Finite Group Databasebeta

← #13172301

Subgroups — #13172301

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
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×C3×#3811C211yesmaximal, characteristic, complemented
3#11723634C211yesmaximal, characteristic, complemented
4C3⋊D3×#217C211yesmaximal, characteristic, complemented
5#11723602C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic, complemented
8#11722995C212yesmaximal, complemented
9#11722967C212yesmaximal, complemented
10#11722962C212yesmaximal, complemented
11#11722947C212yesmaximal, complemented
12#10595234—31nomaximal
13#10595230—31nomaximal
14#10594296—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C3×C3⋊D3C2211yescharacteristic, complemented
17C22×C3×D32C2211yescharacteristic, complemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×#6295—24no—
22C2×#6295C2212yes—
23C2×#6295C2212yescomplemented
24C2×#6290C2212yescomplemented
25C2×Dic3×C3⋊D3C2212yescomplemented
26C3×#3811—24no—
27C2×C3×#626C2211yescharacteristic, complemented
28C2×C3×#626C2211yescharacteristic, complemented
29C2×C3×#626C2212yescomplemented
30C2×C3×#624C2211yescharacteristic, complemented
31#88864C2211yescharacteristic, complemented
32C32×#217C2211yescharacteristic, complemented
33#88806C2212yescomplemented
34#88803C2212yescomplemented
35#88803C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×#3722C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C3×D3×D4—31no—
41C2×C3×D3×D4—31no—
42C2×#3811D311yescharacteristic, complemented
43C22×#626—31no—
44C22×#626—31no—
45C22×#625—31no—
46#64146—31no—
47#64144—31no—
48C22⋊C4×C3⋊D3—31no—
49C3×#937—31no—
50C3×#935—31no—
51C3×#886—31no—
52C3×#882—31no—
53#63981D311yescharacteristic, complemented
54#63977—32no—
55#63976—31no—
56#63976—31no—
57#63976—32no—
58#63976—61no—
59#63971—32no—
60#63970—32no—
61D3×#217—31no—
62D3×#217—31no—
63D3×#217—61no—
64#63962D311yescharacteristic, complemented
65#63961—31no—
66#63961—31no—
67#63961—61no—
68#63922—32no—
69#63916—32no—
70#63912—32no—
71#63905—32no—
72#63886—32no—
73#63885—32no—
74#63854—32no—
75#63850—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⋊D3C2312yes—
82C22×C3×C3⋊D3C2311yescharacteristic
83C22×C3×C3⋊D3C2311yescharacteristic
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—22no—
87C2×C3×D32—42no—
88C2×C3⋊(C3⋊Dic3)C2312yes—
89C2×C3×C3⋊Dic3—22no—
90C2×C3×C3⋊Dic3C2312yes—
91C32×#67—22no—
92C32×#67—22no—
93C2×C32×Dic3C2312yes—
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96#6295—24no—
97#6295—24no—
98#6290—42no—
99Dic3×C3⋊D3—42no—
100C3×#626—22no—
101C3×#626—22no—
102C3×#626—42no—
103C3×#624—22no—
104#5804—91no—
105#5653—91no—
106#5589—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—31no—
114C23×C3×D3—31no—
115C23×C3×D3—61no—
116C23×C3×D3—61no—
117C22×D32C2×D311yescharacteristic, complemented
118C2×C32×D4—31no—
119C2×C32×D4—31no—
120C2×#638—32no—
121C22×C3⋊Dic3C2×D311yescharacteristic, complemented
122C2×C4×C3⋊D3—32no—
123C2×C3×#67—21no—
124C2×C3×#67—21no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—32no—
128C2×C3×#67C2×D311yescharacteristic
129C2×C3×#67C2×D311yescharacteristic
