Finite Group Databasebeta

← #13172855

Subgroups — #13172855

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#88960C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723624C211yesmaximal, characteristic, complemented
5#11723592C211yesmaximal, characteristic, complemented
6C3×#63974C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63969C211yesmaximal, characteristic, complemented
9#11722993C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722961C211yesmaximal, characteristic, complemented
12#11722950C211yesmaximal, characteristic, complemented
13#11722938C211yesmaximal, characteristic, complemented
14#11722930C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595163—31nomaximal
17#10594273—31nomaximal
18#10594272—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic, complemented
26C3⋊D3×#67—24no—
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic, complemented
34C2×C3×#624C2211yescharacteristic, complemented
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88960—24no—
39C3×#3757C2211yescharacteristic, complemented
40C32×#217C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88814C2211yescharacteristic
43#88814C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×#67—61no—
60C2×#3804—31no—
61C2×#3798—31no—
62C2×#3795—31no—
63#64094—31no—
64#64093—31no—
65C3×#939—31no—
66C3×#935—31no—
67C3×#884—31no—
68C3×#883—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63981—31no—
72#63981—31no—
73#63977—31no—
74#63976—31no—
75#63974D311yescharacteristic, complemented
76#63971—31no—
77#63971—31no—
78#63971—61no—
79#63971D311yescharacteristic, complemented
80#63969D311yescharacteristic, complemented
81C2×#3722—31no—
82#63953—31no—
83#63953—31no—
84#63953—61no—
85#63952—31no—
86#63923—31no—
87#63922—31no—
88D3×(C2×D3)⋊C4—31no—
89D3×(C2×D3)⋊C4—31no—
90#63910—31no—
91#63909—31no—
92#63906—31no—
93#63902—31no—
94C4×#625—31no—
95#63899—31no—
96#63897—31no—
97#63896—31no—
98#63881—31no—
99#63881—31no—
100#63879—31no—
101#63865—31no—
102#63850—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—41no—
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—41no—
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C32×#67—22no—
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6295—22no—
129#6295—22no—
130#6293—22no—
131#6292—22no—
132#6292—41no—
133#6290D414yescomplemented
134Dic3×C3⋊D3—22no—
135Dic3×C3⋊D3—22no—
136C3×#626—22no—
137C3×#624—22no—
138C3×#624—41no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5654—91no—
142#5610—91no—
143#5490—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—61no—
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—61no—
158C2×#638—61no—
159C2×#638—61no—
160C2×#638—121no—
161C2×#638C2×D311yescharacteristic, complemented
162D4×C3⋊D3—64no—
163C2×C4⋊(C3⋊D3)—31no—
164C2×C4⋊(C3⋊D3)—31no—
165C2×C4×C3⋊D3—31no—
166C2×C4×C3⋊D3—31no—
167C2×#634—31no—
168C2×C3×#67—21no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—61no—
173C2×C3×#67C2×D311yescharacteristic
174C2×C3×#67C2×D311yescharacteristic
175C22×C3×Dic3—31no—
176C22×C3×Dic3—31no—
177C2×C3×D12—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—31no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×C3×C4×D3—31no—
183C2×C3×C4×D3—31no—
184D3×#67—64no—
185D3×#67—64no—
186D3×#67—68no—
187C2×#627—31no—
188C2×#627—31no—
189C2×#627—61no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—61no—
199C2×#626—61no—
200C2×#626C2×D311yescharacteristic, complemented
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—31no—
204C2×#625—31no—
205C2×#625—61no—
206C2×#624C2×D311yescharacteristic, complemented
207C2×#624C2×D311yescharacteristic, complemented
208#3804—64no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—61no—
214C2×D3×Dic3—61no—
215C2×D3×Dic3C2×D311yescharacteristic, complemented
