Finite Group Databasebeta

← #13172722

Subgroups — #13172722

Order 1728.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89031C211yesmaximal, characteristic, complemented
2C2×#88955C211yesmaximal, characteristic, complemented
3#11723729C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723623C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8C3×#63952C211yesmaximal, characteristic, complemented
9#11723002C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722991C211yesmaximal, characteristic, complemented
12#11722972C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic, complemented
14#11722906C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595296—31nomaximal
17#10595078—31nomaximal
18#10594283—31nomaximal
19C22×#1113C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6289C2211yescharacteristic, complemented
31C2×#6289C2211yescharacteristic, complemented
32#89031—24no—
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#624C2211yescharacteristic
37C2×C3×#624C2211yescharacteristic, complemented
38#88955—24no—
39C32×#217C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3828—31no—
57C2×#3811—31no—
58C2×#3804—31no—
59C2×#3804—31no—
60C2×#3804—61no—
61C2×D3×D12—31no—
62C2×D3×D12—31no—
63#64146—31no—
64#64093—31no—
65C3×#939—31no—
66C3×#938—31no—
67C3×#930—31no—
68C3×C4×#67—31no—
69C3×#884—31no—
70C3×#67⋊C4—31no—
71#63983—31no—
72#63983—31no—
73#63983—31no—
74#63983—31no—
75#63983—31no—
76#63983—61no—
77#63978D311yescharacteristic, complemented
78#63974—31no—
79#63969—31no—
80#63959—31no—
81#63958—31no—
82#63958—31no—
83#63958—61no—
84#63958D311yescharacteristic, complemented
85#63952D311yescharacteristic, complemented
86#63921—31no—
87#63921—31no—
88#63921—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91#63904—31no—
92C4×#626—31no—
93#63897—31no—
94#63895—31no—
95#63894—31no—
96#63884—31no—
97#63860—31no—
98#63857—31no—
99#63854—31no—
100#63853—31no—
101#63853—31no—
102#63852—31no—
103#63851—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×#1113—22no—
111C2×#1113—22no—
112C2×#1113—41no—
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C32×#67—41no—
125C2×C32×Dic3—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6293—22no—
132#6292—22no—
133#6292D414yescomplemented
134#6289—22no—
135#6289—41no—
136Dic3×C3⋊D3—22no—
137C3×#626—22no—
138C3×#626—22no—
139C3×#624—22no—
140C3×#624—41no—
141#5612—91no—
142#5610—91no—
143#5550—91no—
144C23×C3⋊D3—31no—
145C22×D32—31no—
146C22×D32—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—61no—
151C2×C32×D4—31no—
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—61no—
157C2×#638—61no—
158C2×#638—61no—
159C2×#638—121no—
160C2×#638C2×D311yescharacteristic
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163#3828—64no—
164C2×C4⋊(C3⋊D3)—31no—
165C2×C4⋊(C3⋊D3)—31no—
166C2×C4×C3⋊D3—31no—
167C2×C4×C3⋊D3—31no—
168C2×C4×C3⋊D3—31no—
169C2×#634—31no—
170C2×C3×#67—21no—
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—61no—
180C2×C3×#67—61no—
181C2×C3×#67—61no—
182C2×C3×#67C2×D311yescharacteristic, complemented
183C2×C3×#67C2×D311yescharacteristic, complemented
184C22×C3×Dic3—21no—
185C22×C3×Dic3C2×D311yescharacteristic, complemented
186C22×C3×Dic3C2×D311yescharacteristic, complemented
187C2×C3×D12—31no—
188C2×C3×D12—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191C2×C3×C4×D3—31no—
192C2×C3×C4×D3—31no—
193#3811—64no—
194C2×#627—31no—
195C2×#627—31no—
196C2×#627—61no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—61no—
202C2×#626—61no—
203C2×#626C2×D311yescharacteristic
204C2×#626C2×D311yescharacteristic
205C2×#624—31no—
