Finite Group Databasebeta

← #13172049

Subgroups — #13172049

Order 1728.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89031C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723717C211yesmaximal, characteristic, complemented
4#11723635C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8#11723033C211yesmaximal, characteristic, complemented
9#11723030C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11723002C211yesmaximal, characteristic, complemented
12#11722934C211yesmaximal, characteristic, complemented
13#11722933C211yesmaximal, characteristic, complemented
14#11722932C211yesmaximal, characteristic, complemented
15Dic3×#626C211yesmaximal, characteristic, complemented
16#10595155—31nomaximal
17#10595029—31nomaximal
18#10594910—31nomaximal
19C2×#6312C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6293C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32#89031—24no—
33C2×Dic3×C3⋊D3C2211yescharacteristic
34C2×C3×#627C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#626C2211yescharacteristic
37C2×C3×#624C2211yescharacteristic
38C3×#3804—24no—
39C2×C3×D3×Dic3C2211yescharacteristic
40#88815C2211yescharacteristic
41#88814C2211yescharacteristic
42#88814C2211yescharacteristic
43#88807C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C3×Dic32C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C2×#3828—31no—
57C2×C3×#237—31no—
58C2×C3×#235—31no—
59C2×#3804—31no—
60C2×#3804—31no—
61C2×#3804—61no—
62C2×#3804D311yescharacteristic, complemented
63#64148—31no—
64#64139—31no—
65C3×#939—31no—
66C3×#930—31no—
67C2×C3×C4×Dic3—31no—
68C2×C3×C4×Dic3—31no—
69#63980—31no—
70#63979—31no—
71#63978—31no—
72#63978—31no—
73#63978—31no—
74#63978—31no—
75#63978—31no—
76#63978—31no—
77#63978—61no—
78#63978—61no—
79#63978D311yescharacteristic, complemented
80Dic3×#67—31no—
81#63959—31no—
82C2×Dic32D311yescharacteristic, complemented
83#63952—31no—
84#63918—31no—
85#63911—31no—
86#63911—31no—
87#63907—31no—
88#63904—31no—
89C4×#626—31no—
90C4×#626—31no—
91C4×#626—31no—
92C4×#626—31no—
93#63894—31no—
94Dic3×D12—31no—
95#63880—31no—
96#63880—31no—
97#63879—31no—
98#63866—31no—
99#63864—31no—
100#63860—31no—
101#63852—31no—
102#63852—31no—
103#63839—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109#6312—22no—
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638—22no—
112C3×#638—22no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C2×C32×Dic3—22no—
120C2×C32×Dic3D414yescomplemented
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6295—22no—
127#6293—22no—
128#6292—22no—
129#6292—22no—
130#6291—22no—
131#6289—22no—
132Dic3×C3⋊D3—22no—
133C3×#627—22no—
134C3×#626—22no—
135C3×#626—22no—
136C3×#624—22no—
137C3×D3×Dic3—22no—
138#5832—91no—
139#5596—91no—
140#5477—91no—
141C2×C32×D4—31no—
142C22×C32×C4—31no—
143C22×C32×C4—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—61no—
