Finite Group Databasebeta

← #13178310

Subgroups — #13178310

Order 1728.

1424 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89041C211yesmaximal, characteristic, complemented
2C2×#89040C211yesmaximal, characteristic, complemented
3C3×#64106C211yesmaximal, characteristic, complemented
4C3×#64104C211yesmaximal, characteristic, complemented
5C3×#64096C211yesmaximal, characteristic, complemented
6C4×#6295C211yesmaximal, characteristic, complemented
7#11723692C212yesmaximal, complemented
8#11723691C212yesmaximal, complemented
9#11723687C212yesmaximal, complemented
10#11723677C211yesmaximal, characteristic, complemented
11#11723672C212yesmaximal, complemented
12#10594525—31nomaximal
13#10594382—31nomaximal
14#10594329—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#634C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6296C2212yes—
22C2×#6295C2212yes—
23C2×#6295C2211yescharacteristic
24C2×#6294C2212yes—
25C2×#6294C2212yes—
26#89041—24no—
27#89040—24no—
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2212yes—
30C3×#3752C2212yes—
31C3×C4⋊(C3⋊Dic3)C2212yes—
32C3×#3750C2212yes—
33C3×C4×C3⋊Dic3C2212yes—
34C3×C4×C3⋊Dic3C2211yescharacteristic
35#88815C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2212yes—
38#88814C2212yes—
39#88814C2211yescharacteristic
40C2×#3799—31no—
41C2×#3797—31no—
42C2×#3796—31no—
43C2×#3795—31no—
44C2×D3×Dic6—31no—
45C2×D3×Dic6—31no—
46#64106D311yescharacteristic, complemented
47#64104D311yescharacteristic, complemented
48#64096D311yescharacteristic, complemented
49C3×#897—31no—
50C3×#897—31no—
51C3×#897—61no—
52C3×#895—31no—
53C3×#895—31no—
54C3×#895—61no—
55C3×#887—31no—
56C3×#887—31no—
57C3×#887—61no—
58#63915—32no—
59#63910—32no—
60C4×#626—31no—
61C4×#626—31no—
62C4×#625—31no—
63#63899—32no—
64#63898—32no—
65#63895—32no—
66#63894—32no—
67#63893—32no—
68Dic3×D12—32no—
69#63886—32no—
70#63885—32no—
71#63864—31no—
72#63863—31no—
73#63860—31no—
74#63852—32no—
75#63852—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C3×C3⋊D3C2311yescharacteristic
79C2×C33×C4C2312yes—
80C2×C33×C4C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C3×C4⋊(C3⋊D3)—24no—
88C3×C4⋊(C3⋊D3)—22no—
89C3×C4×C3⋊D3—22no—
90C3×C4×C3⋊D3—22no—
91C3×#634—22no—
92C3×#634D414yescomplemented
93#6296—24no—
94#6295—22no—
95#6295—24no—
96#6294—24no—
97#6294—24no—
98#5633—91no—
99#5598—91no—
100#5576—91no—
101C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
102C2×C4⋊(C3⋊D3)C2×D312yes—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×C4×C3⋊D3C2×D311yescharacteristic
105C2×#634C2×D311yescharacteristic
106C2×#634C2×D311yescharacteristic
107C2×C3×D12—31no—
108C2×C3×D12—31no—
109C2×C3×D12—32no—
110C2×C3×D12—32no—
111C2×C3×D12—61no—
112C2×C3×D12—62no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3—61no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—31no—
122C2×C3×Dic6—31no—
123C2×C3×Dic6—61no—
124C2×C3×Dic6—61no—
125C2×#627—32no—
126C2×#627—32no—
127C2×#627—32no—
128C2×#626—32no—
129C2×#626—32no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#625—32no—
133C2×#625—31no—
134C2×#624—32no—
