Finite Group Databasebeta

← #13178717

Subgroups — #13178717

Order 1728.

1504 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64156C211yesmaximal, characteristic, complemented
4C3×#64155C211yesmaximal, characteristic, complemented
5#11723696C211yesmaximal, characteristic, complemented
6#11723695C212yesmaximal, complemented
7C4×#6295C211yesmaximal, characteristic, complemented
8#11723688C212yesmaximal, complemented
9#11723684C212yesmaximal, complemented
10#11723670C212yesmaximal, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595402—31nomaximal
13#10595401—31nomaximal
14#10595362—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C3×Q8×C3⋊D3—24no—
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2212yes—
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#634C2212yes—
22C2×C3×#634C2211yescharacteristic
23C2×#6295C2212yes—
24C2×#6295C2212yes—
25C2×#6295C2211yescharacteristic
26C2×#6294C2212yes—
27#89041—24no—
28C3×#3752C2212yes—
29C3×#3752C2212yes—
30C3×#3752C2212yes—
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C3×#3750C2212yes—
33C3×C4×C3⋊Dic3C2211yescharacteristic
34#88815C2212yes—
35#88815C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2212yes—
38#88814C2211yescharacteristic
39#88813C2212yes—
40C2×Q8×C3⋊D3D311yescharacteristic, complemented
41C2×C3×D3×Q8—31no—
42C2×C3×D3×Q8—31no—
43C2×C3×D3×Q8—61no—
44C2×#3799—31no—
45C2×#3796—31no—
46C2×#3795—31no—
47#64156D311yescharacteristic, complemented
48#64155D311yescharacteristic, complemented
49C3×#947—31no—
50C3×#947—31no—
51C3×#947—61no—
52C3×#946—31no—
53C3×#946—31no—
54C3×#946—61no—
55#63916—31no—
56#63913—32no—
57#63912—32no—
58#63909—31no—
59#63908—31no—
60#63907—32no—
61#63907—32no—
62#63906—32no—
63#63906—32no—
64#63904—32no—
65C4×#626—31no—
66C4×#626—31no—
67C4×#625—31no—
68#63896—32no—
69#63888—32no—
70#63887—32no—
71#63881—32no—
72#63879—32no—
73#63844—31no—
74#63843—31no—
75Dic3×Dic6—31no—
76C22×C3×C3⋊D3C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C3×C3⋊D3C2311yescharacteristic
79C33×Q8—22no—
80C2×C33×C4C2312yes—
81C2×C33×C4C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2312yes—
88C3×C4⋊(C3⋊D3)—22no—
89C3×C4×C3⋊D3—22no—
90C3×C4×C3⋊D3—22no—
91C3×C4×C3⋊D3—24no—
92C3×#634—24no—
93C3×#634D414yescomplemented
94#6295—24no—
95#6295—22no—
96#6295—24no—
97#6294—24no—
98#5817—91no—
99#5677—91no—
100#5633—91no—
101C2×C32×Q8—21no—
102C2×C32×Q8—21no—
103C2×C32×Q8—21no—
104C2×C32×Q8—41no—
105C2×C32×Q8C2×D311yescharacteristic
106C2×C32×Q8C2×D311yescharacteristic
107C2×C32×Q8C2×D311yescharacteristic
108Q8×C3⋊D3—24no—
109C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
110C2×C4×C3⋊D3C2×D311yescharacteristic
111C2×C4×C3⋊D3C2×D312yes—
112C2×C4×C3⋊D3C2×D311yescharacteristic
113C2×#634C2×D312yes—
114C2×#634C2×D311yescharacteristic
115C3×D3×Q8—64no—
116C3×D3×Q8—64no—
117C3×D3×Q8—68no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×D12—61no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—32no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—62no—
128C2×C3×C4×D3—61no—
129C2×C3×C4×D3—61no—
130C2×C3×Dic6—31no—
131C2×C3×Dic6—31no—
132C2×C3×Dic6—32no—
133C2×C3×Dic6—32no—
134C2×C3×Dic6—61no—
135C2×C3×Dic6—62no—
136C2×#626—32no—
