Finite Group Databasebeta

← #13172170

Subgroups — #13172170

Order 1728.

1950 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6289C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723720C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6C3×#63962C211yesmaximal, characteristic, complemented
7C3×#63955C211yesmaximal, characteristic, complemented
8#11722973C212yesmaximal, complemented
9#11722963C212yesmaximal, complemented
10#11722933C212yesmaximal, complemented
11#11722932C212yesmaximal, complemented
12#10595159—31nomaximal
13#10595034—31nomaximal
14#10594079—31nomaximal
15C23×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×#6292C2212yes—
21C2×#6291C2212yes—
22C2×#6289—24no—
23C2×#6289C2212yes—
24C2×#6289C2212yes—
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic, complemented
28C3×#3804—24no—
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C3×#3757C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2212yescomplemented
33#88814C2212yescomplemented
34#88804C2212yes—
35#88804C2212yes—
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C22×C4×C3⋊D3—31no—
41C2×C3×#237—31no—
42C2×C3×#235—31no—
43C22×#624—31no—
44C22×#624—31no—
45C22×#624—61no—
46C2×#3804D311yescharacteristic, complemented
47#64146—31no—
48#64091—31no—
49C3×#935—31no—
50C3×#926—31no—
51C3×#886—31no—
52C3×#877—31no—
53#63981—31no—
54#63981—31no—
55#63981—31no—
56#63981—31no—
57#63981—61no—
58#63981—61no—
59#63966—31no—
60#63962—31no—
61#63962D311yescharacteristic, complemented
62#63961—31no—
63#63958—32no—
64#63955D311yescharacteristic, complemented
65#63952—32no—
66#63916—32no—
67#63910—32no—
68#63904—32no—
69C4×#626—32no—
70C4×#626—32no—
71#63895—32no—
72#63894—32no—
73#63888—32no—
74#63880—32no—
75#63871—32no—
76C23×C33C2311yescharacteristic
77C22×C3⋊(C3⋊D3)—22no—
78C22×C3⋊(C3⋊D3)—24no—
79C22×C3⋊(C3⋊D3)C2312yes—
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C32×D3C2311yescharacteristic
82C3×#638—22no—
83C2×C3×C3⋊Dic3—22no—
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C32×#67—22no—
88C2×C32×Dic3D414yescomplemented
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93#6292—24no—
94#6291—24no—
95#6289—24no—
96#6289—24no—
97C3×#627—22no—
98C3×#626—22no—
99C3×#624—22no—
100C3×D3×Dic3—22no—
101#5828—91no—
102#5656—91no—
103#5524—91no—
104C23×C3⋊D3—31no—
105C23×C3⋊D3—31no—
106C23×C3⋊D3—31no—
107C23×C3⋊D3—61no—
108C23×C3⋊D3—61no—
109C23×C3⋊D3—61no—
110C23×C3⋊D3—121no—
111C2×C32×D4—31no—
112C22×C32×C4—31no—
113C2×#638—32no—
114C2×#638C2×D311yescharacteristic
115C22×C3⋊Dic3C2×D311yescharacteristic
116C2×C4⋊(C3⋊D3)—32no—
117C2×C4×C3⋊D3—32no—
118C2×C4×C3⋊D3—32no—
119C2×C4×C3⋊D3—64no—
120C2×C3×#67—21no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67—61no—
125C2×C3×#67C2×D311yescharacteristic
126C2×C3×#67C2×D311yescharacteristic
127C22×C3×Dic3—21no—
128C22×C3×Dic3—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—61no—
132C22×C3×Dic3C2×D311yescharacteristic
133C22×C3×Dic3C2×D311yescharacteristic
134C3×#237—64no—
135C3×#235—64no—
136C2×C3×D12—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×#627C2×D311yescharacteristic, complemented
