Finite Group Databasebeta

← #13169194

Subgroups — #13169194

Order 1728.

1548 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89018C211yesmaximal, characteristic, complemented
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4#11723516C211yesmaximal, characteristic, complemented
5#11723441C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723003C212yesmaximal, complemented
9#11722973C212yesmaximal, complemented
10#11722959C212yesmaximal, complemented
11#11722932C212yesmaximal, complemented
12#10595342—31nomaximal
13#10594902—31nomaximal
14#10593899—31nomaximal
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6292C2212yes—
21C2×#6291C2212yes—
22C2×#6289C2212yes—
23#89018—24no—
24C2×C3×#627C2212yes—
25C2×C3×#626C2211yescharacteristic
26C2×C3×D3×Dic3C2212yes—
27C3×D3×Dic6—24no—
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30#88815C2212yes—
31#88814C2212yes—
32#88804C2212yes—
33#88804C2212yes—
34#88804C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2211yescharacteristic
37C3×#3722C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×#3832—31no—
41C2×C3×D3×Q8—31no—
42C22×C3×Dic6—31no—
43C2×#3799—31no—
44C2×#3799—31no—
45C2×#3799—61no—
46C2×D3×Dic6D311yescharacteristic, complemented
47#64139—31no—
48#64084—31no—
49C3×Q8×Dic3—31no—
50C3×C4×#67—31no—
51C3×C4×D12—31no—
52C3×C4×Dic6—31no—
53#63978—32no—
54#63952—32no—
55#63909—31no—
56#63909—31no—
57#63909—32no—
58#63909—61no—
59#63907—32no—
60C4×#626—32no—
61C4×#626D311yescharacteristic, complemented
62#63895—32no—
63#63888—32no—
64#63886—32no—
65#63880—32no—
66#63871—31no—
67#63871—32no—
68#63864—31no—
69#63864—31no—
70#63864—32no—
71#63864—61no—
72#63857—31no—
73#63856—31no—
74#63852—32no—
75Dic3×Dic6D311yescharacteristic, complemented
76C22×C3⋊(C3⋊D3)C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C2×C33×C4C2311yescharacteristic
80C4⋊(C3⋊(C3⋊D3))—22no—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3—22no—
85C3×#634—22no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C32×C4×D3—22no—
91C32×Dic6D414yescomplemented
92#6292—24no—
93#6291—24no—
94#6289—24no—
95C3×#627—24no—
96C3×#626—22no—
97C3×D3×Dic3—24no—
98#5817—91no—
99#5576—91no—
100#5552—91no—
101C2×C32×Q8—31no—
102C22×C32×C4—31no—
103C2×#638—32no—
104#3832—64no—
105C2×C4⋊(C3⋊D3)—32no—
106C2×C4⋊(C3⋊D3)—31no—
107C2×C4⋊(C3⋊D3)—31no—
108C2×C4⋊(C3⋊D3)—31no—
109C2×C4⋊(C3⋊D3)—61no—
110C2×C4⋊(C3⋊D3)—61no—
111C2×C4⋊(C3⋊D3)—61no—
112C2×C4⋊(C3⋊D3)—121no—
113C2×C4×C3⋊D3—32no—
114C2×C4×C3⋊D3C2×D311yescharacteristic
115C2×#634C2×D311yescharacteristic
116C2×C3×#67—31no—
117C22×C3×Dic3—32no—
118C3×D3×Q8—64no—
119C2×C3×D12—31no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—61no—
125C2×C3×C4×D3C2×D311yescharacteristic
126C2×C3×C4×D3C2×D311yescharacteristic
127C2×C3×Dic6—21no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—32no—
131C2×C3×Dic6—32no—
132C2×C3×Dic6—64no—
133C2×C3×Dic6—61no—
134C2×C3×Dic6C2×D311yescharacteristic
135C2×C3×Dic6C2×D311yescharacteristic
136C2×#627C2×D312yes—
137C2×#626—32no—
138C2×#626—32no—
139C2×#626—32no—
140C2×#626—32no—
141C2×#626—62no—
142C2×#626—62no—
143C2×#626C2×D311yescharacteristic
144C2×#624—32no—
145C2×#624—32no—
146C2×#624—62no—
147C2×D3×Dic3C2×D312yes—
148#3799—68no—
149#3799—64no—
150#3799—64no—
151D3×Dic6—24no—
152C32×C42—31no—
153#3752—32no—
154#3752—32no—
155#3752—32no—
156C4⋊(C3⋊Dic3)C2×D311yescharacteristic
