Finite Group Databasebeta

← #13172916

Subgroups — #13172916

Order 1728.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×#88960C211yesmaximal, characteristic, complemented
3#11723641C211yesmaximal, characteristic, complemented
4#11723634C211yesmaximal, characteristic, complemented
5C3⋊D3×#217C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63974C211yesmaximal, characteristic, complemented
8C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
9#11723010C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic, complemented
12#11722967C211yesmaximal, characteristic, complemented
13#11722960C211yesmaximal, characteristic, complemented
14#11722957C211yesmaximal, characteristic, complemented
15#11722934C211yesmaximal, characteristic, complemented
16#10595135—31nomaximal
17#10594186—31nomaximal
18#10594184—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C23×C3×C3⋊D3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6295—24no—
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic
28C2×#6293C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic, complemented
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88960—24no—
39#88864C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#626—31no—
57C22×#626—31no—
58C22×#625—31no—
59C2×#3804—31no—
60C2×#3798—31no—
61C2×#3795—31no—
62#64146—31no—
63C22⋊C4×C3⋊D3—31no—
64#64087—31no—
65C3×#937—31no—
66C3×D4×Dic3—31no—
67C3×#882—31no—
68C3×#67⋊C4—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63981D311yescharacteristic, complemented
72#63978—31no—
73#63976—31no—
74#63976—31no—
75#63976—61no—
76#63974D311yescharacteristic, complemented
77#67⋊Dic3D311yescharacteristic, complemented
78#63971—31no—
79D3×#217—31no—
80D3×#217—31no—
81D3×#217—61no—
82#63964—31no—
83#63964—31no—
84#63964—61no—
85#63958—31no—
86#63913—31no—
87#63912—31no—
88#63908—31no—
89#63906—31no—
90#63906—31no—
91#63905—31no—
92C4×#626—31no—
93#63891—31no—
94#63890—31no—
95#63885—31no—
96#63885—31no—
97#63880—31no—
98#63879—31no—
99#63854—31no—
100#63853—31no—
101#63852—31no—
102#63852—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—22no—
109C22×C3×C3⋊D3—41no—
110C22×C3×C3⋊D3—41no—
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C22×C3×C3⋊D3C2311yescharacteristic
114C22×C3×C3⋊D3C2311yescharacteristic
115C22×C32×D3C2311yescharacteristic
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3×C3⋊Dic3—22no—
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C32×#67—22no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6295—22no—
128#6295—22no—
129#6295—22no—
130#6295D414yescomplemented
131#6293—22no—
132#6290—22no—
133#6290—41no—
134Dic3×C3⋊D3—22no—
135Dic3×C3⋊D3—41no—
136C3×#626—22no—
137C3×#626—41no—
138C3×#624—22no—
139C3×#624—41no—
140C3×D3×Dic3—22no—
141#5591—91no—
142#5550—91no—
143#5490—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—61no—
151C23×C3×D3—61no—
152C2×C32×D4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C22×C3⋊Dic3C2×D311yescharacteristic
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×#67C2×D311yescharacteristic
163C2×C3×#67C2×D311yescharacteristic
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C22×C3×Dic3—61no—
