Finite Group Databasebeta

← #13178789

Subgroups — #13178789

Order 1728.

1968 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C2×#89046C211yesmaximal, characteristic, complemented
3C3×#64162C211yesmaximal, characteristic, complemented
4C2×C3×#3757C211yesmaximal, characteristic, complemented
5#11723727C211yesmaximal, characteristic, complemented
6#11723726C211yesmaximal, characteristic, complemented
7#11723726C211yesmaximal, characteristic, complemented
8#11723725C211yesmaximal, characteristic, complemented
9#11723725C211yesmaximal, characteristic, complemented
10#11723724C211yesmaximal, characteristic, complemented
11#11723723C211yesmaximal, characteristic, complemented
12#11723721C211yesmaximal, characteristic, complemented
13#11723720C211yesmaximal, characteristic, complemented
14#11723718C211yesmaximal, characteristic, complemented
15#11723717C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595494—31nomaximal
18#10595493—31nomaximal
19C24×C33C2211yescharacteristic
20C23×C3×C3⋊D3C2211yescharacteristic
21C2×C3×#638—24no—
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C22×C3×C3⋊Dic3C2211yescharacteristic
30C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
31C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
32C2×#6296C2211yescharacteristic, complemented
33C2×#6295C2211yescharacteristic, complemented
34C2×#6295C2211yescharacteristic, complemented
35#89046—24no—
36C2×#6294C2211yescharacteristic, complemented
37C2×#6294C2211yescharacteristic, complemented
38C2×#6294C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3757C2211yescharacteristic
42C3×#3757C2211yescharacteristic, complemented
43C3×#3757C2211yescharacteristic, complemented
44C3×#3757C2211yescharacteristic, complemented
45C3×#3757C2211yescharacteristic, complemented
46#88815C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88815C2211yescharacteristic, complemented
49#88815C2211yescharacteristic, complemented
50#88814C2211yescharacteristic, complemented
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88813C2211yescharacteristic, complemented
56C22×#638D311yescharacteristic, complemented
57C22×C3×#67—31no—
58C22×C3×#67—31no—
59C22×C3×#67—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3804—31no—
63#64162D311yescharacteristic, complemented
64C2×#3757D311yescharacteristic, complemented
65C3×#953—31no—
66C3×#953—31no—
67C3×#953—61no—
68C2×C3×#217—31no—
69C2×C3×#217—31no—
70C2×C3×#217—61no—
71#63982—31no—
72#63981—31no—
73#63980—31no—
74#63978—31no—
75#63978—31no—
76#63977—31no—
77#63976—31no—
78#63975—31no—
79#63974—31no—
80#67⋊Dic3—31no—
81#67⋊Dic3—31no—
82Dic3×#67—31no—
83Dic3×#67—31no—
84#63971—31no—
85#63971—31no—
86#63970—31no—
87#63970—31no—
88#63969—31no—
89#63969—31no—
90D3×#217—31no—
91D3×#217—31no—
92#63966—31no—
93#63964—31no—
94#63964—31no—
95#63962—31no—
96#63961—31no—
97#63959—31no—
98#63959—31no—
99#63958—31no—
100#63958—31no—
101#63953—31no—
102#63952—31no—
103#63952—31no—
104C23×C33—22no—
105C23×C33—22no—
106C23×C33—41no—
107C23×C33C2311yescharacteristic
108C23×C33C2311yescharacteristic
109C23×C33C2311yescharacteristic
110C22×C3×C3⋊D3—22no—
111C22×C3×C3⋊D3—22no—
112C22×C3×C3⋊D3—41no—
113C22×C3×C3⋊D3C2311yescharacteristic
114C22×C3×C3⋊D3C2311yescharacteristic
115C22×C3×C3⋊D3C2311yescharacteristic
116C3×#638—22no—
117C3×#638—22no—
