Finite Group Databasebeta

← #13172853

Subgroups — #13172853

Order 1728.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic, complemented
2C2×#88960C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723642C211yesmaximal, characteristic, complemented
5#11723626C211yesmaximal, characteristic, complemented
6C3×#63977C211yesmaximal, characteristic, complemented
7C3×#63974C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11722992C211yesmaximal, characteristic, complemented
11#11722988C211yesmaximal, characteristic, complemented
12#11722967C211yesmaximal, characteristic, complemented
13#11722960C211yesmaximal, characteristic, complemented
14#11722957C211yesmaximal, characteristic, complemented
15#11722930C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10594184—31nomaximal
18#10594183—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C23×C32×D3C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×#6295C2211yescharacteristic, complemented
24C2×#6295C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6290—24no—
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic, 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
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C22×#625—31no—
58C22×#625—31no—
59C22×#625—61no—
60C2×#3804—31no—
61C2×#3798—31no—
62C2×#3795—31no—
63#64090—31no—
64#64087—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#882—31no—
68C3×D3×C22⋊C4—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63982—31no—
72#63982—31no—
73#63982—61no—
74#63981—31no—
75#63978—31no—
76#63977—31no—
77#63977D311yescharacteristic, complemented
78#63976—31no—
79#63975—31no—
80#63974D311yescharacteristic, complemented
81#67⋊Dic3—31no—
82#67⋊Dic3—31no—
83#67⋊Dic3—61no—
84#63971—31no—
85D3×#217D311yescharacteristic, complemented
86#63966—31no—
87#63958—31no—
88#63953—31no—
89#63952—31no—
90#63915—31no—
91#63913—31no—
92#63912—31no—
93#63908—31no—
94#63906—31no—
95#63906—31no—
96#63905—31no—
97#63905—31no—
98#63905—31no—
99C4×#625—31no—
100#63891—31no—
101#63885—31no—
102#63885—31no—
103#63879—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3—22no—
112C22×C32×D3—22no—
113C22×C32×D3—41no—
114C22×C32×D3C2311yescharacteristic
115C22×C32×D3C2311yescharacteristic
116C2×C3⋊(C3⋊Dic3)—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6295—22no—
128#6295—41no—
129#6293—22no—
130#6290—22no—
131#6290—22no—
132#6290—22no—
133#6290D414yescomplemented
134Dic3×C3⋊D3—22no—
135C3×#626—22no—
136C3×#626—41no—
137C3×#624—22no—
138C3×#624—41no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5591—91no—
142#5490—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—21no—
147C23×C3×D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—61no—
150C23×C3×D3C2×D311yescharacteristic
151C23×C3×D3C2×D311yescharacteristic
152C2×#638—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—64no—
157C2×#638C2×D311yescharacteristic
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—
165C2×C4×C3⋊D3—31no—
166C2×#634—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—61no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3—31no—
174C2×C3×D12—31no—
175C2×C3×D12—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—31no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×#627—31no—
183C2×#627—31no—