157C3×#217—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—32no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—61no—
166C3×Dic3⋊C4—31no—
167C3×Dic3⋊C4—32no—
168C3×C4×Dic3—21no—
169C3×C4×Dic3—32no—
170C3×C4×Dic3—32no—
171C3×C4×Dic3C2×D311yescharacteristic
172C3×C4×Dic3C2×D311yescharacteristic
173#3724—32no—
174Dic3⋊Dic3—32no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3C2×D312yes—
177Dic3⋊Dic3C2×D311yescharacteristic
178#3722—32no—
179#3722—32no—
180#3722—32no—
181#3722—32no—
182#3722—32no—
183#3722—32no—
184#3722—32no—
185#3722—62no—
186#3722—62no—
187#3722—62no—
188#3722C2×D311yescharacteristic
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3C2×D311yescharacteristic
192Dic32C2×D312yes—
193C22×C33C2411yescharacteristic
194C2×C3⋊(C3⋊D3)—22no—
195C2×C3⋊(C3⋊D3)—22no—
196C2×C3⋊(C3⋊D3)—22no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3#4112yescomplemented
203C33×C4C2×D412yes—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C3×C3⋊Dic3—22no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3—21no—
210C32×Dic3C2×D414yes—
211C22×C3×Q8—91no—
212C2×#239—91no—
213C2×#239—91no—
214C2×#239—181no—
215C2×D3×Q8—31no—
216C2×#235—91no—
217C22×Dic6—31no—
218C3×C4×Q8—91no—
219C3×C4×D4—91no—
220#947—92no—
221#947—91no—
222#946—92no—
223#946—91no—
224Q8×Dic3—31no—
225#939—92no—
226#930—92no—
227#930—91no—
228#930—91no—
229#930—181no—
230C4×#67—31no—
231C4×#67—92no—
232#924—91no—
233#897—92no—
234#897—91no—
235#896—92no—
236#895—92no—
237#895—91no—
238#885—92no—
239#67⋊C4—92no—
240#875—92no—
241#875—91no—
242#875—91no—
243#875—181no—
244C4×D12—31no—
245C4×D12—92no—
246C4×Dic6—31no—
247C23×C32—31no—
248C22×C3⋊D3—32no—
249C22×C3⋊D3—32no—
250C22×C3⋊D3—32no—
251C22×C3⋊D3—62no—
252C22×C3⋊D3—62no—
253C22×C3⋊D3—62no—
254C22×C3⋊D3—122no—
255C22×C3⋊D3C22×D311yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3—61no—
260C22×C3×D3C22×D311yescharacteristic
261C22×C3×D3C22×D311yescharacteristic
262C32×Q8—34no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—32no—
267C2×C32×C4—31no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—41no—
271C2×C32×C4—62no—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—64no—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D312yes—
278C2×C3⋊Dic3C22×D311yescharacteristic
279C4⋊(C3⋊D3)—64no—
280C4⋊(C3⋊D3)—62no—
281C4⋊(C3⋊D3)—64no—
282C4⋊(C3⋊D3)—62no—
283C4⋊(C3⋊D3)—62no—
284C4⋊(C3⋊D3)—122no—
285C4⋊(C3⋊D3)—122no—
286C4⋊(C3⋊D3)—124no—
287C4×C3⋊D3—22no—
288C4×C3⋊D3—64no—
289#634—22no—
290C3×#67—62no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—32no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—61no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—62no—
304C2×C3×Dic3—64no—
305C2×C3×Dic3C22×D311yescharacteristic
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D311yescharacteristic
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C22×D311yescharacteristic
311C2×C3×Dic3C22×D312yes—
312C2×C3×Dic3C22×D312yes—
313C3×D12—62no—
314C3×C4×D3—22no—
315C3×C4×D3—22no—
316C3×C4×D3—42no—
317C3×C4×D3—64no—
318C3×C4×D3—64no—
319C3×C4×D3—62no—
320C3×C4×D3—62no—
321C3×Dic6—24no—
322C3×Dic6—64no—
323C3×Dic6—62no—
324C3×Dic6—62no—
325C3×Dic6—64no—
326C3×Dic6—122no—
327C3×Dic6D1214yescomplemented
328C3×Dic6#6714yescomplemented
329#627—24no—
330#626—22no—
331#626—68no—
332#626—64no—
333#626—64no—
334#626—64no—
335#626—64no—
336#626—124no—
