Finite Group Databasebeta

← #13172917

Subgroups — #13172917

Order 1728.

1672 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#88960C211yesmaximal, characteristic, complemented
3#11723631C211yesmaximal, characteristic, complemented
4C3⋊D3×#217C211yesmaximal, characteristic, complemented
5#11723591C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63975C211yesmaximal, characteristic, complemented
8C3×#63971C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722962C211yesmaximal, characteristic, complemented
12#11722951C211yesmaximal, characteristic, complemented
13#11722938C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595294—31nomaximal
17#10594279—31nomaximal
18#10594274—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic, complemented
24#89049—24no—
25C2×#6295C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C2×#6293C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic, complemented
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88960—24no—
39#88864C2211yescharacteristic, complemented
40C32×#217C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×#3722C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3804—31no—
60C2×#3798—31no—
61C2×#3795—31no—
62#64147—31no—
63#64094—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#939—31no—
66C3×#937—31no—
67C3×#884—31no—
68C3×#883—31no—
69C3×#883—31no—
70C3×#882—31no—
71#63983—31no—
72#63981D311yescharacteristic, complemented
73#63975D311yescharacteristic, complemented
74Dic3×#67—31no—
75#63971D311yescharacteristic, complemented
76#63970—31no—
77#63970—31no—
78#63970—31no—
79#63970—61no—
80D3×#217—31no—
81D3×#217—31no—
82D3×#217—61no—
83#63959—31no—
84#63959—31no—
85#63959—61no—
86#63922—31no—
87#63922—31no—
88#63921—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91#63916—31no—
92#63904—31no—
93#63902—31no—
94#63898—31no—
95#63896—31no—
96#63895—31no—
97#63893—31no—
98#63891—31no—
99#63890—31no—
100#63886—31no—
101#63881—31no—
102#63881—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C32×#67—41no—
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6295—22no—
129#6295D414yescomplemented
130#6294—22no—
131#6293—22no—
132#6290—22no—
133Dic3×C3⋊D3—22no—
134Dic3×C3⋊D3—41no—
135Dic3×C3⋊D3—41no—
136C3×#626—22no—
137C3×#626—22no—
138C3×#626—41no—
139C3×#624—22no—
140C3×D3×Dic3—22no—
141#5654—91no—
142#5612—91no—
143#5591—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×C32×D4—31no—
152C2×#638—31no—
153C2×#638C2×D311yescharacteristic
154C2×#638C2×D311yescharacteristic
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×#634—31no—
159C2×C3×#67—21no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—61no—
168C2×C3×#67—61no—
169C2×C3×#67C2×D311yescharacteristic, complemented
170C2×C3×#67C2×D311yescharacteristic, complemented
171C22×C3×Dic3—31no—
172C2×C3×D12—31no—
173C2×C3×D12—31no—
174C2×C3×D12—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178#3811—64no—
179D3×#67—64no—
180D3×#67—64no—
181C2×#627—31no—
182C2×#627—31no—
183C2×#627—61no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626C2×D311yescharacteristic
189C2×#626C2×D311yescharacteristic, complemented
190C2×#626C2×D311yescharacteristic, complemented
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—61no—