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217#3798—64no—
218#3795—64no—
219C32×C22⋊C4—31no—
220C32×C22⋊C4—31no—
221#3757C2×D311yescharacteristic, complemented
222#3752—31no—
223#3752—31no—
224#3752—31no—
225#3750—31no—
226C4×C3⋊Dic3—31no—
227C3×#217—21no—
228C3×#217—21no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—61no—
233C3×#217C2×D311yescharacteristic, complemented
234C3×#217C2×D311yescharacteristic, complemented
235C3×#217C2×D311yescharacteristic, complemented
236C3×#217C2×D311yescharacteristic, complemented
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×C4⋊Dic3—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250#3724—31no—
251#3724—31no—
252#3724—61no—
253#3724C2×D311yescharacteristic, complemented
254#3724C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—61no—
265#3722—61no—
266#3722—61no—
267#3722C2×D311yescharacteristic
268#3722C2×D311yescharacteristic
269#3722C2×D311yescharacteristic, complemented
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—61no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)—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—21no—
292C2×C3×C3⋊D3—44no—
293C2×C3×C3⋊D3C2×D412yes—
294C2×C3×C3⋊D3#4112yescomplemented
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3C2×D412yes—
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)C2×D412yes—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C2×#237—91no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×D3×D4—181no—
313C2×#235—91no—
314C2×#235—91no—
315C3×#123—91no—
316C3×#121—91no—
317C2×C3×C22⋊C4—91no—
318#953—91no—
319#939—31no—
320#939—91no—
321#937—91no—
322#937—91no—
323#935—31no—
324#930—91no—
325#929—91no—
326C4×#67—91no—
327C4×#67—91no—
328C2×(C2×D3)⋊C4—91no—
329C2×(C2×D3)⋊C4—91no—
330#896—91no—
331#896—91no—
332#895—91no—
333#894—91no—
334#894—91no—
335#893—91no—
336#885—91no—
337#885—91no—
338#885—91no—
339#885—181no—
340#884—31no—
341#884—91no—
342#884—91no—
343#884—91no—
344#884—181no—
345#883—31no—
346#882—91no—
347#882—91no—
348#882—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352D3×C22⋊C4—31no—
353D3×C22⋊C4—31no—
354D3×C22⋊C4—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—41no—
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C22×C3⋊D3—22no—
365C22×C3⋊D3—22no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—41no—
370C22×C3⋊D3—61no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—62no—
374C22×C3⋊D3—62no—
375C22×C3⋊D3—121no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3C22×D311yescharacteristic
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—21no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—61no—
388C22×C3×D3—61no—
389C22×C3×D3—61no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—62no—
394C22×C3×D3—64no—
395C22×C3×D3—122no—
396C22×C3×D3—121no—
397C22×C3×D3—121no—
398C22×C3×D3—122no—
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—64no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—122no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—122no—
410C32×D4—62no—
411C2×C32×C4—31no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416#638—34no—
417#638—41no—
418#638—62no—
419#638—62no—
420#638—62no—
421#638—64no—
422#638—122no—
423#638—122no—
424#638—124no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—61no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—121no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C4⋊(C3⋊D3)—62no—
436C4⋊(C3⋊D3)—121no—
437C4×C3⋊D3—62no—
438C4×C3⋊D3—62no—
439#634—62no—
440C3×#67—24no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—62no—
444C3×#67—121no—
445C3×#67—121no—
446C3×#67—122no—
447C2×C3×Dic3—21no—
448C2×C3×Dic3—21no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—61no—
459C2×C3×Dic3—61no—
460C2×C3×Dic3—61no—
461C2×C3×Dic3—62no—
462C2×C3×Dic3—121no—
