Finite Group Databasebeta

← #13178242

Subgroups — #13178242

Order 1728.

1652 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×C4⋊#1113C211yesmaximal, characteristic, complemented
3C3×#64093C212yesmaximal, complemented
4C3×#64090C211yesmaximal, characteristic, complemented
5#11723729C212yesmaximal, complemented
6#11723717C211yesmaximal, characteristic, complemented
7#11723700C212yesmaximal, complemented
8C4×#6295C211yesmaximal, characteristic, complemented
9#11723686C212yesmaximal, complemented
10#11723672C211yesmaximal, characteristic, complemented
11#11723671C211yesmaximal, characteristic, complemented
12#10594283—32nomaximal
13#10594276—31nomaximal
14C22×#1113C2212yes—
15C2×C3×#638C2211yescharacteristic
16C2×C3×#638C2212yescomplemented
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C3×C4⋊(C3⋊D3)C2212yes—
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2212yescomplemented
22C2×#6296C2211yescharacteristic, complemented
23C2×#6295C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25#89046—24no—
26C2×#6294C2212yescomplemented
27C4⋊#1113—24no—
28C33×C22⋊C4C2211yescharacteristic, complemented
29C3×#3752C2211yescharacteristic
30C3×#3752C2212yescomplemented
31C3×#3750C2211yescharacteristic, complemented
32C3×#3750C2212yescomplemented
33C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2212yes—
36#88814C2212yescomplemented
37#88814C2212yescomplemented
38#88814C2212yescomplemented
39C2×#3805—31no—
40C2×#3804—32no—
41C2×#3802—31no—
42C2×D3×D12—32no—
43#64093D312yescomplemented
44#64090D311yescharacteristic, complemented
45C3×#884—32no—
46C3×#884—32no—
47C3×#884—62no—
48C3×#67⋊C4—32no—
49C3×#67⋊C4—61no—
50#63983—32no—
51#63983—32no—
52#63983—32no—
53#63980—31no—
54#63978—32no—
55#63921—32no—
56D3×(C2×D3)⋊C4—32no—
57D3×(C2×D3)⋊C4—32no—
58#63915—31no—
59C4×#626—32no—
60C4×#625—31no—
61#63897—32no—
62#63884—32no—
63#63884—32no—
64#63865—31no—
65#63852—32no—
66#63851—32no—
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3C2312yes—
69C22×C3×C3⋊D3C2312yes—
70C22×C3×C3⋊D3C2311yescharacteristic
71C2×#1113—24no—
72C2×#1113—24no—
73C2×#1113—42no—
74C2×C33×C4C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C3×#638—24no—
77C3×#638—22no—
78C3×#638—42no—
79C2×C3×C3⋊Dic3—22no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)—24no—
86C3×C4×C3⋊D3—22no—
87C3×C4×C3⋊D3—42no—
88#6296—22no—
89#6295—22no—
90#6295D414yescomplemented
91#6294—24no—
92#5610—92no—
93#5550—91no—
94C22×D32—32no—
95C22×D32—32no—
96C22×D32—32no—
97C2×#638C2×D311yescharacteristic
98C2×#638C2×D312yescomplemented
99C2×#638C2×D312yescomplemented
100C22×C3⋊Dic3C2×D311yescharacteristic, complemented
101C2×C4⋊(C3⋊D3)C2×D312yes—
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×C4×C3⋊D3C2×D312yescomplemented
104C2×C3×#67—32no—
105C2×C3×#67—32no—
106C2×C3×#67—32no—
107C2×C3×#67—32no—
108C2×C3×#67—32no—
109C2×C3×#67—61no—
110C2×C3×#67—62no—
111C2×C3×#67—62no—
112C22×C3×Dic3—32no—
113C22×C3×Dic3—61no—
114C2×C3×D12—32no—
115C2×C3×D12—32no—
116C2×C3×D12—62no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—32no—
120C2×C3×C4×D3—61no—
121C2×C3×C4×D3—62no—