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—22no—
121C3×#638—41no—
122C3×#638D414yescomplemented
123C2×C3×C3⋊Dic3—22no—
124C2×C3×C3⋊Dic3—22no—
125C2×C3×C3⋊Dic3—41no—
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C2×C3×C3⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊Dic3C2311yescharacteristic
132C2×C3×C3⋊Dic3C2311yescharacteristic
133C2×C3×C3⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊Dic3C2311yescharacteristic
135#6296—22no—
136#6295—22no—
137#6295—41no—
138#6294—22no—
139#6294—22no—
140#6294—41no—
141#5806—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—21no—
145C24×C32—21no—
146C24×C32—21no—
147C24×C32—41no—
148C24×C32C2×D311yescharacteristic
149C24×C32C2×D311yescharacteristic
150C24×C32C2×D311yescharacteristic
151C23×C3⋊D3C2×D311yescharacteristic
152C23×C3×D3—31no—
153C23×C3×D3—31no—
154C23×C3×D3—61no—
155C2×#638—24no—
156C2×#638C2×D311yescharacteristic
157C2×#638C2×D311yescharacteristic
158C2×#638C2×D311yescharacteristic
159C2×#638C2×D311yescharacteristic
160C2×#638C2×D311yescharacteristic
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163C22×C3⋊Dic3C2×D311yescharacteristic
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165C22×C3⋊Dic3C2×D311yescharacteristic, complemented
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—31no—
180C2×C3×#67—64no—
181C2×C3×#67—64no—
182C2×C3×#67—61no—
183C2×C3×#67—61no—
184C2×C3×#67—61no—
185C2×C3×#67—61no—
186C2×C3×#67—68no—
187C2×C3×#67—61no—
188C2×C3×#67—61no—
189C2×C3×#67—61no—
190C22×C3×Dic3—31no—
191C22×C3×Dic3—31no—
192C22×C3×Dic3—31no—
193C22×C3×Dic3—31no—
194C22×C3×Dic3—31no—
195C22×C3×Dic3—31no—
196C22×C3×Dic3—61no—
197C22×C3×Dic3—61no—
198C22×C3×Dic3—61no—
199C2×#627—31no—
200C2×#627—31no—
201C2×#627—31no—
202C2×#626—31no—
203C2×#626—31no—
204C2×#626—31no—
205C2×#626—31no—
206C2×#625—31no—
207C2×#625—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—31no—
211#3805—64no—
212#3804—64no—
213#3804—64no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—31no—
220#3757C2×D311yescharacteristic
221#3757C2×D311yescharacteristic
222#3757C2×D311yescharacteristic
223#3757C2×D311yescharacteristic, complemented
224#3757C2×D311yescharacteristic, complemented
225#3757C2×D311yescharacteristic, complemented
226#3757C2×D311yescharacteristic, complemented
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—31no—
236C3×#217—31no—
237C3×#217—31no—
238C3×#217—31no—
239C3×#217—31no—
240C3×#217—31no—
241C3×#217—61no—
242C3×#217—61no—
243C3×#217—61no—
244C3×#217—61no—
245C3×#217—61no—
246C3×#217—61no—
247C3×#217—61no—
248#3724—31no—
249#3724—31no—
250#3724—31no—
251#3724—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259Dic3⋊Dic3—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33—21no—
284C22×C33—21no—
285C22×C33—44no—
286C22×C33C2×D412yes—
287C22×C33#4112yescomplemented
288C22×C33C2411yescharacteristic
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—21no—
296C2×C3×C3⋊D3—21no—
297C2×C3×C3⋊D3—44no—
298C2×C3×C3⋊D3C2×D412yes—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3C2×D412yes—
308C22×C3×D4—91no—
309C22×#67—31no—
310C22×#67—31no—
311C22×#67—61no—
312C2×#237—91no—
313C2×#237—91no—
314C2×#235—91no—
315C3×#120—91no—
316C2×C3×C22⋊C4—91no—
317#953—31no—
318#953—31no—
319#953—61no—
320#953—91no—
321C2×#217—31no—
322C2×#217—31no—
323C2×#217—61no—
324C2×#217—91no—
325#939—91no—