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—61no—
210C2×#624—61no—
211C2×#624C2×D311yescharacteristic
212C2×#624C2×D311yescharacteristic, complemented
213#3804—64no—
214#3804—64no—
215#3804—68no—
216C2×D3×Dic3—31no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—61no—
219D3×D12—64no—
220D3×D12—64no—
221C32×C22⋊C4—31no—
222#3757—31no—
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3750—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217C2×D311yescharacteristic, complemented
231C3×#217C2×D311yescharacteristic, complemented
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246#3724C2×D311yescharacteristic, complemented
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3C2×D311yescharacteristic, complemented
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—61no—
258#3722C2×D311yescharacteristic
259#3722C2×D311yescharacteristic, complemented
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—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—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)C2×D412yes—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3C2×D412yes—
293C2×C3×C3⋊D3#4112yescomplemented
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297#1113—44no—
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3C2×D412yes—
308C2×#237—91no—
309C2×D3×D4—91no—
310C2×D3×D4—91no—
311C2×#235—91no—
312C2×#235—91no—
313C2×#235—181no—
314C22×D12—91no—
315C3×#121—91no—
316C3×#121—91no—
317C3×C4×D4—91no—
318#939—31no—
319#938—31no—
320#938—91no—
321#937—91no—
322#937—91no—
323#937—91no—
324#937—91no—
325#937—91no—
326#937—91no—
327#937—181no—
328#936—91no—
329#935—91no—
330#930—31no—
331C4×#67—31no—
332C4×#67—91no—
333C2×(C2×D3)⋊C4—91no—
334#924—91no—
335#897—91no—
336#896—91no—
337#894—91no—
338#894—91no—
339#894—91no—
340#893—91no—
341#885—91no—
342#884—31no—
343#884—91no—
344#884—91no—
345#884—181no—
346#883—91no—
347#883—91no—
348#67⋊C4—31no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#875—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—41no—
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C22×C3⋊D3—31no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—61no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—62no—
371C22×C3⋊D3—62no—
372C22×C3⋊D3—121no—
373C22×C3⋊D3—121no—
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—21no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—61no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3C22×D311yescharacteristic
388C22×C3×D3C22×D311yescharacteristic
389C2×D32—62no—
390C2×D32—62no—
391C2×D32—62no—
392C2×D32—62no—
393C2×D32—62no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—122no—
400C2×D32—122no—
401C2×D32—121no—
402C2×D32—121no—
403C2×D32—122no—
404C2×D32—121no—
405C2×D32—121no—
406C2×D32—121no—
407C32×D4—121no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—62no—
414#638—22no—
415#638—22no—
416#638—41no—
417#638—62no—
418#638—62no—
419#638—62no—
420#638—64no—
421#638—122no—
422#638—122no—
423#638—124no—
424C2×C3⋊Dic3—31no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—61no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—121no—
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C4⋊(C3⋊D3)—34no—
435C4⋊(C3⋊D3)—62no—
436C4×C3⋊D3—62no—
437C4×C3⋊D3—62no—
438C4×C3⋊D3—121no—
439#634—62no—
440C3×#67—41no—
441C3×#67—41no—
442C3×#67—42no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—64no—
449C3×#67—62no—
450C3×#67—122no—
451C3×#67—121no—
452C3×#67—121no—
453C3×#67—122no—
454C2×C3×Dic3—24no—
455C2×C3×Dic3—22no—
456C2×C3×Dic3—22no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
459C2×C3×Dic3—21no—