337#624—68no—
338#624—64no—
339#624—64no—
340D3×Dic3—24no—
341#548—271noSylow
342C2×C33C22×D411yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C2×C332−1+411yescharacteristic
345C3⋊(C3⋊D3)—42no—
346C3×C3⋊D3—41no—
347C32×D3—22no—
348C2×C3×Q8—31no—
349C2×C3×Q8—31no—
350C2×C3×Q8—61no—
351C2×C3×Q8—92no—
352C2×C3×Q8—91no—
353C2×C3×Q8—184no—
354C2×C3×D4—91no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—61no—
358C22×C3×C4—92no—
359C22×C3×C4—91no—
360C2×#67—31no—
361C2×#67—92no—
362C2×#67—92no—
363C2×#67—92no—
364C2×#67—182no—
365C22×Dic3—32no—
366#239—184no—
367#239—184no—
368#239—188no—
369D3×Q8—64no—
370#235—184no—
371C2×D12—31no—
372C2×D12—92no—
373C2×D12—92no—
374C2×D12—92no—
375C2×D12—91no—
376C2×D12—91no—
377C2×D12—91no—
378C2×D12—181no—
379C2×D12—182no—
380C2×D12—181no—
381C2×D12—181no—
382C2×D12—361no—
383C2×C4×D3—32no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—61no—
387C2×C4×D3—92no—
388C2×C4×D3—92no—
389C2×C4×D3—92no—
390C2×C4×D3—182no—
391C2×C4×D3D3211yescharacteristic
392C2×Dic6—31no—
393C2×Dic6—31no—
394C2×Dic6—32no—
395C2×Dic6—32no—
396C2×Dic6—61no—
397C2×Dic6—64no—
398C2×Dic6D3211yescharacteristic
399C3×C4⋊C4—92no—
400C3×C4⋊C4—91no—
401C3×C4⋊C4—91no—
402C3×C22⋊C4—91no—
403C3×C22⋊C4—91no—
404C3×C42—31no—
405C3×C42—31no—
406C3×C42—61no—
407C3×C42—92no—
408#217—31no—
409#217—92no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—92no—
414(C2×D3)⋊C4—92no—
415(C2×D3)⋊C4—92no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—92no—
418(C2×D3)⋊C4—92no—
419(C2×D3)⋊C4—92no—
420(C2×D3)⋊C4—92no—
421(C2×D3)⋊C4—92no—
422(C2×D3)⋊C4—92no—
423(C2×D3)⋊C4—92no—
424(C2×D3)⋊C4—182no—
425(C2×D3)⋊C4—182no—
426(C2×D3)⋊C4—182no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—32no—
431C4⋊Dic3—61no—
432C4⋊Dic3—92no—
433Dic3⋊C4—32no—
434Dic3⋊C4—31no—
435Dic3⋊C4—92no—
436Dic3⋊C4—92no—
437C4×Dic3—32no—
438C4×Dic3—32no—
439C4×Dic3D3211yescharacteristic
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—32no—
444C22×C32—41no—
445C22×C32—61no—
446C22×C32—61no—
447C22×C32C23×D311yescharacteristic
448C22×C32C23×D311yescharacteristic
449C22×C32C23×D311yescharacteristic
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—62no—
454C2×C3⋊D3—64no—
455C2×C3⋊D3—62no—
456C2×C3⋊D3—62no—
457C2×C3⋊D3—62no—
458C2×C3⋊D3—62no—
459C2×C3⋊D3—62no—
460C2×C3⋊D3—62no—
461C2×C3⋊D3—62no—
462C2×C3⋊D3—62no—
463C2×C3⋊D3—122no—
464C2×C3⋊D3—122no—
465C2×C3⋊D3—124no—
466C2×C3⋊D3—122no—
467C2×C3⋊D3—122no—
468C2×C3⋊D3—122no—
469C2×C3⋊D3—122no—
470C2×C3⋊D3—122no—
471C2×C3⋊D3—122no—
472C2×C3⋊D3—242no—
473C2×C3⋊D3—242no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—62no—
482C2×C3×D3—61no—
483C2×C3×D3—61no—
484C2×C3×D3—61no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
488C2×C3×D3—121no—
489C2×C3×D3—121no—
490C2×C3×D3#23512yescomplemented
491C2×C3×D3#23912yescomplemented
492C32×C4—22no—
493C32×C4—22no—
494C32×C4—22no—
495C32×C4—34no—
496C32×C4—42no—
497C32×C4—61no—
498C32×C4—61no—
499C32×C4—61no—
500C32×C4C2×D1212yes—
501C32×C4D3×D412yes—
502C32×C4C2×#6712yes—
503C3⋊Dic3—21no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3×Dic3—21no—
507C3×Dic3—21no—
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—21no—
511C3×Dic3—21no—
512C3×Dic3—24no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C3×Dic3—62no—
517C3×Dic3—61no—
518C3×Dic3—62no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—62no—