137C2×#626—32no—
138C2×#626—32no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#626—32no—
142C2×#625—32no—
143C2×#625—32no—
144C2×#625—31no—
145C2×#624—32no—
146C2×D3×Dic3—32no—
147C2×D3×Dic3—32no—
148#3799—64no—
149#3796—64no—
150#3795—64no—
151#3752C2×D312yes—
152#3752C2×D312yes—
153#3752C2×D312yes—
154C4⋊(C3⋊Dic3)C2×D311yescharacteristic
155#3750C2×D312yes—
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×(C2×D3)⋊C4—32no—
158C3×(C2×D3)⋊C4—32no—
159C3×(C2×D3)⋊C4—32no—
160C3×(C2×D3)⋊C4—32no—
161C3×(C2×D3)⋊C4—32no—
162C3×(C2×D3)⋊C4—32no—
163C3×(C2×D3)⋊C4—62no—
164C3×(C2×D3)⋊C4—62no—
165C3×(C2×D3)⋊C4—62no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—61no—
169C3×Dic3⋊C4—32no—
170C3×Dic3⋊C4—32no—
171C3×Dic3⋊C4—62no—
172C3×C4×Dic3—31no—
173C3×C4×Dic3—31no—
174C3×C4×Dic3—61no—
175#3724—32no—
176#3724—31no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—31no—
180Dic3⋊Dic3—31no—
181#3722—31no—
182#3722—32no—
183#3722—31no—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190Dic32—32no—
191Dic32—32no—
192Dic32—32no—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3#4112yescomplemented
203C33×C4—22no—
204C33×C4C2×D412yes—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—22no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3C2×D414yes—
211C22×C3×Q8—91no—
212C2×#239—91no—
213C2×D3×Q8—31no—
214C2×D3×Q8—31no—
215C2×D3×Q8—61no—
216C2×#237—91no—
217C2×#235—91no—
218C3×#124—91no—
219C3×C22⋊Q8—91no—
220#947—31no—
221#947—31no—
222#947—61no—
223#947—92no—
224#946—31no—
225#946—31no—
226#946—61no—
227#946—92no—
228Q8×Dic3—91no—
229#938—91no—
230#930—91no—
231#930—92no—
232C4×#67—91no—
233C4×#67—91no—
234C4×#67—92no—
235#896—92no—
236#895—91no—
237#893—92no—
238#887—91no—
239#885—92no—
240#885—92no—
241#884—92no—
242#884—92no—
243#67⋊C4—92no—
244#878—92no—
245C4×D12—91no—
246C4×Dic6—91no—
247C22×C3⋊D3C22×D312yes—
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3⋊D3C22×D311yescharacteristic
250C22×C3×D3—31no—
251C22×C3×D3—31no—
252C22×C3×D3—32no—
253C22×C3×D3—32no—
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—61no—
257C22×C3×D3—61no—
258C22×C3×D3—62no—
259C32×Q8—22no—
260C32×Q8—24no—
261C32×Q8—22no—
262C32×Q8—22no—
263C32×Q8—42no—
264C32×Q8—42no—
265C32×Q8—44no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—22no—
269C2×C32×C4—21no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4—41no—
273C2×C32×C4—42no—
274C2×C32×C4C22×D312yes—
275C2×C32×C4C22×D312yes—
276C2×C32×C4C22×D312yes—
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C3⋊Dic3C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D312yes—
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D312yes—
286C4⋊(C3⋊D3)—22no—
287C4×C3⋊D3—22no—
288C4×C3⋊D3—24no—
289C4×C3⋊D3—22no—
290#634—24no—
291#634#6714yescomplemented
292C2×C3×Dic3—32no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—32no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—62no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—62no—
310C3×D12—62no—
311C3×D12—62no—
312C3×D12—122no—
313C3×C4×D3—64no—
314C3×C4×D3—64no—
315C3×C4×D3—68no—
316C3×C4×D3—64no—
317C3×C4×D3—62no—
318C3×C4×D3—62no—
319C3×C4×D3—62no—
320C3×C4×D3—62no—
321C3×C4×D3—122no—
322C3×Dic6—34no—