143C2×#626—32no—
144C2×#626—32no—
145C2×#626—32no—
146C2×#626—32no—
147C2×#626—62no—
148C2×#626—62no—
149C2×#626C2×D311yescharacteristic, complemented
150C2×#624—32no—
151C2×#624—32no—
152C2×#624—32no—
153C2×#624—32no—
154C2×#624—62no—
155C2×#624—62no—
156C2×#624—68no—
157C2×#624—64no—
158C2×#624—64no—
159C2×#624C2×D311yescharacteristic, complemented
160#3804—24no—
161C2×D3×Dic3C2×D311yescharacteristic, complemented
162C32×C22⋊C4—31no—
163#3757C2×D311yescharacteristic
164#3752—32no—
165#3752—32no—
166C3×#217—21no—
167C3×#217—31no—
168C3×#217—31no—
169C3×#217—32no—
170C3×#217—61no—
171C3×#217C2×D311yescharacteristic
172C3×#217C2×D311yescharacteristic
173C3×(C2×D3)⋊C4—32no—
174C3×C4⋊Dic3—32no—
175C3×C4⋊Dic3—32no—
176C3×Dic3⋊C4—32no—
177C3×Dic3⋊C4—32no—
178C3×C4×Dic3—32no—
179C3×C4×Dic3—32no—
180#3724—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—32no—
183Dic3⋊Dic3C2×D312yescomplemented
184Dic3⋊Dic3C2×D312yescomplemented
185#3722—32no—
186#3722—32no—
187#3722—32no—
188#3722—32no—
189#3722—32no—
190#3722—62no—
191#3722—62no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3C2×D312yescomplemented
195Dic32C2×D312yescomplemented
196C22×C33—22no—
197C22×C33C2×D412yes—
198C22×C33C2411yescharacteristic
199C2×C3⋊(C3⋊D3)—28no—
200C2×C3⋊(C3⋊D3)—22no—
201C2×C3⋊(C3⋊D3)—22no—
202C2×C3⋊(C3⋊D3)#4114yescomplemented
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C3×C3⋊Dic3—22no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—22no—
210C32×Dic3—21no—
211C32×Dic3—22no—
212C32×Dic3C2×D412yes—
213C32×Dic3C2×D412yes—
214C2×C3×#41—91no—
215C2×#237—31no—
216C2×#235—31no—
217C22×C4×D3—91no—
218C22×C4×D3—91no—
219C22×C4×D3—91no—
220C22×C4×D3—181no—
221C3×#123—91no—
222C3×#117—91no—
223#946—92no—
224#938—92no—
225#937—91no—
226#937—91no—
227#937—91no—
228#937—181no—
229#935—31no—
230#935—91no—
231#929—91no—
232C4×#67—92no—
233C4×#67—92no—
234#926—31no—
235#897—92no—
236#896—92no—
237#895—92no—
238#893—92no—
239#886—31no—
240#886—91no—
241#884—92no—
242#882—91no—
243#882—91no—
244#882—91no—
245#882—181no—
246#67⋊C4—92no—
247#877—31no—
248C4×D12—92no—
249C4×D12—92no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32—31no—
254C23×C32—41no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—32no—
259C22×C3⋊D3—32no—
260C22×C3⋊D3—32no—
261C22×C3⋊D3—62no—
262C22×C3⋊D3—62no—
263C22×C3⋊D3—62no—
264C22×C3⋊D3—64no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—68no—
269C22×C3⋊D3—64no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—122no—
273C22×C3⋊D3—124no—
274C22×C3⋊D3—124no—
275C22×C3⋊D3—122no—
276C22×C3⋊D3—122no—
277C22×C3⋊D3—124no—
278C22×C3⋊D3—128no—
279C22×C3⋊D3C22×D311yescharacteristic
280C22×C3×D3—21no—
281C22×C3×D3—31no—
282C22×C3×D3—31no—
283C22×C3×D3—61no—
284C22×C3×D3C22×D311yescharacteristic
285C22×C3×D3C22×D311yescharacteristic
286C32×D4—62no—
287C2×C32×C4—34no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—32no—
291C2×C32×C4—31no—
292#638—22no—
293#638—64no—
294C2×C3⋊Dic3—22no—
295C2×C3⋊Dic3C22×D312yes—
296C2×C3⋊Dic3C22×D312yes—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C4⋊(C3⋊D3)—64no—
299C4×C3⋊D3—64no—
