Finite Group Databasebeta

← #13178138

Subgroups — #13178138

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64084C211yesmaximal, characteristic
2C3×C4×#634C211yesmaximal, characteristic, complemented
3C3×C4×#634C211yesmaximal, characteristic, complemented
4#11723691C211yesmaximal, characteristic
5#11723688C212yesmaximal, complemented
6#11723683C212yesmaximal, complemented
7#11723678C211yesmaximal, characteristic, complemented
8#11723677C211yesmaximal, characteristic
9#11723676C212yesmaximal, complemented
10#11723675C212yesmaximal, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10593942—31nomaximal
13#10593932—31nomaximal
14#10593850—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic
19C2×#6294C2212yes—
20C33×C42C2211yescharacteristic
21C3×#3752C2212yes—
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×#3750C2212yes—
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2212yes—
30C3×C4×C3⋊Dic3C2211yescharacteristic
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88813C2212yes—
38#64084D311yescharacteristic
39C4×#634D311yescharacteristic, complemented
40C4×#634D311yescharacteristic, complemented
41C3×#875—31no—
42C3×#875—31no—
43C3×#875—61no—
44C3×C4×Dic6—31no—
45C3×C4×Dic6—31no—
46C3×C4×Dic6—31no—
47C3×C4×Dic6—31no—
48C3×C4×Dic6—61no—
49C3×C4×Dic6—61no—
50#63898—31no—
51#63896—32no—
52#63894—31no—
53Dic3×D12—31no—
54#63888—32no—
55#63887—32no—
56#63878—32no—
57#63877—32no—
58#63873—31no—
59#63868—32no—
60#63866—31no—
61#63866—31no—
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—
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)—22no—
86C3×#634—22no—
87C3×#634—22no—
88C3×#634—22no—
89#6294—24no—
90#5671—91no—
91#5584—91no—
92#5568—91no—
93C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
94C2×#634C2×D311yescharacteristic
95C2×#634C2×D311yescharacteristic
96C2×#634C2×D311yescharacteristic
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—61no—
100C2×C3×Dic6—31no—
101C2×C3×Dic6—31no—
102C2×C3×Dic6—31no—
103C2×C3×Dic6—31no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—61no—
107C2×C3×Dic6—61no—
108C2×C3×Dic6—61no—
109C2×#624—32no—
110C2×D3×Dic3—32no—
111C2×D3×Dic3—32no—
112C32×C42—21no—
113C32×C42—21no—
114C32×C42—21no—
115C32×C42—41no—
116C32×C42C2×D311yescharacteristic
117C32×C42C2×D311yescharacteristic
118C32×C42C2×D311yescharacteristic
119#3752C2×D312yes—
120#3752C2×D312yes—
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123#3750C2×D312yes—
124#3750C2×D311yescharacteristic
125#3750C2×D311yescharacteristic
126C4×C3⋊Dic3C2×D311yescharacteristic
127C4×C3⋊Dic3C2×D312yes—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—62no—
134C3×(C2×D3)⋊C4—62no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3—61no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—61no—
148C3×Dic3⋊C4—62no—
149C3×Dic3⋊C4—61no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—61no—
157C3×C4×Dic3—61no—
158C3×C4×Dic3—62no—
159#3724—32no—
160#3724—32no—
161#3724—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168#3722—32no—
169#3722—32no—
170#3722—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—22no—
184C33×C4—21no—
185C33×C4—21no—
186C33×C4#4112yes—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3#4112yes—
194C3×#124—91no—
195C3×C4×Q8—91no—
196C3×C4×Q8—91no—
197#947—91no—
198#946—92no—
199Q8×Dic3—91no—
200#944—91no—
201#944—91no—
202#936—91no—
203D4×Dic3—91no—
204#898—92no—
205#898—92no—
206#898—92no—
207#896—92no—
208#893—91no—
209#892—92no—
210#887—91no—
211#879—92no—
212#879—92no—
213#878—92no—
214#877—92no—
215#876—92no—
216#875—31no—
217#875—31no—
218#875—61no—
219#875—91no—
220C4×D12—91no—
221#872—92no—
222#869—91no—
223C4×Dic6—31no—
224C4×Dic6—31no—
225C4×Dic6—31no—
226C4×Dic6—31no—
227C4×Dic6—61no—
228C4×Dic6—61no—
229C4×Dic6—91no—
230C22×C3⋊D3C22×D312yes—
231C22×C3×D3—32no—
232C22×C3×D3—32no—
233C22×C3×D3—62no—