135C2×#624—32no—
136C2×D3×Dic3—32no—
137C2×D3×Dic3—32no—
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140#3799—64no—
141#3797—64no—
142#3796—64no—
143#3795—64no—
144D3×Dic6—64no—
145D3×Dic6—64no—
146C32×C4⋊C4—21no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—21no—
149C32×C4⋊C4—41no—
150C32×C4⋊C4C2×D311yescharacteristic
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C2×D311yescharacteristic
153#3752C2×D312yes—
154#3752C2×D312yes—
155C4⋊(C3⋊Dic3)C2×D312yes—
156#3750C2×D312yes—
157C4×C3⋊Dic3C2×D311yescharacteristic
158C4×C3⋊Dic3C2×D312yes—
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×C4⋊Dic3—32no—
166C3×C4⋊Dic3—32no—
167C3×C4⋊Dic3—62no—
168C3×Dic3⋊C4—32no—
169C3×Dic3⋊C4—32no—
170C3×Dic3⋊C4—62no—
171C3×C4×Dic3—32no—
172C3×C4×Dic3—32no—
173C3×C4×Dic3—31no—
174C3×C4×Dic3—31no—
175C3×C4×Dic3—62no—
176C3×C4×Dic3—61no—
177#3724—31no—
178Dic3⋊Dic3—31no—
179Dic3⋊Dic3—31no—
180#3722—31no—
181#3722—32no—
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—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—22no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3#4112yescomplemented
202C33×C4—22no—
203C33×C4C2×D412yes—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C3×C3⋊Dic3—21no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3C2×D414yes—
210C2×#239—91no—
211C2×D3×Q8—91no—
212C2×D3×Q8—91no—
213C2×#237—91no—
214C2×#235—91no—
215C22×Dic6—91no—
216C3×C22⋊Q8—91no—
217C3×#121—91no—
218C3×C4×Q8—91no—
219#947—91no—
220#939—92no—
221#936—91no—
222D4×Dic3—92no—
223C4×#67—91no—
224C4×#67—91no—
225#897—31no—
226#897—31no—
227#897—61no—
228#897—92no—
229#896—92no—
230#895—31no—
231#895—31no—
232#895—61no—
233#895—92no—
234#893—92no—
235#887—31no—
236#887—31no—
237#887—61no—
238#885—92no—
239#885—92no—
240#884—92no—
241#878—92no—
242#875—92no—
243#875—91no—
244C4×D12—92no—
245C4×D12—91no—
246C22×C3⋊D3C22×D312yes—
247C22×C3⋊D3C22×D311yescharacteristic
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3×D3—31no—
250C22×C3×D3—31no—
251C22×C3×D3—32no—
252C22×C3×D3—32no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—61no—
256C22×C3×D3—61no—
257C22×C3×D3—62no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—22no—
262C2×C32×C4—22no—
263C2×C32×C4—22no—
264C2×C32×C4—41no—
265C2×C32×C4—42no—
266C2×C32×C4C22×D312yes—
267C2×C32×C4C22×D312yes—
268C2×C32×C4C22×D312yes—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D311yescharacteristic
277C2×C3⋊Dic3C22×D312yes—
278C4⋊(C3⋊D3)—24no—
279C4⋊(C3⋊D3)—22no—
280C4×C3⋊D3—22no—
281C4×C3⋊D3—22no—
282#634—22no—
283#634D1214yescomplemented
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—61no—
299C2×C3×Dic3—61no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—61no—
302C3×D12—64no—
303C3×D12—64no—
304C3×D12—62no—
305C3×D12—62no—
306C3×D12—122no—
307C3×D12—124no—
308C3×C4×D3—62no—
309C3×C4×D3—62no—
310C3×C4×D3—62no—
311C3×C4×D3—62no—
312C3×C4×D3—122no—
313C3×C4×D3—122no—
314C3×Dic6—34no—
315C3×Dic6—34no—
316C3×Dic6—64no—
317C3×Dic6—62no—
318C3×Dic6—62no—
319C3×Dic6—122no—
320#627—64no—
321#627—64no—
322#627—64no—
323#626—64no—
