Finite Group Databasebeta

← #13178358

Subgroups — #13178358

Order 1728.

1612 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊#1113C211yesmaximal, characteristic, complemented
2C2×#89042C211yesmaximal, characteristic, complemented
3C3×#64103C212yesmaximal, complemented
4C3×#64102C211yesmaximal, characteristic, complemented
5#11723701C212yesmaximal, complemented
6#11723700C212yesmaximal, complemented
7#11723695C211yesmaximal, characteristic, complemented
8#11723687C212yesmaximal, complemented
9#11723685C211yesmaximal, characteristic, complemented
10#11723672C211yesmaximal, characteristic, complemented
11#11723671C211yesmaximal, characteristic, complemented
12#10594619—32nomaximal
13#10594616—31nomaximal
14C22×#1113C2212yes—
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×C4×C3⋊D3C2212yescomplemented
20C2×#6296C2211yescharacteristic, complemented
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6295C2212yescomplemented
24C2×#6295C2212yescomplemented
25C2×#6294C2212yescomplemented
26C4⋊#1113—24no—
27#89042—24no—
28C33×C4⋊C4C2211yescharacteristic, complemented
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic, complemented
31C3×#3752C2212yescomplemented
32C3×#3752C2212yescomplemented
33C3×#3752C2212yescomplemented
34C3×#3750C2212yescomplemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88814C2212yes—
38#88814C2212yescomplemented
39C2×#3802—31no—
40C2×D3×D12—32no—
41C2×#3798—31no—
42C2×#3798—32no—
43#64103D312yescomplemented
44#64102D311yescharacteristic, complemented
45C3×#894—32no—
46C3×#894—32no—
47C3×#894—62no—
48C3×#893—32no—
49C3×#893—61no—
50#63923—32no—
51#63922—32no—
52#63922—32no—
53#63921—32no—
54D3×(C2×D3)⋊C4—32no—
55D3×(C2×D3)⋊C4—32no—
56#63915—31no—
57#63912—31no—
58#63910—32no—
59#63906—32no—
60#63902—31no—
61#63886—32no—
62#63885—32no—
63#63880—32no—
64#63865—31no—
65#63852—32no—
66#63851—32no—
67C22×C3×C3⋊D3C2312yes—
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C3×C3⋊D3C2312yes—
70C22×C3×C3⋊D3C2311yescharacteristic
71C2×#1113—24no—
72C2×#1113—24no—
73C2×#1113—42no—
74C2×C33×C4C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)—24no—
82C3×C4⋊(C3⋊D3)—22no—
83C3×C4×C3⋊D3—24no—
84C3×C4×C3⋊D3—22no—
85C3×C4×C3⋊D3—22no—
86#6296—22no—
87#6295—24no—
88#6295—22no—
89#6295—42no—
90#6295D414yescomplemented
91#6294—42no—
92#5654—92no—
93#5550—91no—
94C22×D32—32no—
95C22×D32—32no—
96C22×D32—32no—
97C2×C4⋊(C3⋊D3)C2×D312yes—
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
101C2×C4×C3⋊D3C2×D312yescomplemented
102C2×C3×D12—32no—
103C2×C3×D12—32no—
104C2×C3×D12—32no—
105C2×C3×D12—61no—
106C2×C3×D12—62no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3—61no—
113C2×C3×C4×D3—62no—
114C2×#627—32no—
115C2×#627—31no—
116C2×#626—32no—
117C2×#626—32no—
118C2×#626—32no—
119C2×#626—32no—
120C2×#626—32no—
121C2×#626—32no—
122C2×#625—31no—
123C2×#625—32no—
124C2×#625—31no—
125C2×#625—32no—
126C2×#624—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129#3802—64no—
130D3×D12—68no—
131#3798—64no—
132#3798—68no—
