Finite Group Databasebeta

← #13178288

Subgroups — #13178288

Order 1728.

1758 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C22×#6295C211yesmaximal, characteristic, complemented
3C3×#64095C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6#11723727C211yesmaximal, characteristic, complemented
7#11723720C211yesmaximal, characteristic, complemented
8#11723701C212yesmaximal, complemented
9#11723696C212yesmaximal, complemented
10#11723695C212yesmaximal, complemented
11#11723690C212yesmaximal, complemented
12#10594296—31nomaximal
13#10594291—31nomaximal
14#10594290—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C3×C3⋊D3C2211yescharacteristic, complemented
17C22×#1113C2211yescharacteristic, complemented
18C2×C3×#638C2211yescharacteristic
19C2×C3×#638C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
22C2×C3×C4×C3⋊D3C2212yescomplemented
23#89049—24no—
24C2×#6295—24no—
25C2×#6295C2212yes—
26C2×#6295C2212yescomplemented
27C2×#6295C2211yescharacteristic, complemented
28C2×#6295C2211yescharacteristic, complemented
29C2×#6295C2212yescomplemented
30C2×#6294C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic, complemented
33C3×#3752C2212yescomplemented
34C3×#3752C2212yescomplemented
35C3×#3752C2212yescomplemented
36C3×C4⋊(C3⋊Dic3)C2212yescomplemented
37#88815C2212yescomplemented
38#88814C2212yescomplemented
39#88814C2212yescomplemented
40C2×#3811—31no—
41C2×D3×#67—31no—
42C2×D3×#67—31no—
43C22×#626—31no—
44C22×#626—31no—
45C22×#625—31no—
46#64095D311yescharacteristic, complemented
47#64091D311yescharacteristic, complemented
48C22⋊C4×C3⋊D3D311yescharacteristic, complemented
49C3×#886—31no—
50C3×#886—31no—
51C3×#886—61no—
52C3×#882—31no—
53C3×#882—31no—
54C3×#882—61no—
55C3×D3×C22⋊C4—31no—
56C3×D3×C22⋊C4—31no—
57C3×D3×C22⋊C4—61no—
58#63981—31no—
59#63977—31no—
60#63976—31no—
61#63966—31no—
62#63962—31no—
63#63961—31no—
64#63923—32no—
65#63922—32no—
66#63922—32no—
67#63916—32no—
68#63912—32no—
69#63909—32no—
70#63908—32no—
71#63906—32no—
72#63906—32no—
73#63891—32no—
74#63890—32no—
75#63854—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3—22no—
78C22×C3×C3⋊D3—42no—
79C22×C3×C3⋊D3—42no—
80C22×C3×C3⋊D3D414yescomplemented
81C22×C3×C3⋊D3C2311yescharacteristic
82C22×C3×C3⋊D3C2312yes—
83C22×C3×C3⋊D3C2311yescharacteristic
84C22×C3×C3⋊D3C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C2×#1113—22no—
87C2×#1113—42no—
88C2×C33×C4C2312yes—
89C3×#638—22no—
90C3×#638—22no—
91C2×C3×C3⋊Dic3—22no—
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊Dic3C2312yes—
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2312yes—
96C3×C4⋊(C3⋊D3)—42no—
97C3×C4×C3⋊D3—42no—
98#6295—24no—
99#6295—24no—
100#6295—22no—
101#6295—22no—
102#6295—42no—
103#6294—22no—
104#5653—91no—
105#5589—91no—
106#5493—91no—
107C23×C3⋊D3C2×D311yescharacteristic
108C23×C3⋊D3C2×D311yescharacteristic, complemented
109C23×C3×D3—31no—
110C23×C3×D3—31no—
111C23×C3×D3—31no—
112C23×C3×D3—31no—
113C23×C3×D3—61no—
114C23×C3×D3—61no—
115C22×D32—31no—
116C22×D32—31no—
117C22×D32—31no—
118C2×#638C2×D311yescharacteristic
119C2×#638C2×D311yescharacteristic
120C22×C3⋊Dic3C2×D311yescharacteristic, complemented
121C2×C4⋊(C3⋊D3)C2×D312yescomplemented
122C2×C4×C3⋊D3C2×D312yescomplemented
