Finite Group Databasebeta

← #13178719

Subgroups — #13178719

Order 1728.

1138 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64155C211yesmaximal, characteristic
2C3×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#64153C211yesmaximal, characteristic, complemented
4C4⋊#6296C211yesmaximal, characteristic, complemented
5#11723692C212yesmaximal
6#11723683C212yesmaximal
7C4×#6294C211yesmaximal, characteristic
8#11723674C211yesmaximal, characteristic
9#11723669C212yesmaximal, complemented
10#11723668C211yesmaximal, characteristic, complemented
11#11723665C212yesmaximal, complemented
12#10595374—31nomaximal
13#10595368—31nomaximal
14#10595367—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×#6296C2212yes—
19C2×#6294C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C3×#3752C2212yes—
22C3×C4⋊(C3⋊Dic3)C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×#3750C2212yes—
26C3×#3750C2212yes—
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2212yes—
30C3×C4×C3⋊Dic3C2211yescharacteristic
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88813C2211yescharacteristic
36#88813C2212yes—
37#88813C2211yescharacteristic
38#64155D311yescharacteristic
39Q8×C3⋊Dic3D311yescharacteristic, complemented
40#64153D311yescharacteristic, complemented
41C3×#946—31no—
42C3×#946—31no—
43C3×#946—61no—
44C3×Q8×Dic3—31no—
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—61no—
47C3×#944—31no—
48C3×#944—31no—
49C3×#944—61no—
50#63919—31no—
51#63918—31no—
52#63918—31no—
53#63899—32no—
54#63895—32no—
55#63893—32no—
56C4×#624—31no—
57#63878—32no—
58#63877—32no—
59C4×D3×Dic3—31no—
60C4×D3×Dic3—31no—
61#63871—31no—
62#63857—31no—
63#63856—31no—
64#63847—32no—
65#63846—32no—
66#63845—32no—
67#63844—31no—
68#63843—31no—
69Dic3×Dic6—31no—
70#63838—32no—
71#63837—32no—
72#63837—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C33×Q8—22no—
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C3×C4×C3⋊D3—22no—
87C3×#634—22no—
88#6296—24no—
89#6294—22no—
90#6294Q814yescomplemented
91#5728—91no—
92#5622—91no—
93#5578—91no—
94C2×C32×Q8—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—21no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2×D311yescharacteristic
99C2×C32×Q8C2×D311yescharacteristic
100C2×C32×Q8C2×D311yescharacteristic
101C2×C4×C3⋊D3C2×D311yescharacteristic
102C2×#634C2×D311yescharacteristic
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—61no—
109C2×#627—32no—
110C2×#627—32no—
111C2×#627—32no—
112C2×#624—31no—
113C2×#624—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118#3752C2×D312yes—
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120C4⋊(C3⋊Dic3)C2×D312yes—
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122#3750C2×D312yes—
123#3750C2×D312yes—
124#3750C2×D312yes—
125C4×C3⋊Dic3C2×D312yes—
126C4×C3⋊Dic3C2×D311yescharacteristic
127C4×C3⋊Dic3C2×D311yescharacteristic
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—62no—
131C3×C4⋊Dic3—32no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—61no—
138C3×C4⋊Dic3—62no—
139C3×C4⋊Dic3—61no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—62no—
147C3×Dic3⋊C4—62no—
148C3×Dic3⋊C4—62no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—61no—
156C3×C4×Dic3—61no—
157C3×C4×Dic3—62no—
158#3724—32no—
159#3724—32no—
160#3724—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167#3722—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170Dic32—32no—
171Dic32—31no—
172Dic32—31no—
173Dic32—32no—
174Dic32—31no—
175Dic32—32no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3C2×Q812yes—
183C33×C4—22no—
184C33×C4#4112yes—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3C2×Q812yes—
191C3×C3⋊Dic3C2×Q812yes—
192C3×C3⋊Dic3#4112yes—
193C3×C4⋊Q8—91no—
194C3×C22⋊Q8—91no—
195C3×C4×Q8—91no—
196#946—31no—
197#946—31no—
198#946—61no—
199#946—91no—
200Q8×Dic3—31no—
201Q8×Dic3—31no—
202Q8×Dic3—61no—
203Q8×Dic3—91no—
204#944—31no—
205#944—31no—
206#944—61no—
207#924—91no—
208C2×C4×Dic3—91no—
209#897—92no—
210#897—91no—
211#896—92no—
212#892—92no—
213#890—92no—
214#889—92no—
215#889—92no—
216#888—91no—
217#888—91no—
218#887—92no—
219#887—92no—
220#887—91no—
221#878—92no—
222#877—92no—
223#872—92no—
224C42×D3—91no—
225C42×D3—91no—
