Finite Group Databasebeta

← #13172707

Subgroups — #13172707

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×#88953C211yesmaximal, characteristic, complemented
3#11723729C211yesmaximal, characteristic, complemented
4#11723637C211yesmaximal, characteristic, complemented
5#11723626C211yesmaximal, characteristic, complemented
6C3×#63983C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63958C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722990C211yesmaximal, characteristic, complemented
12#11722983C211yesmaximal, characteristic, complemented
13#11722930C211yesmaximal, characteristic, complemented
14#11722905C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10595290—31nomaximal
18#10594276—31nomaximal
19C22×#1113C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32#89029—24no—
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88953—24no—
39C32×#217C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
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—
59C2×#3805—31no—
60C2×#3805—31no—
61C2×#3805—61no—
62C2×#3802—31no—
63#64148—31no—
64#64090—31no—
65C3×#939—31no—
66C3×#938—31no—
67C3×#937—31no—
68C3×#937—31no—
69C3×#884—31no—
70C3×#884—31no—
71#63983—31no—
72#63983—31no—
73#63983—31no—
74#63983D311yescharacteristic, complemented
75#63980—31no—
76#63980—31no—
77#63980—61no—
78#67⋊Dic3—31no—
79#67⋊Dic3—31no—
80#67⋊Dic3—61no—
81#63971D311yescharacteristic, complemented
82#63969—31no—
83D3×#217—31no—
84#63962—31no—
85C2×(C2×D3)⋊Dic3—31no—
86#63958D311yescharacteristic, complemented
87#63953—31no—
88#63952—31no—
89#63921—31no—
90D3×(C2×D3)⋊C4—31no—
91D3×(C2×D3)⋊C4—31no—
92D3×(C2×D3)⋊C4—31no—
93#63915—31no—
94#63913—31no—
95C4×#625—31no—
96#63899—31no—
97#63896—31no—
98#63890—31no—
99#63884—31no—
100#63884—31no—
101#63879—31no—
102#63865—31no—
103#63853—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×#1113—22no—
111C2×#1113—22no—
112C2×#1113—41no—
113C2×C3×D32—22no—
114C2×C3×D32—22no—
115C2×C3×D32—41no—
116C2×C3⋊(C3⋊Dic3)—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638—22no—
121C3×#638—41no—
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C32×#67—41no—
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6293—22no—
132#6290—22no—
133#6290D414yescomplemented
134Dic3×C3⋊D3—22no—
135Dic3×C3⋊D3—22no—
136D3×C3⋊Dic3—22no—
137C3×#626—22no—
138C3×#626—22no—
139C3×#624—41no—
140C3×D3×Dic3—41no—
141#5610—91no—
142#5610—91no—
143#5591—91no—
144C23×C3×D3—31no—
145C23×C3×D3—31no—
146C22×D32—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32C2×D311yescharacteristic
150C2×C32×D4—31no—
151C2×C32×D4—31no—
152C2×#638—31no—
153C2×#638—31no—
154C2×#638C2×D311yescharacteristic
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—61no—
162C22×C3⋊Dic3—61no—
163C22×C3⋊Dic3—61no—
164C22×C3⋊Dic3—121no—
165#3830—64no—
166C2×C4×C3⋊D3—31no—
167C2×C4×C3⋊D3—31no—
168C2×#634—31no—
169C2×C3×#67—21no—
170C2×C3×#67—21no—
171C2×C3×#67—31no—
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—31no—
179C2×C3×#67—61no—
180C2×C3×#67—61no—
181C2×C3×#67—61no—
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×D12—31no—
188C2×C3×D12—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191C2×C3×C4×D3—31no—
192D3×#67—64no—
193D3×#67—64no—
194C2×#627—31no—
195C2×#627—31no—
196C2×#627—61no—
