Finite Group Databasebeta

← #13172139

Subgroups — #13172139

Order 1728.

1354 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723723C211yesmaximal, characteristic, complemented
2#11723636C211yesmaximal, characteristic, complemented
3#11723599C211yesmaximal, characteristic, complemented
4#11723592C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63969C211yesmaximal, characteristic, complemented
7C3×#63956C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723002C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722984C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722959C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722927C211yesmaximal, characteristic, complemented
16#10595185—31nomaximal
17#10594232—31nomaximal
18#10594126—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic, complemented
28C2×#6289C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#88804C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64147—31no—
55#64094—31no—
56#64091—31no—
57C3×#937—31no—
58C3×#935—31no—
59C3×#883—31no—
60C3×#882—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63981D311yescharacteristic, complemented
64#63978—31no—
65#63977—31no—
66#63977—31no—
67#63977—61no—
68#63974—31no—
69Dic3×#67—31no—
70#63971—31no—
71#63969D311yescharacteristic, complemented
72D3×#217—31no—
73D3×#217—31no—
74#63959—31no—
75#63958—31no—
76#63958—31no—
77#63958—61no—
78#63956D311yescharacteristic, complemented
79#63953—31no—
80#63953—31no—
81#63953—61no—
82#63910—31no—
83#63909—31no—
84#63904—31no—
85#63898—31no—
86#63897—31no—
87#63896—31no—
88#63895—31no—
89#63894—31no—
90#63893—31no—
91#63886—31no—
92#63886—31no—
93#63881—31no—
94#63880—31no—
95#63862—31no—
96#63861—31no—
97#63860—31no—
98#63854—31no—
99#63853—31no—
100#63852—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—41no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6294—41no—
123#6294—41no—
124#6293—41no—
125#6292—22no—
126#6292—41no—
127#6291—41no—
128#6289—41no—
129C3×#626—22no—
130C3×#626—41no—
131C3×D3×Dic3—41no—
132#5704—91no—
133#5657—91no—
134#5593—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×C32×D4—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—61no—
145C2×#638—61no—
146C2×#638—61no—
147C2×#638—121no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4×C3⋊D3—31no—
151C2×#634—31no—
152C2×C3×#67—21no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67C2×D311yescharacteristic
156C2×C3×#67C2×D311yescharacteristic
157C22×C3×Dic3—31no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×C4×D3—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#627—61no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—61no—
171C2×#626—61no—
172C2×#626—61no—
173C2×#626C2×D311yescharacteristic
174C2×#626C2×D311yescharacteristic
175C2×#624—31no—
176C2×#624—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—61no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3C2×D311yescharacteristic, complemented
185C32×C22⋊C4—31no—
186C32×C22⋊C4—31no—
187#3757—31no—
188#3757C2×D311yescharacteristic
189#3757C2×D311yescharacteristic
190#3752—31no—
191#3752—31no—
192#3752—31no—
193#3752—31no—
194C4⋊(C3⋊Dic3)—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—21no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—61no—
204C3×#217—61no—
205C3×#217C2×D311yescharacteristic
206C3×#217C2×D311yescharacteristic
207C3×#217C2×D311yescharacteristic
208C3×#217C2×D311yescharacteristic
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—31no—
226#3724C2×D311yescharacteristic, complemented
227#3724C2×D311yescharacteristic, complemented
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic, complemented
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233Dic3⋊Dic3C2×D311yescharacteristic, complemented
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—61no—
241#3722—61no—
242#3722C2×D311yescharacteristic
243#3722C2×D311yescharacteristic
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3⋊(C3⋊D3)—21no—
267C2×C3⋊(C3⋊D3)—21no—
268C2×C3⋊(C3⋊D3)—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—44no—
275C2×C3×C3⋊D3#4112yes—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#123—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#939—91no—
295#939—91no—
296#938—91no—
297#938—91no—
298#938—181no—
299#937—31no—
300#936—91no—
301#935—31no—
302D4×Dic3—91no—
303#930—91no—
304C4×#67—91no—
305#898—91no—
306#898—91no—
307#897—91no—
308#896—91no—
309#895—91no—
310#895—91no—
