Finite Group Databasebeta

← #13172849

Subgroups — #13172849

Order 1728.

1968 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6291C211yesmaximal, characteristic, complemented
2C2×#88959C211yesmaximal, characteristic, complemented
3#11723721C211yesmaximal, characteristic, complemented
4#11723638C211yesmaximal, characteristic, complemented
5#11723627C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11723008C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722964C211yesmaximal, characteristic, complemented
13#11722958C211yesmaximal, characteristic, complemented
14#11722958C211yesmaximal, characteristic, complemented
15#11722932C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595135—31nomaximal
18#10594186—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C23×C32×D3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6296C2211yescharacteristic, complemented
24C2×#6291—24no—
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic, complemented
31C2×#6289C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×C3×#625C2211yescharacteristic, complemented
34C2×C3×#625C2211yescharacteristic, complemented
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88959—24no—
39C3×#3757C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#638—31no—
57C22×#626—31no—
58C22×#626—31no—
59C22×#626—61no—
60C2×#3804—31no—
61C2×#3804—31no—
62C2×#3798—31no—
63#64146—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#937—31no—
68C3×D4×Dic3—31no—
69C3×#67⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63982—31no—
72#63981—31no—
73#63981—31no—
74#63981—61no—
75#63978—31no—
76#63978—31no—
77#63976D311yescharacteristic, complemented
78#63975—31no—
79#63974—31no—
80#63974—31no—
81#63974—61no—
82#67⋊Dic3D311yescharacteristic, complemented
83#63971—31no—
84#63971—31no—
85D3×#217D311yescharacteristic, complemented
86#63966—31no—
87#63964—31no—
88#63964—31no—
89#63958—31no—
90#63958—31no—
91#63953—31no—
92#63952—31no—
93#63912—31no—
94#63906—31no—
95#63906—31no—
96C4×#626—31no—
97#63890—31no—
98#63880—31no—
99#63854—31no—
100#63853—31no—
101#63852—31no—
102#63852—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)—22no—
106C22×C3⋊(C3⋊D3)—22no—
107C22×C3⋊(C3⋊D3)—41no—
108C22×C3⋊(C3⋊D3)C2311yescharacteristic
109C22×C3⋊(C3⋊D3)C2311yescharacteristic
110C22×C32×D3—22no—
111C22×C32×D3—22no—
112C22×C32×D3—41no—
113C22×C32×D3C2311yescharacteristic
114C22×C32×D3C2311yescharacteristic
115C22×C32×D3C2311yescharacteristic
116C2×C3×C3⋊Dic3—22no—
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C32×#67—22no—
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6296—22no—
128#6291—22no—
129#6291—22no—
130#6291—22no—
131#6291—22no—
132#6291—41no—
133#6291D414yescomplemented
134#6289—22no—
135#6289—41no—
136C3×#625—22no—
137C3×#625—41no—
138C3×D3×Dic3—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5591—91no—
142#5550—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3—31no—
146C23×C3⋊D3—31no—
147C23×C3⋊D3—31no—
148C23×C3⋊D3—61no—
149C23×C3⋊D3—61no—
150C23×C3⋊D3—61no—
151C23×C3⋊D3—121no—
152C23×C3×D3—21no—
