Finite Group Databasebeta

← #13172698

Subgroups — #13172698

Order 1728.

1742 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic, complemented
2C2×D3×#625C211yesmaximal, characteristic, complemented
3#11723725C211yesmaximal, characteristic, complemented
4#11723637C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#63983C211yesmaximal, characteristic, complemented
8C3×#63970C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722989C211yesmaximal, characteristic, complemented
12#11722980C211yesmaximal, characteristic, complemented
13#11722936C211yesmaximal, characteristic, complemented
14#11722902C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595290—31nomaximal
18#10595225—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6294C2211yescharacteristic, complemented
29C2×#6293C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33#89029—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
36C2×C3×#625C2211yescharacteristic
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38D3×#625—24no—
39C3×#3757C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88814C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic, complemented
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3830—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C22×#625—31no—
60C2×#3805—31no—
61C2×#3805—31no—
62C2×#3805—61no—
63#64148—31no—
64D4×C3⋊Dic3—31no—
65C3×#939—31no—
66C3×#938—31no—
67C3×#937—31no—
68C3×#937—31no—
69C3×#937—31no—
70C3×#937—31no—
71#63983D311yescharacteristic, complemented
72#63983D311yescharacteristic, complemented
73#63982—31no—
74#63980—31no—
75#63980—31no—
76#63980—61no—
77#67⋊Dic3—31no—
78#67⋊Dic3—31no—
79#67⋊Dic3—61no—
80#63971—31no—
81#63970—31no—
82#63970D311yescharacteristic, complemented
83#63969—31no—
84D3×#217—31no—
85D3×#217—31no—
86D3×#217—31no—
87#63962—31no—
88C2×(C2×D3)⋊Dic3—31no—
89#63958—31no—
90#63953—31no—
91#63952—31no—
92#63921—31no—
93D3×(C2×D3)⋊C4—31no—
94#63915—31no—
95#63913—31no—
96#63902—31no—
97#63899—31no—
98#63896—31no—
99#63891—31no—
100#63891—31no—
101#63890—31no—
102#63879—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×C3×D32—22no—
111C2×C3×D32—22no—
112C2×C3×D32—22no—
113C2×C3×D32—22no—
114C2×C3×D32—41no—
115C2×C3×D32—41no—
116C2×C3⋊(C3⋊Dic3)—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C32×#67—22no—
127C32×#67—41no—
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6295—22no—
132#6294—41no—
133#6293—22no—
134#6290—22no—
135#6290D414yescomplemented
136Dic3×C3⋊D3—22no—
137D3×C3⋊Dic3—22no—
138D3×C3⋊Dic3—22no—
139C3×#625—22no—
140C3×D3×Dic3—41no—
141#5610—91no—
142#5591—91no—
143#5591—91no—
144C23×C3×D3—31no—
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C22×D32C2×D311yescharacteristic
149C22×D32C2×D311yescharacteristic
150C2×C32×D4—31no—
151C2×C32×D4—31no—
152C2×C32×D4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638C2×D311yescharacteristic, complemented
156C2×#638C2×D311yescharacteristic, complemented
157C22×C3⋊Dic3—31no—
158C22×C3⋊Dic3—31no—
159C22×C3⋊Dic3—31no—
160C22×C3⋊Dic3—31no—
161C22×C3⋊Dic3—31no—
162C22×C3⋊Dic3—61no—
163C22×C3⋊Dic3—61no—
164C22×C3⋊Dic3—61no—
165C22×C3⋊Dic3—121no—
166#3830—64no—
167C2×C4×C3⋊D3—31no—
168C2×#634—31no—
169C2×C3×#67—21no—
170C2×C3×#67—21no—
