Finite Group Databasebeta

← #13178233

Subgroups — #13178233

Order 1728.

1728 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×#89042C211yesmaximal, characteristic, complemented
3C3×#64090C211yesmaximal, characteristic, complemented
4C3×C22⋊C4×C3⋊D3C212yesmaximal, complemented
5#11723727C212yesmaximal, complemented
6#11723721C211yesmaximal, characteristic, complemented
7#11723695C212yesmaximal, complemented
8#11723695C211yesmaximal, characteristic, complemented
9#11723694C212yesmaximal, complemented
10C4×#6295C211yesmaximal, characteristic, complemented
11#11723672C211yesmaximal, characteristic, complemented
12#10594186—32nomaximal
13#10594183—31nomaximal
14C23×C3×C3⋊D3C2212yes—
15C2×C3×#638C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2212yescomplemented
18C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×C4×C3⋊D3C2212yescomplemented
20C2×#6296C2211yescharacteristic, complemented
21C2×#6295—24no—
22C2×#6295C2211yescharacteristic
23C2×#6295C2212yes—
24C2×#6295C2211yescharacteristic
25C2×#6295C2212yescomplemented
26C2×#6295C2212yescomplemented
27#89042—24no—
28C33×C22⋊C4C2211yescharacteristic
29C3×#3757C2212yes—
30C3×#3752C2212yescomplemented
31C3×#3752C2212yescomplemented
32C3×#3752C2211yescharacteristic, complemented
33C3×#3750C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88815C2212yescomplemented
37#88814C2212yescomplemented
38#88814C2212yescomplemented
39C22×#626—32no—
40C22×#625—31no—
41C2×#3798—31no—
42C2×#3798—32no—
43#64090D311yescharacteristic, complemented
44C22⋊C4×C3⋊D3D312yescomplemented
45C3×#67⋊C4—32no—
46C3×#67⋊C4—61no—
47C3×D3×C22⋊C4—32no—
48C3×D3×C22⋊C4—32no—
49C3×D3×C22⋊C4—62no—
50#63982—31no—
51#63981—32no—
52#63977—32no—
53#63976—32no—
54#63964—32no—
55#63915—31no—
56#63912—31no—
57#63912—32no—
58#63906—32no—
59#63906—32no—
60#63906—32no—
61#63905—32no—
62C4×#626—32no—
63C4×#625—31no—
64#63853—32no—
65#63852—32no—
66#63850—32no—
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3—24no—
69C22×C3×C3⋊D3—24no—
70C22×C3×C3⋊D3—42no—
71C22×C3×C3⋊D3C2312yes—
72C22×C3×C3⋊D3C2311yescharacteristic
73C22×C3×C3⋊D3C2312yes—
74C2×C33×C4C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C3×#638—22no—
77C2×C3×C3⋊Dic3—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—24no—
84C3×C4×C3⋊D3—22no—
85C3×C4×C3⋊D3—42no—
86#6296—22no—
87#6295—24no—
88#6295—24no—
89#6295—22no—
90#6295—42no—
91#6295D414yescomplemented
92#5550—91no—
93#5490—92no—
94C23×C3⋊D3C2×D312yes—
95C23×C3×D3—32no—
96C23×C3×D3—32no—
97C23×C3×D3—62no—
98C2×#638C2×D311yescharacteristic
99C22×C3⋊Dic3C2×D311yescharacteristic
100C2×C4×C3⋊D3C2×D312yescomplemented
101C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
102C2×C4×C3⋊D3C2×D312yescomplemented
103C2×C3×#67—32no—
104C2×C3×#67—61no—
105C22×C3×Dic3—32no—
106C22×C3×Dic3—61no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—62no—
113C2×C3×C4×D3—62no—
114C2×C3×C4×D3—61no—
115C2×#627—32no—
116C2×#627—31no—
117C2×#626—32no—
118C2×#626—32no—
119C2×#626—32no—
120C2×#626—32no—
121C2×#626—32no—
122C2×#626—32no—
123C2×#626—32no—
124C2×#626—32no—
125C2×#626—68no—
126C2×#625—31no—
127C2×#625—32no—
128C2×#625—32no—
129C2×#625—31no—