153C23×C3×D3C2×D311yescharacteristic
154C23×C3×D3C2×D311yescharacteristic
155C2×C32×D4—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—64no—
163C22×C3⋊Dic3C2×D311yescharacteristic
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—21no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67C2×D311yescharacteristic
172C2×C3×#67C2×D311yescharacteristic
173C22×C3×Dic3—31no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—31no—
176C22×C3×Dic3—31no—
177C22×C3×Dic3—31no—
178C22×C3×Dic3—61no—
179C2×C3×C4×D3—31no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×#627—31no—
183C2×#627—31no—
184C2×#627—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—64no—
198C2×#626—64no—
199C2×#626—61no—
200C2×#626—61no—
201C2×#626—61no—
202C2×#626—61no—
203C2×#626—68no—
204C2×#626—61no—
205C2×#626—61no—
206C2×#625C2×D311yescharacteristic, complemented
207C2×#625C2×D311yescharacteristic, complemented
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—31no—
212C2×#624—61no—
213C2×#624—61no—
214#3804—64no—
215#3804—64no—
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217C2×D3×Dic3C2×D311yescharacteristic, complemented
218C2×D3×Dic3C2×D311yescharacteristic, complemented
219#3798—64no—
220C32×C22⋊C4—31no—
221#3757C2×D311yescharacteristic
222#3757C2×D311yescharacteristic
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3752—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—31no—
236C3×#217—31no—
237C3×#217—61no—
238C3×#217—61no—
239C3×#217C2×D311yescharacteristic
240C3×#217C2×D311yescharacteristic
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×C4⋊Dic3—31no—
247C3×Dic3⋊C4—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250#3724—31no—
251#3724—31no—
252#3724—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—31no—
267#3722—31no—
268#3722—61no—
269#3722—61no—
270#3722—61no—
271#3722—61no—
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33#4112yescomplemented
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)—44no—
288C2×C3⋊(C3⋊D3)C2×D412yes—
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×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—44no—
298C2×C32×D3C2×D412yes—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3C2×D412yes—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C22×#67—91no—
310C22×#67—181no—
311C2×#237—91no—
312C2×#235—91no—
313C2×#235—91no—
314C22×D12—91no—
315C3×#120—91no—
316C3×C4×D4—91no—
317C2×C3×C22⋊C4—91no—
318#953—31no—
319C2×#217—31no—
320#939—91no—
321#939—91no—
322#938—91no—
323#937—31no—
324#937—91no—
325#937—91no—
326#937—181no—
327D4×Dic3—31no—
328#930—91no—
329#930—91no—
330#929—91no—
331C4×#67—91no—
332#924—91no—
333#894—91no—
334#894—91no—
335#886—91no—
336#885—91no—
337#885—91no—
338#884—91no—
339#884—91no—
340#884—91no—
341#884—91no—
342#883—91no—
343#883—91no—
344#882—91no—
345#67⋊C4—31no—
346#67⋊C4—91no—
347D3×C22⋊C4—31no—
348D3×C22⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—181no—
352#878—91no—
353#878—91no—
354#875—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32—62no—
364C23×C32—62no—
