Finite Group Databasebeta

← #13178060

Subgroups — #13178060

Order 1728.

2948 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6312C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3C3×#64162C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5#11723642C211yesmaximal, characteristic, complemented
6#11723639C211yesmaximal, characteristic, complemented
7#11723632C211yesmaximal, characteristic, complemented
8#11723628C211yesmaximal, characteristic, complemented
9#11723627C211yesmaximal, characteristic, complemented
10#11723626C211yesmaximal, characteristic, complemented
11#11723624C211yesmaximal, characteristic, complemented
12#11723623C211yesmaximal, characteristic, complemented
13#11723618C211yesmaximal, characteristic, complemented
14#11723612C211yesmaximal, characteristic, complemented
15#11723592C211yesmaximal, characteristic, complemented
16#10595961—31nomaximal
17#10595500—34nomaximal
18C24×C33C2211yescharacteristic
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×#6312—24no—
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic
23C2×#6312C2211yescharacteristic
24C2×#6312C2211yescharacteristic
25C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C22×C32×Dic3C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic, complemented
31C2×#6293C2211yescharacteristic, complemented
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35C2×#6289C2211yescharacteristic, complemented
36#89031—24no—
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C3×#3757C2211yescharacteristic
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic
42C32×#217C2211yescharacteristic
43C32×#217C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88807C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638—31no—
56C22×#638—34no—
57C22×#638—64no—
58C2×#3828—31no—
59C2×#3804—34no—
60C2×C32×C22⋊C4—31no—
61#64162D311yescharacteristic, complemented
62#64139—31no—
63#64138—31no—
64C4×#638—31no—
65#64094—31no—
66#64093—31no—
67#64093—31no—
68#64092—31no—
69#64091—31no—
70#64090—31no—
71C22⋊C4×C3⋊D3—31no—
72#64087—31no—
73C3×#953—34no—
74C2×C3×#217D314yescomplemented
75#63982—34no—
76#63981—34no—
77#63978—34no—
78#63975—34no—
79#63974—34no—
80#67⋊Dic3—34no—
81#63971—34no—
82#63966—34no—
83#63958—34no—
84#63953—34no—
85#63952—34no—
86C23×C33—22no—
87C23×C33—22no—
88C23×C33—41no—
89C23×C33C2311yescharacteristic
90C23×C33C2311yescharacteristic
91C23×C33C2311yescharacteristic
92C22×C3⋊(C3⋊D3)—22no—
93C22×C3⋊(C3⋊D3)—22no—
94C22×C3⋊(C3⋊D3)—41no—
95C22×C3⋊(C3⋊D3)C2311yescharacteristic
96C22×C3⋊(C3⋊D3)C2311yescharacteristic
97C22×C3×C3⋊D3C2311yescharacteristic
98#6312—22no—
99#6312—22no—
100#6312—22no—
101#6312D414yescomplemented
102C2×C3⋊(C3⋊Dic3)—22no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C3×#638—22no—
106C3×#638—22no—
107C3×#638—41no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C32×Dic3—22no—
112C2×C32×Dic3—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6293—22no—
118#6292—22no—
119#6292—41no—
120#6289—22no—
121#6289—41no—
122Dic3×C3⋊D3—22no—
123#5591—91no—