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C2×C3×Dic3C22×D311yescharacteristic
467C2×C3×Dic3C22×D311yescharacteristic
468C2×C3×Dic3C22×D311yescharacteristic
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C3×D12—62no—
474C3×C4×D3—62no—
475C3×C4×D3—62no—
476C3×C4×D3—62no—
477C3×C4×D3—121no—
478C3×C4×D3—121no—
479C3×C4×D3—121no—
480#627—62no—
481#627—62no—
482#627—122no—
483#626—22no—
484#626—62no—
485#626—62no—
486#626—64no—
487#626—62no—
488#626—62no—
489#626—62no—
490#626—62no—
491#626—121no—
492#626—121no—
493#626—122no—
494#625—34no—
495#625—34no—
496#625—64no—
497#625—62no—
498#625—62no—
499#624—22no—
500#624—41no—
501D3×Dic3—22no—
502D3×Dic3—41no—
503D3×Dic3—62no—
504D3×Dic3—62no—
505D3×Dic3—62no—
506D3×Dic3—62no—
507D3×Dic3—64no—
508D3×Dic3—122no—
509#546—271noSylow
510C2×C33—41no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—41no—
515C3×C3⋊D3—22no—
516C3×C3⋊D3—22no—
517C3×C3⋊D3—41no—
518C32×D3—22no—
519C24×C3—91no—
520C23×D3—31no—
521C23×D3—31no—
522C23×D3—61no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—91no—
526C23×D3—181no—
527C2×C3×D4—31no—
528C2×C3×D4—31no—
529C2×C3×D4—61no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C22×C3×C4—91no—
533C22×C3×C4—91no—
534C22×C3×C4—91no—
535C22×C3×C4—91no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—61no—
540C2×#67—91no—
541C2×#67—91no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—181no—
553C2×#67—181no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—184no—
557C2×#67—361no—
558C2×#67D3211yescharacteristic
559C22×Dic3—31no—
560C22×Dic3—31no—
561C22×Dic3—91no—
562C22×Dic3—91no—
563#237—184no—
564D3×D4—184no—
565D3×D4—184no—
566D3×D4—188no—
567#235—184no—
568#235—184no—
569C2×D12—31no—
570C2×D12—91no—
571C2×D12—91no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—91no—
575C2×D12—91no—
576C2×D12—181no—
577C2×D12—181no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
583C2×C4×D3—31no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×C4×D3—181no—
589C2×C4×D3—181no—
590C2×Dic6—91no—
591C2×Dic6—91no—
592C2×Dic6—91no—
593C2×Dic6—181no—
594C3×C4⋊C4—91no—
595C3×C4⋊C4—91no—
596C3×C4⋊C4—91no—
597C3×C22⋊C4—31no—
598C3×C22⋊C4—31no—
599C3×C22⋊C4—31no—
600C3×C22⋊C4—31no—
601C3×C22⋊C4—61no—
602C3×C22⋊C4—61no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605C3×C22⋊C4—91no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—61no—
612#217—91no—
613#217—91no—
614#217D3211yescharacteristic, complemented
615#217D3211yescharacteristic, complemented
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—31no—
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—31no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—181no—
637(C2×D3)⋊C4—181no—
638(C2×D3)⋊C4—181no—
639C4⋊Dic3—31no—
640Dic3⋊C4—31no—
641Dic3⋊C4—31no—
642Dic3⋊C4—31no—
643Dic3⋊C4—31no—
644Dic3⋊C4—31no—
645Dic3⋊C4—91no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—181no—
649C4×Dic3—91no—
650C4×Dic3—91no—
651C4×Dic3—91no—
652C4×Dic3—181no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—32no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—42no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—81no—
680C22×C32—81no—
681C22×C32C23×D311yescharacteristic
682C22×C32C23×D311yescharacteristic
683C22×C32C23×D311yescharacteristic
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—44no—
692C2×C3⋊D3—61no—
693C2×C3⋊D3—62no—
694C2×C3⋊D3—61no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—61no—
697C2×C3⋊D3—61no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—121no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—122no—
705C2×C3⋊D3—121no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—124no—
712C2×C3⋊D3—241no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3#23512yescomplemented
715C2×C3⋊D3D3×D412yes—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—22no—