460C2×C3×Dic3—21no—
461C2×C3×Dic3—21no—
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—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C3×D12—62no—
482C3×D12—62no—
483C3×C4×D3—62no—
484C3×C4×D3—62no—
485C3×C4×D3—121no—
486C3×C4×D3—121no—
487#627—64no—
488#627—62no—
489#627—62no—
490#626—22no—
491#626—22no—
492#626—34no—
493#626—34no—
494#626—64no—
495#626—62no—
496#626—62no—
497#626—122no—
498#624—22no—
499#624—41no—
500#624—62no—
501#624—62no—
502#624—64no—
503#624—121no—
504#624—121no—
505#624—122no—
506D3×Dic3—62no—
507D3×Dic3—62no—
508D3×Dic3—64no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—22no—
515C3×C3⋊D3—22no—
516C3×C3⋊D3—22no—
517C3×C3⋊D3—41no—
518C32×D3—41no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—91no—
522C23×D3—91no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—181no—
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—61no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C22×C3×C4—31no—
535C22×C3×C4—31no—
536C22×C3×C4—61no—
537C22×C3×C4—91no—
538C22×C3×C4—91no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—61no—
548C2×#67—61no—
549C2×#67—61no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—361no—
559C2×#67D3211yescharacteristic, complemented
560C22×Dic3—91no—
561C22×Dic3D3211yescharacteristic, complemented
562#237—184no—
563D3×D4—184no—
564D3×D4—184no—
565#235—184no—
566#235—184no—
567#235—188no—
568C2×D12—31no—
569C2×D12—31no—
570C2×D12—91no—
571C2×D12—91no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—181no—
575C2×D12—181no—
576C2×D12—184no—
577C2×C4×D3—31no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—91no—
589C2×C4×D3—181no—
590C2×C4×D3—181no—
591C2×C4×D3—181no—
592C2×Dic6—91no—
593C2×Dic6—91no—
594C2×Dic6—91no—
595C2×Dic6—181no—
596C3×C4⋊C4—91no—
597C3×C4⋊C4—91no—
598C3×C4⋊C4—91no—
599C3×C22⋊C4—31no—
600C3×C22⋊C4—31no—
601C3×C22⋊C4—61no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C22⋊C4—91no—
606C3×C42—91no—
607#217—31no—
608#217—31no—
609#217—91no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—91no—
614#217—91no—
615#217—91no—
616#217—181no—
617#217D3211yescharacteristic, complemented
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—31no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—181no—
639(C2×D3)⋊C4—181no—
640(C2×D3)⋊C4—181no—
641C4⋊Dic3—31no—
642C4⋊Dic3—31no—
643C4⋊Dic3—91no—
644Dic3⋊C4—31no—
645Dic3⋊C4—31no—
646Dic3⋊C4—31no—
647Dic3⋊C4—31no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—181no—
651C4×Dic3—31no—
652C4×Dic3—31no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—42no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—81no—
680C22×C32—81no—
681C22×C32C23×D311yescharacteristic
682C22×C32C23×D311yescharacteristic
683C22×C32C23×D311yescharacteristic
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—32no—
692C2×C3⋊D3—32no—
693C2×C3⋊D3—32no—
694C2×C3⋊D3—62no—
695C2×C3⋊D3—62no—
696C2×C3⋊D3—62no—
697C2×C3⋊D3—61no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—122no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—124no—
711C2×C3⋊D3—241no—
712C2×C3⋊D3—241no—
713C2×C3⋊D3#23512yescomplemented
714C2×C3⋊D3D3×D412yes—
715C2×C3×D3—22no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—32no—
723C2×C3×D3—32no—
724C2×C3×D3—32no—
725C2×C3×D3—32no—
726C2×C3×D3—41no—
727C2×C3×D3—41no—
728C2×C3×D3—62no—
729C2×C3×D3—62no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—121no—
745C2×C3×D3—121no—
746C2×C3×D3—121no—
747C2×C3×D3—121no—
748C2×C3×D3—121no—
749C2×C3×D3—121no—
750C2×C3×D3—121no—
751D32—124no—
752D32—124no—
753D32—128no—
754D32—124no—
755D32—124no—
756D32—124no—
757C32×C4—32no—