168C2×C3×D12—31no—
169C2×C3×D12—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×#627—31no—
176C2×#627—31no—
177C2×#627—61no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—64no—
187C2×#626—64no—
188C2×#626C2×D311yescharacteristic, complemented
189C2×#626C2×D311yescharacteristic, complemented
190C2×#625—31no—
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—31no—
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—64no—
199C2×#625—61no—
200C2×#625—61no—
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×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—61no—
219#3757—61no—
220#3757—61no—
221#3757—121no—
222#3752—31no—
223#3752—31no—
224#3752—31no—
225#3752—31no—
226C4⋊(C3⋊Dic3)—31no—
227#3750—31no—
228#3750—31no—
229C3×#217—21no—
230C3×#217—21no—
231C3×#217—31no—
232C3×#217C2×D311yescharacteristic
233C3×#217C2×D311yescharacteristic
234C3×#217C2×D311yescharacteristic
235C3×#217C2×D311yescharacteristic
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×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×C4⋊Dic3—31no—
246C3×Dic3⋊C4—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249#3724—31no—
250#3724—31no—
251#3724—61no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259#3722C2×D311yescharacteristic, complemented
260#3722C2×D311yescharacteristic, complemented
261#3722C2×D311yescharacteristic, complemented
262#3722C2×D311yescharacteristic, complemented
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—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276Dic32C2×D311yescharacteristic, complemented
277C22×C33—21no—
278C22×C33—21no—
279C22×C33#4112yescomplemented
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—21no—
291C2×C3×C3⋊D3—44no—
292C2×C3×C3⋊D3—44no—
293C2×C3×C3⋊D3C2×D412yes—
294C2×C3×C3⋊D3C2×D412yes—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
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—
308C22×#67—91no—
309C2×#237—91no—
310C2×#235—91no—
311C2×#235—91no—
312C22×D12—91no—
313C3×#120—91no—
314C3×C4×D4—91no—
315C2×C3×C22⋊C4—91no—
316#953—91no—
317C2×#217—91no—
318#939—91no—
319#939—91no—
320#938—91no—
321#937—31no—
322#937—91no—
323#937—91no—
324#937—181no—
325D4×Dic3—31no—
326#930—91no—
327#930—91no—
328#929—91no—
329C4×#67—91no—
330#924—91no—
331#894—91no—
332#894—91no—
333#886—91no—
334#885—91no—
335#885—91no—
336#884—91no—
337#884—91no—
338#884—91no—
339#884—91no—
340#883—91no—
341#883—91no—
342#882—31no—
343#67⋊C4—31no—
344#67⋊C4—91no—
345D3×C22⋊C4—31no—
346D3×C22⋊C4—31no—
347D3×C22⋊C4—91no—
348D3×C22⋊C4—91no—
349D3×C22⋊C4—181no—
350#878—91no—
351#878—91no—
352#878—181no—
353#875—91no—
354C4×D12—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—22no—
366C22×C3⋊D3—22no—
367C22×C3⋊D3—41no—
368C22×C3⋊D3—41no—
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3⋊D3C22×D311yescharacteristic
371C22×C3⋊D3C22×D311yescharacteristic
372C22×C3⋊D3C22×D311yescharacteristic
373C22×C3×D3—21no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—61no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
388C22×C3×D3—62no—
389C22×C3×D3—62no—
390C22×C3×D3—64no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—62no—
