Finite Group Databasebeta

← #13178302

Subgroups — #13178302

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1113C211yesmaximal, characteristic
2C2×#89040C211yesmaximal, characteristic, complemented
3C3×#64105C212yesmaximal, complemented
4C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5#11723700C211yesmaximal, characteristic
6#11723700C211yesmaximal, characteristic
7#11723692C212yesmaximal, complemented
8#11723688C212yesmaximal, complemented
9#11723682C211yesmaximal, characteristic, complemented
10#11723682C211yesmaximal, characteristic, complemented
11#11723671C212yesmaximal, complemented
12#10594624—31nomaximal
13D3×#896—32nomaximal
14C22×#1113C2211yescharacteristic
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2212yes—
19C2×C3×#634C2212yescomplemented
20C2×#6296C2212yescomplemented
21C2×#6294C2211yescharacteristic
22C2×#6294C2212yes—
23C2×#6294C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C4×#1113—24no—
26#89040—24no—
27C33×C4⋊C4C2211yescharacteristic, complemented
28C3×#3752C2212yes—
29C3×#3752C2212yes—
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×#3750C2211yescharacteristic, complemented
32C3×#3750C2211yescharacteristic, complemented
33C3×#3750C2212yescomplemented
34C3×#3750C2212yescomplemented
35#88815C2212yescomplemented
36#88815C2212yescomplemented
37#88814C2212yes—
38#88814C2212yes—
39C2×C4×D32—32no—
40C2×C4×D32—31no—
41C2×#3797—31no—
42C2×D3×Dic6—32no—
43#64105D312yescomplemented
44C4⋊C4×C3⋊D3D311yescharacteristic, complemented
45C3×#896—32no—
46C3×#896—32no—
47C3×#896—62no—
48C3×D3×C4⋊C4—32no—
49C3×D3×C4⋊C4—61no—
50#63921—31no—
51#63921—31no—
52D3×(C2×D3)⋊C4—32no—
53D3×(C2×D3)⋊C4—32no—
54#63899—32no—
55#63896—32no—
56#63895—32no—
57#63893—32no—
58#63888—32no—
59#63887—32no—
60#63883—31no—
61#63883—31no—
62D3×Dic3⋊C4—32no—
63D3×Dic3⋊C4—32no—
64#63865—32no—
65#63851—32no—
66#63851—32no—
67C22×C3×C3⋊D3C2312yes—
68C22×C3×C3⋊D3C2311yescharacteristic
69C2×#1113—22no—
70C2×#1113—22no—
71C2×#1113Q814yescomplemented
72C2×C33×C4C2311yescharacteristic
73C2×C33×C4C2311yescharacteristic
74C2×C33×C4C2311yescharacteristic
75C2×C3×C3⋊Dic3C2312yes—
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4×C3⋊D3—22no—
82C3×C4×C3⋊D3—22no—
83C3×C4×C3⋊D3—22no—
84C3×C4×C3⋊D3—24no—
85C3×#634—24no—
86#6296—24no—
87#6294—22no—
88#6294—22no—
89#6294—24no—
90#6294D414yes—
91D3×C22⋊Q8—92no—
92C2×#896—91no—
93C22×D32—32no—
94C22×D32—31no—
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×C4×C3⋊D3C2×D311yescharacteristic
97C2×C4×C3⋊D3C2×D312yes—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634C2×D312yescomplemented
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—32no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—61no—
106C2×C3×C4×D3—61no—
107C2×C3×C4×D3—61no—
108C2×C3×C4×D3—62no—
109C2×C3×Dic6—32no—
110C2×C3×Dic6—32no—
111C2×C3×Dic6—62no—
112C2×#627—32no—
113C2×#627—32no—
114C2×#627—32no—
115C2×#624—31no—
116C2×#624—31no—
117C2×#624—32no—
118C2×#624—31no—