300C4×C3⋊D3—64no—
301C3×#67—22no—
302C3×#67—22no—
303C3×#67—42no—
304C3×#67—62no—
305C3×#67—62no—
306C3×#67—62no—
307C3×#67—122no—
308C2×C3×Dic3—24no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—32no—
314C2×C3×Dic3—32no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—32no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—32no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—62no—
322C2×C3×Dic3—64no—
323C2×C3×Dic3—62no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—62no—
326C2×C3×Dic3D1214yescomplemented
327C2×C3×Dic3#6714yescomplemented
328C2×C3×Dic3C22×D312yes—
329C2×C3×Dic3C22×D312yes—
330C2×C3×Dic3C22×D311yescharacteristic
331C2×C3×Dic3C22×D311yescharacteristic
332C2×C3×Dic3C22×D311yescharacteristic
333C2×C3×Dic3C22×D311yescharacteristic
334C2×C3×Dic3C22×D311yescharacteristic
335C2×C3×Dic3C22×D311yescharacteristic
336C3×D12—62no—
337C3×C4×D3—62no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×Dic6—62no—
341C3×Dic6—62no—
342#627—22no—
343#626—22no—
344#626—64no—
345#626—64no—
346#626—64no—
347#626—64no—
348#626—124no—
349#626—124no—
350#624—22no—
351#624—68no—
352#624—68no—
353#624—64no—
354#624—64no—
355#624—64no—
356#624—64no—
357D3×Dic3—22no—
358#525—271noSylow
359C2×C33—22no—
360C2×C33C22×D411yescharacteristic
361C2×C33C2×#4112yes—
362C3⋊(C3⋊D3)—24no—
363C3×C3⋊D3—41no—
364C32×D3—41no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—181no—
369C23×D3—181no—
370C23×D3—181no—
371C23×D3—361no—
372C3×#41—184no—
373C2×C3×Q8—91no—
374C2×C3×D4—31no—
375C2×C3×D4—31no—
376C2×C3×D4—61no—
377C2×C3×D4—91no—
378C2×C3×D4—91no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—61no—
382C22×C3×C4—91no—
383C22×C3×C4—91no—
384C22×C3×C4—91no—
385C2×#67—31no—
386C2×#67—31no—
387C2×#67—31no—
388C2×#67—61no—
389C2×#67—92no—
390C2×#67—92no—
391C2×#67—92no—
392C2×#67—182no—
393C2×#67D3211yescharacteristic
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—61no—
398C22×Dic3D3211yescharacteristic
399#237—64no—
400#235—64no—
401C2×D12—31no—
402C2×D12—92no—
403C2×D12—92no—
404C2×D12—92no—
405C2×D12—182no—
406C2×C4×D3—31no—
407C2×C4×D3—31no—
408C2×C4×D3—31no—
409C2×C4×D3—92no—
410C2×C4×D3—92no—
411C2×C4×D3—92no—
412C2×C4×D3—92no—
413C2×C4×D3—92no—
414C2×C4×D3—92no—
415C2×C4×D3—182no—
416C2×C4×D3—182no—
417C2×C4×D3—184no—
418C2×C4×D3—184no—
419C2×C4×D3—188no—
420C2×C4×D3—184no—
421C2×Dic6—31no—
422C2×Dic6—31no—
423C3×C4⋊C4—92no—
424C3×C4⋊C4—92no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—92no—
429C3×C22⋊C4—91no—
430C3×C42—92no—
431#217—31no—
432#217—31no—
433#217—32no—
434#217—61no—
435#217—92no—
436#217D3211yescharacteristic
437(C2×D3)⋊C4—32no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—92no—
440(C2×D3)⋊C4—92no—
441(C2×D3)⋊C4—92no—
442(C2×D3)⋊C4—92no—
443(C2×D3)⋊C4—92no—
444(C2×D3)⋊C4—92no—
445(C2×D3)⋊C4—92no—
446(C2×D3)⋊C4—182no—
447(C2×D3)⋊C4—182no—
448C4⋊Dic3—32no—
449C4⋊Dic3—32no—
450C4⋊Dic3—92no—
451Dic3⋊C4—32no—
452Dic3⋊C4—32no—
453Dic3⋊C4—92no—
454Dic3⋊C4—92no—
455C4×Dic3—32no—
456C4×Dic3—32no—
457C22×C32—22no—
458C22×C32—24no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—42no—