226#869—91no—
227C4×Dic6—92no—
228C4×Dic6—91no—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
233C32×Q8—22no—
234C32×Q8—24no—
235C32×Q8—22no—
236C32×Q8—22no—
237C32×Q8—42no—
238C32×Q8—42no—
239C32×Q8—44no—
240C2×C32×C4—22no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—22no—
245C2×C32×C4—22no—
246C2×C32×C4—41no—
247C2×C32×C4—42no—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D312yes—
250C2×C32×C4C22×D312yes—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D312yes—
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C4×C3⋊D3—22no—
263#634—22no—
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—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—62no—
288C3×C4×D3—62no—
289C3×C4×D3—62no—
290C3×C4×D3—122no—
291C3×Dic6—62no—
292C3×Dic6—62no—
293C3×Dic6—122no—
294#627—64no—
295#627—64no—
296#627—64no—
297#624—34no—
298#624—62no—
299D3×Dic3—34no—
300D3×Dic3—34no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303#533—271noSylow
304C2×C33C22×Q811yescharacteristic
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C3×C3⋊D3—22no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—41no—
312C2×C3×Q8—91no—
313C2×C3×Q8D3211yescharacteristic
314C2×C3×Q8D3211yescharacteristic
315C2×C3×Q8D3211yescharacteristic
316C22×C3×C4—91no—
317C22×Dic3—91no—
318C22×Dic3—91no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C2×C4×D3—91no—
323C2×C4×D3—91no—
324C2×C4×D3—91no—
325C2×C4×D3—91no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6—92no—
330C2×Dic6—92no—
331C2×Dic6—92no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—92no—
334C3×C4⋊C4—92no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4—92no—
337C3×C4⋊C4—92no—
338C3×C22⋊C4—92no—
339C3×C42—91no—
340C3×C42—92no—
341C3×C42—91no—
342#217—92no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—92no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—32no—
352C4⋊Dic3—31no—
353C4⋊Dic3—32no—
354C4⋊Dic3—62no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—92no—
358C4⋊Dic3—92no—
359C4⋊Dic3—92no—
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—32no—
378C4×Dic3—32no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—62no—
384C4×Dic3—91no—
385C4×Dic3—92no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—92no—
390C4×Dic3—91no—
391C4×Dic3—92no—
392C4×Dic3—91no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—41no—
397C22×C32C23×D311yescharacteristic
398C22×C32C23×D311yescharacteristic
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3D3×Q812yes—
403C2×C3×D3—32no—
404C2×C3×D3—32no—
405C2×C3×D3—62no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408C2×C3×D3—61no—
409C2×C3×D3—61no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
412C32×C4—22no—
413C32×C4—24no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—22no—
417C32×C4—22no—
418C32×C4—22no—
419C32×C4—42no—
420C32×C4—42no—
421C32×C4—42no—
422C32×C4—44no—
423C32×C4#23512yes—
424C32×C4#23712yes—
425C32×C4#23712yes—
426C3⋊Dic3—22no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—22no—
430C3⋊Dic3—22no—
431C3⋊Dic3D3×Q812yes—
432C3⋊Dic3D3×Q812yes—
433C3⋊Dic3#23912yes—
434C3×Dic3—32no—
435C3×Dic3—32no—
436C3×Dic3—32no—
437C3×Dic3—32no—
438C3×Dic3—32no—
439C3×Dic3—32no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—61no—
445C3×Dic3—62no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—61no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—122no—
454C3×Dic3—121no—
455C3×Dic3—122no—
456C3×Dic3—122no—
457C3×Dic3—121no—
458C4⋊Q8—91no—
459C4⋊Q8—271no—
460#125—272no—
461C22⋊Q8—91no—
462C22⋊Q8—272no—
463C22⋊Q8—271no—
464C4×Q8—91no—
465C4×Q8—272no—
466C4×Q8—271no—
467#117—272no—
468C2×C42—271no—
469C33#53311yescharacteristic, complemented, Sylow
470C23×C3—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—61no—
474C3×Q8—24no—
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—42no—
479C3×Q8—42no—
480C3×Q8—44no—
481C3×Q8—182no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—42no—
489C2×C3×C4—41no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—92no—
496C2×C3×C4—92no—
497C2×C3×C4—92no—
498C2×C3×C4—182no—
499C2×C3×C4C2×D3212yes—
500C2×C3×C4C2×D3212yes—
501C2×C3×C4C2×D3212yes—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—62no—