130C2×#625—32no—
131C2×#625—64no—
132#3798—64no—
133#3798—68no—
134C32×C22⋊C4—22no—
135C32×C22⋊C4—21no—
136C32×C22⋊C4—41no—
137C32×C22⋊C4C2×D311yescharacteristic
138C32×C22⋊C4C2×D312yes—
139#3757C2×D312yes—
140#3752C2×D312yescomplemented
141#3752C2×D312yescomplemented
142#3752C2×D311yescharacteristic, complemented
143#3750C2×D311yescharacteristic, complemented
144C4×C3⋊Dic3C2×D311yescharacteristic, complemented
145C3×#217—32no—
146C3×#217—32no—
147C3×#217—62no—
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—62no—
154C3×(C2×D3)⋊C4—62no—
155C3×(C2×D3)⋊C4—61no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—61no—
158C3×C4×Dic3—32no—
159C3×C4×Dic3—61no—
160#3724—32no—
161#3724—31no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
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×C33—21no—
172C22×C33—21no—
173C22×C33#4112yescomplemented
174C22×C33C2411yescharacteristic
175C2×C3×C3⋊D3—22no—
176C2×C3×C3⋊D3—22no—
177C2×C3×C3⋊D3—21no—
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—48no—
184C2×C3×C3⋊D3C2×D414yes—
185C33×C4—21no—
186C33×C4—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3C2×D412yes—
192C22×#67—92no—
193C2×#235—92no—
194C2×#235—91no—
195C22×D12—91no—
196C3×C4×D4—91no—
197C2×C3×C22⋊C4—92no—
198#953—92no—
199#937—92no—
200#930—92no—
201#930—91no—
202#929—92no—
203C4×#67—92no—
204#924—91no—
205#894—92no—
206#885—92no—
207#884—92no—
208#884—92no—
209#884—92no—
210#883—92no—
211#882—92no—
212#67⋊C4—32no—
213#67⋊C4—61no—
214D3×C22⋊C4—32no—
215D3×C22⋊C4—32no—
216D3×C22⋊C4—62no—
217#878—92no—
218#875—91no—
219C4×D12—91no—
220C23×C32—22no—
221C23×C32—21no—
222C23×C32—41no—
223C23×C32C22×D311yescharacteristic
224C23×C32C22×D312yes—
225C22×C3⋊D3—24no—
226C22×C3⋊D3—24no—
227C22×C3⋊D3—42no—
228C22×C3⋊D3C22×D312yes—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3⋊D3C22×D312yes—
231C22×C3×D3—32no—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—32no—
235C22×C3×D3—32no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—61no—
239C22×C3×D3—64no—
240C22×C3×D3—64no—
241C22×C3×D3—68no—
242C22×C3×D3—64no—
243C22×C3×D3—64no—
244C22×C3×D3—124no—
245C22×C3×D3—122no—
246C22×C3×D3—122no—
247C22×C3×D3—124no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—22no—
251C2×C32×C4—22no—
252C2×C32×C4—41no—
253C2×C32×C4—41no—
254C2×C32×C4C22×D312yes—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258#638—22no—
259C2×C3⋊Dic3—22no—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C4×C3⋊D3—24no—
266C4×C3⋊D3—22no—
267C4×C3⋊D3—42no—
268C3×#67—64no—
269C3×#67—64no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—64no—
283C2×C3×Dic3—122no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287C3×C4×D3—122no—
288C3×C4×D3—124no—
289C3×C4×D3—122no—
290C3×C4×D3—122no—
291C3×C4×D3—124no—
292#627—64no—
293#627—62no—
294#626—38no—
295#626—64no—
296#626—64no—
297#626—64no—
298#626—64no—
299#626—64no—
300#626—122no—
301#626—122no—
302#625—34no—
303#625—64no—
304#625—64no—
305#625—62no—
306#625—122no—
307#546—271noSylow
308C2×C33—22no—
309C2×C33C22×D411yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C3×C3⋊D3—24no—
313C3×C3⋊D3—41no—
314C3×C3⋊D3—42no—
315C24×C3—92no—