721C2×C3×D3—32no—
722C2×C3×D3—32no—
723C2×C3×D3—32no—
724C2×C3×D3—32no—
725C2×C3×D3—41no—
726C2×C3×D3—41no—
727C2×C3×D3—62no—
728C2×C3×D3—62no—
729C2×C3×D3—62no—
730C2×C3×D3—62no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—62no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—121no—
747C2×C3×D3—121no—
748C2×C3×D3—121no—
749C2×C3×D3—121no—
750C2×C3×D3—124no—
751C2×C3×D3—124no—
752C2×C3×D3—128no—
753C2×C3×D3D3×D412yes—
754C2×C3×D3D3×D412yes—
755D32—124no—
756D32—124no—
757D32—128no—
758C32×C4—61no—
759C32×C4—61no—
760C32×C4—61no—
761C32×C4—61no—
762C32×C4—61no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—21no—
766C3⋊Dic3—32no—
767C3⋊Dic3—32no—
768C3⋊Dic3—32no—
769C3⋊Dic3—62no—
770C3⋊Dic3—62no—
771C3⋊Dic3—62no—
772C3⋊Dic3—122no—
773C3×Dic3—22no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—21no—
780C3×Dic3—21no—
781C3×Dic3—21no—
782C3×Dic3—21no—
783C3×Dic3—21no—
784C3×Dic3—41no—
785C3×Dic3—41no—
786C3×Dic3—41no—
787C3×Dic3—41no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—121no—
795C3×Dic3—121no—
796C3×Dic3—121no—
797C2×#41—271no—
798C22×D4—271no—
799#124—271no—
800#123—91no—
801#123—271no—
802C22⋊Q8—271no—
803#121—91no—
804#121—271no—
805#121—271no—
806#120—271no—
807#120—271no—
808C4×D4—271no—
809C4×D4—271no—
810C2×C22⋊C4—91no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—41no—
819C23×C3—61no—
820C23×C3—91no—
821C23×C3—91no—
822C23×C3—91no—
823C23×C3—182no—
824C23×C3—182no—
825C23×C3—361no—
826C23×C3C2×D3211yescharacteristic
827C23×C3C2×D3211yescharacteristic
828C23×C3C2×D3211yescharacteristic
829C22×D3—31no—
830C22×D3—31no—
831C22×D3—31no—
832C22×D3—31no—
833C22×D3—31no—
834C22×D3—31no—
835C22×D3—61no—
836C22×D3—61no—
837C22×D3—61no—
838C22×D3—62no—
839C22×D3—62no—
840C22×D3—62no—
841C22×D3—62no—
842C22×D3—64no—
843C22×D3—91no—
844C22×D3—91no—
845C22×D3—91no—
846C22×D3—122no—
847C22×D3—121no—
848C22×D3—121no—
849C22×D3—122no—
850C22×D3—181no—
851C22×D3—181no—
852C22×D3—181no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—182no—
857C22×D3—182no—
858C22×D3—184no—
859C22×D3—182no—
860C22×D3—361no—
861C22×D3—362no—
862C22×D3—361no—
863C22×D3—361no—
864C22×D3—361no—
865C22×D3—362no—
866C22×D3C2×D3211yescharacteristic
867C3×D4—62no—
868C3×D4—62no—
869C3×D4—64no—
870C3×D4—182no—
871C3×D4—361no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—31no—
882C2×C3×C4—61no—
883C2×C3×C4—61no—
884C2×C3×C4—61no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—91no—
888C2×C3×C4—91no—
889C2×C3×C4—91no—
890C2×C3×C4—182no—
891C2×C3×C4—182no—
892C2×C3×C4—361no—
893C2×C3×C4—361no—
894#67—22no—
895#67—62no—
896#67—94no—
897#67—94no—
898#67—94no—
899#67—121no—
900#67—121no—
901#67—122no—
902#67—184no—
903#67—182no—
904#67—182no—
905#67—182no—
906#67—182no—
907#67—182no—
908#67—182no—
909#67—182no—
910#67—182no—
911#67—184no—
912#67—362no—
913#67—362no—
914#67—364no—
915#67—361no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—61no—
923C2×Dic3—61no—
924C2×Dic3—61no—
925C2×Dic3—62no—
926C2×Dic3—91no—
927C2×Dic3—91no—
928C2×Dic3—91no—
929C2×Dic3—121no—
930C2×Dic3—181no—
931C2×Dic3—181no—
932C2×Dic3—181no—
933C2×Dic3—182no—
934C2×Dic3—182no—
935C2×Dic3—361no—
936C2×Dic3C2×D3211yescharacteristic
937C2×Dic3C2×D3211yescharacteristic
938C2×Dic3C2×D3211yescharacteristic
939C2×Dic3C2×D3211yescharacteristic
940C2×Dic3C2×D3211yescharacteristic
941D12—62no—
942D12—182no—
943D12—182no—
944D12—184no—
945D12—182no—
946D12—182no—
947D12—361no—
948D12—361no—
949D12—362no—
950C4×D3—62no—
951C4×D3—62no—
952C4×D3—62no—
953C4×D3—121no—
954C4×D3—121no—
955C4×D3—121no—
956C4×D3—182no—
957C4×D3—182no—
958C4×D3—182no—
959C4×D3—182no—
960C4×D3—184no—
961C4×D3—362no—
962Dic6—182no—
963Dic6—182no—
964Dic6—182no—
965Dic6—362no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—41no—