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—61no—
128C2×C3×#67—61no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—61no—
132C2×C3×D12—32no—
133C2×C3×D12—32no—
134C2×C3×D12—62no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3—62no—
138#3811—64no—
139D3×#67—64no—
140D3×#67—64no—
141C2×#626—32no—
142C2×#626—32no—
143C2×#626—32no—
144C2×#626—32no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#626—32no—
150C2×#626—32no—
151C2×#626—64no—
152C2×#626—64no—
153C2×#625—32no—
154C2×#625—32no—
155C2×#625—31no—
156C2×#625—31no—
157C2×#625—32no—
158C2×#625—64no—
159C2×#624—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C32×C22⋊C4—21no—
163C32×C22⋊C4—21no—
164C32×C22⋊C4—21no—
165C32×C22⋊C4—41no—
166C32×C22⋊C4C2×D311yescharacteristic, complemented
167C32×C22⋊C4C2×D311yescharacteristic, complemented
168C32×C22⋊C4C2×D311yescharacteristic, complemented
169#3757C2×D311yescharacteristic, complemented
170#3752C2×D312yescomplemented
171#3752C2×D312yescomplemented
172#3752C2×D312yescomplemented
173C4⋊(C3⋊Dic3)C2×D312yescomplemented
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—61no—
177C3×(C2×D3)⋊C4—32no—
178C3×(C2×D3)⋊C4—32no—
179C3×(C2×D3)⋊C4—32no—
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182C3×(C2×D3)⋊C4—32no—
183C3×(C2×D3)⋊C4—62no—
184C3×(C2×D3)⋊C4—62no—
185C3×(C2×D3)⋊C4—62no—
186C3×C4⋊Dic3—32no—
187C3×C4⋊Dic3—32no—
188C3×C4⋊Dic3—62no—
189#3724—32no—
190Dic3⋊Dic3—32no—
191Dic3⋊Dic3—32no—
192#3722—32no—
193#3722—32no—
194(C2×D3)⋊Dic3—32no—
195(C2×D3)⋊Dic3—32no—
196(C2×D3)⋊Dic3—32no—
197(C2×D3)⋊Dic3—32no—
198C22×C33—22no—
199C22×C33C2×D412yes—
200C22×C33C2411yescharacteristic
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3—22no—
208C2×C3×C3⋊D3—22no—
209C2×C3×C3⋊D3—22no—
210C2×C3×C3⋊D3—44no—
211C2×C3×C3⋊D3—44no—
212C2×C3×C3⋊D3C2×D412yes—
213C2×C3×C3⋊D3C2×D412yes—
214#1113—44no—
215C33×C4—22no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—21no—
218C3×C3⋊Dic3—22no—
219C3×C3⋊Dic3—22no—
220C22×#67—91no—
221C22×#67—91no—
222C22×#67—91no—
223C2×D3×D4—91no—
224C2×D3×D4—91no—
225C22×D12—91no—
226C3×#123—91no—
227C3×#120—91no—
228C2×C3×C22⋊C4—91no—
229#953—91no—
230#938—92no—
231#937—92no—
232#937—91no—
233#935—91no—
234#930—92no—
235#930—92no—
236#929—91no—
237#895—92no—
238#894—92no—
239#886—31no—
240#886—31no—
241#886—61no—
242#886—92no—
243#886—91no—
244#884—92no—
245#884—92no—
246#883—92no—
247#882—31no—
248#882—31no—
249#882—61no—
250#882—92no—
251#882—92no—
252#882—91no—
253D3×C22⋊C4—31no—
254D3×C22⋊C4—31no—
255D3×C22⋊C4—61no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—41no—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—22no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3D1214yescomplemented
267C22×C3⋊D3C22×D311yescharacteristic
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3⋊D3C22×D312yes—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—34no—
277C22×C3×D3—34no—
278C22×C3×D3—31no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—31no—
282C22×C3×D3—32no—
283C22×C3×D3—32no—
284C22×C3×D3—61no—
285C22×C3×D3—61no—
286C22×C3×D3—62no—
287C22×C3×D3—64no—
288C22×C3×D3—61no—
289C22×C3×D3—61no—
290C22×C3×D3—62no—
291C22×C3×D3—62no—
292C22×C3×D3—122no—
293C22×C3×D3—122no—
294C22×C3×D3—122no—
295C22×C3×D3—122no—