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—21no—
243C2×C32×C4—41no—
244C2×C32×C4—41no—
245C2×C32×C4—41no—
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×C32×C4C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D312yes—
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C4⋊(C3⋊D3)—22no—
263#634—22no—
264#634—22no—
265#634—22no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
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—64no—
293C3×Dic6—64no—
294C3×Dic6—62no—
295C3×Dic6—62no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—122no—
299#624—64no—
300D3×Dic3—64no—
301D3×Dic3—64no—
302#556—271noSylow
303C2×C33C2×#4111yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C2×C332−1+411yescharacteristic
306C3×C3⋊D3—42no—
307C2×C3×Q8—91no—
308C2×C3×Q8—91no—
309C2×C3×Q8—91no—
310C2×C3×D4—91no—
311C22×Dic3—92no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×C4×D3—92no—
316C2×C4×D3—92no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—92no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C22⋊C4—92no—
332C3×C22⋊C4—92no—
333C3×C42—21no—
334C3×C42—21no—
335C3×C42—21no—
336C3×C42—41no—
337C3×C42—91no—
338C3×C42—91no—
339C3×C42—92no—
340C3×C42D3211yescharacteristic
341C3×C42D3211yescharacteristic
342C3×C42D3211yescharacteristic
343#217—92no—
344#217—92no—
345#217—92no—
346(C2×D3)⋊C4—32no—
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—92no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—92no—
365C4⋊Dic3—92no—
366C4⋊Dic3—92no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—32no—
371Dic3⋊C4—31no—
372Dic3⋊C4—32no—
373Dic3⋊C4—61no—
374Dic3⋊C4—62no—
375Dic3⋊C4—61no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382C4×Dic3—32no—
383C4×Dic3—31no—
384C4×Dic3—32no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—62no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—92no—
392C4×Dic3—92no—
393C4×Dic3—92no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—41no—
398C22×C32C23×D311yescharacteristic
399C22×C32C23×D311yescharacteristic
400C22×C32C23×D311yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—62no—
409C2×C3×D3—62no—
410C2×C3×D3—122no—
411C2×C3×D3—122no—
412C2×C3×D3—122no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—22no—
416C32×C4—22no—
417C32×C4—21no—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—22no—
424C32×C4—42no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4—42no—
430C32×C4—42no—
431C32×C4#23512yes—
432C32×C4#23712yes—
433C32×C4#23912yes—
434C3⋊Dic3—22no—
435C3⋊Dic3—21no—
436C3⋊Dic3—22no—
437C3⋊Dic3—22no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3#23512yes—
441C3×Dic3—32no—
442C3×Dic3—32no—
443C3×Dic3—62no—
444C3×Dic3—64no—
445C3×Dic3—62no—
446C3×Dic3—62no—
447C3×Dic3—62no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C3×Dic3—62no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—122no—
459C3×Dic3—121no—
460C3×Dic3—121no—
461C3×Dic3—122no—
462C4⋊Q8—271no—
463#126—272no—
464#126—272no—
465#124—91no—
466#124—271no—
467C22⋊Q8—272no—
468C4×Q8—91no—
469C4×Q8—91no—
470C4×Q8—271no—
471C4×D4—271no—
472#117—272no—
473C33#55611yescharacteristic, complemented, Sylow
474C23×C3—92no—
475C22×D3—32no—
476C22×D3—32no—
477C22×D3—62no—
478C3×Q8—182no—
479C3×Q8—182no—
480C3×Q8—182no—
481C3×D4—182no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—92no—
497C2×C3×C4—92no—
498C2×C3×C4—92no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C2×D3211yescharacteristic
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—31no—
522C2×Dic3—32no—
523C2×Dic3—32no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—62no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—184no—
532D12—62no—
533D12—62no—
534D12—122no—
535C4×D3—184no—
536C4×D3—184no—
537Dic6—62no—
538Dic6—62no—
539Dic6—64no—
540Dic6—64no—
541Dic6—62no—
542Dic6—62no—
543Dic6—62no—
544Dic6—62no—