171C2×C3×#67—21no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—61no—
179C2×C3×#67—61no—
180C2×C3×#67C2×D311yescharacteristic
181C2×C3×#67C2×D311yescharacteristic
182C2×C3×#67C2×D311yescharacteristic, complemented
183C2×C3×#67C2×D311yescharacteristic, complemented
184C2×C3×#67C2×D311yescharacteristic, complemented
185C2×C3×#67C2×D311yescharacteristic, complemented
186C22×C3×Dic3—31no—
187C2×C3×C4×D3—31no—
188D3×#67—64no—
189D3×#67—64no—
190C2×#627—31no—
191C2×#627—31no—
192C2×#627—61no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#625—31no—
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—64no—
201C2×#625—61no—
202C2×#625—61no—
203C2×#625C2×D311yescharacteristic
204C2×#624—31no—
205#3805—64no—
206#3805—64no—
207#3805—68no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—61no—
217C2×D3×Dic3—61no—
218C2×D3×Dic3—61no—
219C2×D3×Dic3C2×D311yescharacteristic, complemented
220#3757—31no—
221#3757—31no—
222#3757C2×D311yescharacteristic, complemented
223#3752—31no—
224C4⋊(C3⋊Dic3)—31no—
225#3750—31no—
226C4×C3⋊Dic3—31no—
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—61no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×C4⋊Dic3—31no—
245C3×Dic3⋊C4—31no—
246#3724—31no—
247#3724—31no—
248#3724—31no—
249#3724—61no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722C2×D311yescharacteristic, complemented
258#3722C2×D311yescharacteristic, complemented
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—61no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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⋊D3C2×D412yes—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3C2×D412yes—
296C2×C32×D3#4112yescomplemented
297C3×D32—44no—
298C3×D32—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3⋊(C3⋊Dic3)C2×D412yes—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C22×#67—91no—
310C2×#237—91no—
311C2×#237—91no—
312C2×#237—91no—
313C2×#237—181no—
314C2×D3×D4—91no—
315C3×#121—91no—
316C3×#120—91no—
317C3×#120—91no—
318C2×#217—91no—
319C2×#217—91no—
320#939—31no—
321#939—91no—
322#939—91no—
323#939—91no—
324#939—91no—
325#939—181no—
326#938—31no—
327#938—91no—
328#937—31no—
329#937—31no—
330#937—31no—
331#937—31no—
332#935—91no—
333D4×Dic3—91no—
334D4×Dic3—91no—
335D4×Dic3—181no—
336C4×#67—91no—
337C2×(C2×D3)⋊C4—91no—
338#896—91no—
339#894—91no—
340#886—91no—
341#886—91no—
342#885—91no—
343#885—91no—
344#885—91no—
345#884—91no—
346#883—91no—
347#883—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C23×C32C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3×D3—21no—
369C22×C3×D3—21no—
370C22×C3×D3—21no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—61no—
376C22×C3×D3—61no—
377C22×C3×D3—62no—
378C22×C3×D3—62no—
379C22×C3×D3—62no—
380C22×C3×D3—62no—
381C22×C3×D3—62no—
382C22×C3×D3—62no—
383C22×C3×D3—62no—
384C22×C3×D3—62no—
385C22×C3×D3—121no—
386C22×C3×D3—121no—
387C22×C3×D3—121no—
388C22×C3×D3—121no—
389C22×C3×D3C22×D311yescharacteristic
390C22×C3×D3C22×D311yescharacteristic
391C22×C3×D3C22×D311yescharacteristic
392C22×C3×D3C22×D311yescharacteristic
393C22×C3×D3C22×D311yescharacteristic
394C22×C3×D3C22×D311yescharacteristic
395C2×D32—22no—
396C2×D32—22no—
397C2×D32—22no—
398C2×D32—22no—
399C2×D32—41no—
400C2×D32—41no—
401C32×D4—62no—
402C32×D4—62no—