124#5490—94no—
125C24×C32—24no—
126C24×C32C2×D314yes—
127C24×C32C2×D311yescharacteristic
128C23×C3⋊D3—31no—
129C23×C3⋊D3—34no—
130C23×C3⋊D3—64no—
131C22×C32×C4—31no—
132C22×C32×C4—31no—
133C2×#638—31no—
134C2×#638—34no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—34no—
140C2×#638—34no—
141C2×#638—64no—
142C2×#638—616no—
143C2×#638—64no—
144C2×#638—64no—
145C2×#638—64no—
146C2×#638—64no—
147C2×#638—632no—
148C2×#638C2×D311yescharacteristic
149C2×#638C2×D311yescharacteristic, complemented
150C2×#638C2×D311yescharacteristic, complemented
151C22×C3⋊Dic3—31no—
152C22×C3⋊Dic3—34no—
153C22×C3⋊Dic3—64no—
154#3828—64no—
155C2×C4⋊(C3⋊D3)—31no—
156C2×C4⋊(C3⋊D3)—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—31no—
160C2×#634—31no—
161C2×C3×#67—34no—
162C2×C3×#67—34no—
163C2×C3×#67—34no—
164C22×C3×Dic3C2×D314yescomplemented
165C22×C3×Dic3C2×D314yescomplemented
166C2×#627—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#624—34no—
170C2×#624—34no—
171#3804—616no—
172C2×D3×Dic3—34no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177#3757C2×D311yescharacteristic
178#3757C2×D311yescharacteristic, complemented
179#3757C2×D311yescharacteristic, complemented
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185C4⋊(C3⋊Dic3)—31no—
186#3750—31no—
187#3750—31no—
188#3750—31no—
189C4×C3⋊Dic3—31no—
190C3×#217—34no—
191C3×#217—34no—
192C3×#217—34no—
193C3×#217C2×D314yes—
194C3×#217C2×D314yes—
195C3×#217C2×D314yescomplemented
196C3×#217C2×D314yescomplemented
197#3724—34no—
198Dic3⋊Dic3—34no—
199Dic3⋊Dic3—34no—
200Dic3⋊Dic3—34no—
201#3722—34no—
202#3722—34no—
203#3722—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206Dic32—34no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33—21no—
214C22×C33—44no—
215C22×C33C2×D412yes—
216C22×C33#4112yescomplemented
217C22×C33C2411yescharacteristic
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3⋊(C3⋊D3)—21no—
221C2×C3⋊(C3⋊D3)—21no—
222C2×C3⋊(C3⋊D3)—21no—
223C2×C3⋊(C3⋊D3)—44no—
224C2×C3⋊(C3⋊D3)C2×D412yes—
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)C2×D412yes—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C32×Dic3—21no—
237C22×#67—94no—
238C22×#67—91no—
239C22×#67—184no—
240C2×#237—91no—
241C2×#235—94no—
242C3×#120—91no—
243C2×C3×C22⋊C4—34no—
244#953—34no—
245C2×#217C3⋊D311yescharacteristic, complemented
246#939—91no—
247#939—91no—
248#938—91no—
249#937—91no—
250D4×Dic3—91no—
251#930—94no—
252#929—94no—
253C4×#67—94no—
254#886—91no—
255#885—94no—
256#885—91no—
257#884—94no—
258#884—94no—
259#883—94no—
260#883—91no—
261#882—94no—
262#67⋊C4—94no—
263#67⋊C4—91no—
264D3×C22⋊C4—94no—
265D3×C22⋊C4—91no—
266#878—94no—
267#878—91no—
268C23×C32—216no—
269C23×C32—28no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—24no—
273C23×C32—24no—
274C23×C32—24no—
275C23×C32—28no—
276C23×C32—48no—
277C23×C32—41no—
278C23×C32—44no—
279C23×C32—48no—
280C23×C32C22×D314yes—
281C23×C32C22×D314yes—
282C23×C32C22×D314yes—
283C23×C32C22×D311yescharacteristic
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3—31no—
287C22×C3⋊D3—31no—