365C23×C32—121no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
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—61no—
378C22×C3⋊D3—61no—
379C22×C3⋊D3—61no—
380C22×C3⋊D3—61no—
381C22×C3⋊D3—62no—
382C22×C3⋊D3—62no—
383C22×C3⋊D3—62no—
384C22×C3⋊D3—62no—
385C22×C3⋊D3—64no—
386C22×C3⋊D3—64no—
387C22×C3⋊D3—62no—
388C22×C3⋊D3—62no—
389C22×C3⋊D3—121no—
390C22×C3⋊D3—121no—
391C22×C3⋊D3—122no—
392C22×C3⋊D3—122no—
393C22×C3⋊D3—122no—
394C22×C3⋊D3—122no—
395C22×C3⋊D3—124no—
396C22×C3⋊D3—124no—
397C22×C3⋊D3—121no—
398C22×C3⋊D3—121no—
399C22×C3⋊D3—121no—
400C22×C3⋊D3—122no—
401C22×C3⋊D3—122no—
402C22×C3⋊D3—122no—
403C22×C3⋊D3—124no—
404C22×C3×D3—24no—
405C22×C3×D3—22no—
406C22×C3×D3—22no—
407C22×C3×D3—22no—
408C22×C3×D3—22no—
409C22×C3×D3—21no—
410C22×C3×D3—21no—
411C22×C3×D3—21no—
412C22×C3×D3—42no—
413C22×C3×D3—41no—
414C22×C3×D3—41no—
415C22×C3×D3—42no—
416C22×C3×D3C22×D311yescharacteristic
417C22×C3×D3C22×D311yescharacteristic
418C22×C3×D3C22×D311yescharacteristic
419C22×C3×D3C22×D311yescharacteristic
420C22×C3×D3C22×D311yescharacteristic
421C22×C3×D3C22×D311yescharacteristic
422C32×D4—62no—
423C2×C32×C4—31no—
424C2×C32×C4—31no—
425C2×C32×C4—31no—
426#638—34no—
427#638—62no—
428#638—62no—
429#638—62no—
430#638—62no—
431#638—121no—
432C2×C3⋊Dic3—22no—
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C4×C3⋊D3—62no—
440C4×C3⋊D3—121no—
441C3×#67—22no—
442C3×#67—22no—
443C3×#67—42no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—121no—
447C3×#67—121no—
448C2×C3×Dic3—21no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—31no—
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—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—61no—
467C2×C3×Dic3—61no—
468C2×C3×Dic3—61no—
469C2×C3×Dic3—62no—
470C2×C3×Dic3—62no—
471C2×C3×Dic3—62no—
472C2×C3×Dic3—62no—
473C2×C3×Dic3—64no—
474C2×C3×Dic3—121no—
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C3×C4×D3—62no—
482C3×C4×D3—62no—
483C3×C4×D3—121no—
484#627—62no—
485#627—62no—
486#627—62no—
487#626—34no—
488#626—34no—
489#626—64no—
490#626—62no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—62no—
496#626—64no—
497#626—64no—
498#626—64no—
499#626—62no—
500#626—62no—
501#626—122no—
502#626—121no—
503#626—121no—
504#626—122no—
505#625—22no—
506#625—41no—
507#624—62no—
508#624—62no—
509#624—122no—
510#624—121no—
511#624—121no—
512#624—122no—
513D3×Dic3—22no—
514D3×Dic3—22no—
515D3×Dic3—41no—
516#546—271noSylow
517C2×C33—22no—
518C2×C33C22×D411yescharacteristic
519C2×C33C2×#4111yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C3⋊(C3⋊D3)—22no—
522C3⋊(C3⋊D3)—41no—
523C32×D3—22no—
524C32×D3—41no—
525C32×D3—41no—
526C24×C3—31no—
527C24×C3—31no—
528C24×C3—61no—
529C23×D3—91no—
530C23×D3—91no—
531C23×D3—91no—
532C23×D3—181no—
533C23×D3—181no—
534C23×D3—181no—
535C23×D3—361no—
536C23×D3D3211yescharacteristic
537C2×C3×D4—31no—
538C2×C3×D4—31no—
539C2×C3×D4—61no—
540C2×C3×D4—91no—
541C2×C3×D4—91no—
542C22×C3×C4—91no—
543C22×C3×C4—91no—
544C22×C3×C4—91no—
545C22×C3×C4—91no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—91no—
560C2×#67—91no—
561C2×#67—91no—
562C2×#67—181no—
