Finite Group Databasebeta

← #13178716

Subgroups — #13178716

Order 1728.

1456 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89040C211yesmaximal, characteristic, complemented
3C3×#64155C211yesmaximal, characteristic, complemented
4C3×#64153C211yesmaximal, characteristic, complemented
5C4×#6295C211yesmaximal, characteristic
6#11723688C212yesmaximal, complemented
7#11723684C212yesmaximal
8#11723674C211yesmaximal, characteristic, complemented
9#11723671C212yesmaximal, complemented
10#11723668C211yesmaximal, characteristic, complemented
11#11723666C212yesmaximal, complemented
12#10595403—31nomaximal
13#10595400—31nomaximal
14#10595361—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C3×Q8×C3⋊D3—24no—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2212yes—
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×C3×#634C2212yes—
22C2×C3×#634C2211yescharacteristic
23C2×#6296C2212yes—
24C2×#6295C2211yescharacteristic
25C2×#6294C2212yes—
26#89040—24no—
27C3×#3752C2212yes—
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3750C2212yes—
30C3×#3750C2212yes—
31C3×#3750C2212yes—
32C3×C4×C3⋊Dic3C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2212yes—
35#88815C2212yes—
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×#3797—31no—
45C2×D3×Dic6—31no—
46C2×D3×Dic6—31no—
47#64155D311yescharacteristic, complemented
48#64153D311yescharacteristic, complemented
49C3×#946—31no—
50C3×#946—31no—
51C3×#946—61no—
52C3×#944—31no—
53C3×#944—31no—
54C3×#944—61no—
55#63904—32no—
56C4×#626—31no—
57C4×#626—31no—
58C4×#625—31no—
59#63896—32no—
60#63888—32no—
61#63887—32no—
62#63881—32no—
63#63879—32no—
64#63871—31no—
65#63865—32no—
66#63857—31no—
67#63856—31no—
68#63851—32no—
69#63851—32no—
70#63844—31no—
71#63843—31no—
72Dic3×Dic6—31no—
73#63840—32no—
74#63839—32no—
75#63839—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C33×Q8—22no—
79C2×C33×C4C2312yes—
80C2×C33×C4C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4×C3⋊D3—22no—
89C3×C4×C3⋊D3—22no—
90C3×C4×C3⋊D3—24no—
91C3×#634—22no—
92C3×#634—24no—
93C3×#634D414yescomplemented
94#6296—24no—
95#6295Q814yescomplemented
96#6294—24no—
97Q8×#67—91no—
98#5727—91no—
99#5632—91no—
100C2×C32×Q8—21no—
101C2×C32×Q8—21no—
102C2×C32×Q8—21no—
103C2×C32×Q8—41no—
104C2×C32×Q8C2×D311yescharacteristic
105C2×C32×Q8C2×D311yescharacteristic
106C2×C32×Q8C2×D311yescharacteristic
107Q8×C3⋊D3—24no—
108C2×C4×C3⋊D3C2×D311yescharacteristic
109C2×C4×C3⋊D3C2×D312yes—
110C2×C4×C3⋊D3C2×D311yescharacteristic
111C2×#634C2×D311yescharacteristic
112C2×#634C2×D312yes—
113C2×#634C2×D311yescharacteristic
114C3×D3×Q8—64no—
115C3×D3×Q8—64no—
116C3×D3×Q8—68no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—32no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—62no—
124C2×C3×C4×D3—61no—
125C2×C3×C4×D3—61no—
126C2×C3×Dic6—31no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—32no—
131C2×C3×Dic6—32no—
132C2×C3×Dic6—61no—
133C2×C3×Dic6—62no—
134C2×C3×Dic6—61no—
135C2×#627—32no—
136C2×#627—32no—
137C2×#627—32no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624—32no—
142C2×D3×Dic3—32no—
143C2×D3×Dic3—32no—