196C2×#624—31no—
197C2×#624C2×D311yescharacteristic, complemented
198#3804—64no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—61no—
208C2×D3×Dic3—61no—
209C2×D3×Dic3—61no—
210C2×D3×Dic3C2×D311yescharacteristic, complemented
211#3798—64no—
212#3795—64no—
213C32×C22⋊C4—31no—
214C32×C22⋊C4—31no—
215#3757—31no—
216#3757—31no—
217#3757—31no—
218#3757—31no—
219#3757—61no—
220#3757—61no—
221#3757—61no—
222#3757—121no—
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3752—31no—
227C4⋊(C3⋊Dic3)—31no—
228C4×C3⋊Dic3—31no—
229C3×#217—21no—
230C3×#217—21no—
231C3×#217C2×D311yescharacteristic, complemented
232C3×#217C2×D311yescharacteristic, complemented
233C3×#217C2×D311yescharacteristic, complemented
234C3×#217C2×D311yescharacteristic, complemented
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×C4⋊Dic3—31no—
244C3×C4⋊Dic3—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255#3722C2×D311yescharacteristic
256#3722C2×D311yescharacteristic, complemented
257#3722C2×D311yescharacteristic, complemented
258#3722C2×D311yescharacteristic, complemented
259(C2×D3)⋊Dic3—31no—
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—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274Dic32—31no—
275Dic32—31no—
276Dic32—61no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2411yescharacteristic
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
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—44no—
291C2×C3×C3⋊D3C2×D412yes—
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—
298C3⋊(C3⋊Dic3)—21no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3C2×D412yes—
302C32×Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C22×#67—91no—
308C2×#237—91no—
309C2×D3×D4—91no—
310C2×D3×D4—91no—
311C2×#235—91no—
312C2×#235—91no—
313C3×#123—91no—
314C3×#121—91no—
315C3×#120—91no—
316C2×#217—91no—
317#939—31no—
318#939—91no—
319#939—91no—
320#938—91no—
321#938—91no—
322#938—91no—
323#938—181no—
324#937—31no—
325#937—91no—
326#937—91no—
327#936—91no—
328D4×Dic3—91no—
329C4×#67—91no—
330C2×(C2×D3)⋊C4—91no—
331#897—91no—
332#896—91no—
333#895—91no—
334#894—91no—
335#893—91no—
336#893—91no—
337#886—91no—
338#885—91no—
339#885—91no—
340#885—181no—
341#884—31no—
342#883—31no—
343#883—31no—
344#883—91no—
345#882—31no—
346#882—91no—
347#67⋊C4—91no—
348#67⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—181no—
354#878—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—31no—
359C23×C32—41no—
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C22×C3⋊D3—22no—
364C22×C3⋊D3—22no—
365C22×C3⋊D3—41no—
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—21no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—61no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—62no—
384C22×C3×D3—62no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—64no—
388C22×C3×D3—122no—
389C22×C3×D3—121no—
390C22×C3×D3—121no—
391C22×C3×D3—122no—
392C22×C3×D3C22×D311yescharacteristic
393C22×C3×D3C22×D311yescharacteristic
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—121no—
401C2×D32—121no—
402C2×D32—121no—
403C32×D4—121no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—31no—
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409#638—22no—
410#638—22no—
411#638—62no—
412C2×C3⋊Dic3—31no—