149C2×#638—61no—
150C2×#638—61no—
151C2×#638—121no—
152C2×#638C2×D311yescharacteristic
153C2×#638C2×D311yescharacteristic
154C22×C3⋊Dic3C2×D311yescharacteristic
155#3828—64no—
156C2×C4⋊(C3⋊D3)—31no—
157C2×C4⋊(C3⋊D3)—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—31no—
160C2×#634—31no—
161C2×C3×#67—21no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—61no—
169C2×C3×#67—61no—
170C2×C3×#67C2×D311yescharacteristic
171C2×C3×#67C2×D311yescharacteristic
172C22×C3×Dic3—21no—
173C22×C3×Dic3—21no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—31no—
176C22×C3×Dic3—31no—
177C22×C3×Dic3—61no—
178C22×C3×Dic3C2×D311yescharacteristic
179C22×C3×Dic3C2×D311yescharacteristic
180C22×C3×Dic3C2×D311yescharacteristic
181C22×C3×Dic3C2×D311yescharacteristic
182C3×#237—64no—
183C3×#235—64no—
184C2×C3×D12—31no—
185C2×C3×D12—31no—
186C2×C3×C4×D3—31no—
187C2×C3×C4×D3—31no—
188C2×C3×C4×D3—31no—
189C2×C3×Dic6—31no—
190C2×C3×Dic6—31no—
191C2×#627—31no—
192C2×#627—31no—
193C2×#627—61no—
194C2×#627C2×D311yescharacteristic
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—61no—
204C2×#626—61no—
205C2×#626—61no—
206C2×#626C2×D311yescharacteristic
207C2×#626C2×D311yescharacteristic
208C2×#625—31no—
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—61no—
212C2×#624C2×D311yescharacteristic
213#3804—24no—
214#3804—68no—
215#3804—64no—
216#3804—64no—
217C2×D3×Dic3—31no—
218C2×D3×Dic3—31no—
219C2×D3×Dic3—61no—
220C2×D3×Dic3C2×D311yescharacteristic
221#3757—31no—
222#3752—31no—
223#3752—31no—
224#3752—31no—
225C4⋊(C3⋊Dic3)—31no—
226#3750—31no—
227C3×#217—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×C4⋊Dic3—31no—
232C3×Dic3⋊C4—31no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—31no—
236C3×C4×Dic3—31no—
237C3×C4×Dic3—31no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—31no—
241#3724—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3C2×D311yescharacteristic
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—61no—
258#3722—61no—
259#3722C2×D311yescharacteristic
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)⋊Dic3C2×D311yescharacteristic
271Dic32C2×D311yescharacteristic
272Dic32C2×D311yescharacteristic
273Dic32C2×D311yescharacteristic
274Dic32C2×D311yescharacteristic
275C22×C33—21no—
276C22×C33—21no—
277C22×C33C2×D412yes—
278C22×C33C2411yescharacteristic
279C2×C3⋊(C3⋊D3)—21no—
280C2×C3⋊(C3⋊D3)—21no—
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×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C3⋊(C3⋊Dic3)—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3#4112yescomplemented
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3C2×D412yes—
299C32×Dic3C2×D412yes—
300C32×Dic3#4112yescomplemented
301C2×C3×#41—91no—
302C2×#237—31no—
303C2×#237—91no—
304C2×#235—31no—
305C2×#235—91no—
306C2×#235—91no—
307C2×#235—181no—