326#939—91no—
327#939—91no—
328#939—91no—
329#938—91no—
330#938—91no—
331#937—91no—
332#936—91no—
333#935—91no—
334#935—91no—
335D4×Dic3—91no—
336D4×Dic3—91no—
337#930—91no—
338#929—91no—
339C4×#67—91no—
340C4×#67—91no—
341#924—91no—
342#886—91no—
343#885—91no—
344#885—91no—
345#884—91no—
346#884—91no—
347#883—91no—
348#883—91no—
349#882—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355#878—91no—
356C23×C32—22no—
357C23×C32—22no—
358C23×C32—24no—
359C23×C32—24no—
360C23×C32—22no—
361C23×C32—22no—
362C23×C32—22no—
363C23×C32—22no—
364C23×C32—21no—
365C23×C32—21no—
366C23×C32—21no—
367C23×C32—21no—
368C23×C32—21no—
369C23×C32—21no—
370C23×C32—21no—
371C23×C32—21no—
372C23×C32—21no—
373C23×C32—41no—
374C23×C32—41no—
375C23×C32—41no—
376C23×C32—42no—
377C23×C32—42no—
378C23×C32—42no—
379C23×C32—42no—
380C23×C32—44no—
381C23×C32—44no—
382C23×C32—41no—
383C23×C32—41no—
384C23×C32—41no—
385C23×C32—42no—
386C23×C32—42no—
387C23×C32—42no—
388C23×C32—44no—
389C23×C32C22×D311yescharacteristic
390C23×C32C22×D311yescharacteristic
391C23×C32C22×D311yescharacteristic
392C23×C32C22×D311yescharacteristic
393C23×C32C22×D311yescharacteristic
394C23×C32C22×D311yescharacteristic
395C23×C32C22×D311yescharacteristic
396C23×C32C22×D311yescharacteristic
397C23×C32C22×D311yescharacteristic
398C22×C3⋊D3—22no—
399C22×C3⋊D3—22no—
400C22×C3⋊D3—41no—
401C22×C3⋊D3C22×D311yescharacteristic
402C22×C3⋊D3C22×D311yescharacteristic
403C22×C3⋊D3C22×D311yescharacteristic
404C22×C3×D3—31no—
405C22×C3×D3—31no—
406C22×C3×D3—31no—
407C22×C3×D3—31no—
408C22×C3×D3—31no—
409C22×C3×D3—31no—
410C22×C3×D3—61no—
411C22×C3×D3—61no—
412C22×C3×D3—61no—
413C22×C3×D3—62no—
414C22×C3×D3—62no—
415C22×C3×D3—64no—
416C22×C3×D3—62no—
417C22×C3×D3—62no—
418C22×C3×D3—122no—
419C22×C3×D3—121no—
420C22×C3×D3—121no—
421C22×C3×D3—122no—
422#638—22no—
423#638—22no—
424#638—22no—
425#638—22no—
426#638—22no—
427#638—41no—
428#638#6714yescomplemented
429C2×C3⋊Dic3—22no—
430C2×C3⋊Dic3—22no—
431C2×C3⋊Dic3—41no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C2×C3⋊Dic3C22×D311yescharacteristic
441C3×#67—34no—
442C3×#67—34no—
443C3×#67—64no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—64no—
449C3×#67—64no—
450C3×#67—64no—
451C3×#67—62no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—62no—
455C3×#67—62no—
456C3×#67—62no—
457C3×#67—122no—
458C3×#67—122no—
459C3×#67—121no—
460C3×#67—121no—
461C3×#67—122no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—31no—
469C2×C3×Dic3—31no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—31no—
476C2×C3×Dic3—31no—
477C2×C3×Dic3—31no—
478C2×C3×Dic3—31no—
479C2×C3×Dic3—31no—
480C2×C3×Dic3—61no—
481C2×C3×Dic3—61no—
482C2×C3×Dic3—61no—
483C2×C3×Dic3—61no—
484C2×C3×Dic3—61no—
485C2×C3×Dic3—61no—
486C2×C3×Dic3—61no—
487C2×C3×Dic3—61no—
488C2×C3×Dic3—61no—
489C2×C3×Dic3—62no—
490C2×C3×Dic3—62no—
491C2×C3×Dic3—64no—
492C2×C3×Dic3—62no—
493C2×C3×Dic3—62no—
494C2×C3×Dic3—122no—
495C2×C3×Dic3—121no—
496C2×C3×Dic3—121no—
497C2×C3×Dic3—122no—
498#627—62no—
499#627—62no—
500#627—62no—
501#626—62no—
502#626—62no—
503#626—121no—
504#626—121no—
505#625—62no—
506#625—121no—
507#624—62no—
508#624—62no—
509#624—121no—
510D3×Dic3—62no—
511D3×Dic3—62no—
512D3×Dic3—62no—
513D3×Dic3—62no—
514D3×Dic3—121no—
515D3×Dic3—121no—
516#546—271noSylow
517C2×C33—22no—
518C2×C33—22no—
519C2×C33—41no—