184C2×#627—61no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626C2×D311yescharacteristic, complemented
190C2×#626C2×D311yescharacteristic, complemented
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—31no—
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—31no—
201C2×#625—64no—
202C2×#625—64no—
203C2×#625—61no—
204C2×#625—61no—
205C2×#625—61no—
206C2×#625—61no—
207C2×#625—68no—
208C2×#624C2×D311yescharacteristic, complemented
209C2×#624C2×D311yescharacteristic, complemented
210#3804—64no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—61no—
214C2×D3×Dic3C2×D311yescharacteristic, complemented
215C2×D3×Dic3C2×D311yescharacteristic, complemented
216#3798—64no—
217#3795—64no—
218C32×C22⋊C4—31no—
219C32×C22⋊C4—31no—
220#3757C2×D311yescharacteristic
221#3752—31no—
222C4⋊(C3⋊Dic3)—31no—
223#3750—31no—
224#3750—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—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—61no—
236C3×#217C2×D311yescharacteristic
237C3×#217C2×D311yescharacteristic
238C3×#217C2×D311yescharacteristic
239C3×#217C2×D311yescharacteristic
240C3×(C2×D3)⋊C4—31no—
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×(C2×D3)⋊C4—31no—
247C3×(C2×D3)⋊C4—31no—
248#3724—31no—
249#3724—31no—
250#3724—61no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3—61no—
260#3722—31no—
261#3722—31no—
262#3722C2×D311yescharacteristic, complemented
263#3722C2×D311yescharacteristic, complemented
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—31no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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#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—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—44no—
291C2×C3×C3⋊D3C2×D412yes—
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)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—
309C22×#67—91no—
310C22×#67—91no—
311C22×#67—181no—
312C2×#237—91no—
313C2×#235—91no—
314C2×#235—91no—
315C3×#120—91no—
316C2×C3×C22⋊C4—91no—
317C2×C3×C22⋊C4—91no—
318#953—31no—
319#953—91no—
320C2×#217—31no—
321#939—91no—
322#939—91no—
323#938—91no—
324#937—91no—
325D4×Dic3—91no—
326#930—91no—
327#930—91no—
328#929—91no—
329#929—91no—
330C4×#67—91no—
331C4×#67—91no—
332#886—91no—
333#885—91no—
334#885—91no—
335#885—91no—
336#884—91no—
337#884—91no—
338#884—91no—
339#884—91no—
340#883—91no—
341#883—91no—
342#883—91no—
343#882—31no—
344#882—91no—
345#67⋊C4—91no—
346#67⋊C4—91no—
347#67⋊C4—91no—
348#67⋊C4—181no—
349D3×C22⋊C4—31no—
350D3×C22⋊C4—31no—
351D3×C22⋊C4—31no—
352#878—91no—
353#878—91no—
354#878—91no—
355#878—181no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32—62no—
363C23×C32—62no—
364C23×C32—121no—
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C22×C3⋊D3—22no—
369C22×C3⋊D3—22no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3C22×D311yescharacteristic
372C22×C3⋊D3C22×D311yescharacteristic
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3×D3—24no—
375C22×C3×D3—22no—
376C22×C3×D3—22no—
377C22×C3×D3—22no—
378C22×C3×D3—22no—
379C22×C3×D3—21no—
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—42no—
388C22×C3×D3—41no—
389C22×C3×D3—41no—
390C22×C3×D3—42no—
391C22×C3×D3—61no—
392C22×C3×D3—61no—
393C22×C3×D3—61no—
394C22×C3×D3—62no—
395C22×C3×D3—62no—