308C3×#121—91no—
309C2×C3×C42—91no—
310#947—91no—
311#944—91no—
312#940—91no—
313#940—91no—
314#939—31no—
315#939—91no—
316#939—91no—
317#939—91no—
318#939—91no—
319#939—91no—
320#939—181no—
321#936—91no—
322D4×Dic3—91no—
323#930—31no—
324#930—91no—
325#930—91no—
326#930—91no—
327#930—91no—
328#930—181no—
329C4×#67—91no—
330C4×#67—91no—
331C4×#67—91no—
332C4×#67—91no—
333C2×C4×Dic3—31no—
334C2×C4×Dic3—31no—
335#893—91no—
336#888—91no—
337#885—91no—
338#885—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#875—91no—
342#875—91no—
343#874—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—91no—
348#869—91no—
349C23×C32—21no—
350C23×C32—21no—
351C23×C32—21no—
352C23×C32—31no—
353C23×C32—41no—
354C23×C32C22×D311yescharacteristic
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C22×C3⋊D3—31no—
358C22×C3⋊D3—31no—
359C22×C3⋊D3—31no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—61no—
363C22×C3⋊D3—121no—
364C22×C3⋊D3C22×D311yescharacteristic
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3×D3—21no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—31no—
370C22×C3×D3—31no—
371C22×C3×D3—61no—
372C22×C3×D3—61no—
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C32×D4—62no—
376C2×C32×C4—34no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—31no—
382C2×C32×C4—62no—
383#638—22no—
384#638—22no—
385#638—62no—
386#638—64no—
387#638—62no—
388#638—62no—
389#638—62no—
390#638—122no—
391#638—122no—
392#638—124no—
393C2×C3⋊Dic3—22no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—121no—
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C4⋊(C3⋊D3)—62no—
406C4⋊(C3⋊D3)—62no—
407C4×C3⋊D3—62no—
408C4×C3⋊D3—62no—
409#634—62no—
410C3×#67—22no—
411C3×#67—22no—
412C3×#67—42no—
413C3×#67—64no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—62no—
417C3×#67—62no—
418C3×#67—62no—
419C3×#67—62no—
420C3×#67—122no—
421C2×C3×Dic3—22no—
422C2×C3×Dic3—22no—
423C2×C3×Dic3—24no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
428C2×C3×Dic3—21no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—42no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3—62no—
445C2×C3×Dic3—122no—
446C2×C3×Dic3D1214yescomplemented
447C2×C3×Dic3#6714yescomplemented
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C3×D12—62no—
459C3×D12—62no—
460C3×C4×D3—62no—
461C3×C4×D3—62no—
462C3×C4×D3—62no—
463C3×Dic6—62no—
464C3×Dic6—62no—
465#627—22no—
466#627—64no—
467#627—62no—
468#627—62no—
469#626—22no—
470#626—22no—
471#626—64no—
472#626—62no—
473#626—62no—
474#626—62no—
475#626—62no—
476#626—62no—
477#626—62no—
478#626—62no—
479#626—62no—
480#626—122no—
481#626—122no—
482#625—62no—
483#624—22no—
484#624—64no—
485#624—62no—
486#624—62no—
487D3×Dic3—22no—
488D3×Dic3—64no—
489D3×Dic3—62no—
490D3×Dic3—62no—
491#532—271noSylow
492C2×C33—22no—
493C2×C33C22×D411yescharacteristic