122C2×#627—32no—
123C2×#627—31no—
124C2×#626—32no—
125C2×#626—32no—
126C2×#625—31no—
127C2×#625—31no—
128C2×#624—32no—
129#3805—64no—
130#3804—68no—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—32no—
133#3802—64no—
134D3×D12—68no—
135C32×C22⋊C4—21no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4—41no—
138C32×C22⋊C4C2×D312yescomplemented
139C32×C22⋊C4C2×D311yescharacteristic, complemented
140#3752C2×D311yescharacteristic
141#3752C2×D312yescomplemented
142#3750C2×D311yescharacteristic, complemented
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—61no—
149C3×(C2×D3)⋊C4—62no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—61no—
154C3×Dic3⋊C4—62no—
155C3×C4×Dic3—32no—
156C3×C4×Dic3—61no—
157#3724—31no—
158Dic3⋊Dic3—32no—
159#3722—32no—
160#3722—32no—
161#3722—32no—
162#3722—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—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—21no—
174C22×C33C2411yescharacteristic
175C2×C3×C3⋊D3—21no—
176C2×C3×C3⋊D3—22no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3—21no—
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3C2×D414yes—
183C2×C3×C3⋊D3#4112yescomplemented
184#1113—48no—
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—
192C2×#237—92no—
193C2×D3×D4—92no—
194C2×#235—91no—
195C22×D12—91no—
196C3×#121—92no—
197C3×C4×D4—91no—
198#939—92no—
199#937—92no—
200#937—92no—
201#937—92no—
202#935—92no—
203#930—91no—
204C4×#67—92no—
205C2×(C2×D3)⋊C4—92no—
206#924—91no—
207#896—92no—
208#894—92no—
209#894—92no—
210#885—92no—
211#884—32no—
212#884—32no—
213#884—62no—
214#67⋊C4—32no—
215#67⋊C4—61no—
216D3×C22⋊C4—92no—
217D3×C22⋊C4—92no—
218#875—91no—
219C4×D12—91no—
220C23×C32—21no—
221C23×C32—22no—
222C23×C32—41no—
223C23×C32C22×D312yes—
224C23×C32C22×D311yescharacteristic
225C22×C3⋊D3C22×D312yes—
226C22×C3⋊D3C22×D311yescharacteristic
227C22×C3⋊D3C22×D312yes—
228C22×C3×D3—32no—
229C22×C3×D3—32no—
230C22×C3×D3—32no—
231C22×C3×D3—32no—
232C22×C3×D3—32no—
233C22×C3×D3—61no—
234C22×C3×D3—62no—
235C22×C3×D3—62no—
236C2×D32—64no—
237C2×D32—64no—
238C2×D32—64no—
239C2×D32—64no—
240C2×D32—64no—
241C2×D32—64no—
242C2×D32—122no—
243C2×D32—122no—
244C2×D32—122no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—22no—
248C2×C32×C4—22no—
249C2×C32×C4—41no—
250C2×C32×C4—41no—
251C2×C32×C4C22×D312yes—
252C2×C32×C4C22×D312yes—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255#638—22no—
256#638—24no—
257#638—42no—
258C2×C3⋊Dic3—22no—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C4⋊(C3⋊D3)—24no—
265C4×C3⋊D3—22no—
266C4×C3⋊D3—42no—
267C3×#67—64no—
268C3×#67—64no—
269C3×#67—64no—
270C3×#67—64no—
271C3×#67—124no—
272C3×#67—122no—
273C3×#67—122no—
274C3×#67—124no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—64no—
288C2×C3×Dic3—122no—
289C3×D12—64no—
290C3×D12—64no—
291C3×D12—124no—
292C3×C4×D3—64no—
293C3×C4×D3—122no—
294C3×C4×D3—122no—
295C3×C4×D3—122no—
296C3×C4×D3—124no—
297#627—64no—
298#627—62no—
299#626—38no—
300#626—64no—
301#625—34no—
302#625—62no—
303#624—64no—
304D3×Dic3—64no—
305D3×Dic3—64no—
306#546—271noSylow
307C2×C33—41no—