288C22×C3⋊D3—34no—
289C22×C3⋊D3—34no—
290C22×C3⋊D3—64no—
291C22×C3⋊D3—64no—
292C22×C3⋊D3—62no—
293C22×C3⋊D3—68no—
294C22×C3⋊D3—616no—
295C22×C3⋊D3—62no—
296C22×C3⋊D3—68no—
297C22×C3⋊D3—128no—
298C22×C3⋊D3—121no—
299C22×C3⋊D3—124no—
300C22×C3⋊D3—128no—
301C22×C3⋊D3C22×D311yescharacteristic
302C22×C3×D3—34no—
303C2×C32×C4—31no—
304C2×C32×C4—31no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—62no—
308C2×C32×C4—121no—
309#638—22no—
310#638—22no—
311#638—34no—
312#638—316no—
313#638—41no—
314#638—616no—
315#638—62no—
316#638—68no—
317#638—62no—
318#638—68no—
319#638—616no—
320#638—616no—
321#638—616no—
322#638—68no—
323#638—62no—
324C2×C3⋊Dic3—31no—
325C2×C3⋊Dic3—31no—
326C2×C3⋊Dic3—34no—
327C2×C3⋊Dic3—34no—
328C2×C3⋊Dic3—64no—
329C2×C3⋊Dic3—64no—
330C2×C3⋊Dic3—62no—
331C2×C3⋊Dic3—68no—
332C2×C3⋊Dic3—616no—
333C2×C3⋊Dic3C22×D311yescharacteristic
334C2×C3⋊Dic3C22×D311yescharacteristic
335C2×C3⋊Dic3C22×D311yescharacteristic
336C4⋊(C3⋊D3)—62no—
337C4⋊(C3⋊D3)—121no—
338C4×C3⋊D3—62no—
339C4×C3⋊D3—62no—
340C4×C3⋊D3—121no—
341#634—62no—
342C3×#67—68no—
343C3×#67—68no—
344C3×#67—124no—
345C2×C3×Dic3—28no—
346C2×C3×Dic3—34no—
347C2×C3×Dic3—34no—
348C2×C3×Dic3—34no—
349C2×C3×Dic3—44no—
350C2×C3×Dic3C22×D314yes—
351C2×C3×Dic3C22×D314yes—
352C2×C3×Dic3C22×D314yes—
353C2×C3×Dic3C22×D314yes—
354#627—68no—
355#626—68no—
356#626—124no—
357#624—68no—
358#624—124no—
359D3×Dic3—68no—
360#546—271noSylow
361C2×C33—22no—
362C2×C33—22no—
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33C2×#4111yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C3⋊(C3⋊D3)—22no—
368C3⋊(C3⋊D3)—41no—
369C3×C3⋊D3—41no—
370C24×C3—24no—
371C24×C3D3214yes—
372C24×C3C2×C3⋊D311yescharacteristic
373C23×D3—94no—
374C23×D3—91no—
375C23×D3—184no—
376C2×C3×D4—91no—
377C2×C3×D4—91no—
378C2×C3×D4—91no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—94no—
385C2×#67—91no—
386C2×#67—94no—
387C2×#67—94no—
388C2×#67—94no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—184no—
395C2×#67—184no—
396C2×#67—184no—
397C2×#67—184no—
398C2×#67—1816no—
399C2×#67—184no—
400C2×#67—1832no—
401C22×Dic3—94no—
402C22×Dic3—91no—
403C22×Dic3—91no—
404C22×Dic3—184no—
405C22×Dic3C2×C3⋊D311yescharacteristic, complemented
406C22×Dic3C2×C3⋊D311yescharacteristic, complemented
407#237—184no—
408#235—1816no—
409C2×D12—94no—
410C2×D12—94no—
411C2×C4×D3—94no—
412C2×C4×D3—94no—
413C2×C4×D3—91no—
414C2×C4×D3—94no—
415C2×C4×D3—91no—
416C2×Dic6—94no—
417C2×Dic6—91no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4—91no—
425#217—34no—
426#217—34no—
427#217—34no—
428#217—91no—
429#217C2×C3⋊D311yescharacteristic
430#217C2×C3⋊D311yescharacteristic
431#217C2×C3⋊D311yescharacteristic, complemented
432#217C2×C3⋊D311yescharacteristic, complemented
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—94no—
435(C2×D3)⋊C4—94no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442C4⋊Dic3—94no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445Dic3⋊C4—94no—
446Dic3⋊C4—94no—
447Dic3⋊C4—94no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450C4×Dic3—94no—