520C2×C33C22×D411yescharacteristic
521C2×C33C2×#4111yescharacteristic
522C2×C33H(5,𝔽2)11yescharacteristic
523C3×C3⋊D3—22no—
524C3×C3⋊D3—41no—
525C3×C3⋊D3—41no—
526C24×C3—21no—
527C24×C3—21no—
528C24×C3—21no—
529C24×C3—41no—
530C24×C3—91no—
531C24×C3D3211yescharacteristic
532C24×C3D3211yescharacteristic
533C24×C3D3211yescharacteristic
534C23×D3—31no—
535C23×D3—31no—
536C23×D3—61no—
537C2×C3×D4—91no—
538C2×C3×D4—91no—
539C2×C3×D4—91no—
540C2×C3×D4—91no—
541C2×C3×D4—91no—
542C2×C3×D4—91no—
543C2×C3×D4—91no—
544C2×C3×D4—184no—
545C22×C3×C4—91no—
546C22×C3×C4—91no—
547C22×C3×C4—91no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—31no—
556C2×#67—31no—
557C2×#67—31no—
558C2×#67—31no—
559C2×#67—31no—
560C2×#67—31no—
561C2×#67—31no—
562C2×#67—61no—
563C2×#67—61no—
564C2×#67—61no—
565C2×#67—61no—
566C2×#67—61no—
567C2×#67—61no—
568C2×#67—61no—
569C2×#67—64no—
570C2×#67—64no—
571C2×#67—68no—
572C2×#67—91no—
573C2×#67—91no—
574C2×#67—91no—
575C2×#67—91no—
576C22×Dic3—31no—
577C22×Dic3—31no—
578C22×Dic3—31no—
579C22×Dic3—31no—
580C22×Dic3—31no—
581C22×Dic3—31no—
582C22×Dic3—61no—
583C22×Dic3—61no—
584C22×Dic3—61no—
585C22×Dic3—91no—
586C22×Dic3—91no—
587C22×Dic3—91no—
588#237—184no—
589#237—184no—
590#235—184no—
591C2×D12—91no—
592C2×D12—91no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—91no—
598C2×C4×D3—91no—
599C2×Dic6—91no—
600C2×Dic6—91no—
601C2×Dic6—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C22⋊C4—91no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608C3×C22⋊C4—91no—
609#217—31no—
610#217—31no—
611#217—31no—
612#217—31no—
613#217—31no—
614#217—31no—
615#217—31no—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—31no—
622#217—31no—
623#217—61no—
624#217—61no—
625#217—61no—
626#217—61no—
627#217—61no—
628#217—61no—
629#217—61no—
630#217—91no—
631#217—91no—
632#217—91no—
633#217—91no—
634#217—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645C4⋊Dic3—91no—
646C4⋊Dic3—91no—
647C4⋊Dic3—91no—
648C4⋊Dic3—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—91no—
651Dic3⋊C4—91no—
652Dic3⋊C4—91no—
653Dic3⋊C4—91no—
654Dic3⋊C4—91no—
655Dic3⋊C4—91no—
656Dic3⋊C4—91no—
657C4×Dic3—91no—
658C4×Dic3—91no—
659C4×Dic3—91no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—22no—
668C22×C32—22no—
669C22×C32—22no—
670C22×C32—22no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—21no—
675C22×C32—21no—
676C22×C32—21no—
677C22×C32—21no—
678C22×C32—21no—
679C22×C32—22no—
680C22×C32—22no—
681C22×C32—22no—
682C22×C32—21no—
683C22×C32—21no—
684C22×C32—21no—
685C22×C32—21no—
686C22×C32—21no—
687C22×C32—21no—
688C22×C32—21no—
689C22×C32—21no—
690C22×C32—21no—
691C22×C32—22no—
692C22×C32—22no—
693C22×C32—22no—
694C22×C32—22no—
695C22×C32—22no—
696C22×C32—22no—
697C22×C32—42no—
698C22×C32—42no—
699C22×C32—41no—
700C22×C32—41no—
701C22×C32—41no—
702C22×C32—41no—
703C22×C32—41no—
704C22×C32—41no—
705C22×C32—41no—
706C22×C32—41no—
707C22×C32—41no—
708C22×C32—41no—
709C22×C32—41no—
710C22×C32—41no—
711C22×C32—41no—
712C22×C32—41no—
713C22×C32—41no—
714C22×C32—42no—
715C22×C32—42no—
716C22×C32—42no—
717C22×C32—42no—
718C22×C32—42no—
719C22×C32—42no—
720C22×C32—42no—
721C22×C32—44no—
722C22×C32—44no—
723C22×C32—44no—
724C22×C32—48no—
725C22×C32—48no—
726C22×C32—48no—
727C22×C32—416no—
728C22×C32#23512yescomplemented
729C22×C32D3×D412yes—
730C22×C32D3×D412yes—
731C22×C32#23712yescomplemented