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×#67C2×D311yescharacteristic
132C22×C3×Dic3—31no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—61no—
135C3×D3×D4—64no—
136C3×D3×D4—64no—
137C2×C3×D12—31no—
138C2×C3×D12—31no—
139C2×C3×D12—32no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142#3811—24no—
143C2×#626—32no—
144C2×#626—32no—
145C2×#626—32no—
146C2×#626—32no—
147C2×#626—64no—
148C2×#626—64no—
149C2×#626C2×D311yescharacteristic, complemented
150C2×#626C2×D311yescharacteristic, complemented
151C2×#626C2×D312yescomplemented
152C2×#625—32no—
153C2×#625—32no—
154C2×#625—32no—
155C2×#625—32no—
156C2×#625—64no—
157C2×#625—62no—
158C2×#624C2×D311yescharacteristic, complemented
159C2×D3×Dic3—32no—
160C2×D3×Dic3—32no—
161C2×D3×Dic3—62no—
162C32×C22⋊C4—31no—
163#3757—31no—
164#3757—31no—
165#3757—31no—
166#3757—32no—
167#3757—61no—
168#3757—61no—
169#3757—61no—
170#3757—121no—
171#3752—32no—
172#3752—32no—
173#3750—32no—
174C3×#217—21no—
175C3×#217—32no—
176C3×#217C2×D311yescharacteristic, complemented
177C3×#217C2×D311yescharacteristic, complemented
178C3×(C2×D3)⋊C4—32no—
179C3×(C2×D3)⋊C4—32no—
180C3×(C2×D3)⋊C4—32no—
181C3×C4⋊Dic3—32no—
182C3×Dic3⋊C4—32no—
183#3724—32no—
184#3724—32no—
185#3724—62no—
186Dic3⋊Dic3C2×D312yescomplemented
187#3722C2×D312yescomplemented
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3—62no—
195(C2×D3)⋊Dic3—62no—
196(C2×D3)⋊Dic3—62no—
197(C2×D3)⋊Dic3C2×D312yescomplemented
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—22no—
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—44no—
207C2×C3×C3⋊D3—44no—
208C2×C3×C3⋊D3C2×D412yes—
209C2×C3×C3⋊D3C2×D412yes—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—22no—
213C2×C32×D3—22no—
214C3×D32—44no—
215C3⋊(C3⋊Dic3)—22no—
216C3×C3⋊Dic3—22no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—22no—
220C22×C3×D4—91no—
221C22×#67—91no—
222C22×#67—91no—
223C2×D3×D4—31no—
224C2×D3×D4—31no—
225C22×D12—91no—
226C3×#123—91no—
227C3×#120—91no—
228#953—92no—
229#953—91no—
230C2×#217—91no—
231#939—92no—
232#939—92no—
233#938—92no—
234#937—31no—
235#937—92no—
236#937—91no—
237#937—91no—
238#937—181no—
239#935—31no—
240#935—91no—
241#935—91no—
242#935—181no—
243#929—92no—
244#929—91no—
245#895—92no—
246#894—92no—
247#886—31no—
248#884—92no—
249#884—92no—
250#883—92no—
251#882—31no—
252#882—92no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4—91no—
255D3×C22⋊C4—181no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—31no—
260C23×C32—31no—
261C23×C32—41no—
262C23×C32C22×D311yescharacteristic
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3—22no—
266C22×C3⋊D3—42no—
267C22×C3⋊D3—42no—
268C22×C3⋊D3#6714yescomplemented
269C22×C3⋊D3C22×D312yes—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—34no—
279C22×C3×D3—34no—
280C22×C3×D3—32no—
281C22×C3×D3—32no—
282C22×C3×D3—61no—
283C22×C3×D3—61no—
284C22×C3×D3—62no—
285C22×C3×D3—64no—
286C22×C3×D3—62no—
287C22×C3×D3—62no—
288C22×C3×D3—62no—
289C22×C3×D3—62no—
290C22×C3×D3—122no—
291C22×C3×D3—122no—
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—
299C22×C3×D3C22×D311yescharacteristic
300C22×C3×D3C22×D311yescharacteristic