396C22×C3×D3—64no—
397C22×C3×D3—62no—
398C22×C3×D3—62no—
399C22×C3×D3—122no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—122no—
403C22×C3×D3C22×D311yescharacteristic
404C22×C3×D3C22×D311yescharacteristic
405C22×C3×D3C22×D311yescharacteristic
406C22×C3×D3C22×D311yescharacteristic
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411#638—22no—
412#638—34no—
413#638—62no—
414#638—62no—
415#638—62no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—31no—
419C2×C3⋊Dic3—31no—
420C2×C3⋊Dic3—31no—
421C2×C3⋊Dic3—31no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—61no—
426C2×C3⋊Dic3—61no—
427C2×C3⋊Dic3—61no—
428C2×C3⋊Dic3—62no—
429C2×C3⋊Dic3—62no—
430C2×C3⋊Dic3—62no—
431C2×C3⋊Dic3—64no—
432C2×C3⋊Dic3—121no—
433C2×C3⋊Dic3—121no—
434C2×C3⋊Dic3—122no—
435C2×C3⋊Dic3—122no—
436C2×C3⋊Dic3—124no—
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C4×C3⋊D3—62no—
441#634—62no—
442C3×#67—62no—
443C3×#67—64no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—121no—
447C2×C3×Dic3—21no—
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—61no—
458C2×C3×Dic3—61no—
459C2×C3×Dic3—61no—
460C2×C3×Dic3—62no—
461C2×C3×Dic3—121no—
462C2×C3×Dic3C22×D311yescharacteristic
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
470C3×D12—62no—
471C3×D12—121no—
472C3×C4×D3—62no—
473C3×C4×D3—62no—
474C3×C4×D3—62no—
475C3×C4×D3—121no—
476C3×C4×D3—121no—
477C3×C4×D3—121no—
478#627—62no—
479#627—62no—
480#627—122no—
481#626—22no—
482#626—41no—
483#626—62no—
484#626—62no—
485#626—121no—
486#626—121no—
487#625—34no—
488#625—34no—
489#625—64no—
490#625—62no—
491#625—62no—
492#625—62no—
493#625—62no—
494#625—62no—
495#625—64no—
496#625—64no—
497#625—64no—
498#625—62no—
499#625—62no—
500#625—121no—
501#624—22no—
502#624—41no—
503D3×Dic3—22no—
504D3×Dic3—41no—
505D3×Dic3—62no—
506D3×Dic3—62no—
507D3×Dic3—122no—
508#546—271noSylow
509C2×C33—22no—
510C2×C33C22×D411yescharacteristic
511C2×C33C2×#4111yescharacteristic
512C2×C33H(5,𝔽2)11yescharacteristic
513C3×C3⋊D3—22no—
514C3×C3⋊D3—41no—
515C3×C3⋊D3—41no—
516C32×D3—22no—
517C32×D3—41no—
518C24×C3—31no—
519C24×C3—31no—
520C24×C3—61no—
521C24×C3—91no—
522C23×D3—31no—
523C23×D3—31no—
524C23×D3—61no—
525C23×D3D3211yescharacteristic
526C2×C3×D4—91no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C22×C3×C4—91no—
530C22×C3×C4—91no—
531C22×C3×C4—91no—
532C22×C3×C4—91no—
533C2×#67—31no—
534C2×#67—31no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—61no—
538C2×#67—91no—
539C2×#67—91no—
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—91no—
553C2×#67—91no—
554C2×#67—181no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—184no—
559C2×#67—184no—
560C2×#67—184no—
561C2×#67—188no—
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—91no—
565C22×Dic3—91no—
566C22×Dic3—91no—
567C22×Dic3—91no—
568C22×Dic3—181no—
569C22×Dic3—181no—
570C22×Dic3—181no—
571C22×Dic3—361no—
572#237—184no—
573#235—184no—
574#235—184no—
575C2×D12—31no—
576C2×D12—31no—
577C2×D12—91no—
578C2×D12—91no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
583C2×C4×D3—31no—
584C2×C4×D3—31no—
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×C22⋊C4—31no—
593C3×C22⋊C4—31no—
594C3×C22⋊C4—31no—
595C3×C22⋊C4—31no—
596C3×C22⋊C4—61no—
597C3×C22⋊C4—61no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C22⋊C4—91no—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—61no—