545Dic6—122no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—41no—
556C2×C32—41no—
557C2×C32—41no—
558C2×C32C2×#23511yescharacteristic
559C2×C32C2×#23511yescharacteristic
560C2×C32C2×#23711yescharacteristic
561C2×C32C2×#23911yescharacteristic
562C2×C32#100711yescharacteristic
563C2×C32D3×#4111yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C2×C32#101011yescharacteristic
566C2×C32#101011yescharacteristic
567C3⋊D3—42no—
568C3×D3—122no—
569C3×D3—122no—
570C3×D3—242no—
571C2×Q8—91no—
572C2×Q8—91no—
573C2×Q8—91no—
574C2×D4—91no—
575C22×C4—272no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—92no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C22⋊C4—92no—
585C22⋊C4—92no—
586C22⋊C4—272no—
587C22⋊C4—272no—
588C22⋊C4—272no—
589C42—92no—
590C42—91no—
591C42—91no—
592C42—272no—
593C42#111311yescharacteristic
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—182no—
599C22×C3—182no—
600C22×C3—182no—
601C22×C3C22×D3211yescharacteristic
602C22×C3C22×D3211yescharacteristic
603C22×C3C22×D3211yescharacteristic
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—62no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—122no—
611C2×D3—122no—
612C2×D3—122no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—92no—
632C3×C4—182no—
633C3×C4—181no—
634C3×C4—181no—
635C3×C4—182no—
636C3×C4—182no—
637C3×C4—181no—
638C3×C4#379512yes—
639C3×C4#379612yes—
640C3×C4#379912yes—
641Dic3—32no—
642Dic3—32no—
643Dic3—62no—
644Dic3—64no—
645Dic3—62no—
646Dic3—62no—
647Dic3—62no—
648Dic3—62no—
649Dic3—61no—
650Dic3—61no—
651Dic3—61no—
652Dic3—61no—
653Dic3—62no—
654Dic3—61no—
655Dic3—61no—
656Dic3—62no—
657Dic3—62no—
658Dic3—122no—
659Dic3—121no—
660Dic3—121no—
661Dic3—122no—
662C32—21no—
663C32—21no—
664C32—21no—
665C32—41no—
666C32#556811yescharacteristic, complemented
667C32#558411yescharacteristic, complemented
668C32#567111yescharacteristic, complemented
669C23—92no—
670Q8—182no—
671Q8—182no—
672Q8—182no—
673D4—182no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—92no—
677C2×C4—91no—
678C2×C4—92no—
679C2×C4—91no—
680C2×C4—92no—
681C2×C4—544no—
682C2×C4C2×#111311yescharacteristic
683C2×C4C2×#111311yescharacteristic
684C2×C4C2×#111311yescharacteristic
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—362no—
698C2×C3C2×#379511yescharacteristic
699C2×C3C2×#379611yescharacteristic
700C2×C3#6429711yescharacteristic
701C2×C3#6429711yescharacteristic
702C2×C3#6429811yescharacteristic
703C2×C3C2×#379911yescharacteristic
704C2×C3D3×#23511yescharacteristic
705C2×C3D3×#23511yescharacteristic
706C2×C3#6430611yescharacteristic
707D3—122no—
708D3—122no—
709D3—242no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22C22×#111311yescharacteristic
714C4—21no—
715C4—21no—
716C4—92no—
717C4—182no—
718C4—182no—
719C4—181no—
720C4—181no—
721C4—182no—
722C4—181no—
723C4#8904112yes—
724C3—21no—
725C3—21no—
726C3—21no—
727C3—41no—
728C3#1059385011yescharacteristic, complemented
729C3#1059393211yescharacteristic, complemented
730C3#1059394211yescharacteristic, complemented
731C2—362no—
732C2C2×#8904111yescharacteristic
733C2#1172461411yescharacteristic
734C2#1172461811yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC42#1113
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#634C2semidirect
3. C3×C4×#634C2semidirect
5. #11723688C2semidirect
6. #11723683C2semidirect
7. #11723678C2semidirect
9. #11723676C2semidirect
10. #11723675C2semidirect
11. #11723668C2semidirect
39. C4×#634D3semidirect
40. C4×#634D3semidirect
473. C33#556semidirect
666. C32#5568semidirect
667. C32#5584semidirect
668. C32#5671semidirect
728. C3#10593850semidirect
729. C3#10593932semidirect
730. C3#10593942semidirect

Maximal subgroups

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

subgroupindex
C3×#640842
C3×C4×#6342
#117236912
#117236882
#117236832
#117236782
#117236772
#117236762
#117236752
#117236682
#105939423
#105939323
#105938503