301C22×C3×D3C22×D311yescharacteristic
302C22×C3×D3C22×D311yescharacteristic
303C2×D32—22no—
304C2×D32—42no—
305C32×D4—62no—
306C32×D4—62no—
307C2×C32×C4—31no—
308C2×C32×C4—32no—
309C2×C32×C4—31no—
310#638—122no—
311C2×C3⋊Dic3—22no—
312C2×C3⋊Dic3—32no—
313C2×C3⋊Dic3—32no—
314C2×C3⋊Dic3—32no—
315C2×C3⋊Dic3—62no—
316C2×C3⋊Dic3—62no—
317C2×C3⋊Dic3—62no—
318C2×C3⋊Dic3—122no—
319C2×C3⋊Dic3C22×D312yes—
320C4×C3⋊D3—122no—
321C3×#67—22no—
322C3×#67—22no—
323C3×#67—22no—
324C3×#67—22no—
325C3×#67—42no—
326C3×#67—42no—
327C3×#67—62no—
328C3×#67—62no—
329C3×#67—122no—
330C2×C3×Dic3—21no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3—32no—
334C2×C3×Dic3—32no—
335C2×C3×Dic3—62no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—62no—
338C2×C3×Dic3—122no—
339C2×C3×Dic3C22×D311yescharacteristic
340C2×C3×Dic3C22×D311yescharacteristic
341C2×C3×Dic3C22×D312yes—
342C2×C3×Dic3C22×D312yes—
343C2×C3×Dic3C22×D311yescharacteristic
344C2×C3×Dic3C22×D311yescharacteristic
345C3×D12—62no—
346C3×D12—62no—
347C3×D12—122no—
348C3×C4×D3—62no—
349C3×C4×D3—62no—
350#626—22no—
351#626—22no—
352#626—42no—
353#626—64no—
354#626—64no—
355#626—64no—
356#626—64no—
357#625—64no—
358#625—64no—
359#625—122no—
360#625—122no—
361#625—124no—
362#624—22no—
363D3×Dic3—122no—
364D3×Dic3—122no—
365D3×Dic3—124no—
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—
373C32×D3—41no—
374C32×D3—41no—
375C24×C3—91no—
376C24×C3—91no—
377C24×C3—91no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—61no—
385C23×D3—61no—
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—31no—
389C2×C3×D4—31no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—91no—
393C2×C3×D4—91no—
394C2×C3×D4—92no—
395C2×C3×D4—184no—
396C22×C3×C4—91no—
397C22×C3×C4—91no—
398C2×#67—31no—
399C2×#67—31no—
400C2×#67—32no—
401C2×#67—92no—
402C2×#67—92no—
403C2×#67—92no—
404C2×#67—92no—
405C2×#67—92no—
406C2×#67—92no—
407C2×#67—92no—
408C2×#67—182no—
409C2×#67—184no—
410C2×#67—184no—
411C2×#67D3211yescharacteristic
412C2×#67D3211yescharacteristic
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—61no—
416C22×Dic3—92no—
417D3×D4—64no—
418D3×D4—64no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—32no—
422C2×D12—92no—
423C2×D12—92no—
424C2×D12—184no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—92no—
428C2×C4×D3—92no—
429C2×C4×D3—182no—
430C3×C4⋊C4—92no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—31no—
433C3×C22⋊C4—61no—
434C3×C22⋊C4—92no—
435C3×C22⋊C4—92no—
436#217—32no—
437#217—92no—
438#217—92no—
439#217—91no—
440#217—91no—
441#217—91no—
442#217—92no—
443#217—92no—
444#217—182no—
445#217—181no—
446#217—181no—
447#217—181no—
448#217—361no—
449#217D3211yescharacteristic, complemented
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—92no—
454(C2×D3)⋊C4—92no—
455(C2×D3)⋊C4—92no—
456(C2×D3)⋊C4—92no—
457(C2×D3)⋊C4—92no—
458(C2×D3)⋊C4—182no—
459(C2×D3)⋊C4—182no—
460C4⋊Dic3—32no—
461Dic3⋊C4—32no—
462Dic3⋊C4—92no—
463Dic3⋊C4—92no—
464Dic3⋊C4—92no—
465Dic3⋊C4—182no—
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—61no—
481C22×C32—61no—
482C22×C32—62no—
483C22×C32—62no—
484C22×C32—82no—
485C22×C32D3×D412yes—