413C2×C3⋊Dic3—31no—
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—61no—
419C2×C3⋊Dic3—61no—
420C2×C3⋊Dic3—61no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—121no—
425C2×C3⋊Dic3—121no—
426C2×C3⋊Dic3C22×D311yescharacteristic
427C2×C3⋊Dic3C22×D311yescharacteristic
428C4×C3⋊D3—62no—
429C4×C3⋊D3—121no—
430C4×C3⋊D3—121no—
431#634—62no—
432C3×#67—41no—
433C3×#67—41no—
434C3×#67—42no—
435C3×#67—62no—
436C3×#67—62no—
437C3×#67—62no—
438C3×#67—62no—
439C3×#67—62no—
440C3×#67—62no—
441C3×#67—122no—
442C3×#67—122no—
443C3×#67—121no—
444C2×C3×Dic3—21no—
445C2×C3×Dic3—21no—
446C2×C3×Dic3—21no—
447C2×C3×Dic3—21no—
448C2×C3×Dic3—21no—
449C2×C3×Dic3—31no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—31no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—61no—
454C2×C3×Dic3—61no—
455C2×C3×Dic3—62no—
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C2×C3×Dic3C22×D311yescharacteristic
459C2×C3×Dic3C22×D311yescharacteristic
460C2×C3×Dic3C22×D311yescharacteristic
461C2×C3×Dic3C22×D311yescharacteristic
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C3×D12—62no—
467C3×D12—62no—
468C3×D12—121no—
469C3×C4×D3—62no—
470C3×C4×D3—62no—
471C3×C4×D3—62no—
472#627—62no—
473#627—62no—
474#627—122no—
475#626—22no—
476#626—22no—
477#626—34no—
478#626—34no—
479#626—41no—
480#626—62no—
481#626—62no—
482#625—34no—
483#625—62no—
484#625—62no—
485#625—62no—
486#625—122no—
487#624—22no—
488#624—62no—
489D3×Dic3—22no—
490D3×Dic3—62no—
491D3×Dic3—62no—
492D3×Dic3—62no—
493D3×Dic3—62no—
494D3×Dic3—122no—
495D3×Dic3—121no—
496D3×Dic3—121no—
497D3×Dic3—121no—
498D3×Dic3—121no—
499D3×Dic3—122no—
500D3×Dic3—122no—
501#546—271noSylow
502C2×C33—41no—
503C2×C33C22×D411yescharacteristic
504C2×C33C2×#4111yescharacteristic
505C2×C33H(5,𝔽2)11yescharacteristic
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—22no—
509C3×C3⋊D3—41no—
510C32×D3—41no—
511C24×C3—91no—
512C23×D3—31no—
513C23×D3—31no—
514C23×D3—61no—
515C23×D3—91no—
516C23×D3—91no—
517C23×D3—91no—
518C2×C3×D4—31no—
519C2×C3×D4—31no—
520C2×C3×D4—61no—
521C2×C3×D4—91no—
522C2×C3×D4—91no—
523C2×C3×D4—91no—
524C2×C3×D4—91no—
525C2×C3×D4—91no—
526C22×C3×C4—91no—
527C22×C3×C4—91no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—31no—
531C2×#67—31no—
532C2×#67—31no—
533C2×#67—31no—
534C2×#67—31no—
535C2×#67—61no—
536C2×#67—61no—
537C2×#67—91no—
538C2×#67—91no—
539C2×#67—91no—
540C2×#67—91no—
541C2×#67—91no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—181no—
545C2×#67—184no—
546C2×#67D3211yescharacteristic, complemented
547C22×Dic3—31no—
548C22×Dic3—91no—
549C22×Dic3—91no—
550C22×Dic3—91no—
551C22×Dic3—91no—
552#237—184no—
553D3×D4—184no—
554D3×D4—184no—
555#235—184no—
556#235—184no—
557C2×D12—31no—
558C2×D12—31no—
559C2×D12—31no—
560C2×D12—91no—
561C2×D12—91no—
562C2×C4×D3—31no—
563C2×C4×D3—31no—
564C2×C4×D3—31no—
565C2×C4×D3—91no—
566C2×C4×D3—91no—
567C2×C4×D3—91no—
568C2×C4×D3—91no—
569C2×C4×D3—91no—
570C2×C4×D3—91no—
571C2×C4×D3—91no—
572C2×C4×D3—91no—
573C2×C4×D3—181no—
574C2×C4×D3—181no—
575C2×C4×D3—181no—
576C2×Dic6—91no—
577C2×Dic6—91no—
578C2×Dic6—91no—
579C2×Dic6—181no—
580C3×C4⋊C4—91no—
581C3×C4⋊C4—91no—
582C3×C4⋊C4—91no—
583C3×C22⋊C4—31no—
584C3×C22⋊C4—31no—
585C3×C22⋊C4—31no—
586C3×C22⋊C4—31no—
587C3×C22⋊C4—61no—