133C32×C4⋊C4—21no—
134C32×C4⋊C4—22no—
135C32×C4⋊C4—41no—
136C32×C4⋊C4C2×D312yescomplemented
137C32×C4⋊C4C2×D311yescharacteristic, complemented
138#3752C2×D311yescharacteristic
139#3752C2×D311yescharacteristic, complemented
140#3752C2×D312yescomplemented
141#3752C2×D312yescomplemented
142#3752C2×D312yescomplemented
143#3750C2×D312yescomplemented
144C4×C3⋊Dic3C2×D311yescharacteristic, complemented
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—61no—
154C3×(C2×D3)⋊C4—61no—
155C3×(C2×D3)⋊C4—62no—
156C3×(C2×D3)⋊C4—62no—
157C3×(C2×D3)⋊C4—62no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—62no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3—61no—
163#3724—31no—
164Dic3⋊Dic3—32no—
165#3722—32no—
166#3722—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171C22×C33C2411yescharacteristic
172C2×C3×C3⋊D3—21no—
173C2×C3×C3⋊D3—22no—
174C2×C3×C3⋊D3—22no—
175C2×C3×C3⋊D3—21no—
176C2×C3×C3⋊D3—21no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3—21no—
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3C2×D414yes—
183C2×C3×C3⋊D3#4112yescomplemented
184#1113—48no—
185C33×C4—21no—
186C33×C4—21no—
187C33×C4—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3C2×D412yes—
192C2×D3×D4—92no—
193C2×#235—92no—
194C2×#235—91no—
195C22×D12—91no—
196C3×#123—92no—
197C3×C4×D4—91no—
198#939—92no—
199#937—92no—
200#930—91no—
201C2×(C2×D3)⋊C4—92no—
202#924—91no—
203#896—92no—
204#895—92no—
205#894—32no—
206#894—32no—
207#894—62no—
208#893—32no—
209#893—61no—
210#885—92no—
211#884—92no—
212#884—92no—
213#882—92no—
214#882—92no—
215#67⋊C4—92no—
216D3×C22⋊C4—92no—
217D3×C22⋊C4—92no—
218#875—91no—
219C4×D12—91no—
220C22×C3⋊D3C22×D312yes—
221C22×C3⋊D3C22×D311yescharacteristic
222C22×C3⋊D3C22×D311yescharacteristic
223C22×C3⋊D3C22×D312yes—
224C22×C3×D3—32no—
225C22×C3×D3—32no—
226C22×C3×D3—32no—
227C22×C3×D3—32no—
228C22×C3×D3—32no—
229C22×C3×D3—32no—
230C22×C3×D3—61no—
231C22×C3×D3—62no—
232C22×C3×D3—61no—
233C22×C3×D3—62no—
234C2×D32—64no—
235C2×D32—64no—
236C2×D32—64no—
237C2×D32—64no—
238C2×D32—64no—
239C2×D32—64no—
240C2×D32—122no—
241C2×D32—122no—
242C2×D32—122no—
243C2×C32×C4—21no—
244C2×C32×C4—22no—
245C2×C32×C4—22no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—22no—
249C2×C32×C4—41no—
250C2×C32×C4—41no—
251C2×C32×C4—41no—
252C2×C32×C4C22×D312yes—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D312yes—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D311yescharacteristic
262C4⋊(C3⋊D3)—22no—
263C4⋊(C3⋊D3)—24no—
264C4×C3⋊D3—24no—
265C4×C3⋊D3—22no—
266C4×C3⋊D3—22no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—62no—
277C3×D12—64no—
278C3×D12—64no—
279C3×D12—64no—
280C3×D12—64no—
281C3×D12—124no—
282C3×C4×D3—64no—
283C3×C4×D3—64no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3—122no—
287C3×C4×D3—122no—
288C3×C4×D3—124no—
289#627—64no—
290#627—62no—
291#626—38no—
292#626—64no—
293#626—64no—
294#626—64no—
295#626—122no—
296#626—122no—
297#625—34no—
298#625—64no—
299#625—62no—
300#625—122no—
301#624—122no—
302D3×Dic3—122no—
303D3×Dic3—122no—