468C22×C32—41no—
469C22×C32—42no—
470C22×C32—42no—
471C22×C32—44no—
472C22×C32—61no—
473C22×C32—62no—
474C22×C32C2×D1212yes—
475C22×C32D3×D412yes—
476C22×C32C2×#6712yes—
477C22×C32C23×D311yescharacteristic
478C22×C32C23×D311yescharacteristic
479C22×C32C23×D311yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—34no—
483C2×C3⋊D3—34no—
484C2×C3⋊D3—34no—
485C2×C3⋊D3—64no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—68no—
489C2×C3⋊D3—62no—
490C2×C3⋊D3—62no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—616no—
493C2×C3⋊D3—68no—
494C2×C3⋊D3—68no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—62no—
497C2×C3⋊D3—62no—
498C2×C3⋊D3—62no—
499C2×C3⋊D3—62no—
500C2×C3⋊D3—124no—
501C2×C3⋊D3—122no—
502C2×C3⋊D3—122no—
503C2×C3⋊D3—122no—
504C2×C3⋊D3—122no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—128no—
508C2×C3⋊D3—128no—
509C2×C3⋊D3—1216no—
510C2×C3×D3—21no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—21no—
514C2×C3×D3—42no—
515C2×C3×D3—41no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—122no—
521C2×C3×D3—121no—
522C32×C4—32no—
523C32×C4—32no—
524C32×C4—61no—
525C32×C4—62no—
526C3⋊Dic3—22no—
527C3⋊Dic3—22no—
528C3⋊Dic3—21no—
529C3×Dic3—21no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—21no—
533C3×Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—42no—
536C3×Dic3—41no—
537C3×Dic3—64no—
538C3×Dic3—62no—
539C3×Dic3—61no—
540C3×Dic3—61no—
541C3×Dic3—62no—
542C3×Dic3—62no—
543C3×Dic3—62no—
544C3×Dic3—122no—
545C3×Dic3—121no—
546C3×Dic3C2×D1212yes—
547C3×Dic3C2×D1212yes—
548C3×Dic3C2×#6712yes—
549C3×Dic3C2×#6712yes—
550C2×#41—91no—
551C23×C4—271no—
552#123—91no—
553#123—271no—
554C22⋊Q8—272no—
555#121—272no—
556#120—271no—
557#120—271no—
558C4×D4—272no—
559C4×D4—272no—
560#117—91no—
561C33#52511yescharacteristic, complemented, Sylow
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—31no—
566C23×C3—31no—
567C23×C3—41no—
568C23×C3—61no—
569C23×C3—91no—
570C23×C3C2×D3211yescharacteristic
571C23×C3C2×D3211yescharacteristic
572C23×C3C2×D3211yescharacteristic
573C22×D3—31no—
574C22×D3—31no—
575C22×D3—61no—
576C22×D3—92no—
577C22×D3—92no—
578C22×D3—92no—
579C22×D3—182no—
580C22×D3—182no—
581C22×D3—182no—
582C22×D3—184no—
583C22×D3—184no—
584C22×D3—184no—
585C22×D3—184no—
586C22×D3—188no—
587C22×D3—182no—
588C22×D3—182no—
589C22×D3—182no—
590C22×D3—362no—
591C22×D3—364no—
592C22×D3—364no—
593C22×D3—362no—
594C22×D3—362no—
595C22×D3—368no—
596C22×D3—364no—
597C22×D3C2×D3211yescharacteristic
598C3×Q8—182no—
599C3×D4—62no—
600C3×D4—62no—
601C3×D4—122no—
602C3×D4—182no—
603C3×D4—182no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—31no—
607C2×C3×C4—31no—
608C2×C3×C4—34no—
609C2×C3×C4—34no—
610C2×C3×C4—32no—
611C2×C3×C4—31no—
612C2×C3×C4—32no—
613C2×C3×C4—31no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—64no—
617C2×C3×C4—61no—
618C2×C3×C4—62no—
619C2×C3×C4—91no—
620C2×C3×C4—92no—
621C2×C3×C4—92no—
622C2×C3×C4—182no—
623C2×C3×C4—182no—
624C2×C3×C4—182no—
625#67—22no—
626#67—62no—
627#67—62no—
628#67—62no—
629#67—122no—
630#67—184no—
631#67—184no—
632#67—184no—
633#67—364no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—31no—