403C32×D4—121no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—31no—
407#638—22no—
408#638—34no—
409#638—41no—
410#638—62no—
411C2×C3⋊Dic3—31no—
412C2×C3⋊Dic3—31no—
413C2×C3⋊Dic3—31no—
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—61no—
418C2×C3⋊Dic3—61no—
419C2×C3⋊Dic3—61no—
420C2×C3⋊Dic3—61no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—62no—
424C2×C3⋊Dic3—62no—
425C2×C3⋊Dic3—62no—
426C2×C3⋊Dic3—62no—
427C2×C3⋊Dic3—62no—
428C2×C3⋊Dic3—64no—
429C2×C3⋊Dic3—121no—
430C2×C3⋊Dic3—121no—
431C2×C3⋊Dic3—122no—
432C2×C3⋊Dic3—122no—
433C2×C3⋊Dic3—124no—
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4×C3⋊D3—62no—
439#634—62no—
440C3×#67—24no—
441C3×#67—24no—
442C3×#67—22no—
443C3×#67—22no—
444C3×#67—22no—
445C3×#67—22no—
446C3×#67—41no—
447C3×#67—41no—
448C3×#67—42no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—64no—
453C3×#67—62no—
454C3×#67—121no—
455C3×#67—121no—
456C3×#67—122no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
459C2×C3×Dic3—21no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3—121no—
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C3×C4×D3—121no—
480#627—62no—
481#627—62no—
482#627—64no—
483#626—62no—
484#626—62no—
485#625—22no—
486#625—34no—
487#625—34no—
488#625—64no—
489#625—62no—
490#625—62no—
491#625—62no—
492#625—122no—
493#624—121no—
494D3×Dic3—41no—
495D3×Dic3—62no—
496D3×Dic3—62no—
497D3×Dic3—64no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—64no—
501D3×Dic3—62no—
502D3×Dic3—62no—
503D3×Dic3—122no—
504D3×Dic3—121no—
505D3×Dic3—121no—
506#546—271noSylow
507C2×C33—41no—
508C2×C33C22×D411yescharacteristic
509C2×C33C2×#4111yescharacteristic
510C2×C33H(5,𝔽2)11yescharacteristic
511C3×C3⋊D3—22no—
512C3×C3⋊D3—41no—
513C32×D3—22no—
514C32×D3—22no—
515C32×D3—41no—
516C24×C3—91no—
517C24×C3—91no—
518C23×D3—31no—
519C23×D3—31no—
520C23×D3—31no—
521C23×D3—31no—
522C2×C3×D4—31no—
523C2×C3×D4—31no—
524C2×C3×D4—31no—
525C2×C3×D4—31no—
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—61no—
529C2×C3×D4—61no—
530C2×C3×D4—61no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
533C2×C3×D4—91no—
534C22×C3×C4—91no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—61no—
542C2×#67—61no—
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—181no—
552C2×#67—181no—
553C2×#67—184no—
554C2×#67—184no—
555C2×#67D3211yescharacteristic
556C2×#67D3211yescharacteristic, complemented
557C2×#67D3211yescharacteristic, complemented
558C22×Dic3—31no—
559C22×Dic3—91no—
560C22×Dic3—91no—
561C22×Dic3—91no—
562C22×Dic3—91no—
563C22×Dic3—91no—
564C22×Dic3—91no—
565C22×Dic3—91no—
566C22×Dic3—91no—
567C22×Dic3—91no—
568C22×Dic3—181no—
569C22×Dic3—181no—
570C22×Dic3—181no—
571C22×Dic3—181no—
572C22×Dic3—181no—
573C22×Dic3—361no—
574#237—184no—
575#237—184no—
576#237—184no—
577#237—188no—
578D3×D4—184no—
579C2×D12—91no—
580C2×C4×D3—31no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—181no—
588C2×Dic6—91no—
589C2×Dic6—91no—
590C2×Dic6—91no—
591C2×Dic6—181no—
592C3×C4⋊C4—91no—
593C3×C22⋊C4—91no—
594C3×C22⋊C4—91no—
595C3×C22⋊C4—91no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601#217—31no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—61no—
609#217—91no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—91no—
614#217—91no—