486C22×C32D3×D412yes—
487C22×C32C2×#6712yes—
488C22×C32C23×D311yescharacteristic
489C22×C32C23×D311yescharacteristic
490C22×C32C23×D311yescharacteristic
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—44no—
497C2×C3⋊D3—44no—
498C2×C3⋊D3C2×#6712yes—
499C2×C3⋊D3C2×#6712yes—
500C2×C3×D3—21no—
501C2×C3×D3—21no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—32no—
509C2×C3×D3—32no—
510C2×C3×D3—32no—
511C2×C3×D3—32no—
512C2×C3×D3—42no—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—42no—
516C2×C3×D3—62no—
517C2×C3×D3—62no—
518C2×C3×D3—64no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—62no—
522C2×C3×D3—62no—
523C2×C3×D3—64no—
524C2×C3×D3—62no—
525C2×C3×D3—62no—
526C2×C3×D3—62no—
527C2×C3×D3—62no—
528C2×C3×D3—62no—
529C2×C3×D3—62no—
530C2×C3×D3—122no—
531C2×C3×D3—122no—
532C2×C3×D3—122no—
533C2×C3×D3—124no—
534C2×C3×D3—124no—
535C2×C3×D3—124no—
536C2×C3×D3—124no—
537C2×C3×D3—128no—
538C2×C3×D3—124no—
539C2×C3×D3—124no—
540C2×C3×D3—128no—
541D32—44no—
542C32×C4—61no—
543C32×C4—61no—
544C32×C4—62no—
545C3⋊Dic3—22no—
546C3⋊Dic3—62no—
547C3⋊Dic3—62no—
548C3⋊Dic3—62no—
549C3⋊Dic3—122no—
550C3⋊Dic3—122no—
551C3⋊Dic3—122no—
552C3⋊Dic3—242no—
553C3×Dic3—21no—
554C3×Dic3—21no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—21no—
558C3×Dic3—21no—
559C3×Dic3—42no—
560C3×Dic3—41no—
561C3×Dic3—41no—
562C3×Dic3—62no—
563C3×Dic3—62no—
564C3×Dic3—122no—
565C22×D4—91no—
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—271no—
576C33#53411yescharacteristic, complemented, Sylow
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—31no—
581C23×C3—31no—
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—41no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—91no—
588C23×C3—91no—
589C23×C3—94no—
590C23×C3—92no—
591C23×C3—182no—
592C23×C3—182no—
593C23×C3—362no—
594C23×C3—362no—
595C23×C3—362no—
596C23×C3C2×D3211yescharacteristic
597C23×C3C2×D3211yescharacteristic
598C23×C3C2×D3211yescharacteristic
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—31no—
603C22×D3—34no—
604C22×D3—34no—
605C22×D3—32no—
606C22×D3—32no—
607C22×D3—61no—
608C22×D3—64no—
609C22×D3—61no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—122no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—122no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3C2×D3211yescharacteristic
625C22×D3C2×D3211yescharacteristic
626C3×D4—62no—
627C3×D4—62no—
628C3×D4—62no—
629C3×D4—62no—
630C3×D4—122no—
631C3×D4—122no—
632C3×D4—182no—
633C3×D4—182no—
634C3×D4—362no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—31no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—62no—
644C2×C3×C4—92no—
645C2×C3×C4—182no—
646C2×C3×C4—182no—
647#67—22no—
648#67—22no—
649#67—62no—
650#67—62no—
651#67—122no—
652#67—184no—
653#67—184no—
654#67—184no—
655#67—184no—
656#67—362no—
657#67—362no—
658#67—362no—
659#67—364no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—92no—
666C2×Dic3—92no—
667C2×Dic3—92no—
668C2×Dic3—122no—
669C2×Dic3—182no—
670C2×Dic3—182no—
671C2×Dic3—182no—
672C2×Dic3—362no—
673C2×Dic3—362no—
674C2×Dic3C2×D3212yes—
675C2×Dic3C2×D3211yescharacteristic
676C2×Dic3C2×D3211yescharacteristic