588C3×C22⋊C4—61no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593#217—91no—
594#217—91no—
595#217—91no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—91no—
600#217—91no—
601#217—91no—
602#217—181no—
603#217—181no—
604#217—181no—
605#217—181no—
606#217—361no—
607#217D3211yescharacteristic, complemented
608#217D3211yescharacteristic, complemented
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—181no—
627(C2×D3)⋊C4—181no—
628(C2×D3)⋊C4—181no—
629(C2×D3)⋊C4—181no—
630C4⋊Dic3—31no—
631C4⋊Dic3—31no—
632C4⋊Dic3—91no—
633C4⋊Dic3—91no—
634C4⋊Dic3—181no—
635Dic3⋊C4—31no—
636Dic3⋊C4—31no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640C4×Dic3—91no—
641C4×Dic3—91no—
642C4×Dic3—91no—
643C4×Dic3—181no—
644C22×C32—21no—
645C22×C32—22no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—41no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—42no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—61no—
668C22×C32—61no—
669C22×C32—61no—
670C22×C32—81no—
671C22×C32—81no—
672C22×C32C23×D311yescharacteristic
673C22×C32C23×D311yescharacteristic
674C22×C32C23×D311yescharacteristic
675C2×C3⋊D3—21no—
676C2×C3⋊D3—21no—
677C2×C3⋊D3—21no—
678C2×C3⋊D3—21no—
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—44no—
685C2×C3⋊D3D3×D412yes—
686C2×C3⋊D3D3×D412yes—
687C2×C3⋊D3#23712yescomplemented
688C2×C3×D3—21no—
689C2×C3×D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—32no—
695C2×C3×D3—32no—
696C2×C3×D3—32no—
697C2×C3×D3—32no—
698C2×C3×D3—32no—
699C2×C3×D3—32no—
700C2×C3×D3—41no—
701C2×C3×D3—41no—
702C2×C3×D3—41no—
703C2×C3×D3—62no—
704C2×C3×D3—62no—
705C2×C3×D3—62no—
706C2×C3×D3—62no—
707C2×C3×D3—62no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—121no—
727C2×C3×D3—121no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—124no—
734C2×C3×D3—124no—
735C2×C3×D3—128no—
736D32—124no—
737D32—124no—
738D32—124no—
739C32×C4—61no—
740C32×C4—61no—
741C32×C4—61no—
742C32×C4—61no—
743C32×C4—61no—
744C3⋊Dic3—21no—
745C3⋊Dic3—61no—
746C3⋊Dic3—61no—
747C3⋊Dic3—61no—
748C3⋊Dic3—61no—
749C3⋊Dic3—61no—
750C3⋊Dic3—61no—
751C3⋊Dic3—121no—
752C3⋊Dic3—121no—
753C3⋊Dic3—121no—
754C3⋊Dic3—121no—
755C3⋊Dic3—121no—
756C3⋊Dic3—121no—
757C3⋊Dic3—241no—
758C3⋊Dic3—241no—
759C3⋊Dic3D3×D412yes—
760C3×Dic3—22no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—21no—
764C3×Dic3—21no—
765C3×Dic3—21no—
766C3×Dic3—21no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—32no—
772C3×Dic3—32no—
773C3×Dic3—41no—
774C3×Dic3—41no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—62no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—121no—
781C2×#41—271no—
782C22×D4—271no—
783#124—271no—
784#123—91no—
785#123—271no—
786C22⋊Q8—271no—
787#121—91no—
788#121—271no—
789#121—271no—
790#120—91no—
791#120—271no—
792C4×D4—271no—
793C4×D4—271no—
794C2×C22⋊C4—271no—
795C2×C22⋊C4—271no—
796C33#54611yescharacteristic, complemented, Sylow
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—21no—
800C23×C3—31no—
801C23×C3—31no—
802C23×C3—41no—
803C23×C3—61no—
804C23×C3—91no—
805C23×C3—91no—
806C23×C3—91no—
807C23×C3—91no—
808C23×C3—182no—
809C23×C3—182no—
810C23×C3—361no—
811C23×C3C2×D3211yescharacteristic
812C23×C3C2×D3211yescharacteristic
813C23×C3C2×D3211yescharacteristic
814C22×D3—31no—