529C2×Dic3—94no—
530C2×Dic3—182no—
531C4×D3—62no—
532C4×D3—62no—
533C4×D3—94no—
534C4×D3—94no—
535C4×D3—122no—
536C4×D3—182no—
537C4×D3—182no—
538Dic6—62no—
539Dic6—62no—
540Dic6—122no—
541Dic6—184no—
542Dic6—184no—
543Dic6—184no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—41no—
554C2×C32—41no—
555C2×C32—41no—
556C2×C32C2×#23511yescharacteristic
557C2×C32C2×#23711yescharacteristic
558C2×C32C2×#23711yescharacteristic
559C2×C32C2×D3×Q811yescharacteristic
560C2×C32C2×D3×Q811yescharacteristic
561C2×C32C2×D3×Q811yescharacteristic
562C2×C32C2×#23911yescharacteristic
563C2×C32D3×#4111yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C3⋊D3—22no—
566C3×D3—62no—
567C3×D3—62no—
568C3×D3—122no—
569C2×Q8—91no—
570C2×Q8—272no—
571C2×Q8#111311yescharacteristic
572C22×C4—91no—
573C22×C4—271no—
574C22×C4—271no—
575C4⋊C4—92no—
576C4⋊C4—92no—
577C4⋊C4—91no—
578C4⋊C4—92no—
579C4⋊C4—91no—
580C4⋊C4—92no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C22⋊C4—92no—
585C22⋊C4—272no—
586C42—91no—
587C42—91no—
588C42—92no—
589C42—271no—
590C42—271no—
591C42—272no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—41no—
596C22×C3—92no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3C22×D3211yescharacteristic
600C22×C3C22×D3211yescharacteristic
601C22×C3C22×D3211yescharacteristic
602C2×D3—32no—
603C2×D3—32no—
604C2×D3—62no—
605C2×D3—61no—
606C2×D3—61no—
607C2×D3—61no—
608C2×D3—61no—
609C2×D3—121no—
610C2×D3—121no—
611C3×C4—24no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—44no—
621C3×C4—42no—
622C3×C4—92no—
623C3×C4—92no—
624C3×C4—92no—
625C3×C4—182no—
626C3×C4—182no—
627C3×C4—181no—
628C3×C4—181no—
629C3×C4—182no—
630C3×C4#380412yes—
631C3×C4#380412yes—
632C3×C4#380512yes—
633Dic3—32no—
634Dic3—32no—
635Dic3—32no—
636Dic3—32no—
637Dic3—32no—
638Dic3—32no—
639Dic3—62no—
640Dic3—62no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—61no—
645Dic3—62no—
646Dic3—62no—
647Dic3—61no—
648Dic3—62no—
649Dic3—61no—
650Dic3—62no—
651Dic3—61no—
652Dic3—122no—
653Dic3—121no—
654Dic3—121no—
655Dic3—122no—
656Dic3—122no—
657C32—21no—
658C32—21no—
659C32—21no—
660C32—41no—
661C32#557811yescharacteristic, complemented
662C32#562211yescharacteristic, complemented
663C32#572811yescharacteristic, complemented
664C23—91no—
665Q8—22no—
666Q8—182no—
667Q8—544no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—92no—
673C2×C4—91no—
674C2×C4—92no—
675C2×C4—92no—
676C2×C4—182no—
677C2×C4—274no—
678C2×C4—542no—
679C2×C4C2×#111312yes—
680C2×C4C2×#111311yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—41no—
693C2×C3—182no—
694C2×C3D32×Q811yescharacteristic
695C2×C3D32×Q811yescharacteristic
696C2×C3D32×Q811yescharacteristic
697C2×C3D3×#23911yescharacteristic
698C2×C3D3×#23911yescharacteristic
699C2×C3#6431911yescharacteristic
700C2×C3C2×#380411yescharacteristic
701C2×C3C2×#380411yescharacteristic
702C2×C3C2×#380511yescharacteristic
703D3—62no—
704D3—62no—
705D3—122no—
706C22—92no—
707C22—181no—
708C22—181no—
709C22C22×#111311yescharacteristic
710C4—22no—
711C4—92no—
712C4—92no—
713C4—92no—
714C4—181no—
715C4—182no—
716C4—182no—
717C4—181no—
718C4—182no—
719C4#8904612yes—
720C3—21no—
721C3—21no—
722C3—21no—
723C3—41no—
724C3#1059536711yescharacteristic, complemented
725C3#1059536811yescharacteristic, complemented
726C3#1059537411yescharacteristic, complemented
727C2—182no—
728C2Q8×#111311yescharacteristic
729C2#1172462611yescharacteristic
730C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×Q8#1113
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×C3⋊Dic3C2semidirect
3. C3×#64153C2semidirect
4. C4⋊#6296C2semidirect
9. #11723669C2semidirect
10. #11723668C2semidirect
11. #11723665C2semidirect
39. Q8×C3⋊Dic3D3semidirect
40. #64153D3semidirect
90. #6294Q8semidirect
469. C33#533semidirect
661. C32#5578semidirect
662. C32#5622semidirect
663. C32#5728semidirect
724. C3#10595367semidirect
725. C3#10595368semidirect
726. C3#10595374semidirect

Maximal subgroups

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

subgroupindex
C3×#641552
C3×Q8×C3⋊Dic32
C3×#641532
C4⋊#62962
#117236922
#117236832
C4×#62942
#117236742
#117236692
#117236682
#117236652
#105953743
#105953683
#105953673