304#546—271noSylow
305C2×C33C22×D411yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C2×C33H(5,𝔽2)11yescharacteristic
308C3×C3⋊D3—22no—
309C3×C3⋊D3—24no—
310C3×C3⋊D3—41no—
311C3×C3⋊D3—42no—
312C23×D3—92no—
313C23×D3—92no—
314C23×D3—92no—
315C2×C3×D4—91no—
316C2×C3×D4—92no—
317C22×C3×C4—91no—
318C22×C3×C4—92no—
319C22×C3×C4—91no—
320C2×#67—92no—
321C2×#67—92no—
322C2×#67—92no—
323C2×#67—92no—
324C2×#67—92no—
325C2×#67—92no—
326C22×Dic3—92no—
327D3×D4—188no—
328#235—184no—
329#235—188no—
330C2×D12—32no—
331C2×D12—32no—
332C2×D12—32no—
333C2×D12—61no—
334C2×D12—62no—
335C2×D12—91no—
336C2×D12—91no—
337C2×D12—92no—
338C2×D12—92no—
339C2×D12—184no—
340C2×C4×D3—32no—
341C2×C4×D3—32no—
342C2×C4×D3—32no—
343C2×C4×D3—32no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—62no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×Dic6—91no—
350C2×Dic6—92no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—92no—
355C3×C4⋊C4D3212yescomplemented
356C3×C4⋊C4D3211yescharacteristic, complemented
357C3×C22⋊C4—91no—
358C3×C22⋊C4—92no—
359C3×C22⋊C4—92no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—91no—
362C3×C42—91no—
363#217—92no—
364#217—92no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—32no—
367(C2×D3)⋊C4—32no—
368(C2×D3)⋊C4—32no—
369(C2×D3)⋊C4—32no—
370(C2×D3)⋊C4—32no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—62no—
377(C2×D3)⋊C4—62no—
378(C2×D3)⋊C4—92no—
379(C2×D3)⋊C4—92no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—92no—
382C4⋊Dic3—91no—
383Dic3⋊C4—32no—
384Dic3⋊C4—32no—
385Dic3⋊C4—62no—
386Dic3⋊C4—92no—
387C4×Dic3—32no—
388C4×Dic3—61no—
389C22×C32—22no—
390C22×C32—21no—
391C22×C32—41no—
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D312yes—
394C2×C3⋊D3—21no—
395C2×C3⋊D3—21no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3#23512yescomplemented
405C2×C3⋊D3D3×D414yes—
406C2×C3×D3—34no—
407C2×C3×D3—34no—
408C2×C3×D3—34no—
409C2×C3×D3—64no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—62no—
417C2×C3×D3—62no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—62no—
427C2×C3×D3—121no—
428C2×C3×D3—121no—
429C2×C3×D3—122no—
430C2×C3×D3—122no—
431C2×C3×D3—121no—
432C2×C3×D3—121no—
433C2×C3×D3—122no—
434C2×C3×D3—122no—
435C2×C3×D3—122no—
436D32—128no—
437D32—128no—
438D32—128no—
439C32×C4—21no—
440C32×C4—22no—
441C32×C4—22no—
442C32×C4—21no—
443C32×C4—22no—
444C32×C4—21no—
445C32×C4—22no—
446C32×C4—42no—
447C32×C4—42no—
448C32×C4—41no—
449C32×C4—42no—
450C32×C4—41no—
451C32×C4—42no—
452C32×C4—81no—
453C32×C4—81no—
454C3⋊Dic3—22no—
455C3⋊Dic3—21no—
456C3⋊Dic3—22no—
457C3⋊Dic3D3×D412yes—
458C3×Dic3—34no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—122no—
466C3×Dic3—121no—
467C3×Dic3—122no—
468C2×#41—271no—
469C22×D4—271no—
470#124—271no—
471#123—92no—
472C22⋊Q8—271no—
473#121—271no—
474#121—272no—
475#120—272no—
476C4×D4—91no—
477C4×D4—271no—
478C2×C22⋊C4—272no—
479C33#54611yescharacteristic, complemented, Sylow
480C23×C3—91no—
481C23×C3—92no—
482C23×C3—92no—
483C23×C3—91no—
484C22×D3—32no—