638C2×Dic3—32no—
639C2×Dic3—31no—
640C2×Dic3—62no—
641C2×Dic3—61no—
642C2×Dic3—62no—
643C2×Dic3—64no—
644C2×Dic3—62no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3#62614yescomplemented
648C2×Dic3C2×D3212yes—
649C2×Dic3C2×D3211yescharacteristic
650C2×Dic3C2×D3211yescharacteristic
651C2×Dic3C2×D3211yescharacteristic
652D12—62no—
653D12—184no—
654D12—184no—
655D12—184no—
656D12—364no—
657C4×D3—62no—
658C4×D3—62no—
659C4×D3—62no—
660C4×D3—184no—
661C4×D3—184no—
662C4×D3—184no—
663C4×D3—184no—
664C4×D3—188no—
665C4×D3—188no—
666C4×D3—184no—
667C4×D3—184no—
668Dic6—62no—
669Dic6—62no—
670C2×C32—22no—
671C2×C32—24no—
672C2×C32—22no—
673C2×C32—22no—
674C2×C32—21no—
675C2×C32—22no—
676C2×C32—22no—
677C2×C32—22no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—41no—
681C2×C32—42no—
682C2×C32—42no—
683C2×C32—42no—
684C2×C32—44no—
685C2×C32—121no—
686C2×C32C22×D1211yescharacteristic
687C2×C32C2×D3×D411yescharacteristic
688C2×C32D3×#4112yes—
689C2×C32D3×#4112yes—
690C2×C32D3×#4112yes—
691C2×C32C22×#6711yescharacteristic
692C3⋊D3—41no—
693C3⋊D3—64no—
694C3⋊D3—68no—
695C3⋊D3—64no—
696C3⋊D3—64no—
697C3⋊D3—124no—
698C3⋊D3—124no—
699C3⋊D3—128no—
700C3×D3—41no—
701C3×D3—41no—
702C3×D3—81no—
703C3×D3—121no—
704C3×D3—121no—
705C3×D3—241no—
706C24—271no—
707#41—184no—
708C2×Q8—91no—
709C2×D4—31no—
710C2×D4—91no—
711C2×D4—91no—
712C2×D4—272no—
713C2×D4—272no—
714C22×C4—31no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—272no—
719C22×C4—272no—
720C22×C4—544no—
721C4⋊C4—92no—
722C4⋊C4—92no—
723C4⋊C4—272no—
724C22⋊C4—31no—
725C22⋊C4—92no—
726C22⋊C4—91no—
727C22⋊C4—272no—
728C22⋊C4—272no—
729C22⋊C4—272no—
730C42—92no—
731C22×C3—24no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—44no—
744C22×C3—41no—
745C22×C3—42no—
746C22×C3—61no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—61no—
750C22×C3—122no—
751C22×C3—121no—
752C22×C3—181no—
753C22×C3—182no—
754C22×C3D3×D1212yes—
755C22×C3C2×#62612yes—
756C22×C3D3×#6712yes—
757C22×C3C22×D3211yescharacteristic
758C22×C3C22×D3211yescharacteristic
759C22×C3C22×D3211yescharacteristic
760C2×D3—22no—
761C2×D3—21no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—94no—
767C2×D3—94no—
768C2×D3—94no—
769C2×D3—122no—
770C2×D3—121no—
771C2×D3—184no—
772C2×D3—184no—
773C2×D3—184no—
774C2×D3—184no—
775C2×D3—188no—
776C2×D3—1816no—
777C2×D3—188no—
778C2×D3—188no—
779C2×D3—184no—
780C2×D3—182no—
781C2×D3—182no—
782C2×D3—182no—
783C2×D3—182no—
784C2×D3—182no—
785C2×D3—182no—
786C2×D3—364no—
787C2×D3—362no—
788C2×D3—362no—
789C2×D3—362no—
790C2×D3—362no—
791C2×D3—368no—
792C2×D3—368no—
793C2×D3—3616no—
794C2×D3—364no—
795C2×D3—364no—
796C3×C4—32no—
797C3×C4—32no—
798C3×C4—32no—
799C3×C4—32no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—61no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—61no—
806C3×C4—122no—
807C3×C4—121no—
808C3×C4—181no—
809C3×C4—182no—
810C3×C4—182no—
811Dic3—22no—
812Dic3—21no—
813Dic3—64no—
814Dic3—62no—
815Dic3—62no—
816Dic3—62no—
817Dic3—61no—
818Dic3—61no—
819Dic3—62no—
820Dic3—121no—
821Dic3—122no—
822Dic3C2×#62612yes—