522C3×Dic3—61no—
523C3×Dic3—122no—
524C3×Dic3—122no—
525C3×Dic3C2×D1214yes—
526C3×Dic3C2×#6714yes—
527C2×#41—271no—
528C22×Q8—91no—
529#124—271no—
530#124—272no—
531C22⋊Q8—272no—
532C22⋊Q8—271no—
533#121—271no—
534#121—272no—
535C4×Q8—91no—
536C4×D4—91no—
537C4×D4—272no—
538C33#54811yescharacteristic, complemented, Sylow
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—91no—
543C22×D3—31no—
544C22×D3—31no—
545C22×D3—61no—
546C22×D3—92no—
547C22×D3—92no—
548C22×D3—92no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—362no—
553C22×D3C2×D3211yescharacteristic
554C3×Q8—34no—
555C3×Q8—34no—
556C3×Q8—64no—
557C3×Q8—184no—
558C3×Q8—182no—
559C3×D4—182no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—62no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4—91no—
579C2×C3×C4—92no—
580C2×C3×C4—92no—
581C2×C3×C4—122no—
582C2×C3×C4—184no—
583C2×C3×C4—182no—
584C2×C3×C4C2×D3211yescharacteristic
585C2×C3×C4C2×D3211yescharacteristic
586C2×C3×C4C2×D3211yescharacteristic
587#67—62no—
588#67—184no—
589#67—184no—
590#67—184no—
591#67—364no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—31no—
595C2×Dic3—32no—
596C2×Dic3—31no—
597C2×Dic3—32no—
598C2×Dic3—61no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—64no—
602C2×Dic3C2×D3211yescharacteristic
603C2×Dic3C2×D3211yescharacteristic
604C2×Dic3C2×D3211yescharacteristic
605C2×Dic3C2×D3212yes—
606D12—62no—
607D12—184no—
608D12—184no—
609D12—184no—
610D12—188no—
611D12—184no—
612D12—182no—
613D12—182no—
614D12—182no—
615D12—362no—
616D12—362no—
617D12—364no—
618C4×D3—22no—
619C4×D3—64no—
620C4×D3—64no—
621C4×D3—62no—
622C4×D3—62no—
623C4×D3—184no—
624C4×D3—184no—
625C4×D3—188no—
626C4×D3—184no—
627Dic6—64no—
628Dic6—62no—
629Dic6—62no—
630Dic6—64no—
631Dic6—122no—
632Dic6#62614yescomplemented
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—62no—
646C2×C32C22×D1211yescharacteristic
647C2×C32C2×#23511yescharacteristic
648C2×C32C2×D3×D411yescharacteristic
649C2×C32C2×#23911yescharacteristic
650C2×C32#100711yescharacteristic
651C2×C32#100711yescharacteristic
652C2×C32D3×#4111yescharacteristic
653C2×C32#101011yescharacteristic
654C2×C32C22×#6711yescharacteristic
655C3⋊D3—41no—
656C3⋊D3—122no—
657C3⋊D3—124no—
658C3⋊D3—122no—
659C3⋊D3—122no—
660C3⋊D3—242no—
661C3⋊D3—242no—
662C3⋊D3—244no—
663C3×D3—22no—
664C3×D3—22no—
665C3×D3—42no—
666C3×D3—122no—
667C3×D3—121no—
668C3×D3—121no—
669#41—544no—
670C2×Q8—31no—
671C2×Q8—92no—
672C2×Q8—91no—
673C2×Q8—184no—
674C2×D4—91no—
675C2×D4—272no—
676C2×D4—272no—
677C2×D4—271no—
678C22×C4—31no—
679C22×C4—92no—
680C22×C4—91no—
681C22×C4—272no—
682C4⋊C4—91no—
683C4⋊C4—92no—
684C4⋊C4—91no—
685C4⋊C4—272no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—272no—
689C22⋊C4—272no—
690C22⋊C4—272no—
691C22⋊C4—272no—
692C42—31no—
693C42—92no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—32no—
698C22×C3—32no—
699C22×C3—41no—
700C22×C3—62no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—181no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3C22×D3211yescharacteristic
711C22×C3C22×D3211yescharacteristic
712C22×C3C22×D3211yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—62no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—184no—
725C2×D3—182no—
726C2×D3—182no—
727C2×D3—182no—
728C2×D3—182no—
729C2×D3—182no—
730C2×D3—182no—
731C2×D3—182no—
732C2×D3—182no—
733C2×D3—182no—
734C2×D3—362no—