732C22×C32#23712yescomplemented
733C22×C32C2×#6712yes—
734C22×C32C23×D311yescharacteristic
735C22×C32C23×D311yescharacteristic
736C22×C32C23×D311yescharacteristic
737C2×C3⋊D3—21no—
738C2×C3⋊D3—21no—
739C2×C3⋊D3—21no—
740C2×C3⋊D3—21no—
741C2×C3⋊D3—21no—
742C2×C3⋊D3—21no—
743C2×C3⋊D3—21no—
744C2×C3⋊D3—21no—
745C2×C3⋊D3—44no—
746C2×C3⋊D3C2×#6712yes—
747C2×C3×D3—32no—
748C2×C3×D3—32no—
749C2×C3×D3—62no—
750C2×C3×D3—61no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—62no—
755C2×C3×D3—61no—
756C2×C3×D3—61no—
757C2×C3×D3—61no—
758C2×C3×D3—61no—
759C2×C3×D3—61no—
760C2×C3×D3—61no—
761C2×C3×D3—61no—
762C2×C3×D3—61no—
763C2×C3×D3—61no—
764C2×C3×D3—61no—
765C2×C3×D3—61no—
766C2×C3×D3—61no—
767C2×C3×D3—121no—
768C2×C3×D3—121no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774C2×C3×D3—124no—
775C2×C3×D3—124no—
776C2×C3×D3—128no—
777C3⋊Dic3—21no—
778C3⋊Dic3—21no—
779C3⋊Dic3—21no—
780C3⋊Dic3—21no—
781C3⋊Dic3—21no—
782C3⋊Dic3—21no—
783C3⋊Dic3—21no—
784C3⋊Dic3—21no—
785C3⋊Dic3C2×#6712yes—
786C3×Dic3—32no—
787C3×Dic3—32no—
788C3×Dic3—62no—
789C3×Dic3—62no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—61no—
795C3×Dic3—61no—
796C3×Dic3—61no—
797C3×Dic3—61no—
798C3×Dic3—61no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—61no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—121no—
807C3×Dic3—121no—
808C3×Dic3—121no—
809C3×Dic3—121no—
810C3×Dic3—121no—
811C3×Dic3—121no—
812C3×Dic3—121no—
813C2×#41—271no—
814C22×D4—91no—
815#124—271no—
816#123—271no—
817#123—271no—
818C22⋊Q8—271no—
819#121—271no—
820#121—271no—
821#121—271no—
822#120—91no—
823#120—271no—
824C4×D4—271no—
825C4×D4—271no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—271no—
828C33#54611yescharacteristic, complemented, Sylow
829C23×C3—24no—
830C23×C3—24no—
831C23×C3—22no—
832C23×C3—22no—
833C23×C3—22no—
834C23×C3—22no—
835C23×C3—22no—
836C23×C3—22no—
837C23×C3—21no—
838C23×C3—21no—
839C23×C3—21no—
840C23×C3—21no—
841C23×C3—21no—
842C23×C3—21no—
843C23×C3—21no—
844C23×C3—21no—
845C23×C3—21no—
846C23×C3—42no—
847C23×C3—42no—
848C23×C3—42no—
849C23×C3—42no—
850C23×C3—44no—
851C23×C3—44no—
852C23×C3—41no—
853C23×C3—41no—
854C23×C3—41no—
855C23×C3—42no—
856C23×C3—42no—
857C23×C3—42no—
858C23×C3—44no—
859C23×C3—41no—
860C23×C3—41no—
861C23×C3—41no—
862C23×C3—91no—
863C23×C3—91no—
864C23×C3—91no—
865C23×C3—182no—
866C23×C3—182no—
867C23×C3—361no—
868C23×C3C2×D3211yescharacteristic
869C23×C3C2×D3211yescharacteristic
870C23×C3C2×D3211yescharacteristic
871C23×C3C2×D3211yescharacteristic
872C23×C3C2×D3211yescharacteristic
873C23×C3C2×D3211yescharacteristic
874C23×C3C2×D3211yescharacteristic
875C23×C3C2×D3211yescharacteristic
876C23×C3C2×D3211yescharacteristic
877C22×D3—31no—
878C22×D3—31no—
879C22×D3—31no—
880C22×D3—31no—
881C22×D3—31no—
882C22×D3—31no—
883C22×D3—61no—
884C22×D3—61no—
885C22×D3—61no—
886C22×D3—62no—
887C22×D3—62no—
888C22×D3—64no—
889C22×D3—62no—
890C22×D3—62no—
891C22×D3—122no—
892C22×D3—121no—
893C22×D3—121no—
894C22×D3—122no—
895C3×D4—94no—
896C3×D4—182no—
897C3×D4—182no—
898C3×D4—182no—
899C3×D4—182no—
900C3×D4—182no—
901C3×D4—361no—
902C2×C3×C4—91no—
903C2×C3×C4—91no—
904C2×C3×C4—91no—
905C2×C3×C4—91no—
906C2×C3×C4—91no—
907C2×C3×C4—91no—
908C2×C3×C4—91no—
909C2×C3×C4—91no—
910C2×C3×C4—91no—
911C2×C3×C4—182no—
912C2×C3×C4—182no—
913C2×C3×C4—361no—
914#67—34no—