394C22×C3×D3—62no—
395C22×C3×D3—122no—
396C22×C3×D3—122no—
397C22×C3×D3—122no—
398C22×C3×D3—121no—
399C22×C3×D3—121no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—122no—
403C22×C3×D3—122no—
404C22×C3×D3C22×D311yescharacteristic
405C22×C3×D3C22×D311yescharacteristic
406C32×D4—62no—
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412#638—62no—
413#638—121no—
414C2×C3⋊Dic3—22no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—31no—
419C2×C3⋊Dic3—31no—
420C2×C3⋊Dic3—31no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—61no—
426C2×C3⋊Dic3—61no—
427C2×C3⋊Dic3—121no—
428C2×C3⋊Dic3—121no—
429C2×C3⋊Dic3C22×D311yescharacteristic
430C2×C3⋊Dic3C22×D311yescharacteristic
431C4×C3⋊D3—62no—
432C4×C3⋊D3—121no—
433#634—62no—
434C3×#67—22no—
435C3×#67—22no—
436C3×#67—42no—
437C3×#67—62no—
438C3×#67—121no—
439C2×C3×Dic3—21no—
440C2×C3×Dic3—21no—
441C2×C3×Dic3—21no—
442C2×C3×Dic3—21no—
443C2×C3×Dic3—21no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—61no—
449C2×C3×Dic3—61no—
450C2×C3×Dic3—62no—
451C2×C3×Dic3—62no—
452C2×C3×Dic3—62no—
453C2×C3×Dic3—122no—
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—
471#627—62no—
472#627—62no—
473#627—122no—
474#626—22no—
475#626—34no—
476#626—34no—
477#626—41no—
478#626—62no—
479#626—62no—
480#626—62no—
481#626—62no—
482#626—62no—
483#626—62no—
484#625—34no—
485#625—62no—
486#625—62no—
487#625—62no—
488#625—62no—
489#625—62no—
490#625—122no—
491#625—121no—
492#625—121no—
493#625—122no—
494#624—22no—
495#624—41no—
496D3×Dic3—22no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—122no—
500D3×Dic3—121no—
501D3×Dic3—121no—
502D3×Dic3—122no—
503#546—271noSylow
504C2×C33—22no—
505C2×C33C22×D411yescharacteristic
506C2×C33C2×#4111yescharacteristic
507C2×C33H(5,𝔽2)11yescharacteristic
508C3×C3⋊D3—22no—
509C3×C3⋊D3—22no—
510C3×C3⋊D3—41no—
511C3×C3⋊D3—41no—
512C32×D3—41no—
513C24×C3—91no—
514C24×C3—91no—
515C23×D3—31no—
516C23×D3—31no—
517C23×D3—31no—
518C23×D3—31no—
519C23×D3—61no—
520C23×D3—61no—
521C2×C3×D4—31no—
522C2×C3×D4—31no—
523C2×C3×D4—61no—
524C2×C3×D4—91no—
525C2×C3×D4—91no—
526C22×C3×C4—91no—
527C22×C3×C4—91no—
528C22×C3×C4—91no—
529C22×C3×C4—91no—
530C2×#67—31no—
531C2×#67—31no—
532C2×#67—91no—
533C2×#67—91no—
534C2×#67—91no—
535C2×#67—91no—
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×#67—184no—
550C2×#67D3211yescharacteristic
551C22×Dic3—31no—
552C22×Dic3—31no—
553C22×Dic3—31no—
554C22×Dic3—61no—
555C22×Dic3—91no—
556C22×Dic3—91no—
557#237—184no—
558#235—184no—
559#235—184no—
560C2×D12—31no—
561C2×D12—31no—
562C2×D12—91no—
563C2×D12—91no—
564C2×D12—91no—
565C2×D12—91no—
566C2×D12—184no—
567C2×C4×D3—31no—
568C2×C4×D3—31no—
569C2×C4×D3—31no—
570C2×C4×D3—31no—
571C2×C4×D3—31no—
572C2×C4×D3—91no—
573C2×C4×D3—91no—
574C2×C4×D3—91no—
575C2×C4×D3—91no—
576C2×C4×D3—181no—
577C2×C4×D3—181no—
578C2×Dic6—91no—
579C2×Dic6—91no—
580C2×Dic6—91no—
581C2×Dic6—181no—
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—
593C3×C22⋊C4—91no—
594C3×C42—91no—
595#217—31no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—91no—
600#217—91no—
601#217—91no—
602#217—91no—
603#217—181no—
604#217—181no—
605#217—181no—
606#217—361no—