758C32×C4—61no—
759C32×C4—61no—
760C32×C4—61no—
761C32×C4—61no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—61no—
766C3⋊Dic3—62no—
767C3⋊Dic3—61no—
768C3⋊Dic3—61no—
769C3⋊Dic3—121no—
770C3⋊Dic3—121no—
771C3⋊Dic3—122no—
772C3×Dic3—22no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—21no—
781C3×Dic3—22no—
782C3×Dic3—41no—
783C3×Dic3—41no—
784C3×Dic3—41no—
785C3×Dic3—62no—
786C3×Dic3—62no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—121no—
794C3×Dic3D3×D412yes—
795C3×Dic3D3×D412yes—
796C2×#41—271no—
797C22×D4—271no—
798#124—271no—
799#123—271no—
800#123—271no—
801C22⋊Q8—271no—
802#121—91no—
803#121—91no—
804#121—271no—
805#120—271no—
806#120—271no—
807C4×D4—91no—
808C4×D4—271no—
809C2×C22⋊C4—271no—
810C2×C22⋊C4—271no—
811C33#54611yescharacteristic, complemented, Sylow
812C23×C3—21no—
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—31no—
816C23×C3—31no—
817C23×C3—41no—
818C23×C3—61no—
819C23×C3—91no—
820C23×C3—91no—
821C23×C3—91no—
822C23×C3C2×D3211yescharacteristic
823C23×C3C2×D3211yescharacteristic
824C23×C3C2×D3211yescharacteristic
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—31no—
829C22×D3—31no—
830C22×D3—31no—
831C22×D3—61no—
832C22×D3—61no—
833C22×D3—61no—
834C22×D3—91no—
835C22×D3—91no—
836C22×D3—91no—
837C22×D3—181no—
838C22×D3—181no—
839C22×D3—181no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—182no—
843C22×D3—182no—
844C22×D3—182no—
845C22×D3—182no—
846C22×D3—182no—
847C22×D3—182no—
848C22×D3—182no—
849C22×D3—182no—
850C22×D3—182no—
851C22×D3—182no—
852C22×D3—361no—
853C22×D3—362no—
854C22×D3—362no—
855C22×D3—361no—
856C22×D3—361no—
857C22×D3—361no—
858C22×D3—361no—
859C22×D3—361no—
860C22×D3—361no—
861C22×D3—362no—
862C22×D3C2×D3211yescharacteristic
863C3×D4—121no—
864C3×D4—121no—
865C3×D4—122no—
866C3×D4—182no—
867C3×D4—182no—
868C3×D4—182no—
869C3×D4—182no—
870C3×D4—361no—
871C2×C3×C4—31no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—61no—
882C2×C3×C4—61no—
883C2×C3×C4—61no—
884C2×C3×C4—61no—
885C2×C3×C4—61no—
886C2×C3×C4—62no—
887C2×C3×C4—62no—
888C2×C3×C4—64no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—91no—
892C2×C3×C4—182no—
893C2×C3×C4—361no—
894#67—41no—
895#67—62no—
896#67—62no—
897#67—62no—
898#67—62no—
899#67—62no—
900#67—64no—
901#67—62no—
902#67—94no—
903#67—122no—
904#67—121no—
905#67—121no—
906#67—122no—
907#67—182no—
908#67—182no—
909#67—182no—
910#67—182no—
911#67—184no—
912#67—362no—
913#67—362no—
914#67—364no—
915C2×Dic3—22no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—61no—
923C2×Dic3—61no—
924C2×Dic3—61no—
925C2×Dic3—91no—
926C2×Dic3—91no—
927C2×Dic3—91no—
928C2×Dic3—181no—
929C2×Dic3—181no—
930C2×Dic3—181no—
931C2×Dic3—182no—
932C2×Dic3—361no—
933C2×Dic3C2×D3211yescharacteristic
934C2×Dic3C2×D3211yescharacteristic
935C2×Dic3C2×D3211yescharacteristic
936C2×Dic3C2×D3211yescharacteristic
937C2×Dic3C2×D3211yescharacteristic
938D12—62no—
939D12—62no—
940D12—94no—
941D12—94no—
942D12—184no—
943D12—182no—
944D12—182no—
945D12—362no—
946C4×D3—62no—
947C4×D3—62no—
948C4×D3—121no—
949C4×D3—121no—
950C4×D3—182no—
951C4×D3—182no—
952C4×D3—182no—
953C4×D3—184no—
954C4×D3—182no—
955C4×D3—182no—
956C4×D3—184no—
957C4×D3—361no—
958C4×D3—361no—
959C4×D3—361no—
960C4×D3—362no—
961Dic6—182no—
962Dic6—182no—
963Dic6—184no—
964Dic6—182no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—41no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—42no—
979C2×C32—41no—
980C2×C32—41no—
981C2×C32—81no—
982C2×C32—81no—
983C2×C32—82no—
984C2×C32—121no—
985C2×C32C2×#23511yescharacteristic
986C2×C32C2×D3×D411yescharacteristic