563C2×#67—181no—
564C2×#67—181no—
565C2×#67—181no—
566C2×#67—181no—
567C2×#67—181no—
568C2×#67—184no—
569C2×#67—184no—
570C2×#67—188no—
571C2×#67D3211yescharacteristic
572C22×Dic3—31no—
573C22×Dic3—31no—
574C22×Dic3—31no—
575C22×Dic3—31no—
576C22×Dic3—31no—
577C22×Dic3—61no—
578#237—184no—
579#235—184no—
580#235—184no—
581C2×D12—91no—
582C2×D12—91no—
583C2×D12—91no—
584C2×D12—91no—
585C2×D12—91no—
586C2×D12—91no—
587C2×D12—184no—
588C2×C4×D3—31no—
589C2×C4×D3—31no—
590C2×C4×D3—31no—
591C2×C4×D3—91no—
592C2×C4×D3—91no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—181no—
598C2×C4×D3—181no—
599C2×Dic6—91no—
600C2×Dic6—91no—
601C2×Dic6—91no—
602C3×C4⋊C4—91no—
603C3×C22⋊C4—31no—
604C3×C22⋊C4—31no—
605C3×C22⋊C4—61no—
606C3×C22⋊C4—91no—
607C3×C22⋊C4—91no—
608C3×C22⋊C4—91no—
609C3×C22⋊C4—91no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C42—91no—
614#217—31no—
615#217—31no—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—31no—
622#217—31no—
623#217—61no—
624#217—61no—
625#217D3211yescharacteristic
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
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—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—181no—
644(C2×D3)⋊C4—181no—
645(C2×D3)⋊C4—181no—
646(C2×D3)⋊C4—181no—
647C4⋊Dic3—31no—
648C4⋊Dic3—91no—
649C4⋊Dic3—91no—
650C4⋊Dic3—91no—
651Dic3⋊C4—31no—
652Dic3⋊C4—91no—
653Dic3⋊C4—91no—
654Dic3⋊C4—91no—
655Dic3⋊C4—91no—
656Dic3⋊C4—91no—
657Dic3⋊C4—91no—
658C4×Dic3—31no—
659C4×Dic3—31no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—22no—
672C22×C32—22no—
673C22×C32—22no—
674C22×C32—32no—
675C22×C32—42no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—42no—
682C22×C32—42no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—61no—
686C22×C32—61no—
687C22×C32—61no—
688C22×C32—61no—
689C22×C32—61no—
690C22×C32—61no—
691C22×C32—124no—
692C22×C32#23512yescomplemented
693C22×C32#23512yescomplemented
694C22×C32#23712yescomplemented
695C22×C32C23×D311yescharacteristic
696C22×C32C23×D311yescharacteristic
697C22×C32C23×D311yescharacteristic
698C2×C3⋊D3—32no—
699C2×C3⋊D3—32no—
700C2×C3⋊D3—32no—
701C2×C3⋊D3—62no—
702C2×C3⋊D3—62no—
703C2×C3⋊D3—62no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—62no—
710C2×C3⋊D3—62no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—61no—
714C2×C3⋊D3—61no—
715C2×C3⋊D3—62no—
716C2×C3⋊D3—62no—
717C2×C3⋊D3—62no—
718C2×C3⋊D3—61no—
719C2×C3⋊D3—61no—
720C2×C3⋊D3—61no—
721C2×C3⋊D3—61no—
722C2×C3⋊D3—61no—
723C2×C3⋊D3—61no—
724C2×C3⋊D3—122no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—121no—
727C2×C3⋊D3—121no—
728C2×C3⋊D3—121no—
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—122no—
736C2×C3⋊D3—122no—
737C2×C3⋊D3—122no—
738C2×C3⋊D3—122no—
739C2×C3⋊D3—122no—
740C2×C3⋊D3—124no—
741C2×C3⋊D3—124no—
742C2×C3⋊D3—124no—
743C2×C3⋊D3—128no—
744C2×C3⋊D3—128no—
745C2×C3⋊D3—128no—
746C2×C3⋊D3—1216no—
747C2×C3×D3—21no—
748C2×C3×D3—21no—
749C2×C3×D3—21no—
750C2×C3×D3—21no—
751C2×C3×D3—22no—
752C2×C3×D3—21no—
753C2×C3×D3—21no—
754C2×C3×D3—21no—
755C2×C3×D3—21no—
756C2×C3×D3—21no—
757C2×C3×D3—21no—