735C2×D3—362no—
736C2×D3—362no—
737C2×D3—362no—
738C2×D3—362no—
739C2×D3—362no—
740C2×D3—362no—
741C2×D3—362no—
742C2×D3—364no—
743C2×D3—722no—
744C2×D3—722no—
745C2×D3#379912yescomplemented
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—34no—
750C3×C4—34no—
751C3×C4—42no—
752C3×C4—64no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—182no—
763C3×C4—182no—
764C3×C4—181no—
765C3×C4D3×D1212yes—
766C3×C4C2×#62612yes—
767C3×C4D3×#6712yes—
768Dic3—21no—
769Dic3—21no—
770Dic3—21no—
771Dic3—62no—
772Dic3—61no—
773Dic3—62no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—61no—
778Dic3—122no—
779Dic3—122no—
780Dic3C2×#62614yes—
781C32—21no—
782C32—21no—
783C32—21no—
784C32—41no—
785C32#555211yescharacteristic, complemented
786C32#557611yescharacteristic, complemented
787C32#581711yescharacteristic, complemented
788C23—31no—
789C23—91no—
790C23—272no—
791Q8—34no—
792Q8—184no—
793Q8—182no—
794D4—182no—
795D4—544no—
796D4—544no—
797D4—542no—
798C2×C4—32no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—62no—
803C2×C4—92no—
804C2×C4—91no—
805C2×C4—92no—
806C2×C4—184no—
807C2×C4—182no—
808C2×C4—544no—
809C2×C4D3311yescharacteristic
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—62no—
823C2×C3—62no—
824C2×C3—122no—
825C2×C3—361no—
826C2×C3#6429711yescharacteristic
827C2×C3#6429711yescharacteristic
828C2×C3C2×#379911yescharacteristic
829C2×C3C2×D3×D1211yescharacteristic
830C2×C3D3×#23511yescharacteristic
831C2×C3#6431611yescharacteristic
832C2×C3D3×#23911yescharacteristic
833C2×C3C22×#62611yescharacteristic
834C2×C3C2×D3×#6711yescharacteristic
835D3—22no—
836D3—122no—
837D3—121no—
838D3—121no—
839D3—364no—
840D3—362no—
841D3—362no—
842D3—362no—
843D3—722no—
844D3—722no—
845D3—724no—
846C22—32no—
847C22—61no—
848C22—61no—
849C22—181no—
850C22—181no—
851C22—181no—
852C22—542no—
853C22—542no—
854C22—542no—
855C22C2×D3311yescharacteristic
856C4—34no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—182no—
861C4—181no—
862C4—182no—
863C4D3×#62612yes—
864C3—21no—
865C3—21no—
866C3—21no—
867C3—41no—
868C3#1059389911yescharacteristic, complemented
869C3#1059490211yescharacteristic, complemented
870C3#1059534211yescharacteristic, complemented
871C2—62no—
872C2—361no—
873C2—1082no—
874C2D3×#379911yescharacteristic
875C2#1172439511yescharacteristic
876C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89018C2semidirect
2. C2×C3×D3×Dic6C2semidirect
3. #11723674C2semidirect
4. #11723516C2semidirect
5. #11723441C2semidirect
6. C3×C4×#626C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723003C2semidirect
9. #11722973C2semidirect
10. #11722959C2semidirect
11. #11722932C2semidirect
46. C2×D3×Dic6D3semidirect
61. C4×#626D3semidirect
75. Dic3×Dic6D3semidirect
91. C32×Dic6D4semidirect
202. C2×C32×D3#41semidirect
327. C3×Dic6D12semidirect
328. C3×Dic6#67semidirect
490. C2×C3×D3#235semidirect
491. C2×C3×D3#239semidirect
538. C33#548semidirect
632. Dic6#626semidirect
745. C2×D3#3799semidirect
785. C32#5552semidirect
786. C32#5576semidirect
787. C32#5817semidirect
868. C3#10593899semidirect
869. C3#10594902semidirect
870. C3#10595342semidirect

Maximal subgroups

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

subgroupindex
C2×#890182
C2×C3×D3×Dic62
#117236742
#117235162
#117234412
C3×C4×#6262
C3×Dic3×Dic62
#117230032
#117229732
#117229592
#117229322
#105953423
#105949023
#105938993