308C2×C33C22×D411yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C3×C3⋊D3—22no—
312C3×C3⋊D3—24no—
313C3×C3⋊D3—42no—
314C23×D3—92no—
315C23×D3—92no—
316C23×D3—92no—
317C2×C3×D4—91no—
318C2×C3×D4—92no—
319C2×C3×D4—92no—
320C2×C3×D4—92no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C22×C3×C4—92no—
324C2×#67—32no—
325C2×#67—32no—
326C2×#67—32no—
327C2×#67—32no—
328C2×#67—32no—
329C2×#67—61no—
330C2×#67—62no—
331C2×#67—62no—
332C2×#67—92no—
333C2×#67—92no—
334C22×Dic3—32no—
335C22×Dic3—61no—
336C22×Dic3—92no—
337#237—188no—
338D3×D4—188no—
339#235—184no—
340C2×D12—32no—
341C2×D12—32no—
342C2×D12—62no—
343C2×D12—91no—
344C2×D12—91no—
345C2×D12—184no—
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—32no—
349C2×C4×D3—61no—
350C2×C4×D3—62no—
351C2×C4×D3—92no—
352C2×C4×D3—92no—
353C2×Dic6—91no—
354C2×Dic6—92no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—92no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—92no—
362C3×C22⋊C4D3212yescomplemented
363C3×C22⋊C4D3211yescharacteristic, complemented
364C3×C42—91no—
365#217—92no—
366#217—92no—
367#217—92no—
368#217—92no—
369(C2×D3)⋊C4—32no—
370(C2×D3)⋊C4—32no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—92no—
375(C2×D3)⋊C4—92no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—92no—
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—32no—
386Dic3⋊C4—61no—
387Dic3⋊C4—62no—
388Dic3⋊C4—92no—
389C4×Dic3—32no—
390C4×Dic3—61no—
391C22×C32—21no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—21no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—22no—
400C22×C32—41no—
401C22×C32—42no—
402C22×C32—42no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—81no—
408C22×C32—81no—
409C22×C32C23×D311yescharacteristic
410C22×C32C23×D312yes—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—22no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3#23512yescomplemented
419C2×C3⋊D3D3×D414yes—
420C2×C3×D3—34no—
421C2×C3×D3—34no—
422C2×C3×D3—34no—
423C2×C3×D3—64no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—62no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—62no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—121no—
438C2×C3×D3—122no—
439C2×C3×D3—122no—
440C2×C3×D3—121no—
441C2×C3×D3—122no—
442C2×C3×D3—122no—
443C2×C3×D3—122no—
444D32—128no—
445D32—128no—
446D32—128no—
447C32×C4—22no—
448C32×C4—21no—
449C32×C4—22no—
450C32×C4—21no—
451C32×C4—41no—
452C32×C4—42no—
453C32×C4—42no—
454C32×C4—41no—
455C32×C4—81no—
456C32×C4—81no—
457C3⋊Dic3—21no—
458C3⋊Dic3—22no—
459C3⋊Dic3—21no—
460C3⋊Dic3—22no—
461C3⋊Dic3D3×D412yes—
462C3×Dic3—34no—
463C3×Dic3—62no—
464C3×Dic3—64no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—121no—
473C3×Dic3—122no—
474C2×#41—271no—
475C22×D4—271no—
476#124—271no—
477#123—272no—
478C22⋊Q8—271no—
479#121—92no—
480#121—271no—
481#120—272no—
482C4×D4—91no—
483C4×D4—271no—
484C2×C22⋊C4—272no—
485C33#54611yescharacteristic, complemented, Sylow
486C23×C3—21no—
487C23×C3—22no—
488C23×C3—41no—
489C23×C3—91no—
490C23×C3—92no—
491C23×C3—92no—
492C23×C3C2×D3212yes—
493C23×C3C2×D3211yescharacteristic
494C22×D3—32no—
495C22×D3—32no—
496C22×D3—32no—