494C2×C33C2×#4111yescharacteristic
495C2×C33C2×#4111yescharacteristic
496C3⋊(C3⋊D3)—41no—
497C3×C3⋊D3—41no—
498C3×C3⋊D3—41no—
499C32×D3—41no—
500C3×#41—184no—
501C2×C3×Q8—91no—
502C2×C3×D4—31no—
503C2×C3×D4—31no—
504C2×C3×D4—61no—
505C2×C3×D4—91no—
506C2×C3×D4—91no—
507C2×C3×D4—91no—
508C2×C3×D4—91no—
509C22×C3×C4—31no—
510C22×C3×C4—31no—
511C22×C3×C4—31no—
512C22×C3×C4—31no—
513C22×C3×C4—61no—
514C22×C3×C4—61no—
515C22×C3×C4—91no—
516C22×C3×C4—91no—
517C22×C3×C4—91no—
518C2×#67—31no—
519C2×#67—31no—
520C2×#67—31no—
521C2×#67—31no—
522C2×#67—31no—
523C2×#67—31no—
524C2×#67—61no—
525C2×#67—61no—
526C2×#67—91no—
527C2×#67—91no—
528C2×#67—91no—
529C2×#67—91no—
530C2×#67—91no—
531C2×#67—91no—
532C2×#67—91no—
533C2×#67—91no—
534C2×#67—91no—
535C2×#67—181no—
536C2×#67—181no—
537C2×#67—181no—
538C2×#67—181no—
539C2×#67—361no—
540C2×#67D3211yescharacteristic
541C22×Dic3—31no—
542C22×Dic3—31no—
543C22×Dic3—31no—
544C22×Dic3—61no—
545C22×Dic3—91no—
546C22×Dic3D3211yescharacteristic
547C22×Dic3D3211yescharacteristic
548#237—64no—
549#237—184no—
550#235—64no—
551#235—184no—
552#235—184no—
553#235—188no—
554C2×D12—31no—
555C2×D12—31no—
556C2×D12—91no—
557C2×D12—91no—
558C2×D12—91no—
559C2×D12—91no—
560C2×D12—91no—
561C2×D12—91no—
562C2×D12—181no—
563C2×D12—181no—
564C2×C4×D3—31no—
565C2×C4×D3—31no—
566C2×C4×D3—31no—
567C2×C4×D3—91no—
568C2×C4×D3—91no—
569C2×C4×D3—91no—
570C2×C4×D3—91no—
571C2×C4×D3—91no—
572C2×C4×D3—181no—
573C2×C4×D3—181no—
574C2×Dic6—31no—
575C2×Dic6—31no—
576C2×Dic6—91no—
577C2×Dic6—91no—
578C2×Dic6—91no—
579C2×Dic6—181no—
580C3×C4⋊C4—91no—
581C3×C22⋊C4—91no—
582C3×C22⋊C4—91no—
583C3×C42—91no—
584C3×C42—91no—
585C3×C42—91no—
586C3×C42—91no—
587#217—31no—
588#217—91no—
589#217—91no—
590#217—91no—
591#217—91no—
592#217—91no—
593#217—181no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—31no—
596(C2×D3)⋊C4—31no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—91no—
607(C2×D3)⋊C4—91no—
608(C2×D3)⋊C4—91no—
609(C2×D3)⋊C4—91no—
610(C2×D3)⋊C4—181no—
611(C2×D3)⋊C4—181no—
612(C2×D3)⋊C4—181no—
613C4⋊Dic3—31no—
614C4⋊Dic3—91no—
615C4⋊Dic3—91no—
616C4⋊Dic3—91no—
617C4⋊Dic3—91no—
618C4⋊Dic3—181no—
619Dic3⋊C4—31no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623Dic3⋊C4—91no—
624Dic3⋊C4—91no—
625Dic3⋊C4—181no—
626C4×Dic3—31no—
627C4×Dic3—31no—
628C4×Dic3—31no—
629C4×Dic3—31no—
630C4×Dic3—31no—
631C4×Dic3—31no—
632C4×Dic3—31no—
633C4×Dic3—31no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—21no—
641C22×C32—21no—
642C22×C32—21no—
643C22×C32—22no—
644C22×C32—22no—
645C22×C32—22no—
646C22×C32—41no—
647C22×C32—42no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—41no—
654C22×C32—61no—
655C22×C32—61no—
656C22×C32—61no—
657C22×C32—81no—
658C22×C32—81no—
659C22×C32C2×D1212yes—
660C22×C32D3×D412yes—
661C22×C32C2×#6712yes—
662C22×C32C23×D311yescharacteristic