144#3797—64no—
145D3×Dic6—64no—
146D3×Dic6—64no—
147#3752C2×D312yes—
148C4⋊(C3⋊Dic3)C2×D311yescharacteristic
149#3750C2×D312yes—
150#3750C2×D312yes—
151#3750C2×D312yes—
152C4×C3⋊Dic3C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×(C2×D3)⋊C4—62no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—61no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—32no—
161C3×Dic3⋊C4—32no—
162C3×Dic3⋊C4—32no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—32no—
165C3×Dic3⋊C4—62no—
166C3×Dic3⋊C4—62no—
167C3×Dic3⋊C4—62no—
168C3×C4×Dic3—31no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—61no—
171#3724—31no—
172#3724—32no—
173#3724—32no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—32no—
180#3722—31no—
181#3722—32no—
182#3722—31no—
183(C2×D3)⋊Dic3—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—
189Dic32—32no—
190Dic32—32no—
191Dic32—32no—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3C2×Q812yescomplemented
198C2×C3×C3⋊D3C2×Q812yescomplemented
199C33×C4—22no—
200C33×C4C2×D412yes—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—22no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C3×C3⋊Dic3C2×D414yes—
207C3×C3⋊Dic3C2×Q812yescomplemented
208C22×C3×Q8—91no—
209C2×D3×Q8—31no—
210C2×D3×Q8—31no—
211C2×D3×Q8—61no—
212C2×D3×Q8—91no—
213C2×D3×Q8—91no—
214C22×Dic6—91no—
215C3×C4⋊Q8—91no—
216C3×C22⋊Q8—91no—
217#946—31no—
218#946—31no—
219#946—61no—
220#946—92no—
221#946—91no—
222Q8×Dic3—91no—
223#944—31no—
224#944—31no—
225#944—61no—
226#944—92no—
227C4×#67—91no—
228C4×#67—91no—
229C4×#67—92no—
230#924—92no—
231#924—91no—
232#897—91no—
233#896—92no—
234#896—92no—
235#896—92no—
236#893—92no—
237#888—92no—
238#888—92no—
239#887—91no—
240#67⋊C4—92no—
241#878—92no—
242C4×D12—91no—
243C4×Dic6—91no—
244C22×C3⋊D3C22×D311yescharacteristic
245C22×C3⋊D3C22×D311yescharacteristic
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—31no—
250C22×C3×D3—61no—
251C22×C3×D3—61no—
252C32×Q8—22no—
253C32×Q8—24no—
254C32×Q8—22no—
255C32×Q8—22no—
256C32×Q8—42no—
257C32×Q8—42no—
258C32×Q8—44no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—22no—
262C2×C32×C4—21no—
263C2×C32×C4—22no—
264C2×C32×C4—22no—
265C2×C32×C4—41no—
266C2×C32×C4—42no—
267C2×C32×C4C22×D312yes—
268C2×C32×C4C22×D312yes—
269C2×C32×C4C22×D312yes—
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D312yes—
274C2×C3⋊Dic3C22×D311yescharacteristic
275C2×C3⋊Dic3C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D311yescharacteristic
279C2×C3⋊Dic3C22×D312yes—
280C4×C3⋊D3—22no—
281C4×C3⋊D3—24no—
282C4×C3⋊D3—22no—
283#634—24no—
284#634—22no—
285#634#6714yescomplemented
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3—61no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—61no—
304C2×C3×Dic3—62no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—62no—
307C3×C4×D3—64no—
308C3×C4×D3—64no—
309C3×C4×D3—68no—
310C3×C4×D3—64no—
311C3×C4×D3—62no—
312C3×C4×D3—62no—
313C3×C4×D3—62no—
314C3×C4×D3—62no—
315C3×C4×D3—122no—
316C3×Dic6—34no—
317C3×Dic6—34no—
318C3×Dic6—64no—
319C3×Dic6—64no—
320C3×Dic6—64no—
321C3×Dic6—68no—
322C3×Dic6—62no—
323C3×Dic6—62no—