497C22×D3—32no—
498C22×D3—32no—
499C22×D3—61no—
500C22×D3—62no—
501C22×D3—62no—
502C22×D3—184no—
503C22×D3—184no—
504C22×D3—184no—
505C22×D3—184no—
506C22×D3—184no—
507C22×D3—184no—
508C22×D3—362no—
509C22×D3—362no—
510C22×D3—362no—
511C3×D4—184no—
512C3×D4—182no—
513C3×D4—184no—
514C3×D4—362no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—91no—
522C2×C3×C4—92no—
523C2×C3×C4—91no—
524C2×C3×C4—92no—
525C2×C3×C4—91no—
526C2×C3×C4—182no—
527C2×C3×C4—182no—
528C2×C3×C4—362no—
529C2×C3×C4C2×D3212yes—
530C2×C3×C4C2×D3212yes—
531C2×C3×C4C2×D3211yescharacteristic
532C2×C3×C4C2×D3211yescharacteristic
533#67—64no—
534#67—64no—
535#67—64no—
536#67—64no—
537#67—98no—
538#67—124no—
539#67—122no—
540#67—122no—
541#67—124no—
542#67—184no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—62no—
553C2×Dic3—61no—
554C2×Dic3—62no—
555C2×Dic3—64no—
556C2×Dic3—122no—
557C2×Dic3—184no—
558D12—64no—
559D12—64no—
560D12—94no—
561D12—124no—
562D12—182no—
563C4×D3—64no—
564C4×D3—122no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3—124no—
568C4×D3—184no—
569C4×D3—184no—
570Dic6—184no—
571Dic6—182no—
572C2×C32—22no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—22no—
576C2×C32—21no—
577C2×C32—22no—
578C2×C32—41no—
579C2×C32—41no—
580C2×C32—41no—
581C2×C32—41no—
582C2×C32—42no—
583C2×C32—42no—
584C2×C32—82no—
585C2×C32—82no—
586C2×C32C2×#23511yescharacteristic
587C2×C32C2×D3×D411yescharacteristic
588C2×C32C2×D3×D412yes—
589C2×C32#100412yes—
590C2×C32D3×#4112yes—
591C2×C32#100911yescharacteristic
592C3⋊D3—22no—
593C3⋊D3—24no—
594C3⋊D3—42no—
595C3×D3—64no—
596C3×D3—64no—
597C3×D3—64no—
598C3×D3—122no—
599C3×D3—124no—
600C3×D3—122no—
601C3×D3—122no—
602C3×D3—242no—
603C24—272no—
604#41—544no—
605C2×Q8—271no—
606C2×D4—91no—
607C2×D4—92no—
608C2×D4—92no—
609C2×D4—92no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—544no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—92no—
616C22×C4—272no—
617C4⋊C4—91no—
618C4⋊C4—92no—
619C4⋊C4—271no—
620C22⋊C4—91no—
621C22⋊C4—92no—
622C22⋊C4—272no—
623C22⋊C4—272no—
624C22⋊C4—272no—
625C22⋊C4—272no—
626C22⋊C4#111311yescharacteristic, complemented
627C42—91no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—22no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—41no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—92no—
647C22×C3—94no—
648C22×C3—182no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—182no—
652C22×C3—182no—
653C22×C3—182no—
654C22×C3—182no—
655C22×C3C22×D3212yes—
656C22×C3C22×D3211yescharacteristic
657C2×D3—34no—
658C2×D3—34no—
659C2×D3—34no—
660C2×D3—64no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—121no—
675C2×D3—122no—
676C2×D3—122no—
677C2×D3—121no—
678C2×D3—122no—
679C2×D3—122no—
680C2×D3—122no—
681C2×D3—368no—
682C2×D3—368no—
683C2×D3—368no—
684C3×C4—22no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—22no—
688C3×C4—41no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—41no—
692C3×C4—81no—
693C3×C4—81no—
694C3×C4—92no—
695C3×C4—181no—
696C3×C4—182no—
697C3×C4—181no—
698C3×C4—182no—
699Dic3—34no—
700Dic3—62no—
701Dic3—64no—
702Dic3—62no—
703Dic3—62no—