915#67—34no—
916#67—64no—
917#67—62no—
918#67—62no—
919#67—62no—
920#67—62no—
921#67—64no—
922#67—64no—
923#67—64no—
924#67—62no—
925#67—62no—
926#67—62no—
927#67—62no—
928#67—62no—
929#67—62no—
930#67—122no—
931#67—122no—
932#67—121no—
933#67—121no—
934#67—122no—
935#67—182no—
936#67—182no—
937#67—361no—
938#67—361no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—31no—
946C2×Dic3—31no—
947C2×Dic3—31no—
948C2×Dic3—31no—
949C2×Dic3—31no—
950C2×Dic3—31no—
951C2×Dic3—31no—
952C2×Dic3—31no—
953C2×Dic3—31no—
954C2×Dic3—31no—
955C2×Dic3—31no—
956C2×Dic3—31no—
957C2×Dic3—61no—
958C2×Dic3—61no—
959C2×Dic3—61no—
960C2×Dic3—61no—
961C2×Dic3—61no—
962C2×Dic3—61no—
963C2×Dic3—61no—
964C2×Dic3—61no—
965C2×Dic3—61no—
966C2×Dic3—62no—
967C2×Dic3—62no—
968C2×Dic3—64no—
969C2×Dic3—62no—
970C2×Dic3—62no—
971C2×Dic3—122no—
972C2×Dic3—121no—
973C2×Dic3—121no—
974C2×Dic3—122no—
975C2×Dic3—182no—
976C2×Dic3—182no—
977C2×Dic3—361no—
978D12—182no—
979D12—361no—
980C4×D3—182no—
981C4×D3—182no—
982C4×D3—182no—
983C4×D3—182no—
984C4×D3—361no—
985C4×D3—361no—
986Dic6—182no—
987Dic6—182no—
988Dic6—182no—
989C2×C32—22no—
990C2×C32—22no—
991C2×C32—24no—
992C2×C32—24no—
993C2×C32—22no—
994C2×C32—22no—
995C2×C32—22no—
996C2×C32—22no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—21no—
1003C2×C32—21no—
1004C2×C32—21no—
1005C2×C32—21no—
1006C2×C32—41no—
1007C2×C32—41no—
1008C2×C32—41no—
1009C2×C32—42no—
1010C2×C32—42no—
1011C2×C32—42no—
1012C2×C32—42no—
1013C2×C32—44no—
1014C2×C32—44no—
1015C2×C32—42no—
1016C2×C32—42no—
1017C2×C32—42no—
1018C2×C32—44no—
1019C2×C32—41no—
1020C2×C32—41no—
1021C2×C32—41no—
1022C2×C32C2×#23511yescharacteristic
1023C2×C32C2×D3×D411yescharacteristic
1024C2×C32C2×D3×D411yescharacteristic
1025C2×C32C2×#23711yescharacteristic
1026C2×C32C2×#23711yescharacteristic
1027C2×C32#100411yescharacteristic
1028C2×C32#100411yescharacteristic
1029C2×C32#100411yescharacteristic
1030C2×C32C22×#6711yescharacteristic
1031C3⋊D3—22no—
1032C3⋊D3—41no—
1033C3⋊D3—41no—
1034C3×D3—62no—
1035C3×D3—62no—
1036C3×D3—122no—
1037C3×D3—122no—
1038C3×D3—121no—
1039C3×D3—121no—
1040C3×D3—121no—
1041C3×D3—121no—
1042C3×D3—241no—
1043C24—91no—
1044C24#111311yescharacteristic
1045#41—544no—
1046C2×Q8—271no—
1047C2×D4—91no—
1048C2×D4—91no—
1049C2×D4—91no—
1050C2×D4—91no—
1051C2×D4—91no—
1052C2×D4—91no—
1053C2×D4—91no—
1054C2×D4—184no—
1055C2×D4—271no—
1056C2×D4—271no—
1057C22×C4—91no—
1058C22×C4—91no—
1059C22×C4—91no—
1060C22×C4—271no—
1061C22×C4—271no—
1062C22×C4—271no—
1063C4⋊C4—271no—
1064C4⋊C4—271no—
1065C4⋊C4—271no—
1066C4⋊C4—271no—
1067C22⋊C4—91no—
1068C22⋊C4—91no—
1069C22⋊C4—91no—
1070C22⋊C4—91no—
1071C22⋊C4—91no—
1072C22⋊C4—91no—
1073C22⋊C4—91no—
1074C22⋊C4—271no—
1075C22⋊C4—271no—
1076C22⋊C4—271no—
1077C22⋊C4—271no—
1078C22⋊C4—271no—
1079C42—271no—
1080C22×C3—22no—
1081C22×C3—22no—
1082C22×C3—22no—
1083C22×C3—22no—
1084C22×C3—21no—
1085C22×C3—21no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—21no—
1092C22×C3—21no—
1093C22×C3—21no—
1094C22×C3—21no—
1095C22×C3—21no—
1096C22×C3—22no—
1097C22×C3—22no—
1098C22×C3—22no—
1099C22×C3—21no—
1100C22×C3—21no—
1101C22×C3—21no—
1102C22×C3—21no—
1103C22×C3—21no—
1104C22×C3—21no—
1105C22×C3—21no—
1106C22×C3—21no—
1107C22×C3—21no—
1108C22×C3—21no—
1109C22×C3—21no—
1110C22×C3—21no—
1111C22×C3—22no—
1112C22×C3—22no—
1113C22×C3—22no—
1114C22×C3—22no—