316C23×D3—32no—
317C23×D3—32no—
318C23×D3—62no—
319C2×C3×D4—91no—
320C22×C3×C4—91no—
321C22×C3×C4—92no—
322C22×C3×C4—91no—
323C22×C3×C4—92no—
324C2×#67—32no—
325C2×#67—61no—
326C2×#67—92no—
327C2×#67—92no—
328C2×#67—92no—
329C2×#67—92no—
330C2×#67—92no—
331C2×#67—92no—
332C2×#67—92no—
333C2×#67—92no—
334C2×#67—188no—
335C22×Dic3—32no—
336C22×Dic3—61no—
337#235—184no—
338#235—188no—
339C2×D12—91no—
340C2×D12—91no—
341C2×D12—92no—
342C2×D12—92no—
343C2×D12—92no—
344C2×D12—184no—
345C2×C4×D3—32no—
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—32no—
349C2×C4×D3—32no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×C4×D3—61no—
353C2×Dic6—91no—
354C2×Dic6—92no—
355C3×C4⋊C4—91no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—92no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—92no—
363C3×C22⋊C4D3211yescharacteristic
364C3×C22⋊C4D3212yes—
365C3×C42—91no—
366#217—32no—
367#217—32no—
368#217—62no—
369#217—92no—
370#217—92no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—32no—
374(C2×D3)⋊C4—32no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—62no—
377(C2×D3)⋊C4—62no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—92no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—92no—
382(C2×D3)⋊C4—92no—
383C4⋊Dic3—91no—
384C4⋊Dic3—92no—
385Dic3⋊C4—32no—
386Dic3⋊C4—61no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389Dic3⋊C4—92no—
390C4×Dic3—32no—
391C4×Dic3—61no—
392C22×C32—22no—
393C22×C32—21no—
394C22×C32—22no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—24no—
400C22×C32—41no—
401C22×C32—42no—
402C22×C32—41no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—41no—
406C22×C32—81no—
407C22×C32—81no—
408C22×C32#23514yescomplemented
409C22×C32#23512yescomplemented
410C22×C32C23×D312yes—
411C22×C32C23×D311yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—22no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—48no—
421C2×C3⋊D3D3×D414yes—
422C2×C3×D3—34no—
423C2×C3×D3—34no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—62no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—64no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—121no—
443C2×C3×D3—121no—
444C2×C3×D3—122no—
445C2×C3×D3—122no—
446C2×C3×D3—128no—
447C2×C3×D3—128no—
448C2×C3×D3—1216no—
449C32×C4—22no—
450C32×C4—21no—
451C32×C4—22no—
452C32×C4—21no—
453C32×C4—41no—
454C32×C4—42no—
455C32×C4—42no—
456C32×C4—41no—
457C32×C4—81no—
458C32×C4—81no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—22no—
462C3⋊Dic3—22no—
463C3⋊Dic3D3×D412yes—
464C3×Dic3—34no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—122no—
474C3×Dic3—122no—
475C3×Dic3—121no—
476C2×#41—271no—
477C22×D4—271no—
478#124—271no—
479#123—272no—
480C22⋊Q8—271no—
481#121—271no—
482#121—272no—
483#120—272no—
484C4×D4—91no—
485C4×D4—271no—
486C2×C22⋊C4—92no—
487C33#54611yescharacteristic, complemented, Sylow
488C23×C3—22no—
489C23×C3—21no—
490C23×C3—41no—
491C23×C3—92no—
492C23×C3—92no—
493C23×C3—91no—
494C23×C3—184no—
495C23×C3—184no—
496C23×C3—362no—
497C23×C3C2×D3211yescharacteristic
498C23×C3C2×D3212yes—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—32no—
502C22×D3—32no—
503C22×D3—32no—