324#626—64no—
325#626—62no—
326#626—62no—
327#625—62no—
328#625—64no—
329#624—64no—
330#624—64no—
331D3×Dic3—64no—
332D3×Dic3—64no—
333D3×Dic3—64no—
334D3×Dic3—64no—
335#548—271noSylow
336C2×C33C22×D411yescharacteristic
337C2×C33C2×#4111yescharacteristic
338C2×C332−1+411yescharacteristic
339C3×C3⋊D3—22no—
340C3×C3⋊D3—41no—
341C3×C3⋊D3—42no—
342C2×C3×Q8—91no—
343C2×C3×Q8—91no—
344C2×C3×D4—92no—
345C2×C3×D4—91no—
346C22×C3×C4—91no—
347C22×C3×C4—91no—
348C2×#67—91no—
349C2×#67—92no—
350C2×#67—92no—
351C2×#67—91no—
352C22×Dic3—92no—
353C22×Dic3—92no—
354#239—184no—
355D3×Q8—184no—
356D3×Q8—184no—
357#237—184no—
358#235—184no—
359C2×D12—32no—
360C2×D12—31no—
361C2×D12—32no—
362C2×D12—31no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—91no—
366C2×D12—92no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—92no—
374C2×C4×D3—92no—
375C2×C4×D3—92no—
376C2×C4×D3—92no—
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—31no—
381C2×Dic6—61no—
382C2×Dic6—61no—
383C2×Dic6—92no—
384C2×Dic6—92no—
385C2×Dic6—92no—
386C2×Dic6—184no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—41no—
391C3×C4⋊C4—92no—
392C3×C4⋊C4—92no—
393C3×C4⋊C4D3211yescharacteristic
394C3×C4⋊C4D3211yescharacteristic
395C3×C4⋊C4D3211yescharacteristic
396C3×C22⋊C4—92no—
397C3×C22⋊C4—92no—
398C3×C42—92no—
399C3×C42—91no—
400#217—92no—
401#217—91no—
402#217—92no—
403#217—91no—
404(C2×D3)⋊C4—32no—
405(C2×D3)⋊C4—32no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—92no—
414(C2×D3)⋊C4—92no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—91no—
418C4⋊Dic3—32no—
419C4⋊Dic3—32no—
420C4⋊Dic3—62no—
421C4⋊Dic3—91no—
422Dic3⋊C4—32no—
423Dic3⋊C4—32no—
424Dic3⋊C4—62no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427C4×Dic3—32no—
428C4×Dic3—32no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—62no—
432C4×Dic3—61no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—41no—
437C22×C32C23×D311yescharacteristic
438C22×C32C23×D311yescharacteristic
439C22×C32C23×D311yescharacteristic
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3—22no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3#23712yescomplemented
449C2×C3×D3—32no—
450C2×C3×D3—32no—
451C2×C3×D3—62no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—62no—
457C2×C3×D3—62no—
458C2×C3×D3—61no—
459C2×C3×D3—62no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—61no—
469C2×C3×D3—121no—
470C2×C3×D3—121no—
471C2×C3×D3—121no—
472C2×C3×D3—121no—
473C2×C3×D3—122no—
474C2×C3×D3—122no—
475C2×C3×D3—122no—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—42no—
483C32×C4—42no—
484C32×C4—42no—
485C32×C4—42no—
486C32×C4—82no—
487C32×C4C2×D1212yes—
488C32×C4D3×D412yes—
489C32×C4D3×D412yes—
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3⋊Dic3—22no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3C2×D1214yes—
496C3×Dic3—34no—
497C3×Dic3—34no—
498C3×Dic3—64no—
499C3×Dic3—62no—
500C3×Dic3—61no—
501C3×Dic3—62no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—62no—
505C3×Dic3—61no—
506C3×Dic3—61no—
507C3×Dic3—61no—
508C3×Dic3—61no—
509C3×Dic3—61no—
510C3×Dic3—122no—