663C22×C32C23×D311yescharacteristic
664C22×C32C23×D311yescharacteristic
665C2×C3⋊D3—21no—
666C2×C3⋊D3—21no—
667C2×C3⋊D3—21no—
668C2×C3⋊D3—21no—
669C2×C3⋊D3—21no—
670C2×C3⋊D3—21no—
671C2×C3⋊D3—61no—
672C2×C3⋊D3—62no—
673C2×C3⋊D3—61no—
674C2×C3⋊D3—61no—
675C2×C3⋊D3—61no—
676C2×C3⋊D3—61no—
677C2×C3⋊D3—61no—
678C2×C3⋊D3—61no—
679C2×C3⋊D3—61no—
680C2×C3⋊D3—61no—
681C2×C3⋊D3—121no—
682C2×C3⋊D3—121no—
683C2×C3⋊D3—122no—
684C2×C3⋊D3—121no—
685C2×C3⋊D3—121no—
686C2×C3⋊D3—121no—
687C2×C3⋊D3—121no—
688C2×C3⋊D3—121no—
689C2×C3⋊D3—121no—
690C2×C3⋊D3—241no—
691C2×C3⋊D3—241no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—41no—
699C2×C3×D3—41no—
700C2×C3×D3—41no—
701C2×C3×D3—62no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
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—121no—
715C2×C3×D3—121no—
716C2×C3×D3—121no—
717C2×C3×D3—121no—
718C2×C3×D3—121no—
719C32×C4—32no—
720C32×C4—32no—
721C32×C4—32no—
722C32×C4—61no—
723C32×C4—61no—
724C3⋊Dic3—21no—
725C3⋊Dic3—21no—
726C3⋊Dic3—21no—
727C3⋊Dic3—61no—
728C3⋊Dic3—62no—
729C3⋊Dic3—61no—
730C3⋊Dic3—61no—
731C3⋊Dic3—121no—
732C3⋊Dic3—121no—
733C3⋊Dic3—122no—
734C3⋊Dic3#23512yescomplemented
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C3×Dic3—32no—
743C3×Dic3—32no—
744C3×Dic3—41no—
745C3×Dic3—41no—
746C3×Dic3—62no—
747C3×Dic3—62no—
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×Dic3C2×D1212yes—
757C3×Dic3C2×D1212yes—
758C3×Dic3#23512yescomplemented
759C3×Dic3#23712yescomplemented
760C3×Dic3C2×#6712yes—
761C3×Dic3C2×#6712yes—
762C2×#41—91no—
763C2×#41—271no—
764C4⋊Q8—271no—
765#127—271no—
766#124—271no—
767#124—271no—
768#121—91no—
769#121—271no—
770#121—271no—
771#121—271no—
772C4×D4—271no—
773C4×D4—271no—
774C4×D4—271no—
775C4×D4—271no—
776C2×C42—91no—
777C33#53211yescharacteristic, complemented, Sylow
778C23×C3—21no—
779C23×C3—21no—
780C23×C3—21no—
781C23×C3—31no—
782C23×C3—31no—
783C23×C3—41no—
784C23×C3—61no—
785C23×C3—91no—
786C23×C3—91no—
787C23×C3C2×D3211yescharacteristic
788C23×C3C2×D3211yescharacteristic
789C23×C3C2×D3211yescharacteristic
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—31no—
793C22×D3—31no—
794C22×D3—61no—
795C22×D3—61no—
796C22×D3—91no—
797C22×D3—91no—
798C22×D3—91no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—181no—
802C22×D3—361no—
803C22×D3C2×D3211yescharacteristic
804C3×Q8—182no—
805C3×D4—62no—
806C3×D4—62no—
807C3×D4—122no—
808C3×D4—182no—
809C3×D4—182no—
810C3×D4—182no—
811C3×D4—182no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—34no—
819C2×C3×C4—34no—
820C2×C3×C4—31no—
821C2×C3×C4—31no—
822C2×C3×C4—31no—
823C2×C3×C4—31no—
824C2×C3×C4—61no—
825C2×C3×C4—61no—
826C2×C3×C4—61no—
827C2×C3×C4—64no—
828C2×C3×C4—61no—
829C2×C3×C4—61no—
830C2×C3×C4—62no—
831C2×C3×C4—62no—
832C2×C3×C4—91no—
833C2×C3×C4—91no—
834C2×C3×C4—91no—
835C2×C3×C4—91no—
836C2×C3×C4—122no—