612#217—91no—
613#217—91no—
614#217—91no—
615#217D3211yescharacteristic
616#217D3211yescharacteristic
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—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—181no—
632C4⋊Dic3—91no—
633C4⋊Dic3—91no—
634C4⋊Dic3—91no—
635C4⋊Dic3—91no—
636C4⋊Dic3—181no—
637Dic3⋊C4—91no—
638Dic3⋊C4—91no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—181no—
646Dic3⋊C4—181no—
647Dic3⋊C4—181no—
648C4×Dic3—91no—
649C4×Dic3—91no—
650C4×Dic3—91no—
651C4×Dic3—181no—
652C22×C32—21no—
653C22×C32—21no—
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—22no—
664C22×C32—22no—
665C22×C32—22no—
666C22×C32—32no—
667C22×C32—42no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—42no—
674C22×C32—42no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—124no—
681C22×C32#23512yescomplemented
682C22×C32#23512yescomplemented
683C22×C32#23712yescomplemented
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⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—21no—
695C2×C3⋊D3—44no—
696C2×C3⋊D3D3×D412yes—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—22no—
702C2×C3×D3—21no—
703C2×C3×D3—21no—
704C2×C3×D3—21no—
705C2×C3×D3—21no—
706C2×C3×D3—21no—
707C2×C3×D3—21no—
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—44no—
716C2×C3×D3—44no—
717C2×C3×D3—48no—
718C2×C3×D3—62no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—62no—
724C2×C3×D3—62no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—61no—
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—121no—
738C2×C3×D3—121no—
739C2×C3×D3—121no—
740C2×C3×D3—121no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—124no—
744C2×C3×D3—124no—
745C2×C3×D3—128no—
746C2×C3×D3D3×D412yes—
747C2×C3×D3D3×D412yes—
748C32×C4—61no—
749C32×C4—61no—
750C32×C4—61no—
751C32×C4—61no—
752C3⋊Dic3—21no—
753C3⋊Dic3—21no—
754C3⋊Dic3—21no—
755C3⋊Dic3—32no—
756C3⋊Dic3—32no—
757C3⋊Dic3—32no—
758C3⋊Dic3—62no—
759C3⋊Dic3—62no—
760C3⋊Dic3—62no—
761C3⋊Dic3—61no—
762C3⋊Dic3—62no—
763C3⋊Dic3—61no—
764C3⋊Dic3—61no—
765C3⋊Dic3—122no—
766C3⋊Dic3—121no—
767C3⋊Dic3—121no—
768C3⋊Dic3—122no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—41no—
778C3×Dic3—41no—
779C3×Dic3—41no—
780C3×Dic3—41no—
781C3×Dic3—62no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—121no—
789C3×Dic3—121no—
790C2×#41—271no—
791C22×D4—271no—
792#124—271no—
793#123—271no—
794#123—271no—
795C22⋊Q8—271no—
796#121—271no—
797#121—271no—
798#121—271no—
799#120—91no—
800#120—271no—
801C4×D4—271no—
802C4×D4—271no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—91no—
805C33#54611yescharacteristic, complemented, Sylow
806C23×C3—21no—
807C23×C3—21no—
808C23×C3—21no—
809C23×C3—31no—
810C23×C3—31no—
811C23×C3—31no—
812C23×C3—31no—
813C23×C3—41no—
814C23×C3—61no—
815C23×C3—61no—
816C23×C3—62no—
817C23×C3—62no—
818C23×C3—64no—
819C23×C3—62no—
820C23×C3—62no—
821C23×C3—91no—
822C23×C3—91no—
823C23×C3—91no—
824C23×C3—122no—
825C23×C3—121no—
826C23×C3—121no—
827C23×C3—122no—
828C23×C3—182no—
829C23×C3—182no—
830C23×C3—361no—
831C23×C3C2×D3211yescharacteristic
832C23×C3C2×D3211yescharacteristic
833C23×C3C2×D3211yescharacteristic
834C22×D3—22no—
835C22×D3—22no—
836C22×D3—31no—
837C22×D3—31no—
838C22×D3—31no—