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—62no—
827C22×D3—62no—
828C22×D3—62no—
829C22×D3—62no—
830C22×D3—64no—
831C22×D3—122no—
832C22×D3—121no—
833C22×D3—121no—
834C22×D3—122no—
835C22×D3—182no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—361no—
842C22×D3—361no—
843C22×D3—361no—
844C22×D3C2×D3211yescharacteristic
845C3×D4—121no—
846C3×D4—121no—
847C3×D4—122no—
848C3×D4—182no—
849C3×D4—182no—
850C3×D4—182no—
851C3×D4—182no—
852C3×D4—361no—
853C2×C3×C4—31no—
854C2×C3×C4—31no—
855C2×C3×C4—31no—
856C2×C3×C4—31no—
857C2×C3×C4—31no—
858C2×C3×C4—31no—
859C2×C3×C4—31no—
860C2×C3×C4—31no—
861C2×C3×C4—31no—
862C2×C3×C4—31no—
863C2×C3×C4—61no—
864C2×C3×C4—61no—
865C2×C3×C4—61no—
866C2×C3×C4—61no—
867C2×C3×C4—61no—
868C2×C3×C4—91no—
869C2×C3×C4—91no—
870C2×C3×C4—182no—
871C2×C3×C4—182no—
872#67—41no—
873#67—62no—
874#67—62no—
875#67—62no—
876#67—62no—
877#67—62no—
878#67—62no—
879#67—94no—
880#67—94no—
881#67—122no—
882#67—122no—
883#67—121no—
884#67—182no—
885#67—182no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—362no—
890C2×Dic3—31no—
891C2×Dic3—31no—
892C2×Dic3—31no—
893C2×Dic3—31no—
894C2×Dic3—61no—
895C2×Dic3—61no—
896C2×Dic3—62no—
897C2×Dic3—91no—
898C2×Dic3—91no—
899C2×Dic3—91no—
900C2×Dic3—91no—
901C2×Dic3—91no—
902C2×Dic3—91no—
903C2×Dic3—181no—
904C2×Dic3—181no—
905C2×Dic3—181no—
906C2×Dic3—181no—
907C2×Dic3—181no—
908C2×Dic3—181no—
909C2×Dic3—182no—
910C2×Dic3—182no—
911C2×Dic3—361no—
912C2×Dic3—361no—
913C2×Dic3—361no—
914C2×Dic3—361no—
915C2×Dic3C2×D3211yescharacteristic
916C2×Dic3C2×D3211yescharacteristic
917C2×Dic3C2×D3211yescharacteristic
918C2×Dic3C2×D3211yescharacteristic
919C2×Dic3C2×D3211yescharacteristic
920D12—62no—
921D12—62no—
922D12—94no—
923D12—121no—
924D12—182no—
925C4×D3—62no—
926C4×D3—62no—
927C4×D3—62no—
928C4×D3—182no—
929C4×D3—182no—
930C4×D3—182no—
931C4×D3—182no—
932C4×D3—362no—
933C4×D3—361no—
934C4×D3—361no—
935C4×D3—361no—
936C4×D3—361no—
937C4×D3—362no—
938C4×D3—362no—
939Dic6—182no—
940Dic6—182no—
941Dic6—182no—
942Dic6—362no—
943C2×C32—21no—
944C2×C32—21no—
945C2×C32—21no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—21no—
951C2×C32—21no—
952C2×C32—41no—
953C2×C32—41no—
954C2×C32—41no—
955C2×C32—41no—
956C2×C32—42no—
957C2×C32—41no—
958C2×C32—41no—
959C2×C32—81no—
960C2×C32—81no—
961C2×C32—82no—
962C2×C32—121no—
963C2×C32C2×D3×D411yescharacteristic
964C2×C32C2×D3×D411yescharacteristic
965C2×C32C2×D3×D411yescharacteristic
966C2×C32C2×#23711yescharacteristic
967C2×C32#100411yescharacteristic
968C2×C32#100411yescharacteristic
969C2×C32D3×#4111yescharacteristic
970C2×C32D3×#4111yescharacteristic
971C2×C32#100911yescharacteristic
972C3⋊D3—22no—
973C3⋊D3—22no—
974C3⋊D3—22no—
975C3⋊D3—41no—
976C3×D3—41no—
977C3×D3—41no—
978C3×D3—64no—
979C3×D3—62no—
980C3×D3—62no—
981C3×D3—62no—
982C3×D3—62no—
983C3×D3—62no—
984C3×D3—62no—
985C3×D3—81no—
986C3×D3—122no—
987C3×D3—122no—
988C3×D3—121no—
989C3×D3—121no—
990C3×D3—241no—
991C24—91no—
992C24—271no—
993#41—544no—
994C2×Q8—271no—
995C2×D4—31no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—91no—
1001C2×D4—271no—
1002C2×D4—271no—
1003C2×D4—271no—
1004C2×D4—544no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—271no—
1008C22×C4—271no—
1009C22×C4—271no—
1010C22×C4—271no—