511C3×Dic3—121no—
512C3×Dic3—121no—
513C3×Dic3—121no—
514C2×#41—271no—
515C22×Q8—271no—
516#124—272no—
517#124—271no—
518C22⋊Q8—91no—
519C22⋊Q8—272no—
520#121—91no—
521#121—272no—
522C4×Q8—91no—
523C4×D4—272no—
524C4×D4—271no—
525C33#54811yescharacteristic, complemented, Sylow
526C23×C3—91no—
527C23×C3—92no—
528C23×C3—91no—
529C22×D3—31no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—62no—
538C3×Q8—94no—
539C3×Q8—182no—
540C3×D4—184no—
541C3×D4—182no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—41no—
549C2×C3×C4—42no—
550C2×C3×C4—92no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—92no—
556C2×C3×C4—182no—
557C2×C3×C4—182no—
558C2×C3×C4C2×D3212yes—
559C2×C3×C4C2×D3212yes—
560C2×C3×C4C2×D3212yes—
561C2×C3×C4C2×D3211yescharacteristic
562C2×C3×C4C2×D3211yescharacteristic
563C2×C3×C4C2×D3211yescharacteristic
564#67—184no—
565#67—184no—
566#67—182no—
567#67—182no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—62no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—62no—
585C2×Dic3—61no—
586C2×Dic3—184no—
587C2×Dic3—184no—
588D12—64no—
589D12—64no—
590D12—62no—
591D12—62no—
592D12—122no—
593D12—124no—
594D12—184no—
595D12—182no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—62no—
600C4×D3—122no—
601C4×D3—122no—
602C4×D3—184no—
603C4×D3—184no—
604C4×D3—184no—
605C4×D3—184no—
606Dic6—34no—
607Dic6—34no—
608Dic6—64no—
609Dic6—62no—
610Dic6—62no—
611Dic6—122no—
612Dic6—184no—
613Dic6—184no—
614Dic6—184no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—41no—
625C2×C32—41no—
626C2×C32—41no—
627C2×C32C22×D1211yescharacteristic
628C2×C32C2×D3×D411yescharacteristic
629C2×C32C2×D3×D411yescharacteristic
630C2×C32C2×#23711yescharacteristic
631C2×C32#100711yescharacteristic
632C2×C32#100711yescharacteristic
633C2×C32D3×#4111yescharacteristic
634C2×C32D3×#4111yescharacteristic
635C2×C32#101011yescharacteristic
636C3⋊D3—22no—
637C3⋊D3—41no—
638C3⋊D3—42no—
639C3×D3—62no—
640C3×D3—62no—
641C3×D3—122no—
642C3×D3—122no—
643C3×D3—122no—
644C3×D3—121no—
645C3×D3—122no—
646C3×D3—121no—
647C3×D3—242no—
648#41—544no—
649C2×Q8—91no—
650C2×Q8—91no—
651C2×Q8—272no—
652C2×Q8—544no—
653C2×D4—92no—
654C2×D4—91no—
655C2×D4—271no—
656C2×D4—272no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—272no—
660C22×C4—272no—
661C4⋊C4—92no—
662C4⋊C4—92no—
663C4⋊C4—271no—
664C4⋊C4#111311yescharacteristic
665C22⋊C4—92no—
666C22⋊C4—92no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—272no—
670C22⋊C4—272no—
671C42—92no—
672C42—91no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—41no—
677C22×C3—92no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—182no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—182no—
684C22×C3—181no—
685C22×C3—182no—
686C22×C3C22×D3211yescharacteristic
687C22×C3C22×D3211yescharacteristic
688C22×C3C22×D3211yescharacteristic
689C2×D3—32no—
690C2×D3—32no—
691C2×D3—62no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—62no—
697C2×D3—61no—
698C2×D3—62no—
699C2×D3—61no—
700C2×D3—62no—
701C2×D3—62no—
702C2×D3—62no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—61no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—122no—