839C22×D3—31no—
840C22×D3—31no—
841C22×D3—31no—
842C22×D3—41no—
843C22×D3—61no—
844C22×D3—61no—
845C22×D3—61no—
846C22×D3—62no—
847C22×D3—62no—
848C22×D3—64no—
849C22×D3—62no—
850C22×D3—62no—
851C22×D3—122no—
852C22×D3—121no—
853C22×D3—121no—
854C22×D3—122no—
855C22×D3C2×D3211yescharacteristic
856C22×D3C2×D3211yescharacteristic
857C3×D4—182no—
858C3×D4—182no—
859C3×D4—361no—
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—31no—
867C2×C3×C4—31no—
868C2×C3×C4—61no—
869C2×C3×C4—61no—
870C2×C3×C4—61no—
871C2×C3×C4—61no—
872C2×C3×C4—91no—
873C2×C3×C4—91no—
874C2×C3×C4—91no—
875C2×C3×C4—182no—
876C2×C3×C4—182no—
877C2×C3×C4—361no—
878C2×C3×C4—361no—
879#67—62no—
880#67—64no—
881#67—62no—
882#67—62no—
883#67—94no—
884#67—94no—
885#67—94no—
886#67—121no—
887#67—184no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—182no—
893#67—182no—
894#67—182no—
895#67—182no—
896#67—182no—
897#67—182no—
898#67—184no—
899#67—184no—
900#67—184no—
901#67—182no—
902#67—361no—
903#67—361no—
904C2×Dic3—31no—
905C2×Dic3—31no—
906C2×Dic3—31no—
907C2×Dic3—31no—
908C2×Dic3—31no—
909C2×Dic3—31no—
910C2×Dic3—61no—
911C2×Dic3—61no—
912C2×Dic3—61no—
913C2×Dic3—62no—
914C2×Dic3—91no—
915C2×Dic3—91no—
916C2×Dic3—91no—
917C2×Dic3—91no—
918C2×Dic3—91no—
919C2×Dic3—91no—
920C2×Dic3—121no—
921C2×Dic3—181no—
922C2×Dic3—181no—
923C2×Dic3—181no—
924C2×Dic3—181no—
925C2×Dic3—181no—
926C2×Dic3—181no—
927C2×Dic3—182no—
928C2×Dic3—182no—
929C2×Dic3—182no—
930C2×Dic3—182no—
931C2×Dic3—184no—
932C2×Dic3—361no—
933C2×Dic3—361no—
934C2×Dic3—362no—
935C2×Dic3—362no—
936C2×Dic3—364no—
937C2×Dic3C2×D3211yescharacteristic
938C2×Dic3C2×D3211yescharacteristic
939C2×Dic3C2×D3211yescharacteristic
940C2×Dic3C2×D3211yescharacteristic
941D12—62no—
942D12—121no—
943D12—182no—
944D12—361no—
945C4×D3—62no—
946C4×D3—62no—
947C4×D3—62no—
948C4×D3—121no—
949C4×D3—121no—
950C4×D3—121no—
951C4×D3—182no—
952C4×D3—182no—
953C4×D3—362no—
954Dic6—182no—
955Dic6—182no—
956Dic6—182no—
957Dic6—362no—
958C2×C32—22no—
959C2×C32—24no—
960C2×C32—22no—
961C2×C32—22no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—41no—
972C2×C32—41no—
973C2×C32—41no—
974C2×C32—42no—
975C2×C32—42no—
976C2×C32—44no—
977C2×C32—62no—
978C2×C32—121no—
979C2×C32C2×#23511yescharacteristic
980C2×C32C2×#23511yescharacteristic
981C2×C32C2×D3×D411yescharacteristic
982C2×C32C2×D3×D411yescharacteristic
983C2×C32C2×D3×D411yescharacteristic
984C2×C32C2×#23711yescharacteristic
985C2×C32#100411yescharacteristic
986C2×C32#100411yescharacteristic
987C2×C32#100411yescharacteristic
988C3⋊D3—22no—
989C3⋊D3—41no—
990C3⋊D3—41no—
991C3×D3—22no—
992C3×D3—22no—
993C3×D3—42no—
994C3×D3—42no—
995C3×D3—41no—
996C3×D3—41no—
997C3×D3—62no—
998C3×D3—62no—
999C3×D3—122no—
1000C3×D3—122no—
1001C3×D3—122no—
1002C3×D3—121no—
1003C3×D3—121no—
1004C3×D3—121no—
1005C3×D3—121no—
1006C24—31no—
1007C24—91no—
1008#41—544no—
1009C2×Q8—271no—
1010C2×D4—91no—
1011C2×D4—91no—
1012C2×D4—91no—
1013C2×D4—271no—
1014C2×D4—271no—
1015C2×D4—271no—
1016C2×D4—271no—
1017C2×D4—271no—
1018C2×D4—271no—
1019C2×D4—544no—
1020C22×C4—91no—
1021C22×C4—91no—
1022C22×C4—91no—
1023C22×C4—91no—
1024C22×C4—271no—
1025C22×C4—271no—
1026C4⋊C4—271no—
1027C4⋊C4—271no—
1028C4⋊C4—271no—
1029C4⋊C4—271no—
1030C22⋊C4—31no—
1031C22⋊C4—31no—