296C22×C3×D3—122no—
297C22×C3×D3—124no—
298C22×C3×D3—124no—
299C2×D32—62no—
300C2×D32—62no—
301C2×D32—62no—
302C2×D32—122no—
303C2×D32—122no—
304C2×D32—122no—
305C2×C32×C4—22no—
306C2×C32×C4—22no—
307C2×C32×C4—22no—
308C2×C32×C4—42no—
309C2×C32×C4C22×D312yes—
310C2×C32×C4C22×D312yes—
311C2×C32×C4C22×D312yes—
312#638—22no—
313#638—22no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3C22×D312yes—
316C2×C3⋊Dic3C22×D311yescharacteristic
317C2×C3⋊Dic3C22×D312yes—
318C2×C3⋊Dic3C22×D311yescharacteristic
319C4⋊(C3⋊D3)—42no—
320C4×C3⋊D3—42no—
321C3×#67—62no—
322C3×#67—62no—
323C3×#67—62no—
324C3×#67—62no—
325C3×#67—122no—
326C3×#67—122no—
327C2×C3×Dic3—32no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—32no—
330C2×C3×Dic3—32no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—31no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—61no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—61no—
338C2×C3×Dic3—62no—
339C2×C3×Dic3—62no—
340C2×C3×Dic3—62no—
341C2×C3×Dic3—122no—
342C3×D12—122no—
343C3×D12—122no—
344C3×D12—124no—
345C3×C4×D3—122no—
346C3×C4×D3—122no—
347C3×C4×D3—124no—
348#626—64no—
349#626—64no—
350#626—62no—
351#626—62no—
352#626—64no—
353#626—64no—
354#626—62no—
355#626—62no—
356#626—122no—
357#626—122no—
358#625—64no—
359#625—64no—
360#625—62no—
361#625—62no—
362#625—122no—
363#624—62no—
364D3×Dic3—62no—
365D3×Dic3—62no—
366#534—271noSylow
367C2×C33—22no—
368C2×C33C22×D411yescharacteristic
369C2×C33H(5,𝔽2)12yes—
370C3×C3⋊D3—22no—
371C3×C3⋊D3—22no—
372C3×C3⋊D3—42no—
373C3×C3⋊D3—41no—
374C3×C3⋊D3—41no—
375C24×C3—91no—
376C24×C3—91no—
377C23×D3—31no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—61no—
382C23×D3—61no—
383C23×D3—91no—
384C23×D3—91no—
385C23×D3—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C2×C3×D4—92no—
389C22×C3×C4—91no—
390C22×C3×C4—92no—
391C2×#67—31no—
392C2×#67—31no—
393C2×#67—31no—
394C2×#67—31no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67—92no—
398C2×#67—92no—
399C2×#67—91no—
400C2×#67—92no—
401C2×#67—91no—
402C2×#67—92no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—92no—
406C2×#67—92no—
407C2×#67—184no—
408C2×#67—184no—
409C2×#67—184no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—61no—
413C22×Dic3—91no—
414D3×D4—184no—
415D3×D4—184no—
416C2×D12—32no—
417C2×D12—32no—
418C2×D12—62no—
419C2×D12—92no—
420C2×D12—91no—
421C2×D12—92no—
422C2×D12—91no—
423C2×D12—92no—
424C2×D12—184no—
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—62no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C3×C4⋊C4—92no—
431C3×C22⋊C4—21no—
432C3×C22⋊C4—21no—
433C3×C22⋊C4—21no—
434C3×C22⋊C4—41no—
435C3×C22⋊C4—91no—
436C3×C22⋊C4—92no—
437C3×C22⋊C4—92no—
438C3×C22⋊C4—92no—
439C3×C22⋊C4D3211yescharacteristic, complemented
440C3×C22⋊C4D3211yescharacteristic, complemented
441C3×C22⋊C4D3211yescharacteristic, complemented
442#217—31no—
443#217—31no—
444#217—61no—
445#217—92no—
446#217—92no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—32no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—92no—
457(C2×D3)⋊C4—92no—
458(C2×D3)⋊C4—92no—
459(C2×D3)⋊C4—92no—
460C4⋊Dic3—32no—
461C4⋊Dic3—32no—
462C4⋊Dic3—62no—
463C4⋊Dic3—92no—
464Dic3⋊C4—92no—
