Finite Group Databasebeta

← #13172918

Subgroups — #13172918

Order 1728.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1302 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#11723634C211yesmaximal, characteristic, complemented
4#11723621C211yesmaximal, characteristic, complemented
5#11723591C211yesmaximal, characteristic, complemented
6C3×#63974C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63958C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722957C211yesmaximal, characteristic, complemented
12#11722951C211yesmaximal, characteristic, complemented
13#11722936C211yesmaximal, characteristic, complemented
14#11722931C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595296—31nomaximal
17#10594278—31nomaximal
18#10594273—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
30C2×#6290C2211yescharacteristic, complemented
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic, complemented
34C2×C3×#624C2211yescharacteristic, complemented
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88960—24no—
39#88864C2211yescharacteristic, complemented
40C32×#217C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3804—31no—
60C2×#3798—31no—
61C2×#3795—31no—
62#64146—31no—
63#64094—31no—
64#64092—31no—
65C3×#939—31no—
66C3×#938—31no—
67C3×#884—31no—
68C3×#884—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63983—31no—
72#63976—31no—
73#63976—31no—
74#63976—61no—
75#63974D311yescharacteristic, complemented
76#63971D311yescharacteristic, complemented
77#63969—31no—
78#63969—31no—
79#63969—61no—
80#63959—31no—
81#63959—31no—
82#63959—61no—
83#63958—31no—
84#63958D311yescharacteristic, complemented
85#63952—31no—
86#63922—31no—
87#63922—31no—
88#63921—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91#63908—31no—
92#63906—31no—
93#63905—31no—
94#63904—31no—
95#63904—31no—
96#63902—31no—
97C4×#625—31no—
98#63896—31no—
99#63895—31no—
100#63893—31no—
101#63879—31no—
102#63854—31no—
103#63850—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—
133#6290—22no—
134Dic3×C3⋊D3—22no—
135C3×#626—22no—
136C3×#626—41no—
137C3×#624—22no—
138C3×#624—41no—
139C3×#624—41no—
140C3×D3×Dic3—22no—
141#5612—91no—
142#5610—91no—
143#5490—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×#638—31no—
154C2×#638C2×D311yescharacteristic
155C2×#638C2×D311yescharacteristic
156C2×C4×C3⋊D3—31no—
157C2×#634—31no—
158C2×C3×#67—21no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×#67C2×D311yescharacteristic, complemented
168C2×C3×#67C2×D311yescharacteristic, complemented
169C22×C3×Dic3—31no—
170C2×C3×D12—31no—
171C2×C3×D12—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179#3811—64no—
180D3×#67—64no—
181D3×#67—64no—
182C2×#627—31no—
183C2×#627—31no—
184C2×#627—61no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626C2×D311yescharacteristic, complemented
190C2×#626C2×D311yescharacteristic, complemented
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—31no—
196C2×#625—31no—
197C2×#625—61no—
198C2×#625—61no—
199C2×#624—31no—