119C2×D3×Dic3—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C4×D32—68no—
125C4×D32—64no—
126#3797—64no—
127D3×Dic6—68no—
128C32×C4⋊C4—21no—
129C32×C4⋊C4—22no—
130C32×C4⋊C4—41no—
131C32×C4⋊C4C2×D312yescomplemented
132C32×C4⋊C4C2×D311yescharacteristic, complemented
133#3752C2×D312yes—
134#3752C2×D312yes—
135C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
136#3750C2×D311yescharacteristic, complemented
137#3750C2×D311yescharacteristic, complemented
138#3750C2×D312yescomplemented
139#3750C2×D312yescomplemented
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—62no—
145C3×(C2×D3)⋊C4—62no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3—61no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—61no—
155C3×Dic3⋊C4—61no—
156C3×Dic3⋊C4—62no—
157C3×Dic3⋊C4—62no—
158#3724—32no—
159#3724—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164#3722—32no—
165#3722—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170C22×C33C2411yescharacteristic
171C2×C3×C3⋊D3—22no—
172C2×C3×C3⋊D3—22no—
173C2×C3×C3⋊D3C2×D412yes—
174C2×C3×C3⋊D3C2×Q812yes—
175C2×C3×C3⋊D3C2×Q814yescomplemented
176C2×C3×C3⋊D3#4112yes—
177#1113—28no—
178C33×C4—21no—
179C33×C4—21no—
180C33×C4—21no—
181C3×C3⋊Dic3—21no—
182C3×C3⋊Dic3—22no—
183C3×C3⋊Dic3—21no—
184C3×C3⋊Dic3—21no—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3C2×D414yes—
187C2×D3×Q8—92no—
188C22×C4×D3—91no—
189C22×C4×D3—92no—
190C22×Dic6—91no—
191C3×C22⋊Q8—92no—
192C2×C3×C4⋊C4—91no—
193#946—92no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196#924—92no—
197C2×Dic3⋊C4—91no—
198C2×Dic3⋊C4—91no—
199#897—92no—
200#896—32no—
201#896—32no—
202#896—62no—
203#896—92no—
204#896—92no—
205#896—92no—
206#896—92no—
207D3×C4⋊C4—32no—
208D3×C4⋊C4—61no—
209D3×C4⋊C4—92no—
210D3×C4⋊C4—92no—
211D3×C22⋊C4—92no—
212D3×C22⋊C4—92no—
213#878—92no—
214#878—92no—
215C22×C3⋊D3C22×D312yes—
216C22×C3⋊D3C22×D311yescharacteristic
217C22×C3×D3—32no—
218C22×C3×D3—32no—
219C22×C3×D3—32no—
220C22×C3×D3—61no—
221C22×C3×D3—62no—
222C2×D32—34no—
223C2×D32—38no—
224C2×D32—64no—
225C2×D32—64no—
226C2×D32—62no—
227C2×D32—62no—
228C2×C32×C4—21no—
229C2×C32×C4—22no—
230C2×C32×C4—21no—
231C2×C32×C4—22no—
232C2×C32×C4—21no—
233C2×C32×C4—22no—
234C2×C32×C4—41no—
235C2×C32×C4—41no—
236C2×C32×C4—41no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D312yes—
240C2×C32×C4C22×D312yes—
241C2×C32×C4C22×D312yes—
242C2×C32×C4C22×D311yescharacteristic
243C2×C3⋊Dic3C22×D311yescharacteristic
244C2×C3⋊Dic3C22×D311yescharacteristic
245C2×C3⋊Dic3C22×D312yes—
246C2×C3⋊Dic3C22×D312yes—
247C2×C3⋊Dic3C22×D311yescharacteristic
248C2×C3⋊Dic3C22×D312yes—
249C4×C3⋊D3—22no—
250C4×C3⋊D3—22no—
251C4×C3⋊D3—22no—
252C4×C3⋊D3—24no—
253#634—24no—
254C2×C3×Dic3—32no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—32no—
257C2×C3×Dic3—32no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—62no—
269C3×C4×D3—64no—
270C3×C4×D3—64no—
271C3×C4×D3—64no—
272C3×C4×D3—64no—
273C3×C4×D3—64no—
274C3×C4×D3—64no—
275C3×C4×D3—124no—