197C2×#626C2×D311yescharacteristic
198C2×#626C2×D311yescharacteristic
199C2×#625—31no—
200C2×#625—31no—
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—61no—
204C2×#625—61no—
205C2×#624C2×D311yescharacteristic, complemented
206#3805—64no—
207#3805—64no—
208#3805—68no—
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—61no—
216C2×D3×Dic3—61no—
217C2×D3×Dic3—61no—
218C2×D3×Dic3C2×D311yescharacteristic, complemented
219#3802—64no—
220C32×C22⋊C4—31no—
221#3757—31no—
222#3752—31no—
223#3752—31no—
224#3750—31no—
225#3750—31no—
226C4×C3⋊Dic3—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217C2×D311yescharacteristic, complemented
232C3×#217C2×D311yescharacteristic, complemented
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244#3724—31no—
245#3724—31no—
246#3724—61no—
247#3724C2×D311yescharacteristic, complemented
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—61no—
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722C2×D311yescharacteristic
256#3722C2×D311yescharacteristic, complemented
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
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⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3C2×D412yes—
290C2×C3×C3⋊D3#4112yescomplemented
291C2×C32×D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3C2×D412yes—
297#1113—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—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C2×#237—91no—
310C2×#237—91no—
311C2×#237—91no—
312C2×#237—181no—
313C2×D3×D4—91no—
314C2×D3×D4—91no—
315C3×#121—91no—
316C3×#121—91no—
317C3×#120—91no—
318C2×#217—91no—
319#939—31no—
320#939—91no—
321#939—91no—
322#939—91no—
323#939—181no—
324#938—31no—
325#937—31no—
326#937—31no—
327#937—91no—
328#937—91no—
329#937—91no—
330#935—91no—
331#935—91no—
332D4×Dic3—91no—
333C4×#67—91no—
334C4×#67—91no—
335C2×(C2×D3)⋊C4—91no—
336C2×(C2×D3)⋊C4—91no—
337#896—91no—
338#896—91no—
339#894—91no—
340#894—91no—
341#886—91no—
342#885—91no—
343#885—91no—
344#885—91no—
345#884—31no—
346#884—31no—
347#883—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351#67⋊C4—181no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354D3×C22⋊C4—91no—
355#878—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3×D3—21no—
369C22×C3×D3—21no—
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—61no—
377C22×C3×D3—61no—
378C22×C3×D3—61no—
379C22×C3×D3—62no—
380C22×C3×D3—62no—
381C22×C3×D3—62no—
382C22×C3×D3—62no—
383C22×C3×D3—121no—
384C22×C3×D3—121no—
385C22×C3×D3C22×D311yescharacteristic
386C22×C3×D3C22×D311yescharacteristic
387C22×C3×D3C22×D311yescharacteristic
388C22×C3×D3C22×D311yescharacteristic
389C2×D32—22no—
390C2×D32—22no—
391C2×D32—41no—
392C2×D32—62no—
393C2×D32—62no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—121no—
399C2×D32—121no—
400C2×D32—121no—
401C32×D4—62no—
402C32×D4—121no—
403C2×C32×C4—31no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—31no—
407#638—22no—
408#638—22no—
409#638—34no—
410#638—41no—
411#638—62no—
412C2×C3⋊Dic3—31no—
413C2×C3⋊Dic3—31no—
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—61no—
419C2×C3⋊Dic3—61no—
420C2×C3⋊Dic3—61no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
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
437C4×C3⋊D3—62no—
438C4×C3⋊D3—62no—