758C2×C3×D3—21no—
759C2×C3×D3—21no—
760C2×C3×D3—21no—
761C2×C3×D3—21no—
762C2×C3×D3—21no—
763C2×C3×D3—21no—
764C2×C3×D3—22no—
765C2×C3×D3—41no—
766C2×C3×D3—41no—
767C2×C3×D3—41no—
768C2×C3×D3—41no—
769C2×C3×D3—41no—
770C2×C3×D3—41no—
771C2×C3×D3—41no—
772C2×C3×D3—44no—
773C2×C3×D3—44no—
774C2×C3×D3—48no—
775C2×C3×D3D3×D412yes—
776C2×C3×D3D3×D412yes—
777C32×C4—61no—
778C32×C4—61no—
779C32×C4—61no—
780C3⋊Dic3—21no—
781C3⋊Dic3—21no—
782C3⋊Dic3—21no—
783C3⋊Dic3—21no—
784C3⋊Dic3—21no—
785C3⋊Dic3D3×D412yes—
786C3×Dic3—21no—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—21no—
790C3×Dic3—21no—
791C3×Dic3—21no—
792C3×Dic3—32no—
793C3×Dic3—32no—
794C3×Dic3—41no—
795C3×Dic3—41no—
796C3×Dic3—41no—
797C3×Dic3—62no—
798C3×Dic3—62no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—61no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—121no—
810C3×Dic3—121no—
811C3×Dic3—121no—
812C3×Dic3—121no—
813C2×#41—271no—
814C22×D4—271no—
815#124—271no—
816#123—271no—
817#123—271no—
818C22⋊Q8—271no—
819#121—271no—
820#121—271no—
821#121—271no—
822#120—91no—
823#120—271no—
824C4×D4—91no—
825C4×D4—271no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—271no—
828C33#54611yescharacteristic, complemented, Sylow
829C23×C3—21no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—31no—
833C23×C3—31no—
834C23×C3—31no—
835C23×C3—31no—
836C23×C3—31no—
837C23×C3—31no—
838C23×C3—41no—
839C23×C3—61no—
840C23×C3—61no—
841C23×C3—61no—
842C23×C3—62no—
843C23×C3—62no—
844C23×C3—64no—
845C23×C3—62no—
846C23×C3—62no—
847C23×C3—122no—
848C23×C3—121no—
849C23×C3—121no—
850C23×C3—122no—
851C23×C3C2×D3211yescharacteristic
852C23×C3C2×D3211yescharacteristic
853C23×C3C2×D3211yescharacteristic
854C22×D3—22no—
855C22×D3—22no—
856C22×D3—41no—
857C22×D3—91no—
858C22×D3—91no—
859C22×D3—91no—
860C22×D3—91no—
861C22×D3—91no—
862C22×D3—91no—
863C22×D3—181no—
864C22×D3—181no—
865C22×D3—181no—
866C22×D3—181no—
867C22×D3—181no—
868C22×D3—181no—
869C22×D3—182no—
870C22×D3—182no—
871C22×D3—182no—
872C22×D3—184no—
873C22×D3—184no—
874C22×D3—182no—
875C22×D3—182no—
876C22×D3—182no—
877C22×D3—361no—
878C22×D3—361no—
879C22×D3—362no—
880C22×D3—362no—
881C22×D3—362no—
882C22×D3—362no—
883C22×D3—364no—
884C22×D3—364no—
885C22×D3—361no—
886C22×D3—361no—
887C22×D3—361no—
888C22×D3—362no—
889C22×D3—362no—
890C22×D3—362no—
891C22×D3—364no—
892C22×D3C2×D3211yescharacteristic
893C22×D3C2×D3211yescharacteristic
894C22×D3C2×D3211yescharacteristic
895C3×D4—62no—
896C3×D4—62no—
897C3×D4—122no—
898C3×D4—182no—
899C3×D4—361no—
900C2×C3×C4—31no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—31no—
906C2×C3×C4—61no—
907C2×C3×C4—61no—
908C2×C3×C4—61no—
909C2×C3×C4—91no—
910C2×C3×C4—91no—
911C2×C3×C4—91no—
912C2×C3×C4—91no—
913C2×C3×C4—91no—
914C2×C3×C4—91no—
915C2×C3×C4—182no—
916C2×C3×C4—182no—
917C2×C3×C4—182no—
918C2×C3×C4—361no—
919#67—22no—
920#67—62no—
921#67—62no—
922#67—94no—
923#67—94no—
924#67—121no—
925#67—121no—
926#67—184no—
927#67—182no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—182no—
934#67—182no—
935#67—184no—
936#67—184no—
937#67—184no—