324C3×Dic6—122no—
325#627—64no—
326#627—64no—
327#627—64no—
328#626—34no—
329#626—34no—
330#625—34no—
331#624—64no—
332D3×Dic3—64no—
333D3×Dic3—64no—
334D4×Q8—271noSylow
335C2×C33C22×D411yescharacteristic
336C2×C33C22×Q811yescharacteristic
337C2×C332−1+411yescharacteristic
338C3×C3⋊D3—22no—
339C3×C3⋊D3—22no—
340C2×C3×Q8—21no—
341C2×C3×Q8—21no—
342C2×C3×Q8—21no—
343C2×C3×Q8—41no—
344C2×C3×Q8—91no—
345C2×C3×Q8—92no—
346C2×C3×Q8—91no—
347C2×C3×Q8—184no—
348C2×C3×Q8D3211yescharacteristic
349C2×C3×Q8D3211yescharacteristic
350C2×C3×Q8D3211yescharacteristic
351C22×C3×C4—92no—
352C22×C3×C4—91no—
353C22×C3×C4—91no—
354C2×#67—91no—
355C2×#67—91no—
356C22×Dic3—92no—
357D3×Q8—64no—
358D3×Q8—64no—
359D3×Q8—68no—
360D3×Q8—184no—
361D3×Q8—184no—
362C2×D12—91no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—32no—
366C2×C4×D3—32no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—62no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—92no—
373C2×C4×D3—92no—
374C2×Dic6—31no—
375C2×Dic6—31no—
376C2×Dic6—32no—
377C2×Dic6—32no—
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C2×Dic6—62no—
382C2×Dic6—61no—
383C2×Dic6—92no—
384C2×Dic6—92no—
385C2×Dic6—92no—
386C2×Dic6—184no—
387C3×C4⋊C4—91no—
388C3×C4⋊C4—92no—
389C3×C4⋊C4—92no—
390C3×C4⋊C4—92no—
391C3×C22⋊C4—92no—
392C3×C42—91no—
393#217—91no—
394#217—91no—
395#217—92no—
396(C2×D3)⋊C4—32no—
397(C2×D3)⋊C4—32no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—92no—
402(C2×D3)⋊C4—92no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—91no—
409C4⋊Dic3—92no—
410C4⋊Dic3—92no—
411Dic3⋊C4—32no—
412Dic3⋊C4—32no—
413Dic3⋊C4—32no—
414Dic3⋊C4—32no—
415Dic3⋊C4—32no—
416Dic3⋊C4—32no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—92no—
421Dic3⋊C4—92no—
422Dic3⋊C4—91no—
423Dic3⋊C4—92no—
424Dic3⋊C4—92no—
425Dic3⋊C4—91no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—61no—
429C4×Dic3—92no—
430C4×Dic3—92no—
431C4×Dic3—92no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32C23×D311yescharacteristic
437C22×C32C23×D311yescharacteristic
438C22×C32C23×D311yescharacteristic
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3D3×Q812yescomplemented
444C2×C3⋊D3D3×Q812yescomplemented
445C2×C3×D3—32no—
446C2×C3×D3—32no—
447C2×C3×D3—32no—
448C2×C3×D3—32no—
449C2×C3×D3—62no—
450C2×C3×D3—62no—
451C2×C3×D3—62no—
452C2×C3×D3—62no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—121no—
462C2×C3×D3—121no—
463C32×C4—22no—
464C32×C4—24no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—22no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—42no—
471C32×C4—42no—
472C32×C4—42no—
473C32×C4—44no—
474C32×C4D3×D412yes—
475C32×C4D3×D412yes—
476C32×C4C2×#6712yes—
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—22no—
480C3⋊Dic3—21no—
481C3⋊Dic3—22no—
482C3⋊Dic3D3×Q812yescomplemented
483C3⋊Dic3C2×#6714yes—
484C3×Dic3—34no—
485C3×Dic3—34no—
486C3×Dic3—32no—
487C3×Dic3—32no—
488C3×Dic3—64no—
489C3×Dic3—62no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—62no—
493C3×Dic3—61no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—62no—
497C3×Dic3—62no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—62no—
