Finite Group Databasebeta

← #13168271

Subgroups — #13168271

Order 1728.

1156 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6296C211yesmaximal, characteristic, complemented
2#11723535C211yesmaximal, characteristic, complemented
3D12×C3⋊Dic3C211yesmaximal, characteristic
4#11723447C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic
6C3×#63898C211yesmaximal, characteristic
7C3×#63872C211yesmaximal, characteristic, complemented
8#11722980C212yesmaximal, complemented
9#11722978C212yesmaximal, complemented
10#11722971C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12#10595272—31nomaximal
13#10594485—31nomaximal
14#10594452—31nomaximal
15C2×C32×D12C2211yescharacteristic
16C2×#6296C2211yescharacteristic
17C2×#6293C2212yes—
18C2×D3×C3⋊Dic3C2212yes—
19C2×C3×D3×Dic3C2212yes—
20C2×C3×D3×Dic3C2212yes—
21C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27#88815C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88807C2212yes—
31#88806C2212yes—
32Dic3⋊(C3⋊Dic3)C2212yes—
33(C2×D3)⋊(C3⋊Dic3)C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38D4×C3⋊Dic3—31no—
39#64099—31no—
40#64097—31no—
41C3×D4×Dic3—31no—
42C3×D4×Dic3—31no—
43C3×#893—31no—
44C3×#893—31no—
45C3×#890—31no—
46C3×#890—31no—
47#63982—32no—
48C2×Dic3⋊Dic3—32no—
49#63964—32no—
50#63964—32no—
51#63918—31no—
52#63918—31no—
53#63918—61no—
54C4×#627—31no—
55C4×#627—31no—
56C4×#627—31no—
57#63899—32no—
58#63899—32no—
59#63898D311yescharacteristic
60#63898D311yescharacteristic
61#63896—32no—
62#63893—32no—
63Dic3×D12—31no—
64Dic3×D12—31no—
65Dic3×D12—61no—
66D3×C4⋊Dic3—32no—
67D3×Dic3⋊C4—32no—
68#63872D311yescharacteristic, complemented
69#63869—31no—
70#63869—31no—
71#63869—61no—
72#63857—32no—
73#63851—32no—
74C22×C32×D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C32×D12Q814yescomplemented
86#6296—22no—
87#6293—42no—
88D3×C3⋊Dic3—42no—
89C3×D3×Dic3—24no—
90C3×D3×Dic3—42no—
91#5690—91no—
92#5543—91no—
93#5539—91no—
94C2×C32×D4—31no—
95C22×C3⋊Dic3—32no—
96C2×#634—32no—
97C22×C3×Dic3—32no—
98C22×C3×Dic3—32no—
99C2×C3×D12—21no—
100C2×C3×D12C2×D311yescharacteristic
101C2×C3×D12C2×D311yescharacteristic
102C2×C3×C4×D3—32no—
103C2×C3×C4×D3—32no—
104C2×#627—31no—
105C2×#627—31no—
106C2×#627—31no—
107C2×#627—32no—
108C2×#627—32no—
109C2×#627—62no—
110C2×D3×Dic3—32no—
111C2×D3×Dic3—32no—
112C2×D3×Dic3—62no—
113C2×D3×Dic3C2×D312yes—
114C2×D3×Dic3C2×D312yes—
115C32×C4⋊C4—31no—
116C32×C4⋊C4—31no—
117#3757—32no—
118C4⋊(C3⋊Dic3)—31no—
119C4⋊(C3⋊Dic3)—31no—
120C4⋊(C3⋊Dic3)—31no—
121C4⋊(C3⋊Dic3)—32no—
122C4⋊(C3⋊Dic3)—61no—
123C4⋊(C3⋊Dic3)—61no—
124C4⋊(C3⋊Dic3)—61no—
125C4⋊(C3⋊Dic3)—121no—
126#3750—32no—
127#3750—32no—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C4×C3⋊Dic3C2×D311yescharacteristic
130C4×C3⋊Dic3C2×D311yescharacteristic
131C3×#217—32no—
132C3×#217—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—61no—
152C3×C4×Dic3—61no—
153C3×C4×Dic3—61no—
154#3724—31no—
155#3724—31no—
156#3724—31no—
157#3724—32no—
158#3724—32no—
159#3724—62no—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—62no—
171Dic3⋊Dic3—62no—
172Dic3⋊Dic3C2×D312yes—