987C2×C32C2×D3×D411yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32#100411yescharacteristic
990C2×C32#100411yescharacteristic
991C2×C32D3×#4111yescharacteristic
992C2×C32D3×#4111yescharacteristic
993C2×C32#100911yescharacteristic
994C3⋊D3—22no—
995C3⋊D3—22no—
996C3⋊D3—41no—
997C3⋊D3—62no—
998C3⋊D3—62no—
999C3⋊D3—62no—
1000C3⋊D3—122no—
1001C3⋊D3—122no—
1002C3⋊D3—122no—
1003C3⋊D3—242no—
1004C3×D3—42no—
1005C3×D3—41no—
1006C3×D3—41no—
1007C3×D3—62no—
1008C3×D3—62no—
1009C3×D3—62no—
1010C3×D3—62no—
1011C3×D3—122no—
1012C3×D3—122no—
1013C3×D3—121no—
1014C3×D3—121no—
1015C3×D3—241no—
1016C24—271no—
1017C24—271no—
1018#41—544no—
1019C2×Q8—271no—
1020C2×D4—31no—
1021C2×D4—91no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—544no—
1030C22×C4—31no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—271no—
1034C22×C4—271no—
1035C22×C4—271no—
1036C4⋊C4—91no—
1037C4⋊C4—91no—
1038C4⋊C4—91no—
1039C4⋊C4—271no—
1040C22⋊C4—31no—
1041C22⋊C4—91no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—271no—
1046C22⋊C4—271no—
1047C22⋊C4—271no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C42—91no—
1053C22×C3—22no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—41no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—42no—
1075C22×C3—41no—
1076C22×C3—62no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—81no—
1084C22×C3—81no—
1085C22×C3—92no—
1086C22×C3—92no—
1087C22×C3—121no—
1088C22×C3—121no—
1089C22×C3—181no—
1090C22×C3—181no—
1091C22×C3—181no—
1092C22×C3—181no—
1093C22×C3—181no—
1094C22×C3—181no—
1095C22×C3—181no—
1096C22×C3C22×D3211yescharacteristic
1097C22×C3C22×D3211yescharacteristic
1098C22×C3C22×D3211yescharacteristic
1099C2×D3—21no—
1100C2×D3—21no—
1101C2×D3—21no—
1102C2×D3—32no—
1103C2×D3—32no—
1104C2×D3—32no—
1105C2×D3—32no—
1106C2×D3—62no—
1107C2×D3—62no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—92no—
1123C2×D3—92no—
1124C2×D3—92no—
1125C2×D3—121no—
1126C2×D3—121no—
1127C2×D3—121no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—121no—
1131C2×D3—121no—
1132C2×D3—182no—
1133C2×D3—182no—
1134C2×D3—182no—
1135C2×D3—181no—
1136C2×D3—181no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—362no—
1142C2×D3—361no—
1143C2×D3—361no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—364no—
1149C2×D3—364no—
1150C2×D3—364no—
1151C2×D3—364no—
1152C2×D3—364no—
1153C2×D3—364no—
1154C2×D3—368no—
1155C2×D3—721no—
1156C2×D3—721no—
1157C3×C4—32no—
1158C3×C4—32no—
1159C3×C4—62no—
1160C3×C4—62no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4—61no—
1168C3×C4—61no—
1169C3×C4—121no—
1170C3×C4—121no—
1171C3×C4—121no—
1172C3×C4—181no—
1173C3×C4—181no—
1174C3×C4—181no—
1175Dic3—21no—
1176Dic3—21no—
1177Dic3—21no—
1178Dic3—21no—
1179Dic3—62no—
1180Dic3—62no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—121no—
1188Dic3—182no—
1189Dic3—181no—
1190Dic3—181no—
1191Dic3—181no—
1192Dic3—361no—
1193Dic3—361no—
1194Dic3—362no—
1195Dic3#381112yes—
1196C32—21no—
1197C32—21no—
1198C32—21no—
1199C32—41no—
1200C32#555011yescharacteristic, complemented
1201C32#561011yescharacteristic, complemented
1202C32#561211yescharacteristic, complemented
1203C23—31no—
1204C23—91no—
1205C23—91no—
1206C23—91no—
1207C23—271no—
1208C23—542no—
1209C23—542no—
1210C23—542no—
1211C23—542no—
1212C23—1081no—
1213C23—1081no—
1214C23D3311yescharacteristic
1215Q8—542no—
1216D4—121no—
1217D4—182no—
1218D4—182no—
1219D4—182no—
1220D4—182no—
1221D4—274no—
1222D4—361no—
1223D4—542no—
1224D4—542no—
1225C2×C4—31no—
1226C2×C4—31no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—62no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—182no—
1235C2×C4—271no—
1236C2×C4—361no—