615#217—181no—
616#217—181no—
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—31no—
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—31no—
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—181no—
633C4⋊Dic3—31no—
634C4⋊Dic3—91no—
635C4⋊Dic3—91no—
636C4⋊Dic3—91no—
637C4⋊Dic3—181no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—181no—
646C4×Dic3—91no—
647C4×Dic3—91no—
648C4×Dic3—91no—
649C4×Dic3—181no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—22no—
654C22×C32—22no—
655C22×C32—22no—
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—32no—
666C22×C32—32no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—42no—
675C22×C32—42no—
676C22×C32—42no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—61no—
683C22×C32—61no—
684C22×C32C23×D311yescharacteristic
685C22×C32C23×D311yescharacteristic
686C22×C32C23×D311yescharacteristic
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3D3×D412yes—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—21no—
702C2×C3×D3—21no—
703C2×C3×D3—21no—
704C2×C3×D3—21no—
705C2×C3×D3—21no—
706C2×C3×D3—21no—
707C2×C3×D3—22no—
708C2×C3×D3—22no—
709C2×C3×D3—32no—
710C2×C3×D3—32no—
711C2×C3×D3—41no—
712C2×C3×D3—41no—
713C2×C3×D3—41no—
714C2×C3×D3—41no—
715C2×C3×D3—41no—
716C2×C3×D3—41no—
717C2×C3×D3—41no—
718C2×C3×D3—62no—
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—121no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—121no—
734C2×C3×D3—124no—
735C2×C3×D3—124no—
736C2×C3×D3—124no—
737C2×C3×D3—124no—
738C2×C3×D3D3×D412yes—
739C2×C3×D3D3×D412yes—
740C2×C3×D3#23712yescomplemented
741C2×C3×D3#23712yescomplemented
742D32—44no—
743D32—44no—
744C32×C4—61no—
745C32×C4—61no—
746C32×C4—61no—
747C3⋊Dic3—21no—
748C3⋊Dic3—21no—
749C3⋊Dic3—21no—
750C3⋊Dic3—21no—
751C3⋊Dic3—32no—
752C3⋊Dic3—32no—
753C3⋊Dic3—32no—
754C3⋊Dic3—62no—
755C3⋊Dic3—62no—
756C3⋊Dic3—62no—
757C3⋊Dic3—61no—
758C3⋊Dic3—62no—
759C3⋊Dic3—61no—
760C3⋊Dic3—61no—
761C3⋊Dic3—122no—
762C3⋊Dic3—121no—
763C3⋊Dic3—121no—
764C3⋊Dic3—122no—
765C3×Dic3—22no—
766C3×Dic3—22no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—41no—
774C3×Dic3—62no—
775C3×Dic3—61no—
776C3×Dic3—61no—
777C3×Dic3—61no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—121no—
784C3×Dic3—121no—
785C3×Dic3—121no—
786C2×#41—271no—
787C22×D4—271no—
788#124—271no—
789#123—271no—
790#123—271no—
791C22⋊Q8—271no—
792#121—91no—
793#121—271no—
794#121—271no—
795#120—91no—
796#120—91no—
797C4×D4—271no—
798C4×D4—271no—
799C2×C22⋊C4—271no—
800C2×C22⋊C4—271no—
801C33#54611yescharacteristic, complemented, Sylow
802C23×C3—21no—
803C23×C3—21no—
804C23×C3—21no—
805C23×C3—31no—
806C23×C3—31no—
807C23×C3—31no—
808C23×C3—31no—
809C23×C3—31no—
810C23×C3—31no—
811C23×C3—41no—
812C23×C3—61no—
813C23×C3—61no—
814C23×C3—61no—
815C23×C3—91no—
816C23×C3—91no—
817C23×C3—182no—
818C23×C3—182no—
819C23×C3—182no—
820C23×C3—182no—
821C23×C3—361no—
822C23×C3—361no—
823C23×C3C2×D3211yescharacteristic
824C23×C3C2×D3211yescharacteristic
825C23×C3C2×D3211yescharacteristic
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—31no—
829C22×D3—31no—
830C22×D3—61no—
831C22×D3—61no—
832C22×D3—62no—
833C22×D3—62no—
834C22×D3—62no—
835C22×D3—62no—
836C22×D3—62no—
837C22×D3—62no—
838C22×D3—62no—
839C22×D3—62no—
840C22×D3—121no—