451C4×Dic3—91no—
452C22×C32—28no—
453C22×C32—28no—
454C22×C32—24no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—24no—
459C22×C32—21no—
460C22×C32—28no—
461C22×C32—24no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—24no—
466C22×C32—28no—
467C22×C32—28no—
468C22×C32—24no—
469C22×C32—24no—
470C22×C32—24no—
471C22×C32—24no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32—44no—
477C22×C32—416no—
478C22×C32—432no—
479C22×C32#23518yescomplemented
480C22×C32D3×D418yes—
481C22×C32D3×D412yes—
482C22×C32#23712yescomplemented
483C22×C32C23×D314yes—
484C22×C32C23×D311yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—32no—
489C2×C3⋊D3—38no—
490C2×C3⋊D3—68no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—61no—
493C2×C3⋊D3—68no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—61no—
496C2×C3⋊D3—61no—
497C2×C3⋊D3—61no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—64no—
501C2×C3⋊D3—64no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—124no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—1216no—
508C2×C3⋊D3—1232no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3—64no—
512C32×C4—61no—
513C32×C4—61no—
514C32×C4—61no—
515C32×C4—61no—
516C3⋊Dic3—21no—
517C3⋊Dic3—21no—
518C3⋊Dic3—21no—
519C3⋊Dic3—32no—
520C3⋊Dic3—38no—
521C3⋊Dic3—68no—
522C3⋊Dic3—68no—
523C3⋊Dic3—64no—
524C3⋊Dic3—61no—
525C3×Dic3—24no—
526C3×Dic3—24no—
527C3×Dic3—24no—
528C3×Dic3—24no—
529C3×Dic3—64no—
530C3×Dic3—64no—
531C3×Dic3—64no—
532C2×#41—271no—
533C22×D4—271no—
534#124—271no—
535#123—271no—
536#123—271no—
537C22⋊Q8—271no—
538#121—271no—
539#121—271no—
540#121—271no—
541#120—91no—
542#120—271no—
543C4×D4—271no—
544C4×D4—271no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—271no—
547C33#54611yescharacteristic, complemented, Sylow
548C23×C3—216no—
549C23×C3—28no—
550C23×C3—28no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—24no—
554C23×C3—24no—
555C23×C3—24no—
556C23×C3—48no—
557C23×C3—44no—
558C23×C3—41no—
559C23×C3—48no—
560C23×C3—91no—
561C23×C3C2×D3214yes—
562C23×C3C2×D3214yes—
563C23×C3C2×D3214yes—
564C23×C3C22×C3⋊D311yescharacteristic
565C23×C3C22×C3⋊D311yescharacteristic
566C23×C3C22×C3⋊D311yescharacteristic
567C22×D3—34no—
568C22×D3—94no—
569C22×D3—91no—
570C22×D3—94no—
571C22×D3—91no—
572C22×D3—184no—
573C22×D3—184no—
574C22×D3—188no—
575C22×D3—182no—
576C22×D3—1816no—
577C22×D3—188no—
578C22×D3—182no—
579C22×D3—368no—
580C22×D3—364no—
581C22×D3—361no—
582C22×D3—368no—
583C3×D4—182no—
584C3×D4—182no—
585C3×D4—361no—
586C2×C3×C4—34no—
587C2×C3×C4—34no—
588C2×C3×C4—34no—
589C2×C3×C4—34no—
590C2×C3×C4—68no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—124no—
595#67—68no—
596#67—68no—
597#67—916no—
598#67—94no—
599#67—124no—
600#67—1816no—
601#67—182no—
602#67—188no—
603#67—182no—
604#67—188no—
605#67—182no—
606#67—1816no—
607#67—1816no—
608#67—1816no—
609#67—188no—
610#67—182no—
611#67—361no—
612C2×Dic3—22no—
613C2×Dic3—34no—
614C2×Dic3—34no—
615C2×Dic3—34no—
616C2×Dic3—41no—
617C2×Dic3—94no—
618C2×Dic3—91no—
619C2×Dic3—94no—