501C3×Dic3—61no—
502C3×Dic3—122no—
503C3×Dic3—121no—
504C3×Dic3—122no—
505C22×Q8—91no—
506C22×Q8—271no—
507C4⋊Q8—91no—
508C4⋊Q8—272no—
509C22⋊Q8—91no—
510C22⋊Q8—272no—
511C22⋊Q8—272no—
512C22⋊Q8—271no—
513C4×Q8—271no—
514C4×D4—271no—
515C4×D4—272no—
516C33D4×Q811yescharacteristic, complemented, Sylow
517C23×C3—91no—
518C23×C3—91no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—61no—
524C22×D3—61no—
525C3×Q8—24no—
526C3×Q8—22no—
527C3×Q8—22no—
528C3×Q8—22no—
529C3×Q8—42no—
530C3×Q8—42no—
531C3×Q8—44no—
532C3×Q8—94no—
533C3×Q8—184no—
534C3×Q8—182no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—22no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—42no—
542C2×C3×C4—41no—
543C2×C3×C4—91no—
544C2×C3×C4—92no—
545C2×C3×C4—92no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—92no—
550C2×C3×C4—184no—
551C2×C3×C4—182no—
552C2×C3×C4—182no—
553C2×C3×C4C2×D3212yes—
554C2×C3×C4C2×D3212yes—
555C2×C3×C4C2×D3212yes—
556C2×C3×C4C2×D3211yescharacteristic
557C2×C3×C4C2×D3211yescharacteristic
558C2×C3×C4C2×D3211yescharacteristic
559#67—94no—
560#67—94no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—31no—
571C2×Dic3—32no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—62no—
578C2×Dic3—61no—
579C2×Dic3—62no—
580C2×Dic3—61no—
581C2×Dic3—62no—
582C2×Dic3—184no—
583D12—94no—
584C4×D3—64no—
585C4×D3—64no—
586C4×D3—68no—
587C4×D3—64no—
588C4×D3—62no—
589C4×D3—62no—
590C4×D3—62no—
591C4×D3—62no—
592C4×D3—122no—
593C4×D3—184no—
594C4×D3—184no—
595Dic6—34no—
596Dic6—34no—
597Dic6—64no—
598Dic6—64no—
599Dic6—64no—
600Dic6—68no—
601Dic6—62no—
602Dic6—62no—
603Dic6—122no—
604Dic6—184no—
605Dic6—184no—
606Dic6—184no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32C2×D3×D411yescharacteristic
620C2×C32C2×D3×D411yescharacteristic
621C2×C32C2×D3×Q811yescharacteristic
622C2×C32C2×D3×Q811yescharacteristic
623C2×C32C2×D3×Q811yescharacteristic
624C2×C32#100711yescharacteristic
625C2×C32#100711yescharacteristic
626C2×C32#101011yescharacteristic
627C2×C32C22×#6711yescharacteristic
628C3⋊D3—22no—
629C3⋊D3—22no—
630C3×D3—64no—
631C3×D3—62no—
632C3×D3—62no—
633C3×D3—62no—
634C3×D3—62no—
635C3×D3—122no—
636C2×Q8—91no—
637C2×Q8—91no—
638C2×Q8—92no—
639C2×Q8—184no—
640C2×Q8—272no—
641C2×Q8—544no—
642C2×Q8#111311yescharacteristic
643C2×D4—271no—
644C22×C4—91no—
645C22×C4—92no—
646C22×C4—91no—
647C22×C4—272no—
648C4⋊C4—92no—
649C4⋊C4—91no—
650C4⋊C4—92no—
651C4⋊C4—92no—
652C4⋊C4—271no—
653C4⋊C4—272no—
654C4⋊C4—272no—
655C22⋊C4—92no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4—272no—
659C42—91no—
660C42—272no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—92no—
666C22×C3—92no—
667C22×C3—181no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3C22×D3211yescharacteristic
672C22×C3C22×D3211yescharacteristic
673C22×C3C22×D3211yescharacteristic
674C2×D3—32no—
675C2×D3—32no—
676C2×D3—32no—
677C2×D3—32no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—121no—
691C2×D3—121no—
692C3×C4—24no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—22no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—22no—
699C3×C4—42no—