1115C22×C3—22no—
1116C22×C3—22no—
1117C22×C3—41no—
1118C22×C3—41no—
1119C22×C3—41no—
1120C22×C3—41no—
1121C22×C3—41no—
1122C22×C3—41no—
1123C22×C3—41no—
1124C22×C3—41no—
1125C22×C3—41no—
1126C22×C3—41no—
1127C22×C3—41no—
1128C22×C3—41no—
1129C22×C3—41no—
1130C22×C3—41no—
1131C22×C3—42no—
1132C22×C3—42no—
1133C22×C3—42no—
1134C22×C3—42no—
1135C22×C3—42no—
1136C22×C3—42no—
1137C22×C3—42no—
1138C22×C3—44no—
1139C22×C3—44no—
1140C22×C3—44no—
1141C22×C3—48no—
1142C22×C3—48no—
1143C22×C3—48no—
1144C22×C3—416no—
1145C22×C3—41no—
1146C22×C3—42no—
1147C22×C3—42no—
1148C22×C3—92no—
1149C22×C3—181no—
1150C22×C3—181no—
1151C22×C3—181no—
1152C22×C3—181no—
1153C22×C3—181no—
1154C22×C3—181no—
1155C22×C3—181no—
1156C22×C3—181no—
1157C22×C3—364no—
1158C22×C3#380412yescomplemented
1159C22×C3#380412yescomplemented
1160C22×C3#380512yescomplemented
1161C22×C3D3×#6712yes—
1162C22×C3D3×#6712yes—
1163C22×C3#381112yes—
1164C22×C3C22×D3211yescharacteristic
1165C22×C3C22×D3211yescharacteristic
1166C22×C3C22×D3211yescharacteristic
1167C2×D3—32no—
1168C2×D3—32no—
1169C2×D3—62no—
1170C2×D3—61no—
1171C2×D3—61no—
1172C2×D3—61no—
1173C2×D3—61no—
1174C2×D3—62no—
1175C2×D3—61no—
1176C2×D3—61no—
1177C2×D3—61no—
1178C2×D3—61no—
1179C2×D3—61no—
1180C2×D3—61no—
1181C2×D3—61no—
1182C2×D3—61no—
1183C2×D3—61no—
1184C2×D3—61no—
1185C2×D3—61no—
1186C2×D3—61no—
1187C2×D3—121no—
1188C2×D3—121no—
1189C2×D3—121no—
1190C2×D3—121no—
1191C2×D3—121no—
1192C2×D3—121no—
1193C2×D3—121no—
1194C2×D3—124no—
1195C2×D3—124no—
1196C2×D3—128no—
1197C3×C4—92no—
1198C3×C4—181no—
1199C3×C4—181no—
1200C3×C4—181no—
1201C3×C4—181no—
1202C3×C4—181no—
1203C3×C4—181no—
1204C3×C4—181no—
1205C3×C4—181no—
1206Dic3—32no—
1207Dic3—32no—
1208Dic3—62no—
1209Dic3—62no—
1210Dic3—61no—
1211Dic3—61no—
1212Dic3—61no—
1213Dic3—61no—
1214Dic3—61no—
1215Dic3—61no—
1216Dic3—61no—
1217Dic3—61no—
1218Dic3—61no—
1219Dic3—61no—
1220Dic3—61no—
1221Dic3—61no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—121no—
1227Dic3—121no—
1228Dic3—121no—
1229Dic3—121no—
1230Dic3—121no—
1231Dic3—121no—
1232Dic3—121no—
1233C32—21no—
1234C32—21no—
1235C32—21no—
1236C32—41no—
1237C32#549011yescharacteristic, complemented
1238C32#559111yescharacteristic, complemented
1239C32#580611yescharacteristic, complemented
1240C23—22no—
1241C23—22no—
1242C23—41no—
1243C23—91no—
1244C23—91no—
1245C23—91no—
1246C23—182no—
1247C23—182no—
1248C23—361no—
1249C23C2×#111311yescharacteristic
1250C23C2×#111311yescharacteristic
1251C23C2×#111311yescharacteristic
1252Q8—542no—
1253D4—94no—
1254D4—182no—
1255D4—182no—
1256D4—182no—
1257D4—182no—
1258D4—182no—
1259D4—361no—
1260D4—542no—
1261D4—1081no—
1262C2×C4—91no—
1263C2×C4—91no—
1264C2×C4—91no—
1265C2×C4—91no—
1266C2×C4—91no—
1267C2×C4—91no—
1268C2×C4—91no—
1269C2×C4—91no—
1270C2×C4—91no—
1271C2×C4—182no—
1272C2×C4—182no—
1273C2×C4—361no—
1274C2×C4—542no—
1275C2×C4—542no—
1276C2×C4—1081no—
1277C2×C3—24no—
1278C2×C3—24no—
1279C2×C3—22no—
1280C2×C3—22no—
1281C2×C3—22no—
1282C2×C3—22no—
1283C2×C3—22no—
1284C2×C3—22no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—21no—
1292C2×C3—21no—
1293C2×C3—21no—
1294C2×C3—42no—
1295C2×C3—42no—
1296C2×C3—42no—
1297C2×C3—42no—
1298C2×C3—44no—
1299C2×C3—44no—
1300C2×C3—42no—
1301C2×C3—42no—
1302C2×C3—42no—
1303C2×C3—44no—
1304C2×C3—41no—
1305C2×C3—41no—
1306C2×C3—41no—
1307C2×C3—41no—
1308C2×C3—41no—