620C2×Dic3—91no—
621C2×Dic3—184no—
622C2×Dic3—184no—
623C2×Dic3—182no—
624C2×Dic3—188no—
625C2×Dic3—182no—
626C2×Dic3—1816no—
627C2×Dic3C22×C3⋊D311yescharacteristic
628C2×Dic3C22×C3⋊D311yescharacteristic
629C2×Dic3C22×C3⋊D311yescharacteristic
630C2×Dic3C22×C3⋊D311yescharacteristic
631D12—188no—
632D12—364no—
633C4×D3—182no—
634C4×D3—188no—
635C4×D3—188no—
636C4×D3—361no—
637C4×D3—364no—
638Dic6—182no—
639Dic6—188no—
640C2×C32—216no—
641C2×C32—28no—
642C2×C32—22no—
643C2×C32—22no—
644C2×C32—24no—
645C2×C32—24no—
646C2×C32—24no—
647C2×C32—28no—
648C2×C32—48no—
649C2×C32—48no—
650C2×C32—44no—
651C2×C32—41no—
652C2×C32C2×#23514yes—
653C2×C32C2×D3×D414yes—
654C2×C32C2×D3×D411yescharacteristic
655C2×C32C2×#23711yescharacteristic
656C2×C32#100414yes—
657C2×C32#100411yescharacteristic
658C3⋊D3—41no—
659C3⋊D3—62no—
660C3⋊D3—68no—
661C3⋊D3—128no—
662C3⋊D3—128no—
663C3⋊D3—124no—
664C3⋊D3—121no—
665C3×D3—124no—
666C24—271no—
667C24D3×C3⋊D311yescharacteristic
668#41—544no—
669C2×Q8—271no—
670C2×D4—91no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—544no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—271no—
683C22×C4—271no—
684C22×C4—271no—
685C22×C4—271no—
686C4⋊C4—271no—
687C4⋊C4—271no—
688C4⋊C4—271no—
689C4⋊C4—271no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—91no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C42—271no—
703C22×C3—28no—
704C22×C3—28no—
705C22×C3—24no—
706C22×C3—24no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—28no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—24no—
721C22×C3—28no—
722C22×C3—28no—
723C22×C3—44no—
724C22×C3—44no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—416no—
729C22×C3—432no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3#380418yescomplemented
734C22×C3#381118yes—
735C22×C3#382812yescomplemented
736C22×C3D4×C3⋊D312yes—
737C22×C3C22×D3214yes—
738C22×C3C23×C3⋊D311yescharacteristic
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—64no—
742C2×D3—98no—
743C2×D3—92no—
744C2×D3—188no—
745C2×D3—184no—
746C2×D3—184no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—188no—
750C2×D3—184no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3—364no—
761C2×D3—3616no—
762C2×D3—3632no—
763C3×C4—64no—
764C3×C4—64no—
765C3×C4—64no—
766C3×C4—64no—
767C3×C4—181no—
768C3×C4—181no—
769C3×C4—181no—
770Dic3—21no—
771Dic3—21no—
772Dic3—21no—
773Dic3—21no—
774Dic3—64no—
775Dic3—64no—
776Dic3—64no—
777Dic3—98no—
778Dic3—92no—
779Dic3—188no—
780Dic3—188no—
781Dic3—184no—
782Dic3—181no—
783C32—24no—
784C32#549014yescomplemented
785C32#559111yescharacteristic, complemented
786C23—22no—
787C23—22no—
788C23—41no—
789C23—91no—
790C23—271no—
791C23—271no—
792C23—542no—
793C23—542no—
794C23—1081no—
795C23C2×D3×C3⋊D311yescharacteristic
796C23C2×D3×C3⋊D311yescharacteristic
797C23C2×D3×C3⋊D311yescharacteristic
798Q8—542no—
799D4—182no—
800D4—182no—
801D4—274no—
802D4—361no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—62no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—121no—
817C2×C4—271no—