607#217D3211yescharacteristic
608#217D3211yescharacteristic
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—31no—
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—91no—
632C4⋊Dic3—91no—
633C4⋊Dic3—91no—
634C4⋊Dic3—181no—
635Dic3⋊C4—31no—
636Dic3⋊C4—91no—
637Dic3⋊C4—91no—
638Dic3⋊C4—91no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—181no—
643Dic3⋊C4—181no—
644C4×Dic3—31no—
645C4×Dic3—31no—
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—22no—
656C22×C32—22no—
657C22×C32—22no—
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×C32#23512yescomplemented
672C22×C32#23512yescomplemented
673C22×C32#23712yescomplemented
674C22×C32C23×D311yescharacteristic
675C22×C32C23×D311yescharacteristic
676C22×C32C23×D311yescharacteristic
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—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—44no—
688C2×C3⋊D3—44no—
689C2×C3⋊D3D3×D412yes—
690C2×C3⋊D3D3×D412yes—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—32no—
698C2×C3×D3—32no—
699C2×C3×D3—32no—
700C2×C3×D3—32no—
701C2×C3×D3—41no—
702C2×C3×D3—41no—
703C2×C3×D3—41no—
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—62no—
717C2×C3×D3—62no—
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—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—121no—
734C2×C3×D3—121no—
735C2×C3×D3—121no—
736C2×C3×D3—124no—
737C2×C3×D3—124no—
738C2×C3×D3—124no—
739C2×C3×D3—124no—
740C2×C3×D3—128no—
741C2×C3×D3—128no—
742C32×C4—61no—
743C32×C4—61no—
744C32×C4—61no—
745C32×C4—61no—
746C32×C4—61no—
747C3⋊Dic3—21no—
748C3⋊Dic3—61no—
749C3⋊Dic3—61no—
750C3⋊Dic3—61no—
751C3⋊Dic3—61no—
752C3⋊Dic3—61no—
753C3⋊Dic3—61no—
754C3⋊Dic3—121no—
755C3⋊Dic3—121no—
756C3⋊Dic3—121no—
757C3⋊Dic3—121no—
758C3⋊Dic3—121no—
759C3⋊Dic3—121no—
760C3⋊Dic3—241no—
761C3⋊Dic3—241no—
762C3⋊Dic3D3×D412yes—
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—21no—
772C3×Dic3—21no—
773C3×Dic3—32no—
774C3×Dic3—32no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—41no—
778C3×Dic3—41no—
779C3×Dic3—41no—
780C3×Dic3—62no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—121no—
784C2×#41—271no—
785C22×D4—271no—
786#124—271no—
787#123—271no—
788#123—271no—
789C22⋊Q8—271no—
790#121—271no—
791#121—271no—
792#121—271no—
793#120—91no—
794#120—271no—
795C4×D4—91no—
796C4×D4—271no—
797C2×C22⋊C4—91no—
798C2×C22⋊C4—271no—
799C33#54611yescharacteristic, complemented, Sylow
800C23×C3—21no—
801C23×C3—21no—
802C23×C3—21no—
803C23×C3—31no—
804C23×C3—31no—
805C23×C3—41no—
806C23×C3—61no—
807C23×C3—91no—
808C23×C3—91no—
809C23×C3—91no—
810C23×C3—91no—
811C23×C3—182no—
812C23×C3—182no—
813C23×C3—182no—
814C23×C3—182no—
815C23×C3—361no—
816C23×C3—361no—
817C23×C3C2×D3211yescharacteristic
818C23×C3C2×D3211yescharacteristic
819C23×C3C2×D3211yescharacteristic
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—61no—
829C22×D3—61no—
830C22×D3—61no—
831C22×D3—61no—
832C22×D3—62no—
833C22×D3—62no—
834C22×D3—62no—
835C22×D3—62no—
836C22×D3—64no—
837C22×D3—62no—
838C22×D3—62no—
839C22×D3—62no—
840C22×D3—62no—
841C22×D3—122no—
842C22×D3—122no—
843C22×D3—122no—
844C22×D3—121no—
845C22×D3—121no—
846C22×D3—121no—
847C22×D3—121no—