938#67—362no—
939#67—361no—
940#67—361no—
941#67—362no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—31no—
946C2×Dic3—31no—
947C2×Dic3—31no—
948C2×Dic3—31no—
949C2×Dic3—31no—
950C2×Dic3—31no—
951C2×Dic3—31no—
952C2×Dic3—31no—
953C2×Dic3—31no—
954C2×Dic3—61no—
955C2×Dic3—61no—
956C2×Dic3—61no—
957C2×Dic3—61no—
958C2×Dic3—61no—
959C2×Dic3—61no—
960C2×Dic3—62no—
961C2×Dic3—62no—
962C2×Dic3—62no—
963C2×Dic3—62no—
964C2×Dic3—64no—
965C2×Dic3—121no—
966C2×Dic3C2×D3211yescharacteristic
967C2×Dic3C2×D3211yescharacteristic
968C2×Dic3C2×D3211yescharacteristic
969D12—94no—
970D12—182no—
971D12—182no—
972D12—182no—
973D12—182no—
974D12—361no—
975C4×D3—62no—
976C4×D3—62no—
977C4×D3—121no—
978C4×D3—182no—
979C4×D3—182no—
980C4×D3—182no—
981C4×D3—362no—
982C4×D3—361no—
983C4×D3—361no—
984C4×D3—361no—
985C4×D3—362no—
986Dic6—182no—
987Dic6—182no—
988Dic6—182no—
989C2×C32—22no—
990C2×C32—24no—
991C2×C32—22no—
992C2×C32—22no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—42no—
1006C2×C32—42no—
1007C2×C32—44no—
1008C2×C32—62no—
1009C2×C32—121no—
1010C2×C32—121no—
1011C2×C32C2×#23511yescharacteristic
1012C2×C32C2×#23511yescharacteristic
1013C2×C32C2×D3×D411yescharacteristic
1014C2×C32C2×D3×D411yescharacteristic
1015C2×C32C2×D3×D411yescharacteristic
1016C2×C32C2×#23711yescharacteristic
1017C2×C32#100411yescharacteristic
1018C2×C32#100411yescharacteristic
1019C2×C32#100911yescharacteristic
1020C3⋊D3—62no—
1021C3⋊D3—64no—
1022C3⋊D3—62no—
1023C3⋊D3—62no—
1024C3⋊D3—122no—
1025C3⋊D3—122no—
1026C3⋊D3—124no—
1027C3⋊D3—122no—
1028C3⋊D3—122no—
1029C3⋊D3—122no—
1030C3⋊D3—124no—
1031C3⋊D3—121no—
1032C3⋊D3—121no—
1033C3⋊D3—121no—
1034C3×D3—22no—
1035C3×D3—22no—
1036C3×D3—42no—
1037C3×D3—42no—
1038C3×D3—41no—
1039C3×D3—41no—
1040C3×D3—41no—
1041C3×D3—41no—
1042C3×D3—81no—
1043C24—31no—
1044C24—271no—
1045#41—544no—
1046C2×Q8—271no—
1047C2×D4—31no—
1048C2×D4—91no—
1049C2×D4—91no—
1050C2×D4—271no—
1051C2×D4—271no—
1052C2×D4—271no—
1053C2×D4—271no—
1054C2×D4—271no—
1055C2×D4—271no—
1056C2×D4—544no—
1057C22×C4—91no—
1058C22×C4—91no—
1059C22×C4—91no—
1060C22×C4—91no—
1061C22×C4—271no—
1062C22×C4—271no—
1063C4⋊C4—91no—
1064C4⋊C4—271no—
1065C4⋊C4—271no—
1066C4⋊C4—271no—
1067C22⋊C4—31no—
1068C22⋊C4—91no—
1069C22⋊C4—91no—
1070C22⋊C4—91no—
1071C22⋊C4—91no—
1072C22⋊C4—91no—
1073C22⋊C4—91no—
1074C22⋊C4—91no—
1075C22⋊C4—271no—
1076C22⋊C4—271no—
1077C22⋊C4—271no—
1078C22⋊C4—271no—
1079C42—91no—
1080C22×C3—22no—
1081C22×C3—22no—
1082C22×C3—21no—
1083C22×C3—21no—
1084C22×C3—21no—
1085C22×C3—21no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—22no—
1092C22×C3—22no—
1093C22×C3—22no—
1094C22×C3—32no—
1095C22×C3—32no—
1096C22×C3—41no—
1097C22×C3—41no—
1098C22×C3—41no—
1099C22×C3—41no—
1100C22×C3—42no—
1101C22×C3—42no—
1102C22×C3—41no—
1103C22×C3—42no—
1104C22×C3—62no—
1105C22×C3—62no—
1106C22×C3—61no—
1107C22×C3—61no—
1108C22×C3—61no—
1109C22×C3—61no—
1110C22×C3—61no—
1111C22×C3—61no—
1112C22×C3—61no—
1113C22×C3—61no—
1114C22×C3—61no—
1115C22×C3—61no—
1116C22×C3—61no—
1117C22×C3—61no—
1118C22×C3—61no—
1119C22×C3—61no—
1120C22×C3—61no—