439#634—62no—
440C3×#67—24no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—41no—
444C3×#67—41no—
445C3×#67—42no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—62no—
449C3×#67—62no—
450C3×#67—62no—
451C3×#67—62no—
452C3×#67—64no—
453C3×#67—64no—
454C3×#67—121no—
455C3×#67—121no—
456C3×#67—122no—
457C2×C3×Dic3—21no—
458C2×C3×Dic3—21no—
459C2×C3×Dic3—21no—
460C2×C3×Dic3—21no—
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—61no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—61no—
470C2×C3×Dic3—121no—
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
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×D12—62no—
480C3×D12—62no—
481C3×C4×D3—121no—
482C3×C4×D3—121no—
483C3×C4×D3—121no—
484#627—62no—
485#627—62no—
486#627—64no—
487#626—22no—
488#626—22no—
489#625—34no—
490#625—34no—
491#625—64no—
492#625—62no—
493#625—62no—
494#625—122no—
495#624—41no—
496D3×Dic3—41no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—62no—
501D3×Dic3—64no—
502D3×Dic3—64no—
503D3×Dic3—62no—
504D3×Dic3—62no—
505D3×Dic3—122no—
506#546—271noSylow
507C2×C33—41no—
508C2×C33C22×D411yescharacteristic
509C2×C33C2×#4111yescharacteristic
510C2×C33H(5,𝔽2)11yescharacteristic
511C3×C3⋊D3—22no—
512C3×C3⋊D3—22no—
513C3×C3⋊D3—41no—
514C32×D3—22no—
515C32×D3—41no—
516C24×C3—91no—
517C23×D3—31no—
518C23×D3—31no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—91no—
522C2×C3×D4—31no—
523C2×C3×D4—31no—
524C2×C3×D4—31no—
525C2×C3×D4—31no—
526C2×C3×D4—61no—
527C2×C3×D4—61no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
533C22×C3×C4—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—31no—
542C2×#67—31no—
543C2×#67—61no—
544C2×#67—61no—
545C2×#67—61no—
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—184no—
555C2×#67D3211yescharacteristic, complemented
556C2×#67D3211yescharacteristic, complemented
557C22×Dic3—31no—
558C22×Dic3—91no—
559C22×Dic3—91no—
560C22×Dic3—91no—
561C22×Dic3—91no—
562C22×Dic3—91no—
563C22×Dic3—91no—
564C22×Dic3—91no—
565C22×Dic3—181no—
566C22×Dic3—181no—
567C22×Dic3—181no—
568C22×Dic3—181no—
569C22×Dic3—361no—
570#237—184no—
571#237—184no—
572#237—184no—
573#237—188no—
574D3×D4—184no—
575D3×D4—184no—
576C2×D12—31no—
577C2×D12—31no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
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—181no—
587C2×C4×D3—181no—
588C2×Dic6—91no—
589C2×Dic6—91no—
590C2×Dic6—91no—
591C2×Dic6—181no—
592C3×C4⋊C4—91no—
593C3×C4⋊C4—91no—
594C3×C22⋊C4—31no—
595C3×C22⋊C4—31no—
596C3×C22⋊C4—61no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—91no—
606#217—91no—
607#217—91no—
608#217—91no—
609#217—91no—
610#217—91no—
611#217—91no—
612#217—181no—
613#217D3211yescharacteristic, complemented
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
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—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—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—
633(C2×D3)⋊C4—181no—
634C4⋊Dic3—31no—
635C4⋊Dic3—91no—
636Dic3⋊C4—31no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—181no—
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—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—42no—
674C22×C32—42no—
675C22×C32—42no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