1237C2×C4—542no—
1238C2×C4—542no—
1239C2×C4—1081no—
1240C2×C3—21no—
1241C2×C3—21no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—42no—
1250C2×C3—41no—
1251C2×C3—41no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—81no—
1257C2×C3—81no—
1258C2×C3—82no—
1259C2×C3—122no—
1260C2×C3—121no—
1261C2×C3—121no—
1262C2×C3—182no—
1263C2×C3—182no—
1264C2×C3—361no—
1265C2×C3D3×#23511yescharacteristic
1266C2×C3D3×#23511yescharacteristic
1267C2×C3#6430711yescharacteristic
1268C2×C3D32×D411yescharacteristic
1269C2×C3D32×D411yescharacteristic
1270C2×C3#6431211yescharacteristic
1271C2×C3#6431411yescharacteristic
1272C2×C3C2×#381111yescharacteristic
1273C2×C3#6433011yescharacteristic
1274D3—41no—
1275D3—62no—
1276D3—62no—
1277D3—62no—
1278D3—62no—
1279D3—122no—
1280D3—122no—
1281D3—121no—
1282D3—121no—
1283D3—182no—
1284D3—182no—
1285D3—182no—
1286D3—241no—
1287D3—362no—
1288D3—362no—
1289D3—362no—
1290D3—722no—
1291C22—21no—
1292C22—21no—
1293C22—21no—
1294C22—61no—
1295C22—61no—
1296C22—61no—
1297C22—92no—
1298C22—92no—
1299C22—181no—
1300C22—181no—
1301C22—181no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—272no—
1307C22—541no—
1308C22—541no—
1309C22—1084no—
1310C22—1084no—
1311C22C2×D3311yescharacteristic
1312C4—32no—
1313C4—61no—
1314C4—61no—
1315C4—61no—
1316C4—61no—
1317C4—181no—
1318C4—181no—
1319C4—181no—
1320C4—541no—
1321C3—21no—
1322C3—21no—
1323C3—21no—
1324C3—41no—
1325C3#1059428311yescharacteristic, complemented
1326C3#1059507811yescharacteristic, complemented
1327C3#1059529611yescharacteristic, complemented
1328C2—41no—
1329C2—121no—
1330C2—182no—
1331C2—182no—
1332C2—361no—
1333C2—542no—
1334C2#1172441011yescharacteristic
1335C2#1172441811yescharacteristic
1336C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89031C2semidirect
2. C2×#88955C2semidirect
3. #11723729C2semidirect
4. #11723643C2semidirect
5. #11723623C2semidirect
6. C3×#63978C2semidirect
7. C3×#63958C2semidirect
8. C3×#63952C2semidirect
9. #11723002C2semidirect
10. #11723000C2semidirect
11. #11722991C2semidirect
12. #11722972C2semidirect
13. #11722933C2semidirect
14. #11722906C2semidirect
15. #11722905C2semidirect
21. C2×#6312C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×#6293C22semidirect
30. C2×#6289C22semidirect
31. C2×#6289C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
37. C2×C3×#624C22semidirect
39. C32×#217C22semidirect
41. #88814C22semidirect
42. #88814C22semidirect
43. #88807C22semidirect
44. #88804C22semidirect
46. #88803C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
77. #63978D3semidirect
84. #63958D3semidirect
85. #63952D3semidirect
133. #6292D4semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
183. C2×C3×#67C2×D3semidirect
185. C22×C3×Dic3C2×D3semidirect
186. C22×C3×Dic3C2×D3semidirect
212. C2×#624C2×D3semidirect
230. C3×#217C2×D3semidirect
231. C3×#217C2×D3semidirect
246. #3724C2×D3semidirect
250. Dic3⋊Dic3C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
259. #3722C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
293. C2×C3×C3⋊D3#41semidirect
559. C2×#67D32semidirect
561. C22×Dic3D32semidirect
617. #217D32semidirect
713. C2×C3⋊D3#235semidirect
811. C33#546semidirect
1200. C32#5550semidirect
1201. C32#5610semidirect
1202. C32#5612semidirect
1325. C3#10594283semidirect
1326. C3#10595078semidirect
1327. C3#10595296semidirect

Maximal subgroups

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

subgroupindex
C2×#890312
C2×#889552
#117237292
#117236432
#117236232
C3×#639782
C3×#639582
C3×#639522
#117230022
#117230002
#117229912
#117229722
#117229332
#117229062
#117229052
#105952963
#105950783
#105942833