700C3×C4—42no—
701C3×C4—44no—
702C3×C4—42no—
703C3×C4—92no—
704C3×C4—94no—
705C3×C4—181no—
706C3×C4—182no—
707C3×C4—181no—
708C3×C4—182no—
709C3×C4—181no—
710C3×C4D3×#6712yes—
711C3×C4D3×#6712yes—
712C3×C4#381112yes—
713Dic3—32no—
714Dic3—32no—
715Dic3—34no—
716Dic3—34no—
717Dic3—64no—
718Dic3—62no—
719Dic3—62no—
720Dic3—62no—
721Dic3—61no—
722Dic3—62no—
723Dic3—62no—
724Dic3—61no—
725Dic3—61no—
726Dic3—61no—
727Dic3—62no—
728Dic3—61no—
729Dic3—62no—
730Dic3—61no—
731Dic3—122no—
732Dic3—121no—
733Dic3—122no—
734C32—21no—
735C32—21no—
736C32—21no—
737C32—41no—
738C32#563211yescharacteristic, complemented
739C32#572711yescharacteristic, complemented
740C32Q8×#6711yescharacteristic, complemented
741C23—91no—
742C23—91no—
743Q8—22no—
744Q8—94no—
745Q8—184no—
746Q8—182no—
747Q8—544no—
748D4—274no—
749C2×C4—91no—
750C2×C4—92no—
751C2×C4—91no—
752C2×C4—92no—
753C2×C4—91no—
754C2×C4—92no—
755C2×C4—91no—
756C2×C4—184no—
757C2×C4—182no—
758C2×C4—182no—
759C2×C4—544no—
760C2×C4C2×#111312yes—
761C2×C4C2×#111311yescharacteristic
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—182no—
775C2×C3—182no—
776C2×C3#6431511yescharacteristic
777C2×C3#6431511yescharacteristic
778C2×C3#6431611yescharacteristic
779C2×C3D32×Q811yescharacteristic
780C2×C3D32×Q811yescharacteristic
781C2×C3D32×Q811yescharacteristic
782C2×C3C2×D3×#6711yescharacteristic
783C2×C3C2×D3×#6711yescharacteristic
784C2×C3C2×#381111yescharacteristic
785D3—64no—
786D3—62no—
787D3—62no—
788D3—62no—
789D3—62no—
790D3—122no—
791C22—92no—
792C22—92no—
793C22—181no—
794C22—181no—
795C22—181no—
796C22—181no—
797C22C22×#111311yescharacteristic
798C4—22no—
799C4—92no—
800C4—94no—
801C4—181no—
802C4—182no—
803C4—181no—
804C4—181no—
805C4—182no—
806C4#8904912yes—
807C3—21no—
808C3—21no—
809C3—21no—
810C3—41no—
811C3#1059536111yescharacteristic, complemented
812C3#1059540011yescharacteristic, complemented
813C3#1059540311yescharacteristic, complemented
814C2—182no—
815C2—182no—
816C2#1172462411yescharacteristic
817C2Q8×#111311yescharacteristic
818C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radicalC2×#6295C22
hypercenterC2×Q8#1113
hypocenterC33D4×Q8
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×#89040C2semidirect
3. C3×#64155C2semidirect
4. C3×#64153C2semidirect
6. #11723688C2semidirect
8. #11723674C2semidirect
9. #11723671C2semidirect
10. #11723668C2semidirect
11. #11723666C2semidirect
40. C2×Q8×C3⋊D3D3semidirect
47. #64155D3semidirect
48. #64153D3semidirect
93. C3×#634D4semidirect
95. #6295Q8semidirect
197. C2×C3×C3⋊D3C2×Q8semidirect
198. C2×C3×C3⋊D3C2×Q8semidirect
207. C3×C3⋊Dic3C2×Q8semidirect
285. #634#67semidirect
443. C2×C3⋊D3D3×Q8semidirect
444. C2×C3⋊D3D3×Q8semidirect
482. C3⋊Dic3D3×Q8semidirect
516. C33D4×Q8semidirect
738. C32#5632semidirect
739. C32#5727semidirect
740. C32Q8×#67semidirect
811. C3#10595361semidirect
812. C3#10595400semidirect
813. C3#10595403semidirect

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×#890402
C3×#641552
C3×#641532
C4×#62952
#117236882
#117236842
#117236742
#117236712
#117236682
#117236662
#105954033
#105954003
#105953613