200C2×#624C2×D311yescharacteristic, complemented
201C2×#624C2×D311yescharacteristic, complemented
202C2×#624C2×D311yescharacteristic, complemented
203#3804—64no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—61no—
209C2×D3×Dic3C2×D311yescharacteristic, complemented
210#3798—64no—
211#3795—64no—
212C32×C22⋊C4—31no—
213C32×C22⋊C4—31no—
214#3757—31no—
215#3757—31no—
216#3757—31no—
217#3757—61no—
218#3757—61no—
219#3757—61no—
220#3757—121no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3752—31no—
225#3752—31no—
226C4⋊(C3⋊Dic3)—31no—
227#3750—31no—
228C4×C3⋊Dic3—31no—
229C3×#217—21no—
230C3×#217—21no—
231C3×#217—31no—
232C3×#217C2×D311yescharacteristic, complemented
233C3×#217C2×D311yescharacteristic, complemented
234C3×#217C2×D311yescharacteristic, complemented
235C3×#217C2×D311yescharacteristic, complemented
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×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247#3724—31no—
248#3724—31no—
249#3724—61no—
250#3724C2×D311yescharacteristic, complemented
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—61no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255#3722C2×D311yescharacteristic
256#3722C2×D311yescharacteristic
257#3722C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3—31no—
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—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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×#121—91no—
314C3×#121—91no—
315C2×C3×C22⋊C4—91no—
316#953—91no—
317#939—31no—
318#938—31no—
319#938—91no—
320#937—91no—
321#937—91no—
322#937—91no—
323#937—91no—
324#937—181no—
325#936—91no—
326#935—91no—
327#930—91no—
328#929—91no—
329C4×#67—91no—
330C4×#67—91no—
331C4×#67—91no—
332C2×(C2×D3)⋊C4—91no—
333#897—91no—
334#896—91no—
335#894—91no—
336#893—91no—
337#885—91no—
338#885—91no—
339#885—181no—
340#884—31no—
341#884—31no—
342#884—91no—
343#883—91no—
344#883—91no—
345#883—91no—
346#883—181no—
347#882—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350D3×C22⋊C4—31no—
351D3×C22⋊C4—31no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
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—122no—
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—
412#638—62no—
413C2×C3⋊Dic3—31no—
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—31no—
419C2×C3⋊Dic3—61no—
420C2×C3⋊Dic3—61no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—121no—
426C2×C3⋊Dic3—121no—
427C2×C3⋊Dic3C22×D311yescharacteristic
428C2×C3⋊Dic3C22×D311yescharacteristic
429C4×C3⋊D3—62no—
430#634—62no—
431C3×#67—41no—
432C3×#67—41no—
433C3×#67—42no—
434C3×#67—62no—
435C3×#67—62no—
436C3×#67—62no—
437C3×#67—62no—
438C3×#67—62no—
439C3×#67—122no—
440C3×#67—122no—
441C3×#67—121no—
442C2×C3×Dic3—21no—
443C2×C3×Dic3—21no—
444C2×C3×Dic3—21no—
445C2×C3×Dic3—21no—
446C2×C3×Dic3—21no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—31no—
449C2×C3×Dic3—31no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—61no—
452C2×C3×Dic3—61no—
453C2×C3×Dic3—62no—
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