837C2×C3×C4—182no—
838C2×C3×C4—182no—
839C2×C3×C4—182no—
840#67—22no—
841#67—64no—
842#67—62no—
843#67—62no—
844#67—62no—
845#67—62no—
846#67—62no—
847#67—62no—
848#67—122no—
849#67—182no—
850#67—182no—
851#67—182no—
852#67—182no—
853#67—184no—
854#67—182no—
855#67—182no—
856#67—182no—
857#67—182no—
858#67—182no—
859#67—362no—
860#67—362no—
861#67—362no—
862#67—364no—
863C2×Dic3—22no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—31no—
867C2×Dic3—31no—
868C2×Dic3—31no—
869C2×Dic3—31no—
870C2×Dic3—31no—
871C2×Dic3—31no—
872C2×Dic3—61no—
873C2×Dic3—61no—
874C2×Dic3—61no—
875C2×Dic3—61no—
876C2×Dic3—62no—
877C2×Dic3—62no—
878C2×Dic3—62no—
879C2×Dic3—91no—
880C2×Dic3—91no—
881C2×Dic3—91no—
882C2×Dic3—122no—
883C2×Dic3—181no—
884C2×Dic3—181no—
885C2×Dic3—181no—
886C2×Dic3—182no—
887C2×Dic3—361no—
888C2×Dic3#62614yescomplemented
889C2×Dic3C2×D3211yescharacteristic
890C2×Dic3C2×D3211yescharacteristic
891C2×Dic3C2×D3211yescharacteristic
892C2×Dic3C2×D3211yescharacteristic
893C2×Dic3C2×D3211yescharacteristic
894D12—62no—
895D12—62no—
896D12—182no—
897D12—182no—
898D12—182no—
899D12—182no—
900D12—184no—
901D12—182no—
902D12—182no—
903D12—362no—
904C4×D3—62no—
905C4×D3—62no—
906C4×D3—62no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—184no—
910C4×D3—182no—
911C4×D3—182no—
912C4×D3—184no—
913C4×D3—182no—
914Dic6—62no—
915Dic6—62no—
916Dic6—182no—
917Dic6—182no—
918Dic6—184no—
919Dic6—182no—
920C2×C32—22no—
921C2×C32—22no—
922C2×C32—22no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—21no—
929C2×C32—21no—
930C2×C32—21no—
931C2×C32—21no—
932C2×C32—41no—
933C2×C32—41no—
934C2×C32—41no—
935C2×C32—42no—
936C2×C32—42no—
937C2×C32—42no—
938C2×C32—82no—
939C2×C32—121no—
940C2×C32C22×D1211yescharacteristic
941C2×C32C2×#23511yescharacteristic
942C2×C32C2×#23511yescharacteristic
943C2×C32C2×D3×D411yescharacteristic
944C2×C32C2×#23711yescharacteristic
945C2×C32D3×#4111yescharacteristic
946C2×C32D3×#4111yescharacteristic
947C2×C32D3×#4111yescharacteristic
948C2×C32C22×#6711yescharacteristic
949C3⋊D3—41no—
950C3⋊D3—41no—
951C3⋊D3—121no—
952C3⋊D3—122no—
953C3⋊D3—121no—
954C3⋊D3—121no—
955C3⋊D3—241no—
956C3⋊D3—241no—
957C3⋊D3—242no—
958C3×D3—41no—
959C3×D3—41no—
960C3×D3—81no—
961C3×D3—122no—
962C3×D3—121no—
963C3×D3—121no—
964C3×D3—121no—
965C3×D3—121no—
966C3×D3—241no—
967#41—184no—
968#41—544no—
969C2×Q8—91no—
970C2×Q8—271no—
971C2×D4—31no—
972C2×D4—91no—
973C2×D4—91no—
974C2×D4—91no—
975C2×D4—91no—
976C2×D4—271no—
977C2×D4—271no—
978C2×D4—271no—
979C2×D4—271no—
980C2×D4—271no—
981C22×C4—31no—
982C22×C4—31no—
983C22×C4—91no—
984C22×C4—91no—
985C22×C4—91no—
986C22×C4—271no—
987C22×C4—271no—
988C4⋊C4—91no—
989C4⋊C4—271no—
990C4⋊C4—271no—
991C4⋊C4—271no—
992C22⋊C4—91no—
993C22⋊C4—91no—
994C22⋊C4—271no—
995C22⋊C4—271no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22⋊C4—271no—