465Dic3⋊C4—92no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—41no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—82no—
481C22×C32C2×D1212yes—
482C22×C32D3×D412yes—
483C22×C32D3×D412yes—
484C22×C32C23×D311yescharacteristic
485C22×C32C23×D311yescharacteristic
486C22×C32C23×D311yescharacteristic
487C2×C3⋊D3—22no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—44no—
497C2×C3⋊D3—44no—
498C2×C3⋊D3C2×D1212yes—
499C2×C3⋊D3C2×D1212yes—
500C2×C3×D3—32no—
501C2×C3×D3—32no—
502C2×C3×D3—32no—
503C2×C3×D3—32no—
504C2×C3×D3—62no—
505C2×C3×D3—62no—
506C2×C3×D3—64no—
507C2×C3×D3—62no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—62no—
511C2×C3×D3—64no—
512C2×C3×D3—62no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—62no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—62no—
522C2×C3×D3—62no—
523C2×C3×D3—62no—
524C2×C3×D3—62no—
525C2×C3×D3—62no—
526C2×C3×D3—122no—
527C2×C3×D3—122no—
528C2×C3×D3—122no—
529C2×C3×D3—122no—
530C2×C3×D3—121no—
531C2×C3×D3—121no—
532C2×C3×D3—122no—
533C2×C3×D3—124no—
534C2×C3×D3—124no—
535C2×C3×D3—128no—
536C2×C3×D3—124no—
537C2×C3×D3—124no—
538C2×C3×D3—128no—
539D32—124no—
540D32—124no—
541D32—124no—
542C32×C4—22no—
543C32×C4—22no—
544C32×C4—22no—
545C32×C4—42no—
546C32×C4—42no—
547C32×C4—42no—
548C32×C4—82no—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—22no—
552C3⋊Dic3—22no—
553C3×Dic3—61no—
554C3×Dic3—61no—
555C3×Dic3—62no—
556C3×Dic3—61no—
557C3×Dic3—61no—
558C3×Dic3—62no—
559C3×Dic3—62no—
560C3×Dic3—62no—
561C3×Dic3—122no—
562C3×Dic3—122no—
563C3×Dic3—121no—
564C3×Dic3—121no—
565C22×D4—271no—
566C22×D4—271no—
567#123—91no—
568#123—272no—
569#123—271no—
570#121—272no—
571#121—272no—
572#120—91no—
573#120—272no—
574#120—271no—
575C2×C22⋊C4—91no—
576C33#53411yescharacteristic, complemented, Sylow
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—41no—
581C23×C3—91no—
582C23×C3—91no—
583C23×C3—94no—
584C23×C3—91no—
585C23×C3—92no—
586C23×C3—91no—
587C23×C3—182no—
588C23×C3—362no—
589C23×C3—362no—
590C23×C3C2×D3211yescharacteristic
591C23×C3C2×D3211yescharacteristic
592C23×C3C2×D3211yescharacteristic
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—31no—
597C22×D3—34no—
598C22×D3—34no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—32no—
602C22×D3—32no—
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—61no—
606C22×D3—64no—
607C22×D3—61no—
608C22×D3—62no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—122no—
614C22×D3—122no—
615C22×D3—122no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—182no—
621C22×D3—182no—
622C22×D3—182no—
623C22×D3—362no—
624C22×D3—362no—
625C22×D3—362no—
626C3×D4—182no—
627C3×D4—182no—
628C3×D4—362no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—42no—
633C2×C3×C4—91no—
634C2×C3×C4—92no—
635C2×C3×C4—92no—
636C2×C3×C4—91no—
637C2×C3×C4—182no—
638C2×C3×C4—362no—
639C2×C3×C4C2×D3212yes—
640C2×C3×C4C2×D3212yes—
641C2×C3×C4C2×D3212yes—
642#67—62no—
643#67—62no—
644#67—62no—
645#67—62no—
646#67—122no—
647#67—122no—
648#67—182no—
649#67—182no—
650#67—184no—
651#67—184no—
652#67—184no—
653#67—184no—
654#67—182no—
655#67—182no—
656#67—362no—
657#67—362no—
658C2×Dic3—31no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—32no—
665C2×Dic3—31no—
666C2×Dic3—61no—
667C2×Dic3—62no—
668C2×Dic3—61no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—122no—