714C2×D3—122no—
715C2×D3—122no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—82no—
727C3×C4—94no—
728C3×C4—181no—
729C3×C4—182no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733C3×C4D3×D1212yes—
734C3×C4D3×D1212yes—
735C3×C4#380212yes—
736Dic3—34no—
737Dic3—34no—
738Dic3—64no—
739Dic3—62no—
740Dic3—62no—
741Dic3—61no—
742Dic3—61no—
743Dic3—62no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—61no—
748Dic3—61no—
749Dic3—61no—
750Dic3—122no—
751Dic3—121no—
752Dic3—121no—
753Dic3—121no—
754C32—21no—
755C32—21no—
756C32—21no—
757C32—41no—
758C32#557611yescharacteristic, complemented
759C32#559811yescharacteristic, complemented
760C32#563311yescharacteristic, complemented
761C23—91no—
762C23—91no—
763C23—92no—
764Q8—94no—
765Q8—182no—
766Q8—544no—
767D4—184no—
768D4—182no—
769D4—544no—
770D4—542no—
771C2×C4—92no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—92no—
776C2×C4—91no—
777C2×C4—182no—
778C2×C4—182no—
779C2×C4—544no—
780C2×C4—544no—
781C2×C4C2×#111312yes—
782C2×C4C2×#111311yescharacteristic
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—182no—
796C2×C3—362no—
797C2×C3—361no—
798C2×C3C2×D3×D1211yescharacteristic
799C2×C3C2×D3×D1211yescharacteristic
800C2×C3C2×#380211yescharacteristic
801C2×C3D3×#23711yescharacteristic
802C2×C3D3×#23711yescharacteristic
803C2×C3#6431211yescharacteristic
804C2×C3#6431511yescharacteristic
805C2×C3#6431511yescharacteristic
806C2×C3#6431611yescharacteristic
807D3—62no—
808D3—62no—
809D3—122no—
810D3—122no—
811D3—121no—
812D3—122no—
813D3—121no—
814D3—122no—
815D3—242no—
816C22—92no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—182no—
821C22—182no—
822C22—181no—
823C22—181no—
824C22—182no—
825C22C22×#111311yescharacteristic
826C4—22no—
827C4—94no—
828C4—181no—
829C4—181no—
830C4—182no—
831C4—181no—
832C4—181no—
833C4C4⋊#111312yes—
834C3—21no—
835C3—21no—
836C3—21no—
837C3—41no—
838C3#1059432911yescharacteristic, complemented
839C3#1059438211yescharacteristic, complemented
840C3#1059452511yescharacteristic, complemented
841C2—182no—
842C2—361no—
843C2—362no—
844C2C2×C4⋊#111311yescharacteristic
845C2#1172462211yescharacteristic
846C2#1172462411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89041C2semidirect
2. C2×#89040C2semidirect
3. C3×#64106C2semidirect
4. C3×#64104C2semidirect
5. C3×#64096C2semidirect
6. C4×#6295C2semidirect
7. #11723692C2semidirect
8. #11723691C2semidirect
9. #11723687C2semidirect
10. #11723677C2semidirect
11. #11723672C2semidirect
46. #64106D3semidirect
47. #64104D3semidirect
48. #64096D3semidirect
92. C3×#634D4semidirect
201. C2×C3×C3⋊D3#41semidirect
283. #634D12semidirect
448. C2×C3⋊D3#237semidirect
525. C33#548semidirect
758. C32#5576semidirect
759. C32#5598semidirect
760. C32#5633semidirect
838. C3#10594329semidirect
839. C3#10594382semidirect
840. C3#10594525semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
C2×#890402
C3×#641062
C3×#641042
C3×#640962
C4×#62952
#117236922
#117236912
#117236872
#117236772
#117236722
#105945253
#105943823
#105943293