704Dic3—62no—
705Dic3—62no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—121no—
710Dic3—122no—
711C32—21no—
712C32—22no—
713C32—41no—
714C32#555011yescharacteristic, complemented
715C32#561012yescomplemented
716C23—91no—
717C23—92no—
718C23—92no—
719C23—544no—
720C23—544no—
721C23—1082no—
722C23C2×#111311yescharacteristic
723Q8—542no—
724D4—184no—
725D4—184no—
726D4—182no—
727D4—274no—
728D4—362no—
729D4—542no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—92no—
734C2×C4—92no—
735C2×C4—182no—
736C2×C4—182no—
737C2×C4—362no—
738C2×C4—544no—
739C2×C4C2×#111311yescharacteristic
740C2×C4C2×#111311yescharacteristic
741C2×C3—21no—
742C2×C3—22no—
743C2×C3—21no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—82no—
754C2×C3—82no—
755C2×C3—182no—
756C2×C3—184no—
757C2×C3—362no—
758C2×C3D3×#23512yes—
759C2×C3#6430611yescharacteristic
760C2×C3D32×D411yescharacteristic
761C2×C3D32×D412yes—
762C2×C3#6431311yescharacteristic
763C2×C3#6431412yes—
764D3—64no—
765D3—64no—
766D3—64no—
767D3—122no—
768D3—124no—
769D3—122no—
770D3—122no—
771D3—242no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—92no—
776C22—94no—
777C22—182no—
778C22—181no—
779C22—182no—
780C22—181no—
781C22—182no—
782C22—182no—
783C22—182no—
784C22—1088no—
785C22C22×#111311yescharacteristic
786C4—21no—
787C4—21no—
788C4—92no—
789C4—181no—
790C4—181no—
791C4—182no—
792C4—182no—
793C3—22no—
794C3—21no—
795C3—41no—
796C3#1059427611yescharacteristic, complemented
797C3#1059428312yescomplemented
798C2—41no—
799C2—182no—
800C2—184no—
801C2—362no—
802C2#1172461811yescharacteristic
803C2D4×#111311yescharacteristic
804C2#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. C2×#89046C2semidirect
2. C2×C4⋊#1113C2semidirect
3. C3×#64093C2semidirect
4. C3×#64090C2semidirect
5. #11723729C2semidirect
6. #11723717C2semidirect
7. #11723700C2semidirect
8. C4×#6295C2semidirect
9. #11723686C2semidirect
10. #11723672C2semidirect
11. #11723671C2semidirect
16. C2×C3×#638C22semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×#6296C22semidirect
26. C2×#6294C22semidirect
28. C33×C22⋊C4C22semidirect
30. C3×#3752C22semidirect
31. C3×#3750C22semidirect
32. C3×#3750C22semidirect
33. C3×C4×C3⋊Dic3C22semidirect
34. #88815C22semidirect
36. #88814C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
43. #64093D3semidirect
44. #64090D3semidirect
90. #6295D4semidirect
98. C2×#638C2×D3semidirect
99. C2×#638C2×D3semidirect
100. C22×C3⋊Dic3C2×D3semidirect
103. C2×C4×C3⋊D3C2×D3semidirect
138. C32×C22⋊C4C2×D3semidirect
139. C32×C22⋊C4C2×D3semidirect
141. #3752C2×D3semidirect
142. #3750C2×D3semidirect
143. #3750C2×D3semidirect
144. C4×C3⋊Dic3C2×D3semidirect
183. C2×C3×C3⋊D3#41semidirect
362. C3×C22⋊C4D32semidirect
363. C3×C22⋊C4D32semidirect
418. C2×C3⋊D3#235semidirect
485. C33#546semidirect
626. C22⋊C4#1113semidirect
714. C32#5550semidirect
715. C32#5610semidirect
796. C3#10594276semidirect
797. C3#10594283semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×C4⋊#11132
C3×#640932
C3×#640902
#117237292
#117237172
#117237002
C4×#62952
#117236862
#117236722
#117236712
#105942833
#105942763