841C22×D3—121no—
842C22×D3—121no—
843C22×D3—121no—
844C22×D3C2×D3211yescharacteristic
845C22×D3C2×D3211yescharacteristic
846C22×D3C2×D3211yescharacteristic
847C3×D4—62no—
848C3×D4—62no—
849C3×D4—62no—
850C3×D4—62no—
851C3×D4—64no—
852C3×D4—64no—
853C3×D4—121no—
854C3×D4—121no—
855C3×D4—122no—
856C3×D4—182no—
857C3×D4—182no—
858C3×D4—361no—
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—61no—
866C2×C3×C4—61no—
867C2×C3×C4—61no—
868C2×C3×C4—91no—
869C2×C3×C4—91no—
870C2×C3×C4—91no—
871C2×C3×C4—91no—
872C2×C3×C4—361no—
873#67—22no—
874#67—22no—
875#67—41no—
876#67—62no—
877#67—62no—
878#67—62no—
879#67—64no—
880#67—62no—
881#67—94no—
882#67—94no—
883#67—94no—
884#67—121no—
885#67—121no—
886#67—122no—
887#67—184no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—182no—
893#67—362no—
894C2×Dic3—31no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—61no—
903C2×Dic3—61no—
904C2×Dic3—61no—
905C2×Dic3—61no—
906C2×Dic3—91no—
907C2×Dic3—91no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—91no—
911C2×Dic3—91no—
912C2×Dic3—121no—
913C2×Dic3—181no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—181no—
918C2×Dic3—181no—
919C2×Dic3—182no—
920C2×Dic3—182no—
921C2×Dic3—182no—
922C2×Dic3—182no—
923C2×Dic3—182no—
924C2×Dic3—184no—
925C2×Dic3—182no—
926C2×Dic3—182no—
927C2×Dic3—182no—
928C2×Dic3—184no—
929C2×Dic3—361no—
930C2×Dic3—361no—
931C2×Dic3—362no—
932C2×Dic3—362no—
933C2×Dic3—362no—
934C2×Dic3—364no—
935C2×Dic3—361no—
936C2×Dic3C2×D3211yescharacteristic
937C2×Dic3C2×D3211yescharacteristic
938C2×Dic3C2×D3211yescharacteristic
939D12—182no—
940C4×D3—121no—
941C4×D3—182no—
942C4×D3—182no—
943C4×D3—182no—
944C4×D3—184no—
945C4×D3—182no—
946C4×D3—361no—
947C4×D3—361no—
948Dic6—182no—
949Dic6—182no—
950Dic6—182no—
951Dic6—184no—
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—21no—
961C2×C32—41no—
962C2×C32—41no—
963C2×C32—41no—
964C2×C32—42no—
965C2×C32—42no—
966C2×C32—42no—
967C2×C32—44no—
968C2×C32—41no—
969C2×C32—41no—
970C2×C32—41no—
971C2×C32—62no—
972C2×C32—62no—
973C2×C32—121no—
974C2×C32C2×D3×D411yescharacteristic
975C2×C32C2×D3×D411yescharacteristic
976C2×C32C2×D3×D411yescharacteristic
977C2×C32C2×#23711yescharacteristic
978C2×C32C2×#23711yescharacteristic
979C2×C32#100411yescharacteristic
980C2×C32#100411yescharacteristic
981C2×C32#100411yescharacteristic
982C2×C32D3×#4111yescharacteristic
983C3⋊D3—22no—
984C3⋊D3—41no—
985C3×D3—22no—
986C3×D3—22no—
987C3×D3—22no—
988C3×D3—22no—
989C3×D3—42no—
990C3×D3—42no—
991C3×D3—41no—
992C3×D3—41no—
993C3×D3—62no—
994C3×D3—62no—
995C3×D3—81no—
996C3×D3—122no—
997C3×D3—121no—
998C3×D3—121no—
999C3×D3—241no—
1000C24—91no—
1001C24—91no—
1002#41—544no—
1003C2×Q8—271no—
1004C2×D4—31no—
1005C2×D4—31no—
1006C2×D4—31no—
1007C2×D4—91no—
1008C2×D4—91no—
1009C2×D4—91no—
1010C2×D4—271no—
1011C2×D4—271no—
1012C2×D4—271no—
1013C2×D4—544no—
1014C22×C4—91no—
1015C22×C4—271no—
1016C22×C4—271no—
1017C22×C4—271no—
1018C22×C4—271no—
1019C22×C4—271no—
1020C4⋊C4—91no—
1021C4⋊C4—271no—
1022C4⋊C4—271no—
1023C4⋊C4—271no—
1024C22⋊C4—91no—
1025C22⋊C4—91no—
1026C22⋊C4—91no—
1027C22⋊C4—91no—
1028C22⋊C4—91no—
1029C22⋊C4—91no—
1030C22⋊C4—91no—
1031C22⋊C4—91no—
1032C22⋊C4—271no—
1033C22⋊C4—271no—
1034C22⋊C4—271no—
1035C22⋊C4—271no—
1036C42—271no—