677D12—62no—
678D12—62no—
679D12—122no—
680D12—184no—
681D12—184no—
682C4×D3—62no—
683C4×D3—62no—
684C4×D3—362no—
685C4×D3—362no—
686C4×D3—364no—
687C2×C32—22no—
688C2×C32—22no—
689C2×C32—22no—
690C2×C32—21no—
691C2×C32—22no—
692C2×C32—22no—
693C2×C32—22no—
694C2×C32—21no—
695C2×C32—21no—
696C2×C32—41no—
697C2×C32—42no—
698C2×C32—42no—
699C2×C32—42no—
700C2×C32—42no—
701C2×C32—82no—
702C2×C32—121no—
703C2×C32—121no—
704C2×C32C2×D3×D411yescharacteristic
705C2×C32C2×D3×D411yescharacteristic
706C2×C32#100412yes—
707C2×C32#100412yes—
708C2×C32#100912yes—
709C2×C32C22×#6711yescharacteristic
710C3⋊D3—22no—
711C3⋊D3—22no—
712C3⋊D3—42no—
713C3×D3—41no—
714C3×D3—41no—
715C3×D3—41no—
716C3×D3—41no—
717C3×D3—64no—
718C3×D3—62no—
719C3×D3—62no—
720C3×D3—62no—
721C3×D3—62no—
722C3×D3—81no—
723C3×D3—81no—
724C3×D3—122no—
725C3×D3—124no—
726C3×D3—122no—
727C3×D3—122no—
728C24—91no—
729C24—91no—
730C24—91no—
731C2×D4—31no—
732C2×D4—31no—
733C2×D4—91no—
734C2×D4—91no—
735C2×D4—92no—
736C2×D4—184no—
737C2×D4—272no—
738C2×D4—272no—
739C2×D4—272no—
740C2×D4—544no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—272no—
744C4⋊C4—92no—
745C4⋊C4—272no—
746C22⋊C4—31no—
747C22⋊C4—92no—
748C22⋊C4—92no—
749C22⋊C4—272no—
750C22⋊C4—272no—
751C22⋊C4—272no—
752C22⋊C4—271no—
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—61no—
768C22×C3—61no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—61no—
774C22×C3—61no—
775C22×C3—82no—
776C22×C3—92no—
777C22×C3—92no—
778C22×C3—122no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—122no—
782C22×C3—182no—
783C22×C3—182no—
784C22×C3—182no—
785C22×C3—182no—
786C22×C3—182no—
787C22×C3—364no—
788C22×C3—364no—
789C22×C3—364no—
790C22×C3#380212yes—
791C22×C3D3×#6712yes—
792C22×C3D3×#6712yes—
793C22×C3C22×D3211yescharacteristic
794C22×C3C22×D3211yescharacteristic
795C22×C3C22×D3211yescharacteristic
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—32no—
801C2×D3—32no—
802C2×D3—32no—
803C2×D3—32no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—64no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—64no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—122no—
821C2×D3—124no—
822C2×D3—124no—
823C2×D3—124no—
824C2×D3—124no—
825C2×D3—128no—
826C2×D3—124no—
827C2×D3—124no—
828C2×D3—128no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—122no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4—182no—
839Dic3—22no—
840Dic3—21no—
841Dic3—21no—
842Dic3—62no—
843Dic3—62no—
844Dic3—122no—
845Dic3—182no—
846Dic3—182no—
847Dic3—182no—
848Dic3—362no—
849Dic3—362no—
850Dic3—362no—
851Dic3—722no—
852C32—21no—
853C32—21no—
854C32—21no—
855C32—41no—
856C32#558911yescharacteristic, complemented
857C32#565311yescharacteristic, complemented
858C32#580411yescharacteristic, complemented
859C23—31no—
860C23—31no—
861C23—91no—
862C23—91no—
863C23—94no—
864C23—92no—
865C23—182no—
866C23—182no—
867C23—362no—
868C23—362no—
869C23—362no—
870C23D3311yescharacteristic
871D4—62no—
872D4—62no—
873D4—182no—
874D4—182no—
875D4—362no—
876D4—544no—
877D4—544no—
878D4—1082no—
879C2×C4—32no—
880C2×C4—31no—
881C2×C4—31no—
882C2×C4—92no—
883C2×C4—182no—