979C2×C32—42no—
980C2×C32—41no—
981C2×C32—41no—
982C2×C32—62no—
983C2×C32—81no—
984C2×C32—81no—
985C2×C32—82no—
986C2×C32C2×#23511yescharacteristic
987C2×C32C2×D3×D411yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32C2×D3×D411yescharacteristic
990C2×C32#100411yescharacteristic
991C2×C32#100411yescharacteristic
992C2×C32D3×#4111yescharacteristic
993C2×C32D3×#4111yescharacteristic
994C2×C32#100911yescharacteristic
995C3⋊D3—22no—
996C3⋊D3—22no—
997C3⋊D3—41no—
998C3⋊D3—121no—
999C3⋊D3—122no—
1000C3⋊D3—121no—
1001C3⋊D3—121no—
1002C3⋊D3—241no—
1003C3⋊D3—241no—
1004C3⋊D3—242no—
1005C3×D3—22no—
1006C3×D3—22no—
1007C3×D3—42no—
1008C3×D3—64no—
1009C3×D3—62no—
1010C3×D3—62no—
1011C3×D3—62no—
1012C3×D3—62no—
1013C3×D3—122no—
1014C3×D3—122no—
1015C3×D3—121no—
1016C3×D3—121no—
1017C24—91no—
1018C24—271no—
1019#41—544no—
1020C2×Q8—271no—
1021C2×D4—31no—
1022C2×D4—91no—
1023C2×D4—91no—
1024C2×D4—271no—
1025C2×D4—271no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4—544no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—91no—
1035C22×C4—271no—
1036C22×C4—271no—
1037C4⋊C4—91no—
1038C4⋊C4—91no—
1039C4⋊C4—91no—
1040C4⋊C4—271no—
1041C22⋊C4—31no—
1042C22⋊C4—31no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—91no—
1046C22⋊C4—91no—
1047C22⋊C4—91no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—271no—
1054C22×C3—22no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—21no—
1067C22×C3—32no—
1068C22×C3—32no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—42no—
1078C22×C3—41no—
1079C22×C3—62no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—81no—
1085C22×C3—81no—
1086C22×C3—92no—
1087C22×C3—92no—
1088C22×C3—121no—
1089C22×C3—121no—
1090C22×C3—181no—
1091C22×C3—181no—
1092C22×C3—181no—
1093C22×C3—181no—
1094C22×C3—181no—
1095C22×C3—181no—
1096C22×C3—181no—
1097C22×C3—364no—
1098C22×C3C22×D3211yescharacteristic
1099C22×C3C22×D3211yescharacteristic
1100C22×C3C22×D3211yescharacteristic
1101C2×D3—21no—
1102C2×D3—21no—
1103C2×D3—32no—
1104C2×D3—32no—
1105C2×D3—32no—
1106C2×D3—32no—
1107C2×D3—62no—
1108C2×D3—62no—
1109C2×D3—62no—
1110C2×D3—62no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—61no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—62no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—121no—
1127C2×D3—121no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—124no—
1131C2×D3—124no—
1132C2×D3—128no—
1133C2×D3—182no—
1134C2×D3—181no—
1135C2×D3—181no—
1136C2×D3—181no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—361no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—361no—
1151C2×D3—362no—
1152C2×D3—364no—
1153C2×D3—364no—
1154C2×D3—364no—
1155C2×D3—368no—
1156C2×D3—721no—
1157C2×D3—721no—
1158C2×D3#381112yes—
1159C3×C4—62no—
1160C3×C4—61no—
1161C3×C4—61no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4—61no—
1168C3×C4—61no—
1169C3×C4—61no—
1170C3×C4—121no—
1171C3×C4—121no—
1172C3×C4—121no—
1173C3×C4—121no—
1174C3×C4—181no—
1175C3×C4—181no—
1176C3×C4—181no—
1177Dic3—21no—
1178Dic3—21no—
1179Dic3—21no—
1180Dic3—21no—
1181Dic3—21no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—61no—
1188Dic3—92no—
1189Dic3—92no—
1190Dic3—92no—
1191Dic3—121no—
1192Dic3—121no—
1193Dic3—121no—
1194Dic3—182no—
1195Dic3—182no—
1196Dic3—182no—
1197Dic3—362no—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#549011yescharacteristic, complemented
1203C32#561011yescharacteristic, complemented
1204C32#565411yescharacteristic, complemented
1205C23—31no—
1206C23—91no—
1207C23—91no—
1208C23—91no—
1209C23—182no—
1210C23—182no—
1211C23—271no—
1212C23—361no—
1213C23—542no—
1214C23—542no—
1215C23—1081no—
1216C23D3311yescharacteristic
1217Q8—542no—
1218D4—62no—
1219D4—182no—
1220D4—274no—
1221D4—361no—
1222D4—542no—
1223D4—542no—
1224D4—542no—
1225D4—542no—
1226D4—1081no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—31no—