1032C22⋊C4—91no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—91no—
1038C22⋊C4—91no—
1039C22⋊C4—271no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C42—271no—
1043C22×C3—22no—
1044C22×C3—22no—
1045C22×C3—21no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—21no—
1053C22×C3—21no—
1054C22×C3—22no—
1055C22×C3—22no—
1056C22×C3—22no—
1057C22×C3—32no—
1058C22×C3—32no—
1059C22×C3—41no—
1060C22×C3—41no—
1061C22×C3—41no—
1062C22×C3—41no—
1063C22×C3—42no—
1064C22×C3—42no—
1065C22×C3—41no—
1066C22×C3—42no—
1067C22×C3—62no—
1068C22×C3—62no—
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—92no—
1080C22×C3—121no—
1081C22×C3—121no—
1082C22×C3—121no—
1083C22×C3—121no—
1084C22×C3—124no—
1085C22×C3—124no—
1086C22×C3—128no—
1087C22×C3—181no—
1088C22×C3—181no—
1089C22×C3—181no—
1090C22×C3—181no—
1091C22×C3—181no—
1092C22×C3—181no—
1093C22×C3—181no—
1094C22×C3—181no—
1095C22×C3—364no—
1096C22×C3#379512yescomplemented
1097C22×C3#379812yescomplemented
1098C22×C3#380412yescomplemented
1099C22×C3C22×D3211yescharacteristic
1100C22×C3C22×D3211yescharacteristic
1101C22×C3C22×D3211yescharacteristic
1102C2×D3—21no—
1103C2×D3—21no—
1104C2×D3—21no—
1105C2×D3—21no—
1106C2×D3—21no—
1107C2×D3—32no—
1108C2×D3—32no—
1109C2×D3—44no—
1110C2×D3—62no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—61no—
1115C2×D3—62no—
1116C2×D3—62no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—121no—
1130C2×D3—121no—
1131C2×D3—121no—
1132C2×D3—121no—
1133C2×D3—121no—
1134C2×D3—121no—
1135C2×D3—124no—
1136C2×D3—124no—
1137C2×D3—128no—
1138C2×D3#381112yes—
1139C3×C4—61no—
1140C3×C4—61no—
1141C3×C4—61no—
1142C3×C4—61no—
1143C3×C4—61no—
1144C3×C4—61no—
1145C3×C4—61no—
1146C3×C4—61no—
1147C3×C4—121no—
1148C3×C4—121no—
1149C3×C4—121no—
1150C3×C4—121no—
1151C3×C4—181no—
1152C3×C4—181no—
1153C3×C4—181no—
1154Dic3—21no—
1155Dic3—21no—
1156Dic3—21no—
1157Dic3—21no—
1158Dic3—62no—
1159Dic3—61no—
1160Dic3—61no—
1161Dic3—61no—
1162Dic3—61no—
1163Dic3—61no—
1164Dic3—61no—
1165Dic3—92no—
1166Dic3—92no—
1167Dic3—92no—
1168Dic3—121no—
1169Dic3—121no—
1170Dic3—182no—
1171Dic3—182no—
1172Dic3—182no—
1173Dic3—182no—
1174Dic3—181no—
1175Dic3—181no—
1176Dic3—181no—
1177Dic3—362no—
1178Dic3—361no—
1179Dic3—361no—
1180Dic3—362no—
1181C32—21no—
1182C32—21no—
1183C32—21no—
1184C32—41no—
1185C32#549011yescharacteristic, complemented
1186C32#549011yescharacteristic, complemented
1187C32#559111yescharacteristic, complemented
1188C23—31no—
1189C23—31no—
1190C23—62no—
1191C23—62no—
1192C23—91no—
1193C23—91no—
1194C23—91no—
1195C23—121no—
1196C23—182no—
1197C23—182no—
1198C23—361no—
1199C23D3311yescharacteristic
1200Q8—542no—
1201D4—182no—
1202D4—182no—
1203D4—274no—
1204D4—361no—
1205D4—542no—
1206D4—542no—
1207D4—542no—
1208D4—542no—
1209D4—1081no—
1210C2×C4—31no—
1211C2×C4—31no—
1212C2×C4—31no—
1213C2×C4—31no—
1214C2×C4—91no—
1215C2×C4—91no—
1216C2×C4—91no—
1217C2×C4—182no—
1218C2×C4—182no—
1219C2×C4—271no—
1220C2×C4—271no—
1221C2×C4—361no—
1222C2×C4—361no—
1223C2×C4—542no—
1224C2×C4—542no—
1225C2×C3—24no—
1226C2×C3—22no—
1227C2×C3—22no—
1228C2×C3—22no—
1229C2×C3—21no—
1230C2×C3—21no—
1231C2×C3—21no—
1232C2×C3—21no—
1233C2×C3—21no—
1234C2×C3—21no—
1235C2×C3—21no—
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—42no—
1239C2×C3—42no—
1240C2×C3—44no—
1241C2×C3—41no—