276C3×C4×D3—122no—
277C3×C4×D3—122no—
278C3×Dic6—64no—
279C3×Dic6—64no—
280C3×Dic6—124no—
281#627—64no—
282#627—64no—
283#627—64no—
284#624—34no—
285#624—64no—
286#624—62no—
287#624—62no—
288D3×Dic3—38no—
289D3×Dic3—64no—
290D3×Dic3—64no—
291D3×Dic3—64no—
292D3×Dic3—64no—
293C2×C22⋊Q8—271noSylow
294C2×C33C22×D411yescharacteristic
295C2×C33C22×Q811yescharacteristic
296C2×C33C2×#4111yescharacteristic
297C3×C3⋊D3—24no—
298C3×C3⋊D3C22⋊Q814yescomplemented
299C23×D3—92no—
300C23×D3—91no—
301C2×C3×Q8—92no—
302C22×C3×C4—91no—
303C22×C3×C4—91no—
304C22×C3×C4—92no—
305C22×C3×C4—91no—
306C22×Dic3—91no—
307C22×Dic3—92no—
308C22×Dic3—91no—
309C22×Dic3—91no—
310D3×Q8—188no—
311C2×C4×D3—32no—
312C2×C4×D3—32no—
313C2×C4×D3—32no—
314C2×C4×D3—32no—
315C2×C4×D3—32no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—62no—
320C2×C4×D3—92no—
321C2×C4×D3—92no—
322C2×C4×D3—92no—
323C2×C4×D3—92no—
324C2×C4×D3—92no—
325C2×C4×D3—188no—
326C2×C4×D3—184no—
327C2×Dic6—32no—
328C2×Dic6—32no—
329C2×Dic6—62no—
330C2×Dic6—92no—
331C2×Dic6—92no—
332C2×Dic6—92no—
333C2×Dic6—184no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—92no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4D3212yescomplemented
343C3×C4⋊C4D3211yescharacteristic, complemented
344C3×C22⋊C4—92no—
345C3×C22⋊C4—92no—
346#217—92no—
347#217—92no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—32no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—92no—
358C4⋊Dic3—32no—
359C4⋊Dic3—61no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362Dic3⋊C4—32no—
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—32no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376C22×C32—22no—
377C22×C32—21no—
378C22×C32—41no—
379C22×C32C23×D311yescharacteristic
380C22×C32C23×D312yes—
381C2×C3⋊D3—22no—
382C2×C3⋊D3—22no—
383C2×C3⋊D3#23512yes—
384C2×C3⋊D3D3×D412yes—
385C2×C3⋊D3D3×Q812yes—
386C2×C3⋊D3D3×Q814yescomplemented
387C2×C3×D3—34no—
388C2×C3×D3—34no—
389C2×C3×D3—34no—
390C2×C3×D3—34no—
391C2×C3×D3—34no—
392C2×C3×D3—62no—
393C2×C3×D3—62no—
394C2×C3×D3—62no—
395C2×C3×D3—64no—
396C2×C3×D3—62no—
397C2×C3×D3—62no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—122no—
401C2×C3×D3—122no—
402D32—616no—
403D32—68no—
404C32×C4—21no—
405C32×C4—22no—
406C32×C4—21no—
407C32×C4—22no—
408C32×C4—21no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—42no—
412C32×C4—42no—
413C32×C4—42no—
414C32×C4—41no—
415C32×C4—42no—
416C32×C4—41no—
417C32×C4—81no—
418C32×C4—81no—
419C3⋊Dic3—21no—
420C3⋊Dic3—21no—
421C3⋊Dic3—22no—
422C3⋊Dic3—21no—
423C3⋊Dic3—22no—
424C3⋊Dic3D3×D414yes—
425C3×Dic3—34no—
426C3×Dic3—34no—
427C3×Dic3—64no—
428C3×Dic3—62no—
429C3×Dic3—62no—
430C3×Dic3—62no—
431C3×Dic3—62no—
432C3×Dic3—62no—
433C3×Dic3—62no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—122no—
437C3×Dic3—121no—
438C3×Dic3—121no—
439C3×Dic3—122no—
440C22×Q8—271no—
441C23×C4—271no—
442C22⋊Q8—92no—
443C22⋊Q8—272no—
444C22⋊Q8—272no—
445C22⋊Q8—272no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—271no—
