⋊(C3⋊Dic3)C2×D311yescharacteristic
118C4⋊(C3⋊Dic3)C2×D311yescharacteristic
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120#3750C2×D312yes—
121#3750C2×D312yes—
122#3750C2×D311yescharacteristic
123#3750C2×D311yescharacteristic
124C4×C3⋊Dic3C2×D311yescharacteristic
125C3×(C2×D3)⋊C4—31no—
126C3×(C2×D3)⋊C4—31no—
127C3×(C2×D3)⋊C4—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—61no—
130C3×(C2×D3)⋊C4—61no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—61no—
142C3×C4⋊Dic3—62no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3—61no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—31no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—62no—
155C3×Dic3⋊C4—62no—
156C3×Dic3⋊C4—61no—
157C3×Dic3⋊C4—61no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—31no—
160C3×C4×Dic3—61no—
161#3724—32no—
162#3724—32no—
163#3724—32no—
164#3724—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—32no—
173#3722—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3C2×Q812yes—
183C33×C4—21no—
184C33×C4—21no—
185C33×C4C2×Q812yes—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3C2×Q812yes—
193C3×C4⋊Q8—91no—
194C3×#125—91no—
195C3×#117—91no—
196#946—92no—
197#944—92no—
198#926—91no—
199C2×C4⋊Dic3—91no—
200#897—92no—
201#896—92no—
202#896—92no—
203#892—91no—
204#892—91no—
205D3×C4⋊C4—91no—
206D3×C4⋊C4—91no—
207#890—91no—
208#890—91no—
209#890—92no—
210#889—92no—
211#889—92no—
212#888—91no—
213#888—91no—
214#888—92no—
215#888—92no—
216#878—92no—
217#878—92no—
218#872—31no—
219#872—31no—
220#872—61no—
221#870—31no—
222#870—31no—
223#870—61no—
224#870—91no—
225#869—31no—
226#869—31no—
227#869—61no—
228#869—91no—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—41no—
243C2×C32×C4—41no—
244C2×C32×C4—41no—
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D312yes—
255C2×C3⋊Dic3C22×D312yes—
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C4×C3⋊D3Dic614yescomplemented
262#634—42no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C3×C4×D3—34no—
285C3×C4×D3—34no—
286C3×C4×D3—64no—
287C3×Dic6—122no—
288C3×Dic6—122no—
289C3×Dic6—124no—
290#627—122no—
291#627—122no—
292#627—122no—
293#624—122no—
294D3×Dic3—122no—
295D3×Dic3—122no—
296#544—271noSylow
297C2×C33C22×Q811yescharacteristic
298C2×C33H(5,𝔽2)11yescharacteristic
299C2×C332−1+411yescharacteristic
300C3×C3⋊D3—22no—
301C2×C3×Q8—92no—
302C22×C3×C4—91no—
303C22×Dic3—92no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—61no—
307C2×C4×D3—92no—
308C2×C4×D3—92no—
309C2×Dic6—32no—
310C2×Dic6—32no—
311C2×Dic6—62no—
312C2×Dic6—92no—
313C2×Dic6—92no—
314C2×Dic6—92no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—92no—
319C3×C4⋊C4—92no—
320C3×C4⋊C4—92no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4—91no—
323C3×C4⋊C4—91no—
324C3×C22⋊C4—91no—
325C3×C22⋊C4—91no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—21no—
329C3×C42—41no—
330C3×C42—91no—
331C3×C42D3211yescharacteristic
332C3×C42D3211yescharacteristic
333C3×C42D3211yescharacteristic
334#217—92no—
335(C2×D3)⋊C4—31no—
336(C2×D3)⋊C4—31no—
337(C2×D3)⋊C4—31no—
338(C2×D3)⋊C4—31no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—92no—
342(C2×D3)⋊C4—92no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—32no—
346C4⋊Dic3—31no—
347C4⋊Dic3—32no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—62no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—92no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—61no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C22×C32—21no—
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—41no—
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D311yescharacteristic
394C22×C32C23×D311yescharacteristic
395C2×C3⋊D3—21no—
396C2×C3⋊D3—21no—
397C2×C3⋊D3C2×Dic612yes—
398C2×C3×D3—32no—
399C2×C3×D3—32no—
400C2×C3×D3—62no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—121no—
406C2×C3×D3—121no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—22no—
416C32×C4—22no—
417C32×C4—22no—
418C32×C4—42no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4—42no—
424C32×C4—42no—
425C32×C4C2×Dic612yes—
426C32×C4D3×Q812yes—
427C32×C4D3×Q812yes—
428C3⋊Dic3—22no—
429C3⋊Dic3—22no—
430C3⋊Dic3—22no—
431C3⋊Dic3—21no—
432C3⋊Dic3—22no—
433C3⋊Dic3—21no—
434C3⋊Dic3C2×Dic612yes—
435C3×Dic3—32no—
436C3×Dic3—32no—
437C3×Dic3—62no—
438C3×Dic3—62no—
439C3×Dic3—61no—
440C3×Dic3—62no—
441C3×Dic3—61no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—62no—
447C3×Dic3—62no—
448C3×Dic3—61no—
449C3×Dic3—62no—
450C3×Dic3—122no—
451C3×Dic3—122no—
452C3×Dic3—122no—
453C3×Dic3—121no—
454C3×Dic3—121no—
455C3×Dic3—122no—
456C4⋊Q8—91no—
457C4⋊Q8—271no—
458C4⋊Q8—272no—