323C3×Dic6—34no—
324C3×Dic6—64no—
325C3×Dic6—64no—
326C3×Dic6—64no—
327C3×Dic6—68no—
328#626—64no—
329#626—64no—
330#626—62no—
331#626—64no—
332#626—64no—
333#626—62no—
334#625—64no—
335#625—62no—
336#625—64no—
337#624—64no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340#548—271noSylow
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C332−1+411yescharacteristic
344C3×C3⋊D3—22no—
345C3×C3⋊D3—41no—
346C3×C3⋊D3—42no—
347C2×C3×Q8—21no—
348C2×C3×Q8—21no—
349C2×C3×Q8—21no—
350C2×C3×Q8—41no—
351C2×C3×Q8—91no—
352C2×C3×Q8—92no—
353C2×C3×Q8—184no—
354C2×C3×Q8D3211yescharacteristic
355C2×C3×Q8D3211yescharacteristic
356C2×C3×Q8D3211yescharacteristic
357C2×C3×D4—91no—
358C22×C3×C4—92no—
359C22×C3×C4—91no—
360C22×C3×C4—91no—
361C2×#67—92no—
362C2×#67—91no—
363C2×#67—92no—
364C2×#67—92no—
365C2×#67—91no—
366C2×#67—92no—
367C22×Dic3—92no—
368#239—184no—
369D3×Q8—64no—
370D3×Q8—64no—
371D3×Q8—68no—
372#237—184no—
373#235—184no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—61no—
377C2×D12—91no—
378C2×D12—92no—
379C2×D12—92no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—32no—
383C2×C4×D3—32no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—62no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—92no—
390C2×C4×D3—92no—
391C2×Dic6—31no—
392C2×Dic6—31no—
393C2×Dic6—32no—
394C2×Dic6—32no—
395C2×Dic6—61no—
396C2×Dic6—62no—
397C3×C4⋊C4—91no—
398C3×C4⋊C4—92no—
399C3×C22⋊C4—92no—
400C3×C22⋊C4—92no—
401C3×C22⋊C4—92no—
402C3×C42—91no—
403#217—92no—
404#217—91no—
405#217—91no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—32no—
411(C2×D3)⋊C4—32no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—92no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—92no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424C4⋊Dic3—91no—
425C4⋊Dic3—92no—
426Dic3⋊C4—32no—
427Dic3⋊C4—32no—
428Dic3⋊C4—62no—
429Dic3⋊C4—92no—
430Dic3⋊C4—92no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—61no—
436C4×Dic3—92no—
437C4×Dic3—92no—
438C4×Dic3—92no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—41no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3#23912yescomplemented
455C2×C3×D3—32no—
456C2×C3×D3—32no—
457C2×C3×D3—62no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—62no—
465C2×C3×D3—62no—
466C2×C3×D3—61no—
467C2×C3×D3—62no—
468C2×C3×D3—61no—
469C2×C3×D3—62no—
470C2×C3×D3—62no—
471C2×C3×D3—61no—
472C2×C3×D3—62no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—62no—
476C2×C3×D3—61no—
477C2×C3×D3—121no—
478C2×C3×D3—121no—
479C2×C3×D3—122no—
480C2×C3×D3—122no—
481C2×C3×D3—122no—
482C32×C4—22no—
483C32×C4—24no—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—22no—
487C32×C4—22no—
488C32×C4—22no—
489C32×C4—42no—
490C32×C4—42no—
491C32×C4—42no—
492C32×C4—44no—
493C32×C4D3×D412yes—
494C32×C4D3×D412yes—
495C32×C4C2×#6712yes—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—22no—
499C3⋊Dic3—21no—
500C3⋊Dic3—21no—
501C3⋊Dic3C2×#6714yes—
502C3×Dic3—34no—
503C3×Dic3—34no—
504C3×Dic3—64no—
505C3×Dic3—62no—
506C3×Dic3—61no—
507C3×Dic3—61no—
508C3×Dic3—61no—
509C3×Dic3—62no—
510C3×Dic3—61no—
511C3×Dic3—61no—
512C3×Dic3—61no—
513C3×Dic3—61no—
514C3×Dic3—62no—
515C3×Dic3—61no—
516C3×Dic3—121no—
517C3×Dic3—121no—