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—32no—
490C22×D3—61no—
491C22×D3—62no—
492C22×D3—61no—
493C22×D3—62no—
494C22×D3—184no—
495C22×D3—184no—
496C22×D3—184no—
497C22×D3—184no—
498C22×D3—184no—
499C22×D3—184no—
500C22×D3—362no—
501C22×D3—362no—
502C22×D3—362no—
503C3×D4—182no—
504C3×D4—184no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—91no—
515C2×C3×C4—92no—
516C2×C3×C4—91no—
517C2×C3×C4—92no—
518C2×C3×C4—182no—
519C2×C3×C4—182no—
520C2×C3×C4—184no—
521C2×C3×C4C2×D3212yes—
522C2×C3×C4C2×D3211yescharacteristic
523C2×C3×C4C2×D3212yes—
524C2×C3×C4C2×D3211yescharacteristic
525C2×C3×C4C2×D3212yes—
526C2×C3×C4C2×D3211yescharacteristic
527#67—98no—
528#67—184no—
529#67—184no—
530#67—184no—
531#67—362no—
532#67—362no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—362no—
544D12—64no—
545D12—64no—
546D12—64no—
547D12—64no—
548D12—94no—
549D12—124no—
550D12—182no—
551D12—184no—
552D12—362no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—64no—
556C4×D3—64no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—124no—
560C4×D3—362no—
561C4×D3—362no—
562Dic6—184no—
563Dic6—182no—
564C2×C32—22no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—22no—
568C2×C32—21no—
569C2×C32—22no—
570C2×C32—41no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32C2×#23511yescharacteristic
574C2×C32C2×D3×D412yes—
575C2×C32C2×D3×D411yescharacteristic
576C2×C32D3×#4112yes—
577C2×C32#100912yes—
578C2×C32#100911yescharacteristic
579C3⋊D3—24no—
580C3⋊D3—22no—
581C3⋊D3—41no—
582C3⋊D3—42no—
583C3×D3—64no—
584C3×D3—64no—
585C3×D3—64no—
586C3×D3—122no—
587C3×D3—124no—
588C3×D3—122no—
589C3×D3—122no—
590C3×D3—122no—
591C3×D3—122no—
592C3×D3—242no—
593C24—272no—
594#41—544no—
595C2×Q8—271no—
596C2×D4—91no—
597C2×D4—92no—
598C2×D4—271no—
599C2×D4—272no—
600C2×D4—271no—
601C2×D4—272no—
602C2×D4—544no—
603C22×C4—92no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—272no—
607C4⋊C4—92no—
608C4⋊C4—271no—
609C4⋊C4#111311yescharacteristic, complemented
610C22⋊C4—91no—
611C22⋊C4—92no—
612C22⋊C4—91no—
613C22⋊C4—92no—
614C22⋊C4—92no—
615C22⋊C4—272no—
616C22⋊C4—272no—
617C42—91no—
618C22×C3—21no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—92no—
622C22×C3—94no—
623C22×C3—182no—
624C22×C3—181no—
625C22×C3—182no—
626C22×C3—181no—
627C22×C3—182no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—182no—
631C22×C3—181no—
632C22×C3—182no—
633C22×C3C22×D3212yes—
634C22×C3C22×D3211yescharacteristic
635C2×D3—34no—
636C2×D3—34no—
637C2×D3—34no—
638C2×D3—64no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—122no—
663C2×D3—122no—
664C2×D3—122no—
665C2×D3—368no—
666C2×D3—368no—
667C2×D3—368no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—92no—
684C3×C4—182no—
685C3×C4—181no—
686C3×C4—182no—
687Dic3—34no—
688Dic3—62no—
689Dic3—62no—
690Dic3—62no—
691Dic3—62no—
692Dic3—62no—
693Dic3—62no—
694Dic3—122no—
695Dic3—121no—
696Dic3—122no—
697C32—21no—
698C32—22no—
699C32—41no—
700C32#555011yescharacteristic, complemented
701C32#565412yescomplemented
702C23—91no—