848C22×D3—122no—
849C22×D3—122no—
850C22×D3C2×D3211yescharacteristic
851C3×D4—62no—
852C3×D4—62no—
853C3×D4—122no—
854C3×D4—182no—
855C3×D4—361no—
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—31no—
864C2×C3×C4—31no—
865C2×C3×C4—31no—
866C2×C3×C4—61no—
867C2×C3×C4—61no—
868C2×C3×C4—61no—
869C2×C3×C4—61no—
870C2×C3×C4—61no—
871C2×C3×C4—91no—
872C2×C3×C4—91no—
873C2×C3×C4—182no—
874C2×C3×C4—182no—
875C2×C3×C4—182no—
876C2×C3×C4—361no—
877#67—22no—
878#67—62no—
879#67—94no—
880#67—94no—
881#67—121no—
882#67—182no—
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—361no—
893#67—361no—
894#67—361no—
895#67—362no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—61no—
901C2×Dic3—61no—
902C2×Dic3—62no—
903C2×Dic3—62no—
904C2×Dic3—62no—
905C2×Dic3—91no—
906C2×Dic3—91no—
907C2×Dic3—91no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—91no—
911C2×Dic3—122no—
912C2×Dic3—181no—
913C2×Dic3—181no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—181no—
918C2×Dic3—182no—
919C2×Dic3—361no—
920C2×Dic3—361no—
921C2×Dic3—361no—
922C2×Dic3C2×D3211yescharacteristic
923C2×Dic3C2×D3211yescharacteristic
924C2×Dic3C2×D3211yescharacteristic
925C2×Dic3C2×D3211yescharacteristic
926C2×Dic3C2×D3211yescharacteristic
927D12—62no—
928D12—94no—
929D12—121no—
930D12—182no—
931D12—182no—
932D12—182no—
933C4×D3—62no—
934C4×D3—62no—
935C4×D3—62no—
936C4×D3—121no—
937C4×D3—121no—
938C4×D3—182no—
939C4×D3—182no—
940C4×D3—362no—
941C4×D3—361no—
942C4×D3—361no—
943C4×D3—362no—
944Dic6—182no—
945Dic6—182no—
946Dic6—182no—
947Dic6—362no—
948C2×C32—22no—
949C2×C32—22no—
950C2×C32—22no—
951C2×C32—21no—
952C2×C32—21no—
953C2×C32—21no—
954C2×C32—21no—
955C2×C32—21no—
956C2×C32—21no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—41no—
961C2×C32—41no—
962C2×C32—41no—
963C2×C32—42no—
964C2×C32—42no—
965C2×C32—42no—
966C2×C32—82no—
967C2×C32—121no—
968C2×C32C2×#23511yescharacteristic
969C2×C32C2×#23511yescharacteristic
970C2×C32C2×D3×D411yescharacteristic
971C2×C32C2×D3×D411yescharacteristic
972C2×C32C2×D3×D411yescharacteristic
973C2×C32C2×#23711yescharacteristic
974C2×C32#100411yescharacteristic
975C2×C32#100411yescharacteristic
976C2×C32#100911yescharacteristic
977C3⋊D3—22no—
978C3⋊D3—22no—
979C3⋊D3—41no—
980C3⋊D3—41no—
981C3×D3—41no—
982C3×D3—41no—
983C3×D3—64no—
984C3×D3—62no—
985C3×D3—62no—
986C3×D3—62no—
987C3×D3—62no—
988C3×D3—81no—
989C3×D3—122no—
990C3×D3—122no—
991C3×D3—122no—
992C3×D3—121no—
993C3×D3—121no—
994C3×D3—121no—
995C3×D3—121no—
996C24—91no—
997C24—91no—
998#41—544no—
999C2×Q8—271no—
1000C2×D4—31no—
1001C2×D4—91no—
1002C2×D4—91no—
1003C2×D4—271no—
1004C2×D4—271no—
1005C2×D4—271no—
1006C2×D4—271no—
1007C2×D4—271no—
1008C2×D4—271no—
1009C2×D4—544no—
1010C22×C4—91no—
1011C22×C4—91no—
1012C22×C4—91no—
1013C22×C4—91no—
1014C22×C4—271no—
1015C22×C4—271no—
1016C4⋊C4—91no—
1017C4⋊C4—271no—
1018C4⋊C4—271no—
1019C4⋊C4—271no—
1020C22⋊C4—31no—
1021C22⋊C4—31no—
1022C22⋊C4—91no—
1023C22⋊C4—91no—
1024C22⋊C4—91no—
1025C22⋊C4—91no—
1026C22⋊C4—91no—
1027C22⋊C4—271no—
1028C22⋊C4—271no—
1029C22⋊C4—271no—
1030C22⋊C4—271no—
1031C22⋊C4—271no—
1032C42—91no—
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—21no—