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⋊D3D3×D412yes—
692C2×C3⋊D3#23712yescomplemented
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—22no—
704C2×C3×D3—32no—
705C2×C3×D3—32no—
706C2×C3×D3—32no—
707C2×C3×D3—32no—
708C2×C3×D3—41no—
709C2×C3×D3—41no—
710C2×C3×D3—41no—
711C2×C3×D3—41no—
712C2×C3×D3—41no—
713C2×C3×D3—62no—
714C2×C3×D3—62no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—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—121no—
735C2×C3×D3—121no—
736C2×C3×D3—124no—
737C2×C3×D3—124no—
738C2×C3×D3D3×D412yes—
739C2×C3×D3D3×D412yes—
740D32—44no—
741D32—124no—
742D32—124no—
743D32—124no—
744C32×C4—61no—
745C32×C4—61no—
746C32×C4—61no—
747C32×C4—61no—
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—21no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—41no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—62no—
778C3×Dic3—62no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
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—91no—
794#121—271no—
795#120—91no—
796#120—271no—
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—41no—
810C23×C3—61no—
811C23×C3—61no—
812C23×C3—91no—
813C23×C3—91no—
814C23×C3—91no—
815C23×C3—182no—
816C23×C3—182no—
817C23×C3—361no—
818C23×C3C2×D3211yescharacteristic
819C23×C3C2×D3211yescharacteristic
820C23×C3C2×D3211yescharacteristic
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—61no—
828C22×D3—61no—
829C22×D3—61no—
830C22×D3—62no—
831C22×D3—62no—
832C22×D3—62no—
833C22×D3—62no—
834C22×D3—121no—
835C22×D3—121no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—361no—
843C22×D3—361no—
844C22×D3—361no—
845C22×D3C2×D3211yescharacteristic
846C22×D3C2×D3211yescharacteristic
847C3×D4—62no—
848C3×D4—62no—
849C3×D4—64no—
850C3×D4—121no—
851C3×D4—121no—
852C3×D4—122no—
853C3×D4—182no—
854C3×D4—182no—
855C3×D4—182no—
856C3×D4—182no—
857C3×D4—361no—
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—91no—
871C2×C3×C4—91no—
872C2×C3×C4—91no—
873C2×C3×C4—361no—
874C2×C3×C4—361no—
875#67—22no—
876#67—41no—
877#67—62no—
878#67—62no—
879#67—62no—
880#67—62no—
881#67—62no—
882#67—62no—
883#67—64no—
884#67—64no—
885#67—94no—
886#67—94no—
887#67—94no—
888#67—121no—
889#67—121no—
890#67—122no—
891#67—184no—
892#67—182no—
893#67—182no—
894#67—182no—
895#67—362no—
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—91no—
906C2×Dic3—91no—
907C2×Dic3—91no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—91no—
911C2×Dic3—121no—
912C2×Dic3—181no—
913C2×Dic3—181no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—181no—
918C2×Dic3—182no—
919C2×Dic3—182no—
920C2×Dic3—182no—
921C2×Dic3—182no—
922C2×Dic3—184no—
923C2×Dic3—182no—
924C2×Dic3—182no—
925C2×Dic3—182no—
926C2×Dic3—184no—
927C2×Dic3—361no—
928C2×Dic3—361no—
929C2×Dic3—362no—
930C2×Dic3—362no—
931C2×Dic3—364no—
932C2×Dic3C2×D3211yescharacteristic
933C2×Dic3C2×D3211yescharacteristic
934C2×Dic3C2×D3211yescharacteristic
935C2×Dic3C2×D3211yescharacteristic
936D12—62no—
937D12—62no—
938C4×D3—121no—
939C4×D3—121no—
940C4×D3—121no—
941C4×D3—182no—
942C4×D3—182no—
943C4×D3—182no—
944C4×D3—182no—
945C4×D3—184no—
946C4×D3—182no—
947C4×D3—362no—
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—121no—
973C2×C32C2×D3×D411yescharacteristic
974C2×C32C2×D3×D411yescharacteristic