1121C22×C3—61no—
1122C22×C3—121no—
1123C22×C3—121no—
1124C22×C3—121no—
1125C22×C3—121no—
1126C22×C3—121no—
1127C22×C3—121no—
1128C22×C3—121no—
1129C22×C3—124no—
1130C22×C3—124no—
1131C22×C3—128no—
1132C22×C3#379812yescomplemented
1133C22×C3#380412yescomplemented
1134C22×C3#380412yescomplemented
1135C22×C3C22×D3211yescharacteristic
1136C22×C3C22×D3211yescharacteristic
1137C22×C3C22×D3211yescharacteristic
1138C2×D3—21no—
1139C2×D3—21no—
1140C2×D3—21no—
1141C2×D3—21no—
1142C2×D3—21no—
1143C2×D3—21no—
1144C2×D3—21no—
1145C2×D3—21no—
1146C2×D3—44no—
1147C2×D3—92no—
1148C2×D3—92no—
1149C2×D3—92no—
1150C2×D3—182no—
1151C2×D3—182no—
1152C2×D3—182no—
1153C2×D3—182no—
1154C2×D3—182no—
1155C2×D3—181no—
1156C2×D3—181no—
1157C2×D3—181no—
1158C2×D3—181no—
1159C2×D3—181no—
1160C2×D3—181no—
1161C2×D3—182no—
1162C2×D3—182no—
1163C2×D3—182no—
1164C2×D3—181no—
1165C2×D3—181no—
1166C2×D3—181no—
1167C2×D3—181no—
1168C2×D3—181no—
1169C2×D3—181no—
1170C2×D3—181no—
1171C2×D3—181no—
1172C2×D3—181no—
1173C2×D3—362no—
1174C2×D3—361no—
1175C2×D3—361no—
1176C2×D3—361no—
1177C2×D3—361no—
1178C2×D3—361no—
1179C2×D3—361no—
1180C2×D3—361no—
1181C2×D3—361no—
1182C2×D3—361no—
1183C2×D3—361no—
1184C2×D3—362no—
1185C2×D3—362no—
1186C2×D3—362no—
1187C2×D3—362no—
1188C2×D3—362no—
1189C2×D3—364no—
1190C2×D3—364no—
1191C2×D3—364no—
1192C2×D3—368no—
1193C2×D3—368no—
1194C2×D3—368no—
1195C2×D3—3616no—
1196C2×D3#381112yes—
1197C3×C4—61no—
1198C3×C4—61no—
1199C3×C4—61no—
1200C3×C4—61no—
1201C3×C4—61no—
1202C3×C4—61no—
1203C3×C4—92no—
1204C3×C4—121no—
1205C3×C4—121no—
1206C3×C4—121no—
1207C3×C4—181no—
1208C3×C4—181no—
1209C3×C4—181no—
1210C3×C4—181no—
1211C3×C4—181no—
1212Dic3—21no—
1213Dic3—21no—
1214Dic3—21no—
1215Dic3—32no—
1216Dic3—32no—
1217Dic3—62no—
1218Dic3—62no—
1219Dic3—61no—
1220Dic3—61no—
1221Dic3—61no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—121no—
1230Dic3—121no—
1231Dic3—121no—
1232Dic3—121no—
1233C32—21no—
1234C32—21no—
1235C32—21no—
1236C32—41no—
1237C32#549011yescharacteristic, complemented
1238C32#555011yescharacteristic, complemented
1239C32#559111yescharacteristic, complemented
1240C23—31no—
1241C23—31no—
1242C23—31no—
1243C23—62no—
1244C23—62no—
1245C23—121no—
1246C23—271no—
1247C23—271no—
1248C23—542no—
1249C23—542no—
1250C23—1081no—
1251C23D3311yescharacteristic
1252Q8—542no—
1253D4—62no—
1254D4—182no—
1255D4—274no—
1256D4—361no—
1257D4—542no—
1258D4—542no—
1259D4—542no—
1260D4—542no—
1261D4—1081no—
1262C2×C4—31no—
1263C2×C4—31no—
1264C2×C4—31no—
1265C2×C4—91no—
1266C2×C4—91no—
1267C2×C4—91no—
1268C2×C4—91no—
1269C2×C4—91no—
1270C2×C4—91no—
1271C2×C4—182no—
1272C2×C4—182no—
1273C2×C4—182no—
1274C2×C4—361no—
1275C2×C4—542no—
1276C2×C4—1081no—
1277C2×C3—24no—
1278C2×C3—22no—
1279C2×C3—22no—
1280C2×C3—22no—
1281C2×C3—21no—
1282C2×C3—21no—
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—42no—
1291C2×C3—42no—
1292C2×C3—44no—
1293C2×C3—41no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—62no—
1297C2×C3—62no—
1298C2×C3—122no—
1299C2×C3—122no—
1300C2×C3—121no—
1301C2×C3—121no—
1302C2×C3—121no—
1303C2×C3—121no—