504C22×D3—62no—
505C22×D3—62no—
506C22×D3—61no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—68no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—124no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—124no—
516C3×D4—182no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—92no—
526C2×C3×C4—92no—
527C2×C3×C4—91no—
528C2×C3×C4—182no—
529C2×C3×C4—184no—
530C2×C3×C4—182no—
531C2×C3×C4—362no—
532C2×C3×C4C2×D3212yes—
533C2×C3×C4C2×D3212yes—
534C2×C3×C4C2×D3211yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536#67—64no—
537#67—64no—
538#67—98no—
539#67—184no—
540#67—184no—
541#67—184no—
542#67—184no—
543#67—184no—
544#67—362no—
545#67—362no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—32no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—64no—
559C2×Dic3—122no—
560D12—94no—
561D12—182no—
562D12—184no—
563D12—184no—
564D12—362no—
565C4×D3—64no—
566C4×D3—64no—
567C4×D3—64no—
568C4×D3—122no—
569C4×D3—124no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—124no—
573Dic6—184no—
574Dic6—182no—
575C2×C32—24no—
576C2×C32—22no—
577C2×C32—21no—
578C2×C32—22no—
579C2×C32—21no—
580C2×C32—22no—
581C2×C32—21no—
582C2×C32—22no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—44no—
587C2×C32—42no—
588C2×C32—82no—
589C2×C32C2×#23512yes—
590C2×C32C2×#23511yescharacteristic
591C2×C32C2×D3×D412yes—
592C2×C32C2×D3×D411yescharacteristic
593C2×C32#100412yes—
594C2×C32#100911yescharacteristic
595C3⋊D3—24no—
596C3⋊D3—42no—
597C3⋊D3—41no—
598C3×D3—68no—
599C3×D3—64no—
600C3×D3—64no—
601C3×D3—122no—
602C3×D3—124no—
603C3×D3—122no—
604C3×D3—122no—
605C3×D3—122no—
606C24—92no—
607#41—544no—
608C2×Q8—271no—
609C2×D4—91no—
610C2×D4—271no—
611C2×D4—272no—
612C2×D4—272no—
613C2×D4—271no—
614C2×D4—272no—
615C2×D4—544no—
616C22×C4—91no—
617C22×C4—92no—
618C22×C4—91no—
619C22×C4—92no—
620C4⋊C4—91no—
621C4⋊C4—271no—
622C4⋊C4—272no—
623C22⋊C4—92no—
624C22⋊C4—92no—
625C22⋊C4—92no—
626C22⋊C4—91no—
627C22⋊C4—272no—
628C22⋊C4—272no—
629C22⋊C4#111311yescharacteristic
630C42—91no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—24no—
639C22×C3—41no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—42no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—94no—
648C22×C3—182no—
649C22×C3—182no—
650C22×C3—181no—
651C22×C3—182no—
652C22×C3—181no—
653C22×C3—182no—
654C22×C3—181no—
655C22×C3—182no—
656C22×C3—368no—
657C22×C3#379814yescomplemented
658C22×C3#379812yescomplemented
659C22×C3C22×D3211yescharacteristic
660C22×C3C22×D3212yes—
661C2×D3—34no—
662C2×D3—34no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—64no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—62no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—121no—
682C2×D3—122no—
683C2×D3—122no—
684C2×D3—121no—
685C2×D3—128no—
686C2×D3—128no—
687C2×D3—1216no—
688C3×C4—21no—
689C3×C4—22no—
690C3×C4—21no—
691C3×C4—22no—
692C3×C4—41no—
693C3×C4—42no—
694C3×C4—42no—
695C3×C4—41no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4—92no—
699C3×C4—181no—
700C3×C4—182no—
701C3×C4—181no—
702C3×C4—182no—
703Dic3—34no—
704Dic3—62no—
705Dic3—62no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—62no—