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
464C3×D12—62no—
465C3×D12—121no—
466C3×C4×D3—62no—
467C3×C4×D3—62no—
468C3×C4×D3—62no—
469C3×C4×D3—121no—
470C3×C4×D3—121no—
471C3×C4×D3—121no—
472C3×C4×D3—121no—
473#627—62no—
474#627—62no—
475#627—122no—
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—62no—
487#625—62no—
488#625—122no—
489#625—122no—
490#624—22no—
491#624—41no—
492#624—41no—
493#624—62no—
494D3×Dic3—22no—
495D3×Dic3—62no—
496D3×Dic3—62no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—122no—
500#546—271noSylow
501C2×C33—41no—
502C2×C33C22×D411yescharacteristic
503C2×C33C2×#4111yescharacteristic
504C2×C33H(5,𝔽2)11yescharacteristic
505C3×C3⋊D3—22no—
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—41no—
509C32×D3—41no—
510C24×C3—91no—
511C23×D3—31no—
512C23×D3—31no—
513C23×D3—61no—
514C23×D3—91no—
515C23×D3—91no—
516C23×D3—91no—
517C2×C3×D4—31no—
518C2×C3×D4—31no—
519C2×C3×D4—61no—
520C2×C3×D4—91no—
521C2×C3×D4—91no—
522C2×C3×D4—91no—
523C2×C3×D4—91no—
524C22×C3×C4—91no—
525C22×C3×C4—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—61no—
535C2×#67—61no—
536C2×#67—91no—
537C2×#67—91no—
538C2×#67—91no—
539C2×#67—91no—
540C2×#67—91no—
541C2×#67—91no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—181no—
547C2×#67—181no—
548C2×#67—184no—
549C2×#67D3211yescharacteristic, complemented
550C22×Dic3—31no—
551C22×Dic3—91no—
552C22×Dic3—91no—
553#237—184no—
554D3×D4—184no—
555D3×D4—184no—
556#235—184no—
557#235—184no—
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—31no—
566C2×C4×D3—31no—
567C2×C4×D3—31no—
568C2×C4×D3—31no—
569C2×C4×D3—91no—
570C2×C4×D3—91no—
571C2×C4×D3—91no—
572C2×C4×D3—91no—
573C2×C4×D3—181no—
574C2×Dic6—91no—
575C2×Dic6—91no—
576C2×Dic6—91no—
577C2×Dic6—181no—
578C3×C4⋊C4—91no—
579C3×C4⋊C4—91no—
580C3×C22⋊C4—31no—
581C3×C22⋊C4—31no—
582C3×C22⋊C4—31no—
583C3×C22⋊C4—31no—
584C3×C22⋊C4—61no—
585C3×C22⋊C4—61no—
586C3×C22⋊C4—91no—
587C3×C22⋊C4—91no—
588C3×C22⋊C4—91no—
589C3×C22⋊C4—91no—
590#217—31no—
591#217—91no—
592#217—91no—
593#217—91no—
594#217—91no—
595#217—91no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—181no—
600#217—181no—
601#217—181no—
602#217—361no—
603#217D3211yescharacteristic, complemented
604#217D3211yescharacteristic, complemented
605(C2×D3)⋊C4—31no—
606(C2×D3)⋊C4—31no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—91no—
613(C2×D3)⋊C4—91no—
614(C2×D3)⋊C4—91no—
615(C2×D3)⋊C4—91no—
616(C2×D3)⋊C4—91no—
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—181no—
623(C2×D3)⋊C4—181no—
624(C2×D3)⋊C4—181no—
625(C2×D3)⋊C4—181no—
626(C2×D3)⋊C4—181no—
627C4⋊Dic3—31no—
628C4⋊Dic3—91no—
629C4⋊Dic3—91no—
630C4⋊Dic3—181no—
631Dic3⋊C4—31no—
632Dic3⋊C4—31no—
633Dic3⋊C4—31no—
634Dic3⋊C4—91no—
635Dic3⋊C4—91no—
636Dic3⋊C4—91no—
637Dic3⋊C4—91no—
638Dic3⋊C4—181no—
639C4×Dic3—91no—
640C4×Dic3—91no—
641C4×Dic3—91no—
642C4×Dic3—181no—
643C22×C32—21no—
644C22×C32—22no—
645C22×C32—21no—
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—41no—
657C22×C32—41no—
658C22×C32—41no—