173Dic3⋊Dic3C2×D312yes—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—62no—
177(C2×D3)⋊Dic3C2×D312yes—
178(C2×D3)⋊Dic3C2×D312yes—
179C22×C33C2411yescharacteristic
180C2×C32×D3—22no—
181C2×C32×D3—22no—
182C2×C32×D3C2×Q814yes—
183C33×C4C2×Q812yes—
184C3⋊(C3⋊Dic3)—22no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3#4112yes—
191C32×Dic3—22no—
192C32×Dic3—22no—
193C3×#125—91no—
194C3×C4×D4—91no—
195C3×C4×D4—91no—
196D4×Dic3—31no—
197D4×Dic3—31no—
198D4×Dic3—91no—
199D4×Dic3—91no—
200D4×Dic3—181no—
201C2×C4⋊Dic3—92no—
202#924—92no—
203#924—92no—
204C2×Dic3⋊C4—92no—
205#897—92no—
206#896—92no—
207#896—92no—
208#893—31no—
209#893—31no—
210D3×C4⋊C4—92no—
211#890—31no—
212#890—31no—
213#890—91no—
214#890—91no—
215#890—181no—
216#888—91no—
217#888—91no—
218#888—181no—
219#878—92no—
220#878—92no—
221#878—92no—
222#878—92no—
223C4×D12—91no—
224#870—91no—
225#869—91no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C23×C32—32no—
230C22×C3×D3—22no—
231C22×C3×D3C22×D312yes—
232C22×C3×D3C22×D312yes—
233C32×D4—34no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—32no—
238C2×C32×C4—32no—
239C2×C32×C4—41no—
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C3⋊Dic3—32no—
244C2×C3⋊Dic3—32no—
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—62no—
247C2×C3⋊Dic3—62no—
248C2×C3⋊Dic3—62no—
249C2×C3⋊Dic3—122no—
250C2×C3⋊Dic3—122no—
251C2×C3⋊Dic3C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257#634—122no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—64no—
279C2×C3×Dic3—122no—
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D312yes—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C3×D12—24no—
285C3×D12Dic614yescomplemented
286C3×D12Dic614yescomplemented
287C3×C4×D3—64no—
288C3×C4×D3—122no—
289#627—62no—
290#627—62no—
291#627—62no—
292#627—122no—
293#627—122no—
294#627—124no—
295D3×Dic3—24no—
296D3×Dic3—42no—
297D3×Dic3—122no—
298D3×Dic3—122no—
299D3×Dic3—124no—
300#554—271noSylow
301C2×C33C22×Q811yescharacteristic
302C2×C33C2×#4111yescharacteristic
303C2×C33H(5,𝔽2)11yescharacteristic
304C32×D3—24no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C22×C3×C4—92no—
309C22×C3×C4—92no—
310C22×Dic3—32no—
311C22×Dic3—32no—
312C22×Dic3—92no—
313C22×Dic3—92no—
314C22×Dic3—182no—
315C2×D12D3211yescharacteristic
316C2×C4×D3—32no—
317C2×C4×D3—32no—
318C2×C4×D3—92no—
319C2×Dic6—91no—
320C2×Dic6—91no—
321C2×Dic6—91no—
322C2×Dic6—92no—
323C2×Dic6—92no—
324C2×Dic6—92no—
325C2×Dic6—182no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—92no—
333C3×C4⋊C4—92no—
334C3×C22⋊C4—92no—
335C3×C22⋊C4—92no—
336C3×C42—91no—
337C3×C42—91no—
338C3×C42—91no—
339#217—32no—
340#217—32no—
341#217—92no—
342#217—92no—
343#217—182no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—92no—
347C4⋊Dic3—32no—
348C4⋊Dic3—32no—
349C4⋊Dic3—91no—
350C4⋊Dic3—91no—
351C4⋊Dic3—91no—
352C4⋊Dic3—92no—
353C4⋊Dic3—92no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—92no—
358C4⋊Dic3—182no—
359C4⋊Dic3—181no—
360C4⋊Dic3—181no—
361C4⋊Dic3—181no—
362C4⋊Dic3—361no—
363C4⋊Dic3D3211yescharacteristic
364C4⋊Dic3D3211yescharacteristic