1000C42—91no—
1001C42—91no—
1002C42—91no—
1003C42—91no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—21no—
1013C22×C3—22no—
1014C22×C3—22no—
1015C22×C3—22no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—41no—
1019C22×C3—41no—
1020C22×C3—41no—
1021C22×C3—41no—
1022C22×C3—41no—
1023C22×C3—42no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—61no—
1028C22×C3—61no—
1029C22×C3—61no—
1030C22×C3—81no—
1031C22×C3—81no—
1032C22×C3—121no—
1033C22×C3—121no—
1034C22×C3—121no—
1035C22×C3—181no—
1036C22×C3—181no—
1037C22×C3—181no—
1038C22×C3—181no—
1039C22×C3—181no—
1040C22×C3—181no—
1041C22×C3D3×D1212yes—
1042C22×C3C2×#62612yes—
1043C22×C3D3×#6712yes—
1044C22×C3C22×D3211yescharacteristic
1045C22×C3C22×D3211yescharacteristic
1046C22×C3C22×D3211yescharacteristic
1047C2×D3—21no—
1048C2×D3—21no—
1049C2×D3—21no—
1050C2×D3—62no—
1051C2×D3—61no—
1052C2×D3—61no—
1053C2×D3—61no—
1054C2×D3—61no—
1055C2×D3—61no—
1056C2×D3—61no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—182no—
1069C2×D3—181no—
1070C2×D3—181no—
1071C2×D3—181no—
1072C2×D3—181no—
1073C2×D3—181no—
1074C2×D3—181no—
1075C2×D3—181no—
1076C2×D3—181no—
1077C2×D3—181no—
1078C2×D3—361no—
1079C2×D3—361no—
1080C2×D3—361no—
1081C2×D3—361no—
1082C2×D3—361no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—362no—
1087C2×D3—721no—
1088C2×D3—721no—
1089C3×C4—32no—
1090C3×C4—32no—
1091C3×C4—32no—
1092C3×C4—32no—
1093C3×C4—32no—
1094C3×C4—32no—
1095C3×C4—62no—
1096C3×C4—62no—
1097C3×C4—62no—
1098C3×C4—61no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—61no—
1102C3×C4—92no—
1103C3×C4—121no—
1104C3×C4—121no—
1105C3×C4—181no—
1106C3×C4—181no—
1107C3×C4—181no—
1108Dic3—21no—
1109Dic3—21no—
1110Dic3—32no—
1111Dic3—32no—
1112Dic3—62no—
1113Dic3—62no—
1114Dic3—61no—
1115Dic3—61no—
1116Dic3—61no—
1117Dic3—61no—
1118Dic3—61no—
1119Dic3—61no—
1120Dic3—121no—
1121Dic3—121no—
1122Dic3—182no—
1123Dic3—181no—
1124Dic3—181no—
1125Dic3—181no—
1126Dic3—361no—
1127Dic3—361no—
1128Dic3—362no—
1129Dic3#380412yescomplemented
1130Dic3C2×#62612yes—
1131Dic3C2×#62612yes—
1132C32—21no—
1133C32—21no—
1134C32—21no—
1135C32—41no—
1136C32#547711yescharacteristic, complemented
1137C32#559611yescharacteristic, complemented
1138C32#583211yescharacteristic, complemented
1139C23—31no—
1140C23—91no—
1141C23—91no—
1142C23—271no—
1143C23D3311yescharacteristic
1144Q8—182no—
1145Q8—542no—
1146D4—62no—
1147D4—182no—
1148D4—182no—
1149D4—182no—
1150D4—182no—
1151D4—542no—
1152D4—542no—
1153D4—542no—
1154D4—542no—
1155D4—542no—
1156C2×C4—31no—
1157C2×C4—31no—
1158C2×C4—31no—
1159C2×C4—34no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—62no—
1163C2×C4—91no—
1164C2×C4—91no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—182no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—271no—
1171C2×C4—542no—
1172C2×C4—542no—
1173C2×C3—22no—