518C3×Dic3—122no—
519C3×Dic3—121no—
520C2×#41—271no—
521C22×Q8—91no—
522#124—91no—
523#124—272no—
524C22⋊Q8—91no—
525C22⋊Q8—272no—
526#121—272no—
527#121—271no—
528C4×Q8—271no—
529C4×D4—271no—
530C4×D4—272no—
531C33#54811yescharacteristic, complemented, Sylow
532C23×C3—91no—
533C23×C3—92no—
534C23×C3—91no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—31no—
539C22×D3—32no—
540C22×D3—32no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—62no—
544C3×Q8—24no—
545C3×Q8—22no—
546C3×Q8—22no—
547C3×Q8—22no—
548C3×Q8—42no—
549C3×Q8—42no—
550C3×Q8—44no—
551C3×Q8—94no—
552C3×Q8—184no—
553C3×D4—182no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—42no—
561C2×C3×C4—41no—
562C2×C3×C4—92no—
563C2×C3×C4—91no—
564C2×C3×C4—92no—
565C2×C3×C4—91no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—184no—
569C2×C3×C4—182no—
570C2×C3×C4—182no—
571C2×C3×C4C2×D3212yes—
572C2×C3×C4C2×D3212yes—
573C2×C3×C4C2×D3212yes—
574C2×C3×C4C2×D3211yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577#67—184no—
578#67—184no—
579#67—182no—
580#67—184no—
581#67—182no—
582#67—184no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—62no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—62no—
601C2×Dic3—184no—
602D12—62no—
603D12—62no—
604D12—122no—
605D12—184no—
606D12—184no—
607D12—182no—
608C4×D3—64no—
609C4×D3—64no—
610C4×D3—68no—
611C4×D3—64no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—62no—
615C4×D3—62no—
616C4×D3—122no—
617C4×D3—184no—
618C4×D3—184no—
619Dic6—34no—
620Dic6—34no—
621Dic6—64no—
622Dic6—64no—
623Dic6—64no—
624Dic6—68no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—41no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32C2×D3×D411yescharacteristic
638C2×C32C2×D3×D411yescharacteristic
639C2×C32C2×#23911yescharacteristic
640C2×C32#100711yescharacteristic
641C2×C32#100711yescharacteristic
642C2×C32D3×#4111yescharacteristic
643C2×C32D3×#4111yescharacteristic
644C2×C32#101011yescharacteristic
645C2×C32C22×#6711yescharacteristic
646C3⋊D3—22no—
647C3⋊D3—41no—
648C3⋊D3—42no—
649C3×D3—64no—
650C3×D3—62no—
651C3×D3—62no—
652C3×D3—122no—
653C3×D3—122no—
654C3×D3—121no—
655C3×D3—122no—
656C3×D3—121no—
657C3×D3—242no—
658#41—544no—
659C2×Q8—91no—
660C2×Q8—92no—
661C2×Q8—184no—
662C2×Q8#111311yescharacteristic
663C2×D4—91no—
664C2×D4—271no—
665C2×D4—272no—
666C2×D4—272no—
667C22×C4—92no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—272no—
671C4⋊C4—92no—
672C4⋊C4—91no—
673C4⋊C4—271no—
674C4⋊C4—272no—
675C22⋊C4—92no—
676C22⋊C4—92no—
677C22⋊C4—92no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—272no—
681C42—91no—
682C42—272no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—41no—
687C22×C3—92no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—182no—
692C22×C3—181no—
693C22×C3—182no—
694C22×C3—182no—
695C22×C3—181no—
696C22×C3C22×D3211yescharacteristic
697C22×C3C22×D3211yescharacteristic
698C22×C3C22×D3211yescharacteristic
699C2×D3—32no—
700C2×D3—32no—
701C2×D3—62no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—62no—
709C2×D3—61no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—61no—
713C2×D3—62no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—62no—
717C2×D3—61no—
718C2×D3—62no—
719C2×D3—61no—