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—182no—
380Dic3⋊C4—182no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—34no—
394C22×C32—41no—
395C22×C32—62no—
396C22×C32—62no—
397C22×C32C23×D311yescharacteristic
398C22×C32C23×D311yescharacteristic
399C22×C32C23×D311yescharacteristic
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—24no—
405C2×C3×D3—42no—
406C2×C3×D3—42no—
407C2×C3×D3C2×Dic614yes—
408C2×C3×D3C2×Dic614yes—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—42no—
413C32×C4—62no—
414C32×C4—62no—
415C32×C4C2×Dic612yes—
416C32×C4C2×Dic612yes—
417C32×C4D3×Q812yes—
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—21no—
421C3⋊Dic3—21no—
422C3⋊Dic3—21no—
423C3⋊Dic3—62no—
424C3⋊Dic3—62no—
425C3⋊Dic3—62no—
426C3⋊Dic3—122no—
427C3⋊Dic3—122no—
428C3⋊Dic3—122no—
429C3⋊Dic3—242no—
430C3⋊Dic3#23712yes—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—32no—
436C3×Dic3—32no—
437C3×Dic3—42no—
438C3×Dic3—42no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—61no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C3×Dic3—121no—
453C3×Dic3—121no—
454C3×Dic3—121no—
455C4⋊Q8—271no—
456#125—91no—
457#125—271no—
458C22⋊Q8—272no—
459C22⋊Q8—272no—
460C22⋊Q8—272no—
461C4×Q8—271no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—271no—
465C2×C4⋊C4—272no—
466C33#55411yescharacteristic, complemented, Sylow
467C23×C3—32no—
468C23×C3—32no—
469C23×C3—62no—
470C22×D3C2×D3212yes—
471C3×D4—34no—
472C3×D4—34no—
473C3×D4—64no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—41no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—184no—
491C2×C3×C4—362no—
492C2×C3×C4C2×D3211yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—64no—
514C2×Dic3—92no—
515C2×Dic3—92no—
516C2×Dic3—92no—
517C2×Dic3—122no—
518C2×Dic3—182no—
519C2×Dic3—182no—
520C2×Dic3—182no—
521C2×Dic3—362no—
522C2×Dic3—362no—
523C2×Dic3—362no—
524C2×Dic3—364no—
525C2×Dic3C2×D3212yes—
526C2×Dic3C2×D3212yes—
527D12#62714yescomplemented
528C4×D3—64no—
529C4×D3—122no—
530C4×D3—362no—
531Dic6—182no—
532Dic6—182no—
533Dic6—182no—
534Dic6—362no—
535Dic6—362no—
536Dic6—362no—
537Dic6—364no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—41no—
548C2×C32—41no—
549C2×C32—41no—
550C2×C32—64no—
551C2×C32C22×Dic611yescharacteristic
552C2×C32C22×Dic611yescharacteristic
553C2×C32C2×#23711yescharacteristic
554C2×C32#100411yescharacteristic
555C2×C32C2×D3×Q811yescharacteristic
556C2×C32D3×#4111yescharacteristic
557C2×C32D3×#4111yescharacteristic
558C2×C32#100911yescharacteristic
559C2×C32#100911yescharacteristic
560C3×D3—24no—
561C3×D3—24no—
562C3×D3—44no—
563C2×Q8—272no—
564C2×Q8—271no—
565C2×D4—31no—
566C22×C4—92no—
567C22×C4—92no—
568C22×C4—272no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—92no—
572C4⋊C4—92no—
573C4⋊C4—272no—
574C4⋊C4—272no—
575C4⋊C4—272no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C22⋊C4—92no—
581C22⋊C4—92no—
582C22⋊C4—272no—
583C42—91no—
584C42—91no—
585C42—91no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—34no—
590C22×C3—34no—
591C22×C3—41no—
592C22×C3—64no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—122no—