448C2×C4⋊C4—271no—
449C2×C22⋊C4—271no—
450C2×C22⋊C4—271no—
451C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
452C23×C3—91no—
453C23×C3—92no—
454C22×D3—32no—
455C22×D3—32no—
456C22×D3—32no—
457C22×D3—61no—
458C22×D3—62no—
459C22×D3—98no—
460C22×D3—94no—
461C22×D3—184no—
462C22×D3—184no—
463C22×D3—182no—
464C22×D3—182no—
465C3×Q8—184no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—92no—
476C2×C3×C4—91no—
477C2×C3×C4—91no—
478C2×C3×C4—92no—
479C2×C3×C4—92no—
480C2×C3×C4—91no—
481C2×C3×C4—184no—
482C2×C3×C4—182no—
483C2×C3×C4—182no—
484C2×C3×C4—182no—
485C2×C3×C4C2×D3211yescharacteristic
486C2×C3×C4C2×D3212yes—
487C2×C3×C4C2×D3211yescharacteristic
488C2×C3×C4C2×D3212yes—
489C2×C3×C4C2×D3212yes—
490C2×C3×C4C2×D3211yescharacteristic
491C2×Dic3—32no—
492C2×Dic3—32no—
493C2×Dic3—32no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—32no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—61no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—62no—
506C2×Dic3—94no—
507C2×Dic3—184no—
508C2×Dic3—182no—
509C2×Dic3—182no—
510C4×D3—64no—
511C4×D3—64no—
512C4×D3—64no—
513C4×D3—64no—
514C4×D3—64no—
515C4×D3—64no—
516C4×D3—98no—
517C4×D3—124no—
518C4×D3—122no—
519C4×D3—122no—
520C4×D3—184no—
521C4×D3—184no—
522C4×D3—184no—
523C4×D3—184no—
524Dic6—64no—
525Dic6—64no—
526Dic6—124no—
527Dic6—184no—
528Dic6—184no—
529Dic6—184no—
530C2×C32—22no—
531C2×C32—21no—
532C2×C32—22no—
533C2×C32—21no—
534C2×C32—22no—
535C2×C32—21no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32C2×#23511yescharacteristic
540C2×C32C2×D3×D411yescharacteristic
541C2×C32C2×D3×D412yes—
542C2×C32C2×D3×Q811yescharacteristic
543C2×C32C2×D3×Q812yes—
544C2×C32D3×#4112yes—
545C3⋊D3—24no—
546C3⋊D3#89614yescomplemented
547C3×D3—38no—
548C3×D3—64no—
549C3×D3—64no—
550C3×D3—64no—
551C3×D3—124no—
552C24—271no—
553C2×Q8—92no—
554C2×Q8—272no—
555C2×Q8—544no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—92no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—272no—
564C22×C4—544no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—92no—
569C4⋊C4—92no—
570C4⋊C4—272no—
571C4⋊C4—272no—
572C4⋊C4#111311yescharacteristic, complemented
573C22⋊C4—92no—
574C22⋊C4—92no—
575C22⋊C4—272no—
576C22⋊C4—272no—
577C22×C3—21no—
578C22×C3—22no—
579C22×C3—41no—
580C22×C3—92no—
581C22×C3—92no—
582C22×C3—92no—
583C22×C3—94no—
584C22×C3—182no—
585C22×C3—182no—
586C22×C3C22×D3212yes—
587C22×C3C22×D3211yescharacteristic
588C2×D3—34no—
589C2×D3—34no—
590C2×D3—34no—
591C2×D3—34no—
592C2×D3—34no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—64no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—1816no—
604C2×D3—188no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—21no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—81no—
619C3×C4—81no—
620C3×C4—94no—
621C3×C4—182no—
622C3×C4—181no—
623C3×C4—181no—
624C3×C4—182no—
625C3×C4—181no—
626Dic3—34no—
627Dic3—34no—
628Dic3—64no—
629Dic3—62no—
630Dic3—62no—
631Dic3—62no—