673C2×Dic3—182no—
674D12—122no—
675D12—122no—
676D12—124no—
677D12—184no—
678D12—184no—
679D12—182no—
680D12—182no—
681D12—362no—
682C4×D3—122no—
683C4×D3—122no—
684C4×D3—124no—
685C4×D3—182no—
686C4×D3—182no—
687C2×C32—22no—
688C2×C32—22no—
689C2×C32—22no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—22no—
694C2×C32—22no—
695C2×C32—22no—
696C2×C32—41no—
697C2×C32—42no—
698C2×C32—42no—
699C2×C32—42no—
700C2×C32—42no—
701C2×C32—82no—
702C2×C32C22×D1211yescharacteristic
703C2×C32C2×D3×D411yescharacteristic
704C2×C32C2×D3×D411yescharacteristic
705C2×C32#100412yes—
706C2×C32#100412yes—
707C2×C32#100912yes—
708C3⋊D3—22no—
709C3⋊D3—22no—
710C3⋊D3—42no—
711C3⋊D3—41no—
712C3⋊D3—41no—
713C3×D3—64no—
714C3×D3—62no—
715C3×D3—62no—
716C3×D3—62no—
717C3×D3—62no—
718C3×D3—122no—
719C3×D3—124no—
720C3×D3—121no—
721C3×D3—122no—
722C3×D3—121no—
723C3×D3—121no—
724C3×D3—122no—
725C3×D3—121no—
726C3×D3—241no—
727C3×D3—241no—
728C24—91no—
729C24—91no—
730C24—271no—
731C2×D4—91no—
732C2×D4—91no—
733C2×D4—92no—
734C2×D4—272no—
735C2×D4—271no—
736C2×D4—272no—
737C2×D4—271no—
738C2×D4—272no—
739C2×D4—544no—
740C2×D4—544no—
741C22×C4—91no—
742C22×C4—92no—
743C22×C4—271no—
744C4⋊C4—92no—
745C4⋊C4—272no—
746C22⋊C4—91no—
747C22⋊C4—92no—
748C22⋊C4—92no—
749C22⋊C4—92no—
750C22⋊C4—272no—
751C22⋊C4—272no—
752C22⋊C4#111311yescharacteristic, complemented
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—41no—
766C22×C3—42no—
767C22×C3—82no—
768C22×C3—92no—
769C22×C3—92no—
770C22×C3—182no—
771C22×C3—182no—
772C22×C3—182no—
773C22×C3—181no—
774C22×C3—181no—
775C22×C3—182no—
776C22×C3—182no—
777C22×C3—182no—
778C22×C3—182no—
779C22×C3—364no—
780C22×C3—364no—
781C22×C3D3×D1212yes—
782C22×C3D3×D1212yes—
783C22×C3#380212yes—
784C22×C3C22×D3211yescharacteristic
785C22×C3C22×D3211yescharacteristic
786C22×C3C22×D3211yescharacteristic
787C2×D3—32no—
788C2×D3—32no—
789C2×D3—32no—
790C2×D3—32no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—64no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—64no—
799C2×D3—62no—
800C2×D3—61no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—122no—
814C2×D3—122no—
815C2×D3—122no—
816C2×D3—122no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—122no—
820C2×D3—124no—
821C2×D3—124no—
822C2×D3—128no—
823C2×D3—124no—
824C2×D3—124no—
825C2×D3—128no—
826C2×D3—364no—
827C2×D3—364no—
828C2×D3—364no—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—22no—
832C3×C4—42no—
833C3×C4—42no—
834C3×C4—42no—
835C3×C4—82no—
836C3×C4—181no—
837C3×C4—181no—
838C3×C4—182no—
839C3×C4—182no—
840Dic3—61no—
841Dic3—61no—
842Dic3—62no—
843Dic3—62no—
844Dic3—61no—
845Dic3—61no—
846Dic3—62no—
847Dic3—62no—
848Dic3—122no—
849Dic3—122no—
850Dic3—121no—
851Dic3—121no—
852C32—21no—
853C32—21no—
854C32—21no—
855C32—41no—
856C32#549311yescharacteristic, complemented
857C32#558911yescharacteristic, complemented
858C32#565311yescharacteristic, complemented
859C23—91no—
860C23—91no—
861C23—94no—
862C23—91no—
863C23—92no—
864C23—91no—
865C23—182no—
866C23—362no—
867C23—362no—
868C23—542no—
869C23—1082no—
870C23C2×#111311yescharacteristic
871D4—182no—
872D4—182no—
873D4—362no—
874D4—544no—
875D4—544no—
876D4—542no—
877D4—542no—
878D4—1082no—
879C2×C4—92no—