1037C22×C3—22no—
1038C22×C3—22no—
1039C22×C3—22no—
1040C22×C3—21no—
1041C22×C3—21no—
1042C22×C3—21no—
1043C22×C3—21no—
1044C22×C3—21no—
1045C22×C3—21no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—32no—
1053C22×C3—32no—
1054C22×C3—32no—
1055C22×C3—32no—
1056C22×C3—41no—
1057C22×C3—41no—
1058C22×C3—41no—
1059C22×C3—41no—
1060C22×C3—41no—
1061C22×C3—41no—
1062C22×C3—42no—
1063C22×C3—42no—
1064C22×C3—42no—
1065C22×C3—41no—
1066C22×C3—62no—
1067C22×C3—62no—
1068C22×C3—61no—
1069C22×C3—61no—
1070C22×C3—61no—
1071C22×C3—61no—
1072C22×C3—61no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—61no—
1076C22×C3—61no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—92no—
1083C22×C3—121no—
1084C22×C3—121no—
1085C22×C3—121no—
1086C22×C3—121no—
1087C22×C3—121no—
1088C22×C3—121no—
1089C22×C3—121no—
1090C22×C3—181no—
1091C22×C3—181no—
1092C22×C3—181no—
1093C22×C3—181no—
1094C22×C3—181no—
1095C22×C3—364no—
1096C22×C3—364no—
1097C22×C3C22×D3211yescharacteristic
1098C22×C3C22×D3211yescharacteristic
1099C22×C3C22×D3211yescharacteristic
1100C2×D3—21no—
1101C2×D3—21no—
1102C2×D3—21no—
1103C2×D3—21no—
1104C2×D3—21no—
1105C2×D3—21no—
1106C2×D3—21no—
1107C2×D3—32no—
1108C2×D3—32no—
1109C2×D3—62no—
1110C2×D3—61no—
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—61no—
1120C2×D3—121no—
1121C2×D3—121no—
1122C2×D3—121no—
1123C2×D3—121no—
1124C2×D3—121no—
1125C2×D3—124no—
1126C2×D3—124no—
1127C2×D3—124no—
1128C2×D3—124no—
1129C2×D3#380512yescomplemented
1130C2×D3#381112yes—
1131C3×C4—62no—
1132C3×C4—62no—
1133C3×C4—61no—
1134C3×C4—61no—
1135C3×C4—61no—
1136C3×C4—61no—
1137C3×C4—61no—
1138C3×C4—61no—
1139C3×C4—121no—
1140C3×C4—181no—
1141C3×C4—181no—
1142C3×C4—181no—
1143C3×C4—181no—
1144Dic3—21no—
1145Dic3—21no—
1146Dic3—21no—
1147Dic3—62no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—61no—
1151Dic3—61no—
1152Dic3—61no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—92no—
1157Dic3—92no—
1158Dic3—92no—
1159Dic3—121no—
1160Dic3—121no—
1161Dic3—121no—
1162Dic3—182no—
1163Dic3—182no—
1164Dic3—182no—
1165Dic3—182no—
1166Dic3—181no—
1167Dic3—181no—
1168Dic3—181no—
1169Dic3—362no—
1170Dic3—361no—
1171Dic3—361no—
1172Dic3—362no—
1173C32—21no—
1174C32—21no—
1175C32—21no—
1176C32—41no—
1177C32#559111yescharacteristic, complemented
1178C32#559111yescharacteristic, complemented
1179C32#561011yescharacteristic, complemented
1180C23—31no—
1181C23—31no—
1182C23—31no—
1183C23—91no—
1184C23—91no—
1185C23—182no—
1186C23—182no—
1187C23—182no—
1188C23—182no—
1189C23—361no—
1190C23—361no—
1191C23D3311yescharacteristic
1192Q8—542no—
1193D4—62no—
1194D4—62no—
1195D4—121no—
1196D4—182no—
1197D4—182no—
1198D4—274no—
1199D4—361no—
1200D4—542no—
1201D4—542no—
1202C2×C4—31no—
1203C2×C4—31no—
1204C2×C4—31no—
1205C2×C4—91no—
1206C2×C4—91no—
1207C2×C4—91no—
1208C2×C4—91no—
1209C2×C4—271no—
1210C2×C4—271no—
1211C2×C4—361no—
1212C2×C4—542no—
1213C2×C4—542no—
1214C2×C4—542no—
1215C2×C4—542no—
1216C2×C4—1081no—
1217C2×C3—21no—
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—42no—
1227C2×C3—42no—
1228C2×C3—42no—
1229C2×C3—44no—
1230C2×C3—41no—
1231C2×C3—41no—
1232C2×C3—41no—
1233C2×C3—41no—
1234C2×C3—41no—
1235C2×C3—41no—
1236C2×C3—62no—
1237C2×C3—62no—
1238C2×C3—62no—
1239C2×C3—62no—
1240C2×C3—122no—
1241C2×C3—122no—