710Dic3—62no—
711Dic3—62no—
712Dic3—122no—
713Dic3—122no—
714Dic3—121no—
715C32—21no—
716C32—22no—
717C32—41no—
718C32#549012yescomplemented
719C32#555011yescharacteristic, complemented
720C23—92no—
721C23—92no—
722C23—91no—
723C23—184no—
724C23—184no—
725C23—362no—
726C23C2×#111311yescharacteristic
727Q8—542no—
728D4—182no—
729D4—274no—
730D4—542no—
731D4—544no—
732D4—544no—
733D4—1082no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—92no—
737C2×C4—92no—
738C2×C4—91no—
739C2×C4—182no—
740C2×C4—184no—
741C2×C4—182no—
742C2×C4—362no—
743C2×C4C2×#111311yescharacteristic
744C2×C4C2×#111311yescharacteristic
745C2×C3—22no—
746C2×C3—24no—
747C2×C3—21no—
748C2×C3—22no—
749C2×C3—21no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—44no—
754C2×C3—42no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—82no—
759C2×C3—184no—
760C2×C3—361no—
761C2×C3—362no—
762C2×C3C2×#379811yescharacteristic
763C2×C3C2×#379812yes—
764C2×C3D32×D411yescharacteristic
765C2×C3D32×D412yes—
766C2×C3#6431311yescharacteristic
767C2×C3#6431412yes—
768D3—68no—
769D3—64no—
770D3—64no—
771D3—124no—
772D3—122no—
773D3—122no—
774D3—122no—
775D3—122no—
776C22—21no—
777C22—21no—
778C22—94no—
779C22—182no—
780C22—182no—
781C22—181no—
782C22—182no—
783C22—181no—
784C22—182no—
785C22—181no—
786C22—182no—
787C22—368no—
788C22#8904212yescomplemented
789C22C22×#111311yescharacteristic
790C4—21no—
791C4—21no—
792C4—92no—
793C4—181no—
794C4—181no—
795C4—182no—
796C4—182no—
797C3—22no—
798C3—21no—
799C3—41no—
800C3#1059418311yescharacteristic, complemented
801C3#1059418612yescomplemented
802C2—22no—
803C2—184no—
804C2—362no—
805C2—361no—
806C2C2×#8904211yescharacteristic
807C2D4×#111311yescharacteristic
808C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6295C2semidirect
2. C2×#89042C2semidirect
3. C3×#64090C2semidirect
4. C3×C22⋊C4×C3⋊D3C2semidirect
5. #11723727C2semidirect
6. #11723721C2semidirect
7. #11723695C2semidirect
8. #11723695C2semidirect
9. #11723694C2semidirect
10. C4×#6295C2semidirect
11. #11723672C2semidirect
17. C2×C3×C4×C3⋊D3C22semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
20. C2×#6296C22semidirect
25. C2×#6295C22semidirect
26. C2×#6295C22semidirect
30. C3×#3752C22semidirect
31. C3×#3752C22semidirect
32. C3×#3752C22semidirect
33. C3×#3750C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
43. #64090D3semidirect
44. C22⋊C4×C3⋊D3D3semidirect
91. #6295D4semidirect
100. C2×C4×C3⋊D3C2×D3semidirect
101. C2×C4×C3⋊D3C2×D3semidirect
102. C2×C4×C3⋊D3C2×D3semidirect
140. #3752C2×D3semidirect
141. #3752C2×D3semidirect
142. #3752C2×D3semidirect
143. #3750C2×D3semidirect
144. C4×C3⋊Dic3C2×D3semidirect
173. C22×C33#41semidirect
408. C22×C32#235semidirect
409. C22×C32#235semidirect
487. C33#546semidirect
657. C22×C3#3798semidirect
658. C22×C3#3798semidirect
718. C32#5490semidirect
719. C32#5550semidirect
788. C22#89042semidirect
800. C3#10594183semidirect
801. C3#10594186semidirect

Maximal subgroups

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

subgroupindex
C22×#62952
C2×#890422
C3×#640902
C3×C22⋊C4×C3⋊D32
#117237272
#117237212
#117236952
#117236942
C4×#62952
#117236722
#105941863
#105941833