720C2×D3—62no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—122no—
724C2×D3—122no—
725C2×D3—122no—
726C3×C4—24no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—44no—
736C3×C4—42no—
737C3×C4—94no—
738C3×C4—181no—
739C3×C4—182no—
740C3×C4—181no—
741C3×C4—181no—
742C3×C4—181no—
743C3×C4D3×#6712yes—
744C3×C4D3×#6712yes—
745C3×C4#381112yes—
746Dic3—34no—
747Dic3—34no—
748Dic3—64no—
749Dic3—62no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—62no—
754Dic3—61no—
755Dic3—62no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761Dic3—121no—
762Dic3—122no—
763Dic3—121no—
764C32—21no—
765C32—21no—
766C32—21no—
767C32—41no—
768C32#563311yescharacteristic, complemented
769C32#567711yescharacteristic, complemented
770C32#581711yescharacteristic, complemented
771C23—91no—
772C23—91no—
773C23—92no—
774Q8—22no—
775Q8—94no—
776Q8—184no—
777D4—182no—
778D4—544no—
779D4—542no—
780D4—544no—
781C2×C4—92no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—92no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—184no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—544no—
791C2×C4C2×#111312yes—
792C2×C4C2×#111311yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—182no—
806C2×C3—361no—
807C2×C3—362no—
808C2×C3#6431511yescharacteristic
809C2×C3#6431511yescharacteristic
810C2×C3#6431611yescharacteristic
811C2×C3D3×#23911yescharacteristic
812C2×C3D3×#23911yescharacteristic
813C2×C3#6431911yescharacteristic
814C2×C3C2×D3×#6711yescharacteristic
815C2×C3C2×D3×#6711yescharacteristic
816C2×C3C2×#381111yescharacteristic
817D3—64no—
818D3—62no—
819D3—62no—
820D3—122no—
821D3—121no—
822D3—122no—
823D3—122no—
824D3—121no—
825D3—242no—
826C22—92no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—182no—
831C22—181no—
832C22—182no—
833C22—181no—
834C22—182no—
835C22C22×#111311yescharacteristic
836C4—22no—
837C4—94no—
838C4—181no—
839C4—181no—
840C4—182no—
841C4—181no—
842C4—181no—
843C4#8904912yes—
844C3—21no—
845C3—21no—
846C3—21no—
847C3—41no—
848C3#1059536211yescharacteristic, complemented
849C3#1059540111yescharacteristic, complemented
850C3#1059540211yescharacteristic, complemented
851C2—182no—
852C2—361no—
853C2—362no—
854C2#1172462411yescharacteristic
855C2#1172462611yescharacteristic
856C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
hypercenterC2×Q8#1113
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×C3⋊D3C2semidirect
2. C2×#89041C2semidirect
3. C3×#64156C2semidirect
4. C3×#64155C2semidirect
5. #11723696C2semidirect
6. #11723695C2semidirect
7. C4×#6295C2semidirect
8. #11723688C2semidirect
9. #11723684C2semidirect
10. #11723670C2semidirect
11. #11723668C2semidirect
40. C2×Q8×C3⋊D3D3semidirect
47. #64156D3semidirect
48. #64155D3semidirect
93. C3×#634D4semidirect
202. C2×C3×C3⋊D3#41semidirect
291. #634#67semidirect
454. C2×C3⋊D3#239semidirect
531. C33#548semidirect
768. C32#5633semidirect
769. C32#5677semidirect
770. C32#5817semidirect
848. C3#10595362semidirect
849. C3#10595401semidirect
850. C3#10595402semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×C3⋊D32
C2×#890412
C3×#641562
C3×#641552
#117236962
#117236952
C4×#62952
#117236882
#117236842
#117236702
#117236682
#105954023
#105954013
#105953623