1242C2×C3—121no—
1243C2×C3—121no—
1244C2×C3—182no—
1245C2×C3—241no—
1246C2×C3—361no—
1247C2×C3D32×D411yescharacteristic
1248C2×C3D32×D411yescharacteristic
1249C2×C3D3×#23711yescharacteristic
1250C2×C3D3×#23711yescharacteristic
1251C2×C3#6431311yescharacteristic
1252C2×C3#6431311yescharacteristic
1253C2×C3C2×#380511yescharacteristic
1254C2×C3C2×#381111yescharacteristic
1255C2×C3#6433011yescharacteristic
1256D3—22no—
1257D3—22no—
1258D3—41no—
1259D3—62no—
1260D3—62no—
1261D3—122no—
1262D3—121no—
1263D3—121no—
1264D3—241no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—32no—
1269C22—32no—
1270C22—61no—
1271C22—61no—
1272C22—61no—
1273C22—61no—
1274C22—61no—
1275C22—61no—
1276C22—61no—
1277C22—92no—
1278C22—181no—
1279C22—181no—
1280C22—181no—
1281C22—181no—
1282C22—181no—
1283C22—364no—
1284C22—364no—
1285C22C2×D3311yescharacteristic
1286C4—61no—
1287C4—61no—
1288C4—61no—
1289C4—181no—
1290C4—181no—
1291C4—181no—
1292C4—181no—
1293C4—272no—
1294C4—541no—
1295C3—21no—
1296C3—21no—
1297C3—21no—
1298C3—41no—
1299C3#1059522511yescharacteristic, complemented
1300C3#1059529011yescharacteristic, complemented
1301C3#1059530711yescharacteristic, complemented
1302C2—41no—
1303C2—62no—
1304C2—62no—
1305C2—121no—
1306C2—182no—
1307C2—361no—
1308C2D3×#380511yescharacteristic
1309C2#1172441511yescharacteristic
1310C2D3×#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×#89029C2semidirect
2. C2×D3×#625C2semidirect
3. #11723725C2semidirect
4. #11723637C2semidirect
5. #67⋊(C3⋊Dic3)C2semidirect
6. C3×#63983C2semidirect
7. C3×#63983C2semidirect
8. C3×#63970C2semidirect
9. #11723009C2semidirect
10. #11722997C2semidirect
11. #11722989C2semidirect
12. #11722980C2semidirect
13. #11722936C2semidirect
14. #11722902C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×#67C22semidirect
28. C2×#6294C22semidirect
29. C2×#6293C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
35. C2×D3×C3⋊Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C3×#3757C22semidirect
40. #88815C22semidirect
41. #88814C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. #88803C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×#3722C22semidirect
50. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
71. #63983D3semidirect
72. #63983D3semidirect
82. #63970D3semidirect
135. #6290D4semidirect
155. C2×#638C2×D3semidirect
156. C2×#638C2×D3semidirect
182. C2×C3×#67C2×D3semidirect
183. C2×C3×#67C2×D3semidirect
184. C2×C3×#67C2×D3semidirect
185. C2×C3×#67C2×D3semidirect
219. C2×D3×Dic3C2×D3semidirect
222. #3757C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
257. #3722C2×D3semidirect
258. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
296. C2×C32×D3#41semidirect
556. C2×#67D32semidirect
557. C2×#67D32semidirect
740. C2×C3×D3#237semidirect
741. C2×C3×D3#237semidirect
801. C33#546semidirect
1129. C2×D3#3805semidirect
1177. C32#5591semidirect
1178. C32#5591semidirect
1179. C32#5610semidirect
1299. C3#10595225semidirect
1300. C3#10595290semidirect
1301. C3#10595307semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
C2×D3×#6252
#117237252
#117236372
#67⋊(C3⋊Dic3)2
C3×#639832
C3×#639702
#117230092
#117229972
#117229892
#117229802
#117229362
#117229022
D3×(C2×D3)⋊Dic32
#105953073
#105952903
#105952253