659C22×C32—42no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—61no—
667C22×C32—61no—
668C22×C32—61no—
669C22×C32—81no—
670C22×C32—81no—
671C22×C32C23×D311yescharacteristic
672C22×C32C23×D311yescharacteristic
673C22×C32C23×D311yescharacteristic
674C2×C3⋊D3—21no—
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—44no—
684C2×C3⋊D3#23512yescomplemented
685C2×C3⋊D3D3×D412yes—
686C2×C3⋊D3D3×D412yes—
687C2×C3×D3—21no—
688C2×C3×D3—21no—
689C2×C3×D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—32no—
694C2×C3×D3—32no—
695C2×C3×D3—32no—
696C2×C3×D3—32no—
697C2×C3×D3—32no—
698C2×C3×D3—32no—
699C2×C3×D3—41no—
700C2×C3×D3—41no—
701C2×C3×D3—41no—
702C2×C3×D3—62no—
703C2×C3×D3—62no—
704C2×C3×D3—62no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
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—121no—
724C2×C3×D3—121no—
725C2×C3×D3—121no—
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—124no—
733C2×C3×D3—124no—
734C2×C3×D3—128no—
735D32—124no—
736D32—124no—
737D32—124no—
738C32×C4—61no—
739C32×C4—61no—
740C32×C4—61no—
741C32×C4—61no—
742C32×C4—61no—
743C3⋊Dic3—21no—
744C3⋊Dic3—61no—
745C3⋊Dic3—61no—
746C3⋊Dic3—61no—
747C3⋊Dic3—61no—
748C3⋊Dic3—61no—
749C3⋊Dic3—61no—
750C3⋊Dic3—121no—
751C3⋊Dic3—121no—
752C3⋊Dic3—121no—
753C3⋊Dic3—121no—
754C3⋊Dic3—121no—
755C3⋊Dic3—121no—
756C3⋊Dic3—241no—
757C3⋊Dic3—241no—
758C3⋊Dic3D3×D412yes—
759C3×Dic3—21no—
760C3×Dic3—21no—
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—32no—
770C3×Dic3—32no—
771C3×Dic3—41no—
772C3×Dic3—41no—
773C3×Dic3—41no—
774C3×Dic3—41no—
775C3×Dic3—41no—
776C3×Dic3—62no—
777C3×Dic3—61no—
778C3×Dic3—61no—
779C3×Dic3—121no—
780C2×#41—271no—
781C22×D4—271no—
782#124—271no—
783#123—271no—
784#123—271no—
785C22⋊Q8—271no—
786#121—91no—
787#121—91no—
788#121—271no—
789#120—271no—
790#120—271no—
791C4×D4—271no—
792C4×D4—271no—
793C2×C22⋊C4—91no—
794C2×C22⋊C4—271no—
795C33#54611yescharacteristic, complemented, Sylow
796C23×C3—21no—
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—31no—
800C23×C3—31no—
801C23×C3—41no—
802C23×C3—61no—
803C23×C3—91no—
804C23×C3—91no—
805C23×C3—91no—
806C23×C3—91no—
807C23×C3—182no—
808C23×C3—182no—
809C23×C3—361no—
810C23×C3C2×D3211yescharacteristic
811C23×C3C2×D3211yescharacteristic
812C23×C3C2×D3211yescharacteristic
813C22×D3—31no—
814C22×D3—31no—
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—61no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—62no—
826C22×D3—62no—
827C22×D3—62no—
828C22×D3—62no—
829C22×D3—122no—
830C22×D3—122no—
831C22×D3—121no—
832C22×D3—121no—
833C22×D3—122no—
834C22×D3—182no—
835C22×D3—182no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—361no—
841C22×D3—361no—
842C22×D3—361no—
843C22×D3C2×D3211yescharacteristic
844C3×D4—121no—
845C3×D4—121no—
846C3×D4—122no—
847C3×D4—182no—
848C3×D4—182no—
849C3×D4—182no—
850C3×D4—361no—
851C2×C3×C4—31no—
852C2×C3×C4—31no—
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—61no—
862C2×C3×C4—61no—
863C2×C3×C4—61no—
864C2×C3×C4—61no—
865C2×C3×C4—61no—
866C2×C3×C4—91no—