1042C22×C3—22no—
1043C22×C3—22no—
1044C22×C3—22no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—41no—
1050C22×C3—41no—
1051C22×C3—41no—
1052C22×C3—42no—
1053C22×C3—61no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—61no—
1057C22×C3—61no—
1058C22×C3—61no—
1059C22×C3—81no—
1060C22×C3—81no—
1061C22×C3—92no—
1062C22×C3—92no—
1063C22×C3—121no—
1064C22×C3—121no—
1065C22×C3—121no—
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—181no—
1075C22×C3—181no—
1076C22×C3—364no—
1077C22×C3—364no—
1078C22×C3#379512yescomplemented
1079C22×C3#379812yescomplemented
1080C22×C3#380412yescomplemented
1081C22×C3C22×D3211yescharacteristic
1082C22×C3C22×D3211yescharacteristic
1083C22×C3C22×D3211yescharacteristic
1084C2×D3—21no—
1085C2×D3—21no—
1086C2×D3—21no—
1087C2×D3—32no—
1088C2×D3—32no—
1089C2×D3—32no—
1090C2×D3—32no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
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—62no—
1104C2×D3—62no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
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—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—121no—
1122C2×D3—121no—
1123C2×D3—124no—
1124C2×D3—124no—
1125C2×D3—124no—
1126C2×D3—124no—
1127C2×D3—128no—
1128C2×D3—128no—
1129C3×C4—61no—
1130C3×C4—61no—
1131C3×C4—61no—
1132C3×C4—61no—
1133C3×C4—61no—
1134C3×C4—61no—
1135C3×C4—61no—
1136C3×C4—61no—
1137C3×C4—61no—
1138C3×C4—61no—
1139C3×C4—92no—
1140C3×C4—121no—
1141C3×C4—121no—
1142C3×C4—121no—
1143C3×C4—121no—
1144C3×C4—121no—
1145C3×C4—181no—
1146Dic3—21no—
1147Dic3—21no—
1148Dic3—21no—
1149Dic3—21no—
1150Dic3—21no—
1151Dic3—32no—
1152Dic3—32no—
1153Dic3—62no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—121no—
1157Dic3—181no—
1158Dic3—181no—
1159Dic3—181no—
1160Dic3—181no—
1161Dic3—181no—
1162Dic3—181no—
1163Dic3—361no—
1164Dic3—361no—
1165Dic3—361no—
1166Dic3—361no—
1167Dic3—361no—
1168Dic3—361no—
1169Dic3—721no—
1170Dic3—721no—
1171C32—21no—
1172C32—21no—
1173C32—21no—
1174C32—41no—
1175C32#549011yescharacteristic, complemented
1176C32#555011yescharacteristic, complemented
1177C32#559111yescharacteristic, complemented
1178C23—31no—
1179C23—91no—
1180C23—91no—
1181C23—91no—
1182C23—91no—
1183C23—182no—
1184C23—182no—
1185C23—182no—
1186C23—182no—
1187C23—361no—
1188C23—361no—
1189C23D3311yescharacteristic
1190Q8—542no—
1191D4—62no—
1192D4—182no—
1193D4—274no—
1194D4—361no—
1195D4—542no—
1196D4—542no—
1197D4—542no—
1198D4—542no—
1199D4—1081no—
1200C2×C4—31no—
1201C2×C4—31no—
1202C2×C4—31no—
1203C2×C4—31no—
1204C2×C4—31no—
1205C2×C4—91no—
1206C2×C4—91no—
1207C2×C4—182no—
1208C2×C4—182no—
1209C2×C4—182no—
1210C2×C4—271no—
1211C2×C4—271no—
1212C2×C4—361no—
1213C2×C4—542no—
1214C2×C4—1081no—
1215C2×C3—22no—
1216C2×C3—22no—
1217C2×C3—22no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—21no—
1221C2×C3—21no—
1222C2×C3—21no—
1223C2×C3—21no—
1224C2×C3—21no—
1225C2×C3—21no—
1226C2×C3—21no—
1227C2×C3—42no—
1228C2×C3—42no—
1229C2×C3—42no—
1230C2×C3—41no—
1231C2×C3—41no—
1232C2×C3—41no—
1233C2×C3—82no—
1234C2×C3—121no—
1235C2×C3—121no—
1236C2×C3—182no—
1237C2×C3—182no—
1238C2×C3—241no—
1239C2×C3—361no—
1240C2×C3—361no—