598C22×C3—122no—
599C22×C3C22×D3211yescharacteristic
600C22×C3C22×D3211yescharacteristic
601C22×C3C22×D3211yescharacteristic
602C2×D3—22no—
603C2×D3—22no—
604C2×D3C2×#62714yes—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—42no—
609C3×C4—62no—
610C3×C4—62no—
611C3×C4—62no—
612C3×C4—62no—
613C3×C4—92no—
614C3×C4—122no—
615C3×C4—122no—
616C3×C4—181no—
617C3×C4—181no—
618C3×C4—181no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4D3×Dic612yes—
622C3×C4D3×Dic612yes—
623C3×C4C2×#62712yes—
624Dic3—22no—
625Dic3—22no—
626Dic3—32no—
627Dic3—32no—
628Dic3—62no—
629Dic3—62no—
630Dic3—62no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—61no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—121no—
642Dic3—121no—
643Dic3—121no—
644Dic3—182no—
645Dic3—182no—
646Dic3—182no—
647Dic3—362no—
648Dic3—362no—
649Dic3—362no—
650Dic3—722no—
651C32—21no—
652C32—21no—
653C32—21no—
654C32—41no—
655C32#553911yescharacteristic, complemented
656C32#554311yescharacteristic, complemented
657C32#569011yescharacteristic, complemented
658C23—32no—
659Q8—542no—
660Q8—1082no—
661D4—34no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—184no—
671C2×C4—272no—
672C2×C4—362no—
673C2×C4—1082no—
674C2×C4D3311yescharacteristic
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—41no—
687C2×C3—64no—
688C2×C3—64no—
689C2×C3—124no—
690C2×C3C2×D3×Dic611yescharacteristic
691C2×C3C2×D3×Dic611yescharacteristic
692C2×C3D3×#23711yescharacteristic
693C2×C3D3×#23711yescharacteristic
694C2×C3#6431411yescharacteristic
695C2×C3#6431411yescharacteristic
696C2×C3#6431911yescharacteristic
697C2×C3#6432011yescharacteristic
698C2×C3C22×#62711yescharacteristic
699D3—24no—
700C22—34no—
701C22—62no—
702C22—62no—
703C22C2×D3311yescharacteristic
704C4—62no—
705C4—62no—
706C4—92no—
707C4—181no—
708C4—181no—
709C4—181no—
710C4—181no—
711C4—181no—
712C4—542no—
713C4D3×#62712yes—
714C3—21no—
715C3—21no—
716C3—21no—
717C3—41no—
718C3#1059445211yescharacteristic, complemented
719C3#1059448511yescharacteristic, complemented
720C3#1059527211yescharacteristic, complemented
721C2—64no—
722C2#1172437411yescharacteristic
723C2#1172438611yescharacteristic
724C2C2×D3×#62711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C32×D12C22
hypercenterC2×C4D33
hypocenterC33#554
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. #11723535C2semidirect
4. #11723447C2semidirect
7. C3×#63872C2semidirect
8. #11722980C2semidirect
9. #11722978C2semidirect
10. #11722971C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
68. #63872D3semidirect
85. C32×D12Q8semidirect
285. C3×D12Dic6semidirect
286. C3×D12Dic6semidirect
466. C33#554semidirect
527. D12#627semidirect
655. C32#5539semidirect
656. C32#5543semidirect
657. C32#5690semidirect
718. C3#10594452semidirect
719. C3#10594485semidirect
720. C3#10595272semidirect

Maximal subgroups

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

subgroupindex
C4×#62962
#117235352
D12×C3⋊Dic32
#117234472
C3×#638982
C3×#638722
#117229802
#117229782
#117229712
D3×Dic3⋊Dic32
#105952723
#105944853
#105944523