867C2×C3×C4—91no—
868C2×C3×C4—182no—
869C2×C3×C4—182no—
870C2×C3×C4—361no—
871C2×C3×C4—361no—
872#67—41no—
873#67—62no—
874#67—62no—
875#67—62no—
876#67—62no—
877#67—62no—
878#67—94no—
879#67—94no—
880#67—122no—
881#67—122no—
882#67—121no—
883#67—182no—
884#67—182no—
885#67—182no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—362no—
892#67—362no—
893C2×Dic3—31no—
894C2×Dic3—31no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—61no—
898C2×Dic3—61no—
899C2×Dic3—62no—
900C2×Dic3—91no—
901C2×Dic3—91no—
902C2×Dic3—91no—
903C2×Dic3—91no—
904C2×Dic3—91no—
905C2×Dic3—91no—
906C2×Dic3—181no—
907C2×Dic3—181no—
908C2×Dic3—181no—
909C2×Dic3—181no—
910C2×Dic3—181no—
911C2×Dic3—181no—
912C2×Dic3—182no—
913C2×Dic3—182no—
914C2×Dic3—361no—
915C2×Dic3—361no—
916C2×Dic3C2×D3211yescharacteristic
917C2×Dic3C2×D3211yescharacteristic
918C2×Dic3C2×D3211yescharacteristic
919C2×Dic3C2×D3211yescharacteristic
920C2×Dic3C2×D3211yescharacteristic
921D12—62no—
922D12—94no—
923D12—121no—
924D12—182no—
925C4×D3—62no—
926C4×D3—62no—
927C4×D3—62no—
928C4×D3—121no—
929C4×D3—121no—
930C4×D3—121no—
931C4×D3—121no—
932C4×D3—182no—
933C4×D3—182no—
934C4×D3—182no—
935C4×D3—182no—
936C4×D3—362no—
937Dic6—182no—
938Dic6—182no—
939Dic6—182no—
940Dic6—362no—
941C2×C32—21no—
942C2×C32—21no—
943C2×C32—21no—
944C2×C32—21no—
945C2×C32—21no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—41no—
951C2×C32—41no—
952C2×C32—41no—
953C2×C32—41no—
954C2×C32—42no—
955C2×C32—41no—
956C2×C32—41no—
957C2×C32—81no—
958C2×C32—81no—
959C2×C32—82no—
960C2×C32—121no—
961C2×C32C2×#23511yescharacteristic
962C2×C32C2×D3×D411yescharacteristic
963C2×C32C2×D3×D411yescharacteristic
964C2×C32C2×D3×D411yescharacteristic
965C2×C32#100411yescharacteristic
966C2×C32#100411yescharacteristic
967C2×C32#100411yescharacteristic
968C2×C32D3×#4111yescharacteristic
969C2×C32D3×#4111yescharacteristic
970C3⋊D3—22no—
971C3⋊D3—22no—
972C3⋊D3—22no—
973C3⋊D3—41no—
974C3×D3—41no—
975C3×D3—41no—
976C3×D3—62no—
977C3×D3—62no—
978C3×D3—62no—
979C3×D3—62no—
980C3×D3—62no—
981C3×D3—62no—
982C3×D3—81no—
983C3×D3—122no—
984C3×D3—122no—
985C3×D3—122no—
986C3×D3—121no—
987C3×D3—121no—
988C3×D3—241no—
989C24—91no—
990C24—271no—
991#41—544no—
992C2×Q8—271no—
993C2×D4—31no—
994C2×D4—91no—
995C2×D4—91no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—271no—
999C2×D4—271no—
1000C2×D4—271no—
1001C2×D4—271no—
1002C2×D4—544no—
1003C22×C4—91no—
1004C22×C4—91no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—271no—
1008C22×C4—271no—
1009C4⋊C4—91no—
1010C4⋊C4—91no—
1011C4⋊C4—271no—
1012C4⋊C4—271no—
1013C22⋊C4—31no—
1014C22⋊C4—31no—
1015C22⋊C4—91no—
1016C22⋊C4—91no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—271no—
1020C22⋊C4—271no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4—271no—
1025C42—271no—
1026C22×C3—22no—
1027C22×C3—21no—
1028C22×C3—21no—
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—41no—
1040C22×C3—41no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—42no—
1048C22×C3—41no—
1049C22×C3—61no—
1050C22×C3—61no—