1241C2×C3C2×#379511yescharacteristic
1242C2×C3C2×#379811yescharacteristic
1243C2×C3D32×D411yescharacteristic
1244C2×C3D32×D411yescharacteristic
1245C2×C3D32×D411yescharacteristic
1246C2×C3#6431311yescharacteristic
1247C2×C3#6431411yescharacteristic
1248C2×C3#6431411yescharacteristic
1249C2×C3C2×#380411yescharacteristic
1250D3—41no—
1251D3—64no—
1252D3—62no—
1253D3—62no—
1254D3—62no—
1255D3—62no—
1256D3—122no—
1257D3—122no—
1258D3—122no—
1259D3—121no—
1260D3—121no—
1261D3—121no—
1262D3—121no—
1263C22—21no—
1264C22—21no—
1265C22—61no—
1266C22—61no—
1267C22—61no—
1268C22—92no—
1269C22—92no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—181no—
1275C22—181no—
1276C22—181no—
1277C22—181no—
1278C22—181no—
1279C22—181no—
1280C22—364no—
1281C22—364no—
1282C22#8896012yescomplemented
1283C22C2×D3311yescharacteristic
1284C4—61no—
1285C4—61no—
1286C4—61no—
1287C4—61no—
1288C4—61no—
1289C4—92no—
1290C4—181no—
1291C4—541no—
1292C4—541no—
1293C3—21no—
1294C3—21no—
1295C3—21no—
1296C3—41no—
1297C3#1059418411yescharacteristic, complemented
1298C3#1059418611yescharacteristic, complemented
1299C3#1059513511yescharacteristic, complemented
1300C2—22no—
1301C2—121no—
1302C2—182no—
1303C2—182no—
1304C2—361no—
1305C2—361no—
1306C2#1172441611yescharacteristic
1307C2C2×#8896011yescharacteristic
1308C2#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. C22×#6295C2semidirect
2. C2×#88960C2semidirect
3. #11723641C2semidirect
4. #11723634C2semidirect
5. C3⋊D3×#217C2semidirect
6. C3×#63981C2semidirect
7. C3×#63974C2semidirect
8. C3×#67⋊Dic3C2semidirect
9. #11723010C2semidirect
10. #11722997C2semidirect
11. #11722995C2semidirect
12. #11722967C2semidirect
13. #11722960C2semidirect
14. #11722957C2semidirect
15. #11722934C2semidirect
28. C2×#6293C22semidirect
29. C2×#6290C22semidirect
30. C2×#6290C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×#624C22semidirect
37. C2×C3×D3×Dic3C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. #88803C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
71. #63981D3semidirect
76. #63974D3semidirect
77. #67⋊Dic3D3semidirect
130. #6295D4semidirect
188. C2×#626C2×D3semidirect
189. C2×#626C2×D3semidirect
201. C2×#624C2×D3semidirect
202. C2×#624C2×D3semidirect
210. C2×D3×Dic3C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
259. #3722C2×D3semidirect
260. #3722C2×D3semidirect
261. #3722C2×D3semidirect
262. #3722C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. Dic32C2×D3semidirect
279. C22×C33#41semidirect
671. C22×C32#235semidirect
672. C22×C32#235semidirect
673. C22×C32#237semidirect
799. C33#546semidirect
1078. C22×C3#3795semidirect
1079. C22×C3#3798semidirect
1080. C22×C3#3804semidirect
1175. C32#5490semidirect
1176. C32#5550semidirect
1177. C32#5591semidirect
1282. C22#88960semidirect
1297. C3#10594184semidirect
1298. C3#10594186semidirect
1299. C3#10595135semidirect

Maximal subgroups

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

subgroupindex
C22×#62952
C2×#889602
#117236412
#117236342
C3⋊D3×#2172
C3×#639812
C3×#639742
C3×#67⋊Dic32
#117230102
#117229972
#117229952
#117229672
#117229602
#117229572
#117229342
#105951353
#105941863
#105941843