632Dic3—62no—
633Dic3—62no—
634Dic3—62no—
635Dic3—62no—
636Dic3—62no—
637Dic3—122no—
638Dic3—121no—
639Dic3—121no—
640Dic3—122no—
641C32—22no—
642C32—21no—
643C32—41no—
644C32C2×#89611yescharacteristic, complemented
645C32D3×C22⋊Q812yescomplemented
646C23—91no—
647C23—92no—
648C23—274no—
649C23—542no—
650C23—542no—
651Q8—184no—
652Q8—544no—
653C2×C4—92no—
654C2×C4—92no—
655C2×C4—92no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—91no—
659C2×C4—184no—
660C2×C4—182no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4—274no—
664C2×C4—544no—
665C2×C4—542no—
666C2×C4—542no—
667C2×C4C2×#111311yescharacteristic
668C2×C4C2×#111311yescharacteristic
669C2×C4C2×#111311yescharacteristic
670C2×C3—21no—
671C2×C3—22no—
672C2×C3—22no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—22no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—94no—
680C2×C3—184no—
681C2×C3D3×#23512yes—
682C2×C3#6430611yescharacteristic
683C2×C3D32×D412yes—
684C2×C3D32×D411yescharacteristic
685C2×C3D32×Q812yes—
686C2×C3D32×Q811yescharacteristic
687D3—38no—
688D3—64no—
689D3—64no—
690D3—64no—
691D3—124no—
692C22—92no—
693C22—92no—
694C22—92no—
695C22—94no—
696C22—182no—
697C22—182no—
698C22—548no—
699C22C22×#111311yescharacteristic
700C4—21no—
701C4—21no—
702C4—21no—
703C4—94no—
704C4—181no—
705C4—182no—
706C4—181no—
707C4—181no—
708C4—182no—
709C3—21no—
710C3—22no—
711C3—41no—
712C3D3×#89612yescomplemented
713C3#1059462411yescharacteristic, complemented
714C2—94no—
715C2—184no—
716C2#1172461811yescharacteristic
717C2D4×#111311yescharacteristic
718C2Q8×#111311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×#1113C22
hypercenterC4⋊C4#1113
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#89040C2semidirect
3. C3×#64105C2semidirect
4. C3×C4⋊C4×C3⋊D3C2semidirect
7. #11723692C2semidirect
8. #11723688C2semidirect
9. #11723682C2semidirect
10. #11723682C2semidirect
11. #11723671C2semidirect
19. C2×C3×#634C22semidirect
20. C2×#6296C22semidirect
27. C33×C4⋊C4C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C3×#3750C22semidirect
32. C3×#3750C22semidirect
33. C3×#3750C22semidirect
34. C3×#3750C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
43. #64105D3semidirect
44. C4⋊C4×C3⋊D3D3semidirect
71. C2×#1113Q8semidirect
99. C2×#634C2×D3semidirect
131. C32×C4⋊C4C2×D3semidirect
132. C32×C4⋊C4C2×D3semidirect
135. C4⋊(C3⋊Dic3)C2×D3semidirect
136. #3750C2×D3semidirect
137. #3750C2×D3semidirect
138. #3750C2×D3semidirect
139. #3750C2×D3semidirect
175. C2×C3×C3⋊D3C2×Q8semidirect
298. C3×C3⋊D3C22⋊Q8semidirect
342. C3×C4⋊C4D32semidirect
343. C3×C4⋊C4D32semidirect
386. C2×C3⋊D3D3×Q8semidirect
451. C33C2×C22⋊Q8semidirect
546. C3⋊D3#896semidirect
572. C4⋊C4#1113semidirect
644. C32C2×#896semidirect
645. C32D3×C22⋊Q8semidirect
712. C3D3×#896semidirect
713. C3#10594624semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#11132
C2×#890402
C3×#641052
C3×C4⋊C4×C3⋊D32
#117237002
#117236922
#117236882
#117236822
#117236712
#105946243
D3×#8963