1309C2×C3—41no—
1310C2×C3—182no—
1311C2×C3—361no—
1312C2×C3—361no—
1313C2×C3C2×#380411yescharacteristic
1314C2×C3C2×#380411yescharacteristic
1315C2×C3C2×#380511yescharacteristic
1316C2×C3C2×D3×#6711yescharacteristic
1317C2×C3C2×D3×#6711yescharacteristic
1318C2×C3C2×#381111yescharacteristic
1319C2×C3#6433011yescharacteristic
1320C2×C3#6433011yescharacteristic
1321C2×C3#6433011yescharacteristic
1322D3—62no—
1323D3—62no—
1324D3—122no—
1325D3—122no—
1326D3—121no—
1327D3—121no—
1328D3—121no—
1329D3—121no—
1330D3—241no—
1331C22—21no—
1332C22—21no—
1333C22—21no—
1334C22—21no—
1335C22—21no—
1336C22—21no—
1337C22—21no—
1338C22—44no—
1339C22—92no—
1340C22—181no—
1341C22—181no—
1342C22—181no—
1343C22—181no—
1344C22—181no—
1345C22—181no—
1346C22—181no—
1347C22—181no—
1348C22—364no—
1349C22#8904612yescomplemented
1350C22#8904912yes—
1351C22C22×#111311yescharacteristic
1352C4—92no—
1353C4—181no—
1354C4—181no—
1355C4—181no—
1356C4—181no—
1357C4—181no—
1358C4—181no—
1359C4—181no—
1360C4—181no—
1361C3—21no—
1362C3—21no—
1363C3—21no—
1364C3—41no—
1365C3#1059549311yescharacteristic, complemented
1366C3#1059549411yescharacteristic, complemented
1367C3#1059550011yescharacteristic, complemented
1368C2—22no—
1369C2—22no—
1370C2—41no—
1371C2—182no—
1372C2—361no—
1373C2—361no—
1374C2C2×#8904611yescharacteristic
1375C2C2×#8904911yescharacteristic
1376C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24#1113
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×C3×#638C2semidirect
2. C2×#89046C2semidirect
3. C3×#64162C2semidirect
4. C2×C3×#3757C2semidirect
5. #11723727C2semidirect
6. #11723726C2semidirect
7. #11723726C2semidirect
8. #11723725C2semidirect
9. #11723725C2semidirect
10. #11723724C2semidirect
11. #11723723C2semidirect
12. #11723721C2semidirect
13. #11723720C2semidirect
14. #11723718C2semidirect
15. #11723717C2semidirect
27. C2×C3×#638C22semidirect
28. C2×C3×#638C22semidirect
30. C22×C3×C3⋊Dic3C22semidirect
31. C22×C3×C3⋊Dic3C22semidirect
32. C2×#6296C22semidirect
33. C2×#6295C22semidirect
34. C2×#6295C22semidirect
36. C2×#6294C22semidirect
37. C2×#6294C22semidirect
38. C2×#6294C22semidirect
42. C3×#3757C22semidirect
43. C3×#3757C22semidirect
44. C3×#3757C22semidirect
45. C3×#3757C22semidirect
46. #88815C22semidirect
47. #88815C22semidirect
48. #88815C22semidirect
49. #88815C22semidirect
50. #88814C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88813C22semidirect
56. C22×#638D3semidirect
63. #64162D3semidirect
64. C2×#3757D3semidirect
122. C3×#638D4semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
164. C22×C3⋊Dic3C2×D3semidirect
165. C22×C3⋊Dic3C2×D3semidirect
223. #3757C2×D3semidirect
224. #3757C2×D3semidirect
225. #3757C2×D3semidirect
226. #3757C2×D3semidirect
287. C22×C33#41semidirect
428. #638#67semidirect
728. C22×C32#235semidirect
731. C22×C32#237semidirect
732. C22×C32#237semidirect
828. C33#546semidirect
1158. C22×C3#3804semidirect
1159. C22×C3#3804semidirect
1160. C22×C3#3805semidirect
1237. C32#5490semidirect
1238. C32#5591semidirect
1239. C32#5806semidirect
1349. C22#89046semidirect
1365. C3#10595493semidirect
1366. C3#10595494semidirect
1367. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C2×#890462
C3×#641622
C2×C3×#37572
#117237272
#117237262
#117237252
#117237242
#117237232
#117237212
#117237202
#117237182
#117237172
#105955003
#105954943
#105954933