1051C22×C3—61no—
1052C22×C3—61no—
1053C22×C3—61no—
1054C22×C3—61no—
1055C22×C3—81no—
1056C22×C3—81no—
1057C22×C3—92no—
1058C22×C3—92no—
1059C22×C3—92no—
1060C22×C3—121no—
1061C22×C3—121no—
1062C22×C3—121no—
1063C22×C3—181no—
1064C22×C3—181no—
1065C22×C3—181no—
1066C22×C3—181no—
1067C22×C3—181no—
1068C22×C3—181no—
1069C22×C3—181no—
1070C22×C3—181no—
1071C22×C3—181no—
1072C22×C3—364no—
1073C22×C3C22×D3211yescharacteristic
1074C22×C3C22×D3211yescharacteristic
1075C22×C3C22×D3211yescharacteristic
1076C2×D3—21no—
1077C2×D3—21no—
1078C2×D3—21no—
1079C2×D3—32no—
1080C2×D3—32no—
1081C2×D3—32no—
1082C2×D3—32no—
1083C2×D3—32no—
1084C2×D3—32no—
1085C2×D3—62no—
1086C2×D3—62no—
1087C2×D3—62no—
1088C2×D3—61no—
1089C2×D3—61no—
1090C2×D3—61no—
1091C2×D3—61no—
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—121no—
1107C2×D3—121no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—124no—
1116C2×D3—124no—
1117C2×D3—128no—
1118C2×D3—364no—
1119C2×D3—364no—
1120C2×D3—364no—
1121C3×C4—61no—
1122C3×C4—61no—
1123C3×C4—61no—
1124C3×C4—61no—
1125C3×C4—61no—
1126C3×C4—61no—
1127C3×C4—61no—
1128C3×C4—61no—
1129C3×C4—61no—
1130C3×C4—61no—
1131C3×C4—92no—
1132C3×C4—121no—
1133C3×C4—121no—
1134C3×C4—121no—
1135C3×C4—121no—
1136C3×C4—121no—
1137C3×C4—181no—
1138Dic3—21no—
1139Dic3—21no—
1140Dic3—21no—
1141Dic3—21no—
1142Dic3—21no—
1143Dic3—32no—
1144Dic3—32no—
1145Dic3—62no—
1146Dic3—61no—
1147Dic3—61no—
1148Dic3—121no—
1149Dic3—181no—
1150Dic3—181no—
1151Dic3—181no—
1152Dic3—181no—
1153Dic3—181no—
1154Dic3—181no—
1155Dic3—361no—
1156Dic3—361no—
1157Dic3—361no—
1158Dic3—361no—
1159Dic3—361no—
1160Dic3—361no—
1161Dic3—721no—
1162Dic3—721no—
1163C32—21no—
1164C32—21no—
1165C32—21no—
1166C32—41no—
1167C32#549011yescharacteristic, complemented
1168C32#561011yescharacteristic, complemented
1169C32#561211yescharacteristic, complemented
1170C23—31no—
1171C23—91no—
1172C23—91no—
1173C23—91no—
1174C23—91no—
1175C23—182no—
1176C23—182no—
1177C23—361no—
1178C23—542no—
1179C23—542no—
1180C23—1081no—
1181C23D3311yescharacteristic
1182Q8—542no—
1183D4—121no—
1184D4—182no—
1185D4—182no—
1186D4—182no—
1187D4—274no—
1188D4—361no—
1189D4—542no—
1190D4—542no—
1191D4—542no—
1192C2×C4—31no—
1193C2×C4—31no—
1194C2×C4—31no—
1195C2×C4—31no—
1196C2×C4—31no—
1197C2×C4—91no—
1198C2×C4—91no—
1199C2×C4—182no—
1200C2×C4—182no—
1201C2×C4—271no—
1202C2×C4—271no—
1203C2×C4—361no—
1204C2×C4—361no—
1205C2×C4—542no—
1206C2×C4—542no—
1207C2×C3—21no—
1208C2×C3—21no—
1209C2×C3—21no—
1210C2×C3—21no—
1211C2×C3—21no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—42no—
1217C2×C3—41no—
1218C2×C3—41no—
1219C2×C3—41no—
1220C2×C3—41no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—81no—
1224C2×C3—81no—
1225C2×C3—82no—
1226C2×C3—121no—
1227C2×C3—121no—
1228C2×C3—182no—
1229C2×C3—182no—
1230C2×C3—182no—
1231C2×C3—241no—
1232C2×C3—361no—
1233C2×C3D3×#23511yescharacteristic
1234C2×C3D3×#23511yescharacteristic
1235C2×C3D32×D411yescharacteristic
1236C2×C3D32×D411yescharacteristic
1237C2×C3D32×D411yescharacteristic