975C2×C32C2×D3×D411yescharacteristic
976C2×C32C2×#23711yescharacteristic
977C2×C32#100411yescharacteristic
978C2×C32#100411yescharacteristic
979C2×C32#100411yescharacteristic
980C2×C32D3×#4111yescharacteristic
981C2×C32D3×#4111yescharacteristic
982C3⋊D3—22no—
983C3⋊D3—22no—
984C3⋊D3—41no—
985C3×D3—22no—
986C3×D3—22no—
987C3×D3—42no—
988C3×D3—41no—
989C3×D3—41no—
990C3×D3—62no—
991C3×D3—62no—
992C3×D3—62no—
993C3×D3—62no—
994C3×D3—81no—
995C3×D3—122no—
996C3×D3—122no—
997C3×D3—121no—
998C3×D3—121no—
999C3×D3—241no—
1000C24—91no—
1001C24—271no—
1002#41—544no—
1003C2×Q8—271no—
1004C2×D4—31no—
1005C2×D4—31no—
1006C2×D4—91no—
1007C2×D4—91no—
1008C2×D4—91no—
1009C2×D4—91no—
1010C2×D4—91no—
1011C2×D4—271no—
1012C2×D4—271no—
1013C2×D4—544no—
1014C22×C4—91no—
1015C22×C4—91no—
1016C22×C4—271no—
1017C22×C4—271no—
1018C22×C4—271no—
1019C22×C4—271no—
1020C4⋊C4—91no—
1021C4⋊C4—91no—
1022C4⋊C4—271no—
1023C4⋊C4—271no—
1024C22⋊C4—31no—
1025C22⋊C4—91no—
1026C22⋊C4—91no—
1027C22⋊C4—91no—
1028C22⋊C4—91no—
1029C22⋊C4—91no—
1030C22⋊C4—271no—
1031C22⋊C4—271no—
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—41no—
1055C22×C3—41no—
1056C22×C3—41no—
1057C22×C3—41no—
1058C22×C3—41no—
1059C22×C3—41no—
1060C22×C3—42no—
1061C22×C3—42no—
1062C22×C3—42no—
1063C22×C3—41no—
1064C22×C3—62no—
1065C22×C3—61no—
1066C22×C3—61no—
1067C22×C3—61no—
1068C22×C3—61no—
1069C22×C3—61no—
1070C22×C3—61no—
1071C22×C3—61no—
1072C22×C3—61no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—92no—
1076C22×C3—92no—
1077C22×C3—121no—
1078C22×C3—121no—
1079C22×C3—121no—
1080C22×C3—121no—
1081C22×C3—121no—
1082C22×C3—181no—
1083C22×C3—181no—
1084C22×C3—181no—
1085C22×C3—181no—
1086C22×C3—181no—
1087C22×C3—181no—
1088C22×C3—181no—
1089C22×C3—364no—
1090C22×C3C22×D3211yescharacteristic
1091C22×C3C22×D3211yescharacteristic
1092C22×C3C22×D3211yescharacteristic
1093C2×D3—21no—
1094C2×D3—21no—
1095C2×D3—21no—
1096C2×D3—21no—
1097C2×D3—21no—
1098C2×D3—32no—
1099C2×D3—32no—
1100C2×D3—32no—
1101C2×D3—32no—
1102C2×D3—62no—
1103C2×D3—62no—
1104C2×D3—61no—
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—61no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—121no—
1122C2×D3—121no—
1123C2×D3—121no—
1124C2×D3—121no—
1125C2×D3—124no—
1126C2×D3—124no—
1127C2×D3—364no—
1128C2×D3—364no—
1129C2×D3—364no—
1130C2×D3#381112yes—
1131C3×C4—62no—
1132C3×C4—61no—
1133C3×C4—61no—
1134C3×C4—61no—
1135C3×C4—61no—
1136C3×C4—61no—
1137C3×C4—61no—
1138C3×C4—61no—
1139C3×C4—61no—
1140C3×C4—121no—
1141C3×C4—121no—
1142C3×C4—121no—
1143C3×C4—181no—
1144C3×C4—181no—
1145C3×C4—181no—
1146Dic3—21no—
1147Dic3—21no—
1148Dic3—21no—
1149Dic3—21no—
1150Dic3—62no—
1151Dic3—62no—
1152Dic3—61no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—61no—
1157Dic3—61no—
1158Dic3—92no—
1159Dic3—92no—
1160Dic3—92no—
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#561011yescharacteristic, complemented
1179C32#561011yescharacteristic, complemented
1180C23—31no—
1181C23—31no—
1182C23—91no—
1183C23—91no—
1184C23—91no—
1185C23—182no—
1186C23—182no—
1187C23—361no—
1188C23—542no—
1189C23—542no—
1190C23—1081no—
1191C23D3311yescharacteristic
1192Q8—542no—
1193D4—62no—
1194D4—121no—
1195D4—182no—
1196D4—182no—
1197D4—182no—
1198D4—182no—
1199D4—274no—
1200D4—361no—
1201D4—542no—
1202C2×C4—31no—