1242C2×C3—41no—
1243C2×C3—41no—
1244C2×C3—62no—
1245C2×C3—62no—
1246C2×C3—122no—
1247C2×C3—122no—
1248C2×C3—121no—
1249C2×C3—121no—
1250C2×C3—182no—
1251C2×C3—361no—
1252C2×C3—361no—
1253C2×C3C2×#379511yescharacteristic
1254C2×C3C2×#379811yescharacteristic
1255C2×C3D32×D411yescharacteristic
1256C2×C3D32×D411yescharacteristic
1257C2×C3#6431311yescharacteristic
1258C2×C3#6431311yescharacteristic
1259C2×C3C2×#380411yescharacteristic
1260C2×C3C2×#381111yescharacteristic
1261C2×C3#6433011yescharacteristic
1262D3—22no—
1263D3—41no—
1264D3—62no—
1265D3—62no—
1266D3—122no—
1267D3—122no—
1268D3—122no—
1269D3—121no—
1270D3—121no—
1271D3—121no—
1272D3—121no—
1273C22—21no—
1274C22—21no—
1275C22—32no—
1276C22—61no—
1277C22—61no—
1278C22—61no—
1279C22—61no—
1280C22—61no—
1281C22—92no—
1282C22—124no—
1283C22—181no—
1284C22—181no—
1285C22—181no—
1286C22—181no—
1287C22—181no—
1288C22—181no—
1289C22—181no—
1290C22—181no—
1291C22—364no—
1292C22#8896012yescomplemented
1293C22C2×D3311yescharacteristic
1294C4—61no—
1295C4—61no—
1296C4—61no—
1297C4—61no—
1298C4—181no—
1299C4—181no—
1300C4—181no—
1301C4—272no—
1302C4—541no—
1303C3—21no—
1304C3—21no—
1305C3—21no—
1306C3—41no—
1307C3#1059418311yescharacteristic, complemented
1308C3#1059418411yescharacteristic, complemented
1309C3#1059550011yescharacteristic, complemented
1310C2—22no—
1311C2—62no—
1312C2—121no—
1313C2—182no—
1314C2—361no—
1315C2—361no—
1316C2#1172441511yescharacteristic
1317C2C2×#8896011yescharacteristic
1318C2D3×#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×#6290C2semidirect
2. C2×#88960C2semidirect
3. #11723727C2semidirect
4. #11723642C2semidirect
5. #11723626C2semidirect
6. C3×#63977C2semidirect
7. C3×#63974C2semidirect
8. C3×D3×#217C2semidirect
9. #11723009C2semidirect
10. #11722992C2semidirect
11. #11722988C2semidirect
12. #11722967C2semidirect
13. #11722960C2semidirect
14. #11722957C2semidirect
15. #11722930C2semidirect
23. C2×#6295C22semidirect
24. C2×#6295C22semidirect
25. C2×#6293C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×C3×#626C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#624C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88807C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88803C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
77. #63977D3semidirect
80. #63974D3semidirect
85. D3×#217D3semidirect
133. #6290D4semidirect
189. C2×#626C2×D3semidirect
190. C2×#626C2×D3semidirect
208. C2×#624C2×D3semidirect
209. C2×#624C2×D3semidirect
214. C2×D3×Dic3C2×D3semidirect
215. C2×D3×Dic3C2×D3semidirect
262. #3722C2×D3semidirect
263. #3722C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
280. C22×C33#41semidirect
681. C22×C32#235semidirect
682. C22×C32#235semidirect
683. C22×C32#237semidirect
805. C33#546semidirect
1096. C22×C3#3795semidirect
1097. C22×C3#3798semidirect
1098. C22×C3#3804semidirect
1185. C32#5490semidirect
1186. C32#5490semidirect
1187. C32#5591semidirect
1292. C22#88960semidirect
1307. C3#10594183semidirect
1308. C3#10594184semidirect
1309. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C22×#62902
C2×#889602
#117237272
#117236422
#117236262
C3×#639772
C3×#639742
C3×D3×#2172
#117230092
#117229922
#117229882
#117229672
#117229602
#117229572
#117229302
#105955003
#105941843
#105941833