818C2×C4—271no—
819C2×C4—542no—
820C2×C4—542no—
821C2×C4—542no—
822C2×C4—1081no—
823C2×C3—216no—
824C2×C3—22no—
825C2×C3—22no—
826C2×C3—28no—
827C2×C3—28no—
828C2×C3—24no—
829C2×C3—24no—
830C2×C3—24no—
831C2×C3—48no—
832C2×C3—48no—
833C2×C3—41no—
834C2×C3—44no—
835C2×C3—361no—
836C2×C3C2×#380414yes—
837C2×C3C2×#381114yes—
838C2×C3#6433014yes—
839C2×C3C2×#382811yescharacteristic
840C2×C3C2×D4×C3⋊D311yescharacteristic
841C2×C3#6436111yescharacteristic
842D3—124no—
843D3—182no—
844D3—188no—
845D3—368no—
846D3—368no—
847D3—361no—
848D3—364no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—44no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—272no—
861C22—541no—
862C22—541no—
863C22—541no—
864C22—541no—
865C22—541no—
866C22—1084no—
867C22#8903112yescomplemented
868C22#8903912yes—
869C22C22×D3×C3⋊D311yescharacteristic
870C4—61no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—181no—
875C4—181no—
876C4—181no—
877C4—272no—
878C4—541no—
879C3—24no—
880C3#1059550014yescomplemented
881C3#1059596111yescharacteristic, complemented
882C2—22no—
883C2—22no—
884C2—41no—
885C2—361no—
886C2—542no—
887C2—1081no—
888C2C2×#8903111yescharacteristic
889C2C2×#8903911yescharacteristic
890C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6312C2semidirect
2. C2×#89031C2semidirect
3. C3×#64162C2semidirect
4. C2×C32×#217C2semidirect
5. #11723642C2semidirect
6. #11723639C2semidirect
7. #11723632C2semidirect
8. #11723628C2semidirect
9. #11723627C2semidirect
10. #11723626C2semidirect
11. #11723624C2semidirect
12. #11723623C2semidirect
13. #11723618C2semidirect
14. #11723612C2semidirect
15. #11723592C2semidirect
27. C2×C3×#638C22semidirect
28. C2×C3×#638C22semidirect
29. C22×C32×Dic3C22semidirect
30. C22×C32×Dic3C22semidirect
31. C2×#6293C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6289C22semidirect
35. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
43. C32×#217C22semidirect
44. C32×#217C22semidirect
45. #88807C22semidirect
46. #88807C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
61. #64162D3semidirect
74. C2×C3×#217D3semidirect
101. #6312D4semidirect
149. C2×#638C2×D3semidirect
150. C2×#638C2×D3semidirect
164. C22×C3×Dic3C2×D3semidirect
165. C22×C3×Dic3C2×D3semidirect
178. #3757C2×D3semidirect
179. #3757C2×D3semidirect
195. C3×#217C2×D3semidirect
196. C3×#217C2×D3semidirect
216. C22×C33#41semidirect
245. C2×#217C3⋊D3semidirect
405. C22×Dic3C2×C3⋊D3semidirect
406. C22×Dic3C2×C3⋊D3semidirect
431. #217C2×C3⋊D3semidirect
432. #217C2×C3⋊D3semidirect
479. C22×C32#235semidirect
482. C22×C32#237semidirect
547. C33#546semidirect
733. C22×C3#3804semidirect
735. C22×C3#3828semidirect
784. C32#5490semidirect
785. C32#5591semidirect
867. C22#89031semidirect
880. C3#10595500semidirect
881. C3#10595961semidirect

Maximal subgroups

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

subgroupindex
C22×#63122
C2×#890312
C3×#641622
C2×C32×#2172
#117236422
#117236392
#117236322
#117236282
#117236272
#117236262
#117236242
#117236232
#117236182
#117236122
#117235922
#105959613
#105955003