1238C2×C3#6431211yescharacteristic
1239C2×C3#6431311yescharacteristic
1240C2×C3#6431311yescharacteristic
1241C2×C3#6433011yescharacteristic
1242D3—41no—
1243D3—62no—
1244D3—62no—
1245D3—62no—
1246D3—62no—
1247D3—62no—
1248D3—62no—
1249D3—122no—
1250D3—122no—
1251D3—122no—
1252D3—121no—
1253D3—121no—
1254D3—241no—
1255C22—21no—
1256C22—21no—
1257C22—21no—
1258C22—61no—
1259C22—61no—
1260C22—61no—
1261C22—92no—
1262C22—92no—
1263C22—92no—
1264C22—181no—
1265C22—181no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—364no—
1274C22—1084no—
1275C22C2×D3311yescharacteristic
1276C4—61no—
1277C4—61no—
1278C4—61no—
1279C4—61no—
1280C4—61no—
1281C4—92no—
1282C4—181no—
1283C4—541no—
1284C4—541no—
1285C3—21no—
1286C3—21no—
1287C3—21no—
1288C3—41no—
1289C3#1059427311yescharacteristic, complemented
1290C3#1059427811yescharacteristic, complemented
1291C3#1059529611yescharacteristic, complemented
1292C2—41no—
1293C2—121no—
1294C2—182no—
1295C2—182no—
1296C2—182no—
1297C2—361no—
1298C2#1172441011yescharacteristic
1299C2#1172441511yescharacteristic
1300C2#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. #11723634C2semidirect
4. #11723621C2semidirect
5. #11723591C2semidirect
6. C3×#63974C2semidirect
7. C3×#63971C2semidirect
8. C3×#63958C2semidirect
9. #11722995C2semidirect
10. #11722984C2semidirect
11. #11722957C2semidirect
12. #11722951C2semidirect
13. #11722936C2semidirect
14. #11722931C2semidirect
15. #11722905C2semidirect
23. C2×C32×#67C22semidirect
28. C2×#6293C22semidirect
30. C2×#6290C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×C3×#626C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#624C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×#624C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. #88864C22semidirect
40. C32×#217C22semidirect
41. C32×#217C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. #88803C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
75. #63974D3semidirect
76. #63971D3semidirect
84. #63958D3semidirect
129. #6295D4semidirect
167. C2×C3×#67C2×D3semidirect
168. C2×C3×#67C2×D3semidirect
189. C2×#626C2×D3semidirect
190. C2×#626C2×D3semidirect
200. C2×#624C2×D3semidirect
201. C2×#624C2×D3semidirect
202. C2×#624C2×D3semidirect
209. C2×D3×Dic3C2×D3semidirect
232. C3×#217C2×D3semidirect
233. C3×#217C2×D3semidirect
234. C3×#217C2×D3semidirect
235. C3×#217C2×D3semidirect
250. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
257. #3722C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
293. C2×C3×C3⋊D3#41semidirect
549. C2×#67D32semidirect
603. #217D32semidirect
604. #217D32semidirect
684. C2×C3⋊D3#235semidirect
795. C33#546semidirect
1167. C32#5490semidirect
1168. C32#5610semidirect
1169. C32#5612semidirect
1289. C3#10594273semidirect
1290. C3#10594278semidirect
1291. C3#10595296semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#889602
#117236342
#117236212
#117235912
C3×#639742
C3×#639712
C3×#639582
#117229952
#117229842
#117229572
#117229512
#117229362
#117229312
#117229052
#105952963
#105942783
#105942733