1304C2×C3—241no—
1305C2×C3C2×#379811yescharacteristic
1306C2×C3D32×D411yescharacteristic
1307C2×C3D32×D411yescharacteristic
1308C2×C3#6431411yescharacteristic
1309C2×C3#6431411yescharacteristic
1310C2×C3C2×#380411yescharacteristic
1311C2×C3C2×#380411yescharacteristic
1312C2×C3C2×#381111yescharacteristic
1313C2×C3#6433011yescharacteristic
1314D3—22no—
1315D3—41no—
1316D3—41no—
1317D3—184no—
1318D3—182no—
1319D3—182no—
1320D3—182no—
1321D3—362no—
1322D3—362no—
1323D3—364no—
1324D3—362no—
1325D3—362no—
1326D3—362no—
1327D3—364no—
1328D3—361no—
1329D3—361no—
1330D3—361no—
1331C22—21no—
1332C22—21no—
1333C22—32no—
1334C22—61no—
1335C22—61no—
1336C22—61no—
1337C22—61no—
1338C22—61no—
1339C22—61no—
1340C22—61no—
1341C22—61no—
1342C22—124no—
1343C22—272no—
1344C22—541no—
1345C22—541no—
1346C22—541no—
1347C22—541no—
1348C22—541no—
1349C22—1084no—
1350C22#8895912yescomplemented
1351C22C2×D3311yescharacteristic
1352C4—61no—
1353C4—61no—
1354C4—61no—
1355C4—92no—
1356C4—181no—
1357C4—181no—
1358C4—181no—
1359C4—181no—
1360C4—181no—
1361C3—21no—
1362C3—21no—
1363C3—21no—
1364C3—41no—
1365C3#1059418611yescharacteristic, complemented
1366C3#1059513511yescharacteristic, complemented
1367C3#1059550011yescharacteristic, complemented
1368C2—22no—
1369C2—62no—
1370C2—121no—
1371C2—121no—
1372C2—542no—
1373C2—1081no—
1374C2#1172441911yescharacteristic
1375C2C2×#8895911yescharacteristic
1376C2D3×#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. C22×#6291C2semidirect
2. C2×#88959C2semidirect
3. #11723721C2semidirect
4. #11723638C2semidirect
5. #11723627C2semidirect
6. C3×#63976C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. C3×D3×#217C2semidirect
9. #11723008C2semidirect
10. #11722996C2semidirect
11. #11722987C2semidirect
12. #11722964C2semidirect
13. #11722958C2semidirect
14. #11722958C2semidirect
15. #11722932C2semidirect
23. C2×#6296C22semidirect
29. C2×#6291C22semidirect
30. C2×#6291C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
33. C2×C3×#625C22semidirect
34. C2×C3×#625C22semidirect
35. C2×C3×D3×Dic3C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
44. #88815C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
77. #63976D3semidirect
82. #67⋊Dic3D3semidirect
85. D3×#217D3semidirect
133. #6291D4semidirect
206. C2×#625C2×D3semidirect
207. C2×#625C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
217. C2×D3×Dic3C2×D3semidirect
218. C2×D3×Dic3C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
280. C22×C33#41semidirect
692. C22×C32#235semidirect
693. C22×C32#235semidirect
694. C22×C32#237semidirect
828. C33#546semidirect
1132. C22×C3#3798semidirect
1133. C22×C3#3804semidirect
1134. C22×C3#3804semidirect
1237. C32#5490semidirect
1238. C32#5550semidirect
1239. C32#5591semidirect
1350. C22#88959semidirect
1365. C3#10594186semidirect
1366. C3#10595135semidirect
1367. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C22×#62912
C2×#889592
#117237212
#117236382
#117236272
C3×#639762
C3×#67⋊Dic32
C3×D3×#2172
#117230082
#117229962
#117229872
#117229642
#117229582
#117229322
#105955003
#105951353
#105941863