703C23—92no—
704C23—92no—
705C23—91no—
706C23—544no—
707C23—544no—
708C23—1082no—
709Q8—542no—
710D4—184no—
711D4—182no—
712D4—274no—
713D4—542no—
714D4—544no—
715D4—1082no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—92no—
719C2×C4—92no—
720C2×C4—182no—
721C2×C4—182no—
722C2×C4—184no—
723C2×C4—1082no—
724C2×C4C2×#111311yescharacteristic
725C2×C4C2×#111311yescharacteristic
726C2×C4C2×#111311yescharacteristic
727C2×C3—21no—
728C2×C3—22no—
729C2×C3—21no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—22no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3—41no—
736C2×C3—182no—
737C2×C3—184no—
738C2×C3—361no—
739C2×C3—362no—
740C2×C3D3×#23512yes—
741C2×C3#6430611yescharacteristic
742C2×C3D32×D411yescharacteristic
743C2×C3D32×D412yes—
744C2×C3#6432011yescharacteristic
745C2×C3#6432012yes—
746D3—64no—
747D3—64no—
748D3—64no—
749D3—122no—
750D3—124no—
751D3—122no—
752D3—122no—
753D3—122no—
754D3—122no—
755D3—242no—
756C22—92no—
757C22—94no—
758C22—182no—
759C22—181no—
760C22—182no—
761C22—181no—
762C22—181no—
763C22—182no—
764C22—181no—
765C22—182no—
766C22—181no—
767C22—182no—
768C22—1088no—
769C22C22×#111311yescharacteristic
770C4—21no—
771C4—21no—
772C4—21no—
773C4—92no—
774C4—182no—
775C4—181no—
776C4—182no—
777C3—21no—
778C3—22no—
779C3—41no—
780C3#1059461611yescharacteristic, complemented
781C3#1059461912yescomplemented
782C2—182no—
783C2—184no—
784C2—362no—
785C2—361no—
786C2#1172461811yescharacteristic
787C2D4×#111311yescharacteristic
788C2#1172462711yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#1113C2semidirect
2. C2×#89042C2semidirect
3. C3×#64103C2semidirect
4. C3×#64102C2semidirect
5. #11723701C2semidirect
6. #11723700C2semidirect
7. #11723695C2semidirect
8. #11723687C2semidirect
9. #11723685C2semidirect
10. #11723672C2semidirect
11. #11723671C2semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
20. C2×#6296C22semidirect
23. C2×#6295C22semidirect
24. C2×#6295C22semidirect
25. C2×#6294C22semidirect
28. C33×C4⋊C4C22semidirect
30. C3×#3752C22semidirect
31. C3×#3752C22semidirect
32. C3×#3752C22semidirect
33. C3×#3752C22semidirect
34. C3×#3750C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
36. #88815C22semidirect
38. #88814C22semidirect
43. #64103D3semidirect
44. #64102D3semidirect
90. #6295D4semidirect
100. C2×C4×C3⋊D3C2×D3semidirect
101. C2×C4×C3⋊D3C2×D3semidirect
136. C32×C4⋊C4C2×D3semidirect
137. C32×C4⋊C4C2×D3semidirect
139. #3752C2×D3semidirect
140. #3752C2×D3semidirect
141. #3752C2×D3semidirect
142. #3752C2×D3semidirect
143. #3750C2×D3semidirect
144. C4×C3⋊Dic3C2×D3semidirect
183. C2×C3×C3⋊D3#41semidirect
355. C3×C4⋊C4D32semidirect
356. C3×C4⋊C4D32semidirect
404. C2×C3⋊D3#235semidirect
479. C33#546semidirect
609. C4⋊C4#1113semidirect
700. C32#5550semidirect
701. C32#5654semidirect
780. C3#10594616semidirect
781. C3#10594619semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#11132
C2×#890422
C3×#641032
C3×#641022
#117237012
#117237002
#117236952
#117236872
#117236852
#117236722
#117236712
#105946193
#105946163