1174C2×C3—22no—
1175C2×C3—22no—
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—42no—
1186C2×C3—42no—
1187C2×C3—42no—
1188C2×C3—41no—
1189C2×C3—41no—
1190C2×C3—41no—
1191C2×C3—82no—
1192C2×C3—121no—
1193C2×C3—121no—
1194C2×C3—241no—
1195C2×C3—361no—
1196C2×C3—361no—
1197C2×C3C2×D3×D1211yescharacteristic
1198C2×C3D3×#23511yescharacteristic
1199C2×C3D3×#23511yescharacteristic
1200C2×C3D3×#23511yescharacteristic
1201C2×C3D3×#23711yescharacteristic
1202C2×C3#6431211yescharacteristic
1203C2×C3C2×#380411yescharacteristic
1204C2×C3C22×#62611yescharacteristic
1205C2×C3C2×D3×#6711yescharacteristic
1206D3—41no—
1207D3—122no—
1208D3—121no—
1209D3—121no—
1210D3—121no—
1211D3—121no—
1212D3—241no—
1213D3—362no—
1214D3—361no—
1215D3—361no—
1216D3—361no—
1217D3—721no—
1218D3—721no—
1219D3—722no—
1220C22—21no—
1221C22—21no—
1222C22—61no—
1223C22—61no—
1224C22—61no—
1225C22—181no—
1226C22—181no—
1227C22—181no—
1228C22—181no—
1229C22—181no—
1230C22—181no—
1231C22—541no—
1232C22—541no—
1233C22—541no—
1234C22D3×#62612yes—
1235C22C2×D3311yescharacteristic
1236C4—32no—
1237C4—32no—
1238C4—32no—
1239C4—61no—
1240C4—61no—
1241C4—92no—
1242C4—181no—
1243C4—181no—
1244C4—181no—
1245C4—541no—
1246C3—21no—
1247C3—21no—
1248C3—21no—
1249C3—41no—
1250C3#1059491011yescharacteristic, complemented
1251C3#1059502911yescharacteristic, complemented
1252C3#1059515511yescharacteristic, complemented
1253C2—22no—
1254C2—121no—
1255C2—361no—
1256C2—361no—
1257C2—1081no—
1258C2D3×#380411yescharacteristic
1259C2#1172441011yescharacteristic
1260C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#532
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×C3×#3804C2semidirect
3. #11723717C2semidirect
4. #11723635C2semidirect
5. #11723632C2semidirect
6. C3×#63978C2semidirect
7. C2×C3×Dic32C2semidirect
8. #11723033C2semidirect
9. #11723030C2semidirect
10. #11723003C2semidirect
11. #11723002C2semidirect
12. #11722934C2semidirect
13. #11722933C2semidirect
14. #11722932C2semidirect
15. Dic3×#626C2semidirect
62. C2×#3804D3semidirect
79. #63978D3semidirect
82. C2×Dic32D3semidirect
120. C2×C32×Dic3D4semidirect
295. C3×C3⋊Dic3#41semidirect
300. C32×Dic3#41semidirect
446. C2×C3×Dic3D12semidirect
447. C2×C3×Dic3#67semidirect
734. C3⋊Dic3#235semidirect
758. C3×Dic3#235semidirect
759. C3×Dic3#237semidirect
777. C33#532semidirect
888. C2×Dic3#626semidirect
1129. Dic3#3804semidirect
1136. C32#5477semidirect
1137. C32#5596semidirect
1138. C32#5832semidirect
1250. C3#10594910semidirect
1251. C3#10595029semidirect
1252. C3#10595155semidirect

Maximal subgroups

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

subgroupindex
C2×#890312
C2×C3×#38042
#117237172
#117236352
#117236322
C3×#639782
C2×C3×Dic322
#117230332
#117230302
#117230032
#117230022
#117229342
#117229332
#117229322
Dic3×#6262
#105951553
#105950293
#105949103