1203C2×C4—31no—
1204C2×C4—31no—
1205C2×C4—31no—
1206C2×C4—91no—
1207C2×C4—91no—
1208C2×C4—91no—
1209C2×C4—271no—
1210C2×C4—271no—
1211C2×C4—361no—
1212C2×C4—361no—
1213C2×C4—542no—
1214C2×C4—542no—
1215C2×C4—542no—
1216C2×C4—542no—
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—122no—
1239C2×C3—121no—
1240C2×C3—121no—
1241C2×C3—182no—
1242C2×C3—182no—
1243C2×C3—241no—
1244C2×C3—361no—
1245C2×C3#6430611yescharacteristic
1246C2×C3D32×D411yescharacteristic
1247C2×C3D32×D411yescharacteristic
1248C2×C3D3×#23711yescharacteristic
1249C2×C3D3×#23711yescharacteristic
1250C2×C3#6431311yescharacteristic
1251C2×C3#6431311yescharacteristic
1252C2×C3C2×#381111yescharacteristic
1253C2×C3#6433011yescharacteristic
1254D3—22no—
1255D3—41no—
1256D3—62no—
1257D3—62no—
1258D3—62no—
1259D3—62no—
1260D3—122no—
1261D3—122no—
1262D3—121no—
1263D3—121no—
1264D3—241no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—32no—
1269C22—61no—
1270C22—61no—
1271C22—61no—
1272C22—61no—
1273C22—61no—
1274C22—92no—
1275C22—92no—
1276C22—181no—
1277C22—181no—
1278C22—181no—
1279C22—181no—
1280C22—181no—
1281C22—181no—
1282C22—181no—
1283C22—364no—
1284C22—1084no—
1285C22C2×D3311yescharacteristic
1286C4—61no—
1287C4—61no—
1288C4—61no—
1289C4—61no—
1290C4—181no—
1291C4—181no—
1292C4—181no—
1293C4—272no—
1294C4—541no—
1295C3—21no—
1296C3—21no—
1297C3—21no—
1298C3—41no—
1299C3#1059427611yescharacteristic, complemented
1300C3#1059529011yescharacteristic, complemented
1301C3#1059530711yescharacteristic, complemented
1302C2—41no—
1303C2—62no—
1304C2—121no—
1305C2—182no—
1306C2—182no—
1307C2—361no—
1308C2#1172440711yescharacteristic
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×#88953C2semidirect
3. #11723729C2semidirect
4. #11723637C2semidirect
5. #11723626C2semidirect
6. C3×#63983C2semidirect
7. C3×#63971C2semidirect
8. C3×#63958C2semidirect
9. #11723009C2semidirect
10. #11722991C2semidirect
11. #11722990C2semidirect
12. #11722983C2semidirect
13. #11722930C2semidirect
14. #11722905C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×#67C22semidirect
27. C2×#6293C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
36. C2×C3×#624C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C32×#217C22semidirect
41. #88814C22semidirect
42. #88814C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
46. #88803C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
74. #63983D3semidirect
81. #63971D3semidirect
86. #63958D3semidirect
133. #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
205. C2×#624C2×D3semidirect
218. C2×D3×Dic3C2×D3semidirect
231. C3×#217C2×D3semidirect
232. C3×#217C2×D3semidirect
247. #3724C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
256. #3722C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
290. C2×C3×C3⋊D3#41semidirect
555. C2×#67D32semidirect
556. C2×#67D32semidirect
613. #217D32semidirect
692. C2×C3⋊D3#237semidirect
801. C33#546semidirect
1177. C32#5591semidirect
1178. C32#5610semidirect
1179. C32#5610semidirect
1299. C3#10594276semidirect
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×#889532
#117237292
#117236372
#117236262
C3×#639832
C3×#639712
C3×#639582
#117230092
#117229912
#117229902
#117229832
#117229302
#117229052
D3×(C2×D3)⋊Dic32
#105953073
#105952903
#105942763