1011C4⋊C4—91no—
1012C4⋊C4—91no—
1013C4⋊C4—91no—
1014C4⋊C4—271no—
1015C22⋊C4—31no—
1016C22⋊C4—31no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—91no—
1020C22⋊C4—91no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4—271no—
1025C22⋊C4—271no—
1026C22⋊C4—271no—
1027C42—271no—
1028C22×C3—22no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—21no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—21no—
1038C22×C3—21no—
1039C22×C3—21no—
1040C22×C3—21no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—42no—
1050C22×C3—41no—
1051C22×C3—61no—
1052C22×C3—61no—
1053C22×C3—61no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—61no—
1057C22×C3—81no—
1058C22×C3—81no—
1059C22×C3—92no—
1060C22×C3—92no—
1061C22×C3—92no—
1062C22×C3—121no—
1063C22×C3—121no—
1064C22×C3—121no—
1065C22×C3—181no—
1066C22×C3—181no—
1067C22×C3—181no—
1068C22×C3—181no—
1069C22×C3—181no—
1070C22×C3—181no—
1071C22×C3—181no—
1072C22×C3—181no—
1073C22×C3—181no—
1074C22×C3—364no—
1075C22×C3C22×D3211yescharacteristic
1076C22×C3C22×D3211yescharacteristic
1077C22×C3C22×D3211yescharacteristic
1078C2×D3—21no—
1079C2×D3—21no—
1080C2×D3—21no—
1081C2×D3—32no—
1082C2×D3—32no—
1083C2×D3—32no—
1084C2×D3—32no—
1085C2×D3—32no—
1086C2×D3—32no—
1087C2×D3—62no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—62no—
1092C2×D3—61no—
1093C2×D3—61no—
1094C2×D3—61no—
1095C2×D3—61no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—124no—
1118C2×D3—124no—
1119C2×D3—128no—
1120C2×D3—364no—
1121C2×D3—364no—
1122C2×D3—364no—
1123C3×C4—62no—
1124C3×C4—61no—
1125C3×C4—61no—
1126C3×C4—61no—
1127C3×C4—61no—
1128C3×C4—61no—
1129C3×C4—61no—
1130C3×C4—61no—
1131C3×C4—61no—
1132C3×C4—61no—
1133C3×C4—61no—
1134C3×C4—92no—
1135C3×C4—121no—
1136C3×C4—121no—
1137C3×C4—121no—
1138C3×C4—121no—
1139C3×C4—181no—
1140Dic3—21no—
1141Dic3—21no—
1142Dic3—21no—
1143Dic3—21no—
1144Dic3—21no—
1145Dic3—32no—
1146Dic3—32no—
1147Dic3—62no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—121no—
1151Dic3—181no—
1152Dic3—181no—
1153Dic3—181no—
1154Dic3—181no—
1155Dic3—181no—
1156Dic3—181no—
1157Dic3—361no—
1158Dic3—361no—
1159Dic3—361no—
1160Dic3—361no—
1161Dic3—361no—
1162Dic3—361no—
1163Dic3—721no—
1164Dic3—721no—
1165C32—21no—
1166C32—21no—
1167C32—21no—
1168C32—41no—
1169C32#559111yescharacteristic, complemented
1170C32#561211yescharacteristic, complemented
1171C32#565411yescharacteristic, complemented
1172C23—31no—
1173C23—91no—
1174C23—91no—
1175C23—91no—
1176C23—91no—
1177C23—182no—
1178C23—182no—
1179C23—361no—
1180C23—542no—
1181C23—542no—
1182C23—1081no—
1183C23D3311yescharacteristic
1184Q8—542no—
1185D4—121no—
1186D4—182no—
1187D4—182no—
1188D4—182no—
1189D4—182no—
1190D4—274no—
1191D4—361no—
1192D4—542no—
1193D4—542no—
1194C2×C4—31no—
1195C2×C4—31no—
1196C2×C4—31no—
1197C2×C4—31no—
1198C2×C4—31no—
1199C2×C4—91no—
1200C2×C4—91no—
1201C2×C4—182no—
1202C2×C4—182no—
1203C2×C4—271no—
1204C2×C4—271no—
1205C2×C4—542no—
1206C2×C4—542no—
1207C2×C4—1081no—
1208C2×C4—1081no—
1209C2×C3—21no—
1210C2×C3—21no—
1211C2×C3—21no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—21no—
1217C2×C3—21no—
1218C2×C3—42no—
1219C2×C3—41no—
1220C2×C3—41no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—41no—
1224C2×C3—41no—
1225C2×C3—81no—