884C2×C4—182no—
885C2×C4—272no—
886C2×C4—1082no—
887C2×C3—22no—
888C2×C3—22no—
889C2×C3—22no—
890C2×C3—22no—
891C2×C3—22no—
892C2×C3—22no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—42no—
897C2×C3—42no—
898C2×C3—42no—
899C2×C3—42no—
900C2×C3—41no—
901C2×C3—82no—
902C2×C3—121no—
903C2×C3—121no—
904C2×C3—121no—
905C2×C3—121no—
906C2×C3—182no—
907C2×C3—182no—
908C2×C3—241no—
909C2×C3—241no—
910C2×C3—362no—
911C2×C3C2×#380211yescharacteristic
912C2×C3#6431312yes—
913C2×C3#6431412yes—
914C2×C3#6431412yes—
915C2×C3C2×D3×#6711yescharacteristic
916C2×C3C2×D3×#6711yescharacteristic
917D3—41no—
918D3—41no—
919D3—64no—
920D3—62no—
921D3—62no—
922D3—62no—
923D3—62no—
924D3—122no—
925D3—124no—
926D3—122no—
927D3—122no—
928C22—22no—
929C22—62no—
930C22—62no—
931C22—61no—
932C22—61no—
933C22—92no—
934C22—92no—
935C22—182no—
936C22—182no—
937C22—182no—
938C22—182no—
939C22—182no—
940C22—364no—
941C22—364no—
942C22—364no—
943C22#8895312yes—
944C22C2×D3311yescharacteristic
945C4—62no—
946C4—61no—
947C4—61no—
948C4—182no—
949C4—542no—
950C3—21no—
951C3—21no—
952C3—21no—
953C3—41no—
954C3#1059429611yescharacteristic, complemented
955C3#1059523011yescharacteristic, complemented
956C3#1059523411yescharacteristic, complemented
957C2—22no—
958C2—121no—
959C2—121no—
960C2—182no—
961C2—182no—
962C2—362no—
963C2#1172441612yes—
964C2C2×#8895311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6295C2semidirect
2. C2×C3×#3811C2semidirect
3. #11723634C2semidirect
4. C3⋊D3×#217C2semidirect
5. #11723602C2semidirect
6. C3×#63981C2semidirect
7. C3×#63962C2semidirect
8. #11722995C2semidirect
9. #11722967C2semidirect
10. #11722962C2semidirect
11. #11722947C2semidirect
16. C23×C3×C3⋊D3C22semidirect
17. C22×C3×D32C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
23. C2×#6295C22semidirect
24. C2×#6290C22semidirect
25. C2×Dic3×C3⋊D3C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#626C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#624C22semidirect
31. #88864C22semidirect
32. C32×#217C22semidirect
33. #88806C22semidirect
34. #88803C22semidirect
35. #88803C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
38. C3×#3722C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
42. C2×#3811D3semidirect
53. #63981D3semidirect
64. #63962D3semidirect
80. C22×C3×C3⋊D3D4semidirect
108. C23×C3⋊D3C2×D3semidirect
117. C22×D32C2×D3semidirect
121. C22×C3⋊Dic3C2×D3semidirect
149. C2×#626C2×D3semidirect
150. C2×#626C2×D3semidirect
151. C2×#626C2×D3semidirect
158. C2×#624C2×D3semidirect
176. C3×#217C2×D3semidirect
177. C3×#217C2×D3semidirect
186. Dic3⋊Dic3C2×D3semidirect
187. #3722C2×D3semidirect
197. (C2×D3)⋊Dic3C2×D3semidirect
268. C22×C3⋊D3#67semidirect
449. #217D32semidirect
576. C33#534semidirect
856. C32#5589semidirect
857. C32#5653semidirect
858. C32#5804semidirect
954. C3#10594296semidirect
955. C3#10595230semidirect
956. C3#10595234semidirect

Maximal subgroups

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

subgroupindex
C22×#62952
C2×C3×#38112
#117236342
C3⋊D3×#2172
#117236022
C3×#639812
C3×#639622
#117229952
#117229672
#117229622
#117229472
#105952343
#105952303
#105942963