823Dic3C2×#62612yes—
824C32—21no—
825C32—21no—
826C32—21no—
827C32—41no—
828C32#552411yescharacteristic, complemented
829C32#565611yescharacteristic, complemented
830C32#582811yescharacteristic, complemented
831C23—31no—
832C23—91no—
833C23—272no—
834C23—544no—
835C23—542no—
836C23D3311yescharacteristic
837Q8—182no—
838D4—62no—
839D4—182no—
840D4—182no—
841D4—544no—
842D4—544no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—34no—
846C2×C4—32no—
847C2×C4—31no—
848C2×C4—92no—
849C2×C4—92no—
850C2×C4—91no—
851C2×C4—182no—
852C2×C4—182no—
853C2×C4—182no—
854C2×C4—544no—
855C2×C4—544no—
856C2×C3—24no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—22no—
862C2×C3—22no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—42no—
868C2×C3—44no—
869C2×C3—42no—
870C2×C3—41no—
871C2×C3—121no—
872C2×C3—121no—
873C2×C3—241no—
874C2×C3—361no—
875C2×C3C2×D3×D1211yescharacteristic
876C2×C3#6430612yes—
877C2×C3#6431212yes—
878C2×C3#6431212yes—
879C2×C3C22×#62611yescharacteristic
880C2×C3C2×D3×#6711yescharacteristic
881D3—41no—
882D3—121no—
883D3—121no—
884D3—188no—
885D3—184no—
886D3—184no—
887D3—184no—
888D3—241no—
889D3—364no—
890D3—364no—
891D3—368no—
892C22—22no—
893C22—62no—
894C22—61no—
895C22—182no—
896C22—181no—
897C22—274no—
898C22—548no—
899C22—542no—
900C22—542no—
901C22D3×#62612yes—
902C22C2×D3311yescharacteristic
903C4—32no—
904C4—32no—
905C4—62no—
906C4—61no—
907C4—182no—
908C4—182no—
909C4—181no—
910C3—21no—
911C3—21no—
912C3—21no—
913C3—41no—
914C3#1059407911yescharacteristic, complemented
915C3#1059503411yescharacteristic, complemented
916C3#1059515911yescharacteristic, complemented
917C2—22no—
918C2—121no—
919C2—361no—
920C2—544no—
921C2#1172441112yes—
922C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6289C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723720C2semidirect
4. #11723639C2semidirect
5. #11723638C2semidirect
6. C3×#63962C2semidirect
7. C3×#63955C2semidirect
8. #11722973C2semidirect
9. #11722963C2semidirect
10. #11722933C2semidirect
11. #11722932C2semidirect
25. C2×C3×#627C22semidirect
26. C2×C3×#626C22semidirect
27. C2×C3×#624C22semidirect
29. C2×C3×D3×Dic3C22semidirect
32. #88815C22semidirect
33. #88814C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
46. C2×#3804D3semidirect
61. #63962D3semidirect
64. #63955D3semidirect
88. C2×C32×Dic3D4semidirect
142. C2×#627C2×D3semidirect
149. C2×#626C2×D3semidirect
159. C2×#624C2×D3semidirect
161. C2×D3×Dic3C2×D3semidirect
183. Dic3⋊Dic3C2×D3semidirect
184. Dic3⋊Dic3C2×D3semidirect
194. (C2×D3)⋊Dic3C2×D3semidirect
195. Dic32C2×D3semidirect
202. C2×C3⋊(C3⋊D3)#41semidirect
326. C2×C3×Dic3D12semidirect
327. C2×C3×Dic3#67semidirect
561. C33#525semidirect
647. C2×Dic3#626semidirect
828. C32#5524semidirect
829. C32#5656semidirect
830. C32#5828semidirect
914. C3#10594079semidirect
915. C3#10595034semidirect
916. C3#10595159semidirect

Maximal subgroups

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

subgroupindex
C22×#62892
C2×C3×#38042
#117237202
#117236392
#117236382
C3×#639622
C3×#639552
#117229732
#117229632
#117229332
#117229322
#105951593
#105950343
#105940793