459#125—91no—
460#125—271no—
461#125—272no—
462C22⋊Q8—272no—
463C22⋊Q8—272no—
464#117—91no—
465#117—271no—
466C2×C4⋊C4—271no—
467C33#54411yescharacteristic, complemented, Sylow
468C23×C3—91no—
469C22×D3—31no—
470C22×D3—31no—
471C22×D3—61no—
472C3×Q8—362no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—91no—
486C2×C3×C4—94no—
487C2×C3×C4—92no—
488C2×C3×C4—92no—
489C2×C3×C4—91no—
490C2×C3×C4—92no—
491C2×C3×C4—91no—
492C2×C3×C4—92no—
493C2×C3×C4C2×D3211yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C2×D3211yescharacteristic
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—362no—
524C4×D3—34no—
525C4×D3—34no—
526C4×D3—64no—
527C4×D3—362no—
528C4×D3—362no—
529Dic6—122no—
530Dic6—122no—
531Dic6—124no—
532Dic6—362no—
533Dic6—362no—
534Dic6—362no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—41no—
545C2×C32—41no—
546C2×C32—41no—
547C2×C32C22×Dic611yescharacteristic
548C2×C32#100411yescharacteristic
549C2×C32C2×D3×Q811yescharacteristic
550C2×C32C2×D3×Q811yescharacteristic
551C2×C32#100711yescharacteristic
552C2×C32#100911yescharacteristic
553C2×C32#100911yescharacteristic
554C2×C32#101011yescharacteristic
555C2×C32#101011yescharacteristic
556C3⋊D3—22no—
557C3×D3—62no—
558C3×D3—62no—
559C3×D3—122no—
560C2×Q8—92no—
561C2×Q8—272no—
562C22×C4—91no—
563C22×C4—272no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—92no—
571C4⋊C4—92no—
572C4⋊C4—92no—
573C4⋊C4—272no—
574C4⋊C4—272no—
575C4⋊C4—272no—
576C4⋊C4—272no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—272no—
580C42—91no—
581C42—272no—
582C42#111311yescharacteristic
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—41no—
587C22×C3—92no—
588C22×C3—181no—
589C22×C3—181no—
590C22×C3C22×D3211yescharacteristic
591C22×C3C22×D3211yescharacteristic
592C22×C3C22×D3211yescharacteristic
593C2×D3—32no—
594C2×D3—32no—
595C2×D3—62no—
596C2×D3—61no—
597C2×D3—61no—
598C2×D3—61no—
599C2×D3—61no—
600C2×D3—121no—
601C2×D3—121no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—92no—
621C3×C4—181no—
622C3×C4—182no—
623C3×C4—181no—
624C3×C4—182no—
625C3×C4—182no—
626C3×C4—182no—
627C3×C4D3×Dic612yes—
628C3×C4D3×Dic612yes—
629C3×C4#379712yes—
630Dic3—32no—
631Dic3—32no—
632Dic3—62no—
633Dic3—62no—
634Dic3—61no—
635Dic3—61no—
636Dic3—62no—
637Dic3—62no—
638Dic3—62no—
639Dic3—62no—
640Dic3—62no—
641Dic3—61no—
642Dic3—62no—
643Dic3—61no—
644Dic3—62no—
645Dic3—122no—
646Dic3—122no—
647Dic3—122no—
648Dic3—121no—
649Dic3—122no—
650Dic3—121no—
651C32—21no—
652C32—21no—
653C32—21no—
654C32—41no—
655C32#551911yescharacteristic, complemented
656C32#568911yescharacteristic, complemented
657C32#572911yescharacteristic, complemented
658C23—91no—
659Q8—362no—
660Q8—1082no—
661C2×C4—91no—
662C2×C4—94no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—92no—
666C2×C4—92no—
667C2×C4—92no—
668C2×C4—92no—
669C2×C4—1082no—
670C2×C4C2×#111311yescharacteristic
671C2×C4C2×#111311yescharacteristic
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—182no—
686C2×C3C2×D3×Dic611yescharacteristic
687C2×C3C2×D3×Dic611yescharacteristic
688C2×C3#6429711yescharacteristic
689C2×C3#6429711yescharacteristic
690C2×C3#6429811yescharacteristic
691C2×C3C2×#379711yescharacteristic
692C2×C3#6430711yescharacteristic
693C2×C3#6430711yescharacteristic
694C2×C3#6430811yescharacteristic
695D3—62no—
696D3—62no—
697D3—122no—
698C22—92no—
699C22—181no—
700C22—181no—
701C22C22×#111311yescharacteristic
702C4—21no—
703C4—21no—
704C4—92no—
705C4—181no—
706C4—182no—
707C4—182no—
708C4—182no—
709C4—182no—
710C4—181no—
711C4#8904012yes—
712C3—21no—
713C3—21no—
714C3—21no—
715C3—41no—
716C3#1059385511yescharacteristic, complemented
717C3#1059395411yescharacteristic, complemented
718C3#1059395911yescharacteristic, complemented
719C2—182no—
720C2C2×#8904011yescharacteristic
721C2#1172461411yescharacteristic
722C2#1172461911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC42#1113
hypocenterC33#544
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×#64079C2semidirect
3. C3×#64078C2semidirect
4. C4⋊#6296C2semidirect
8. #11723680C2semidirect
9. #11723669C2semidirect
11. #11723666C2semidirect
39. #64079D3semidirect
40. #64078D3semidirect
85. C3×C4×C3⋊D3Q8semidirect
261. C4×C3⋊D3Dic6semidirect
467. C33#544semidirect
655. C32#5519semidirect
656. C32#5689semidirect
657. C32#5729semidirect
716. C3#10593855semidirect
717. C3#10593954semidirect
718. C3#10593959semidirect

Maximal subgroups

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

subgroupindex
C3×#640812
C3×#640792
C3×#640782
C4⋊#62962
#117236922
#117236892
#117236882
#117236802
#117236692
#117236672
#117236662
#105939593
#105939543
#105938553