1226C2×C3—81no—
1227C2×C3—82no—
1228C2×C3—121no—
1229C2×C3—121no—
1230C2×C3—182no—
1231C2×C3—182no—
1232C2×C3—182no—
1233C2×C3—241no—
1234C2×C3—361no—
1235C2×C3#6430611yescharacteristic
1236C2×C3#6430711yescharacteristic
1237C2×C3D32×D411yescharacteristic
1238C2×C3D32×D411yescharacteristic
1239C2×C3D32×D411yescharacteristic
1240C2×C3D3×#23711yescharacteristic
1241C2×C3D3×#23711yescharacteristic
1242C2×C3#6431411yescharacteristic
1243C2×C3#6433011yescharacteristic
1244D3—41no—
1245D3—64no—
1246D3—62no—
1247D3—62no—
1248D3—62no—
1249D3—62no—
1250D3—62no—
1251D3—62no—
1252D3—122no—
1253D3—122no—
1254D3—121no—
1255D3—121no—
1256D3—241no—
1257C22—21no—
1258C22—21no—
1259C22—21no—
1260C22—61no—
1261C22—61no—
1262C22—61no—
1263C22—92no—
1264C22—92no—
1265C22—92no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—181no—
1275C22—364no—
1276C22—1084no—
1277C22C2×D3311yescharacteristic
1278C4—61no—
1279C4—61no—
1280C4—61no—
1281C4—61no—
1282C4—61no—
1283C4—92no—
1284C4—181no—
1285C4—541no—
1286C4—541no—
1287C3—21no—
1288C3—21no—
1289C3—21no—
1290C3—41no—
1291C3#1059427411yescharacteristic, complemented
1292C3#1059427911yescharacteristic, complemented
1293C3#1059529411yescharacteristic, complemented
1294C2—41no—
1295C2—121no—
1296C2—182no—
1297C2—182no—
1298C2—182no—
1299C2—361no—
1300C2#1172440711yescharacteristic
1301C2#1172441811yescharacteristic
1302C2#1172444011yescharacteristic
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×#89049C2semidirect
2. C2×#88960C2semidirect
3. #11723631C2semidirect
4. C3⋊D3×#217C2semidirect
5. #11723591C2semidirect
6. C3×#63981C2semidirect
7. C3×#63975C2semidirect
8. C3×#63971C2semidirect
9. #11722997C2semidirect
10. #11722984C2semidirect
11. #11722962C2semidirect
12. #11722951C2semidirect
13. #11722938C2semidirect
14. #11722927C2semidirect
15. #11722905C2semidirect
23. C2×C32×#67C22semidirect
28. C2×#6293C22semidirect
29. C2×#6290C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#624C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. #88864C22semidirect
40. C32×#217C22semidirect
41. C32×#217C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
54. C3×#3722C22semidirect
55. C3×#3722C22semidirect
72. #63981D3semidirect
73. #63975D3semidirect
75. #63971D3semidirect
129. #6295D4semidirect
169. C2×C3×#67C2×D3semidirect
170. C2×C3×#67C2×D3semidirect
189. C2×#626C2×D3semidirect
190. C2×#626C2×D3semidirect
197. C2×#624C2×D3semidirect
210. C2×D3×Dic3C2×D3semidirect
231. C3×#217C2×D3semidirect
232. C3×#217C2×D3semidirect
233. C3×#217C2×D3semidirect
234. C3×#217C2×D3semidirect
249. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
256. #3722C2×D3semidirect
257. #3722C2×D3semidirect
258. #3722C2×D3semidirect
293. C2×C3×C3⋊D3#41semidirect
546. C2×#67D32semidirect
607. #217D32semidirect
608. #217D32semidirect
687. C2×C3⋊D3#237semidirect
796. C33#546semidirect
1169. C32#5591semidirect
1170. C32#5612semidirect
1171. C32#5654semidirect
1291. C3#10594274semidirect
1292. C3#10594279semidirect
1293. C3#10595294semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#889602
#117236312
C3⋊D3×#2172
#117235912
C3×#639812
C3×#639752
C3×#639712
#117229972
#117229842
#117229622
#117229512
#117229382
#117229272
#117229052
#105952943
#105942793
#105942743