1231C2×C4—31no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—182no—
1236C2×C4—182no—
1237C2×C4—271no—
1238C2×C4—361no—
1239C2×C4—361no—
1240C2×C4—542no—
1241C2×C4—542no—
1242C2×C3—21no—
1243C2×C3—21no—
1244C2×C3—21no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—42no—
1252C2×C3—41no—
1253C2×C3—41no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—41no—
1257C2×C3—41no—
1258C2×C3—62no—
1259C2×C3—62no—
1260C2×C3—81no—
1261C2×C3—81no—
1262C2×C3—82no—
1263C2×C3—122no—
1264C2×C3—182no—
1265C2×C3—182no—
1266C2×C3—361no—
1267C2×C3D3×#23511yescharacteristic
1268C2×C3D3×#23511yescharacteristic
1269C2×C3D32×D411yescharacteristic
1270C2×C3D32×D411yescharacteristic
1271C2×C3#6431211yescharacteristic
1272C2×C3#6431311yescharacteristic
1273C2×C3#6431411yescharacteristic
1274C2×C3#6431411yescharacteristic
1275C2×C3C2×#381111yescharacteristic
1276D3—22no—
1277D3—64no—
1278D3—62no—
1279D3—62no—
1280D3—62no—
1281D3—62no—
1282D3—122no—
1283D3—122no—
1284D3—121no—
1285D3—121no—
1286D3—362no—
1287D3—361no—
1288D3—361no—
1289D3—361no—
1290D3—721no—
1291D3—721no—
1292D3—722no—
1293C22—21no—
1294C22—21no—
1295C22—21no—
1296C22—32no—
1297C22—61no—
1298C22—61no—
1299C22—92no—
1300C22—92no—
1301C22—181no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—181no—
1307C22—181no—
1308C22—364no—
1309C22—541no—
1310C22—541no—
1311C22—541no—
1312C22—1084no—
1313C22C2×D3311yescharacteristic
1314C4—61no—
1315C4—61no—
1316C4—61no—
1317C4—61no—
1318C4—61no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—272no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059427211yescharacteristic, complemented
1328C3#1059427311yescharacteristic, complemented
1329C3#1059516311yescharacteristic, complemented
1330C2—41no—
1331C2—62no—
1332C2—182no—
1333C2—182no—
1334C2—361no—
1335C2—1081no—
1336C2#1172441011yescharacteristic
1337C2#1172441611yescharacteristic
1338C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#88960C2semidirect
3. #11723727C2semidirect
4. #11723624C2semidirect
5. #11723592C2semidirect
6. C3×#63974C2semidirect
7. C3×#63971C2semidirect
8. C3×#63969C2semidirect
9. #11722993C2semidirect
10. #11722983C2semidirect
11. #11722961C2semidirect
12. #11722950C2semidirect
13. #11722938C2semidirect
14. #11722930C2semidirect
15. D3×#3722C2semidirect
22. C2×C3×#638C22semidirect
25. C2×#6295C22semidirect
27. C2×#6293C22semidirect
29. C2×#6292C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#624C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. C32×#217C22semidirect
41. C32×#217C22semidirect
43. #88814C22semidirect
44. #88806C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×#3724C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
75. #63974D3semidirect
79. #63971D3semidirect
80. #63969D3semidirect
133. #6290D4semidirect
161. C2×#638C2×D3semidirect
200. C2×#626C2×D3semidirect
206. C2×#624C2×D3semidirect
207. C2×#624C2×D3semidirect
215. C2×D3×Dic3C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
221. #3757C2×D3semidirect
233. C3×#217C2×D3semidirect
234. C3×#217C2×D3semidirect
235. C3×#217C2×D3semidirect
236. C3×#217C2×D3semidirect
253. #3724C2×D3semidirect
254. #3724C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
269. #3722C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
294. C2×C3×C3⋊D3#41semidirect
614. #217D32semidirect
615. #217D32semidirect
714. C2×C3⋊D3#235semidirect
812. C33#546semidirect
1202. C32#5490semidirect
1203. C32#5610semidirect
1204. C32#5654semidirect
1327. C3#10594272semidirect
1328. C3#10594273semidirect
1329. C3#10595163semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#889602
#117237272
#117236242
#117235922
C3×#639742
C3×#639712
C3×#639692
#117229932
#117229832
#117229612
#117229502
#117229382
#117229302
D3×#37222
#105951633
#105942733
#105942723