880C2×C4—91no—
881C2×C4—92no—
882C2×C4—91no—
883C2×C4—182no—
884C2×C4—362no—
885C2×C4—542no—
886C2×C4C2×#111312yes—
887C2×C3—22no—
888C2×C3—22no—
889C2×C3—22no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—22no—
894C2×C3—22no—
895C2×C3—22no—
896C2×C3—42no—
897C2×C3—42no—
898C2×C3—42no—
899C2×C3—41no—
900C2×C3—42no—
901C2×C3—82no—
902C2×C3—182no—
903C2×C3—182no—
904C2×C3—361no—
905C2×C3—361no—
906C2×C3—362no—
907C2×C3C2×D3×D1211yescharacteristic
908C2×C3C2×D3×D1211yescharacteristic
909C2×C3C2×#380211yescharacteristic
910C2×C3#6431312yes—
911C2×C3#6431412yes—
912C2×C3#6431412yes—
913D3—64no—
914D3—62no—
915D3—62no—
916D3—62no—
917D3—62no—
918D3—122no—
919D3—124no—
920D3—122no—
921D3—121no—
922D3—121no—
923D3—122no—
924D3—121no—
925D3—121no—
926D3—241no—
927D3—241no—
928C22—22no—
929C22—92no—
930C22—92no—
931C22—182no—
932C22—182no—
933C22—181no—
934C22—181no—
935C22—182no—
936C22—182no—
937C22—182no—
938C22—182no—
939C22—182no—
940C22—364no—
941C22—364no—
942C22—1084no—
943C22C4⋊#111312yes—
944C22C22×#111311yescharacteristic
945C4—22no—
946C4—182no—
947C4—181no—
948C4—181no—
949C4—182no—
950C3—21no—
951C3—21no—
952C3—21no—
953C3—41no—
954C3#1059429011yescharacteristic, complemented
955C3#1059429111yescharacteristic, complemented
956C3#1059429611yescharacteristic, complemented
957C2—22no—
958C2—182no—
959C2—182no—
960C2—362no—
961C2—361no—
962C2—361no—
963C2C2×C4⋊#111311yescharacteristic
964C2#1172462312yes—
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C22×#6295C2semidirect
3. C3×#64095C2semidirect
4. C3×#64091C2semidirect
5. C3×C22⋊C4×C3⋊D3C2semidirect
6. #11723727C2semidirect
7. #11723720C2semidirect
8. #11723701C2semidirect
9. #11723696C2semidirect
10. #11723695C2semidirect
11. #11723690C2semidirect
16. C23×C3×C3⋊D3C22semidirect
17. C22×#1113C22semidirect
20. C22×C3×C3⋊Dic3C22semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
26. C2×#6295C22semidirect
27. C2×#6295C22semidirect
28. C2×#6295C22semidirect
29. C2×#6295C22semidirect
30. C2×#6294C22semidirect
31. C33×C22⋊C4C22semidirect
32. C3×#3757C22semidirect
33. C3×#3752C22semidirect
34. C3×#3752C22semidirect
35. C3×#3752C22semidirect
36. C3×C4⋊(C3⋊Dic3)C22semidirect
37. #88815C22semidirect
38. #88814C22semidirect
39. #88814C22semidirect
46. #64095D3semidirect
47. #64091D3semidirect
48. C22⋊C4×C3⋊D3D3semidirect
80. C22×C3×C3⋊D3D4semidirect
108. C23×C3⋊D3C2×D3semidirect
120. C22×C3⋊Dic3C2×D3semidirect
121. C2×C4⋊(C3⋊D3)C2×D3semidirect
122. C2×C4×C3⋊D3C2×D3semidirect
166. C32×C22⋊C4C2×D3semidirect
167. C32×C22⋊C4C2×D3semidirect
168. C32×C22⋊C4C2×D3semidirect
169. #3757C2×D3semidirect
170. #3752C2×D3semidirect
171. #3752C2×D3semidirect
172. #3752C2×D3semidirect
173. C4⋊(C3⋊Dic3)C2×D3semidirect
266. C22×C3⋊D3D12semidirect
439. C3×C22⋊C4D32semidirect
440. C3×C22⋊C4D32semidirect
441. C3×C22⋊C4D32semidirect
576. C33#534semidirect
752. C22⋊C4#1113semidirect
856. C32#5493semidirect
857. C32#5589semidirect
858. C32#5653semidirect
954. C3#10594290semidirect
955. C3#10594291semidirect
956. C3#10594296semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C22×#62952
C3×#640952
C3×#640912
C3×C22⋊C4×C3⋊D32
#117237272
#117237202
#117237012
#117236962
#117236952
#117236902
#105942963
#105942913
#105942903