311#894—91no—
312#894—91no—
313#893—91no—
314#893—91no—
315#885—91no—
316#885—91no—
317#885—91no—
318#885—91no—
319#885—181no—
320#884—91no—
321#884—91no—
322#883—31no—
323#883—91no—
324#882—31no—
325#882—91no—
326#882—91no—
327#882—181no—
328#67⋊C4—91no—
329D3×C22⋊C4—91no—
330D3×C22⋊C4—91no—
331#879—31no—
332#879—31no—
333#879—91no—
334#878—91no—
335#875—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3—22no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—31no—
349C22×C3⋊D3—41no—
350C22×C3⋊D3—41no—
351C22×C3⋊D3—61no—
352C22×C3⋊D3—61no—
353C22×C3⋊D3—61no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—61no—
363C22×C3×D3—61no—
364C22×C3×D3—62no—
365C22×C3×D3—62no—
366C22×C3×D3—122no—
367C22×C3×D3—121no—
368C22×C3×D3—121no—
369C22×C3×D3—121no—
370C22×C3×D3—121no—
371C22×C3×D3—122no—
372C22×C3×D3—122no—
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C32×D4—121no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381#638—121no—
382#638—121no—
383#638—121no—
384#638—121no—
385#638—122no—
386#638—122no—
387#638—122no—
388#638—124no—
389C2×C3⋊Dic3—31no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—61no—
393C2×C3⋊Dic3—61no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C4⋊(C3⋊D3)—62no—
401C4⋊(C3⋊D3)—121no—
402C4×C3⋊D3—121no—
403#634—121no—
404C3×#67—41no—
405C3×#67—41no—
406C3×#67—42no—
407C3×#67—62no—
408C3×#67—121no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
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—121no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C3×D12—62no—
438C3×D12—121no—
439C3×C4×D3—121no—
440#627—121no—
441#627—121no—
442#627—122no—
443#626—22no—
444#626—41no—
445#626—62no—
446#626—62no—
447#626—122no—
448#626—121no—
449#626—121no—
450#626—122no—
451#626—121no—
452#626—121no—
453#626—122no—
454#624—121no—
455#624—121no—
456#624—122no—
457#624—121no—
458#624—121no—
459D3×Dic3—41no—
460D3×Dic3—121no—
461D3×Dic3—121no—
462D3×Dic3—121no—
463D3×Dic3—121no—
464#538—271noSylow
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3⋊(C3⋊D3)—41no—
470C3×C3⋊D3—22no—
471C3×C3⋊D3—41no—
472C32×D3—41no—
473C24×C3—91no—
474C23×D3—31no—
475C23×D3—31no—
476C23×D3—61no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—61no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C22×C3×C4—91no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—181no—
493C2×#67—181no—
494C2×#67—181no—
495C2×#67—181no—
496C2×#67—361no—
497C2×#67D3211yescharacteristic
498C22×Dic3—31no—
499C22×Dic3—91no—
500C22×Dic3—91no—
501C2×D12—31no—
502C2×D12—31no—
503C2×D12—91no—
504C2×D12—91no—
505C2×D12—91no—
506C2×D12—91no—
507C2×D12—91no—
508C2×D12—181no—
509C2×D12—181no—
510C2×C4×D3—31no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—181no—
519C2×Dic6—91no—
520C2×Dic6—91no—
521C2×Dic6—91no—
522C2×Dic6—181no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C4⋊C4—91no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—31no—
531C3×C22⋊C4—31no—
532C3×C22⋊C4—61no—
533C3×C22⋊C4—61no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C22⋊C4—91no—
539C3×C42—91no—
540#217—31no—
541#217—31no—
542#217—31no—
543#217—31no—
544#217—31no—
545#217—61no—
546#217—61no—
547#217—91no—
548#217—91no—
549#217—91no—
550#217—91no—
551#217—91no—
552#217—91no—
553#217—181no—
554#217D3211yescharacteristic
555#217D3211yescharacteristic
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—91no—
575(C2×D3)⋊C4—91no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578(C2×D3)⋊C4—181no—
579(C2×D3)⋊C4—181no—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3—31no—
583C4⋊Dic3—91no—
584C4⋊Dic3—91no—
585C4⋊Dic3—181no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4—31no—
592Dic3⋊C4—31no—
593Dic3⋊C4—91no—
594C4×Dic3—31no—
595C4×Dic3—31no—
596C4×Dic3—91no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C4×Dic3—181no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—42no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—81no—
627C22×C32—81no—
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—44no—
637C2×C3⋊D3—61no—
638C2×C3⋊D3—62no—
639C2×C3⋊D3—61no—
640C2×C3⋊D3—61no—
641C2×C3⋊D3—61no—
642C2×C3⋊D3—61no—
643C2×C3⋊D3—61no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—61no—
646C2×C3⋊D3—61no—
647C2×C3⋊D3—121no—
648C2×C3⋊D3—121no—
649C2×C3⋊D3—122no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—241no—
657C2×C3⋊D3—241no—
658C2×C3⋊D3#23712yes—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—32no—
666C2×C3×D3—32no—
667C2×C3×D3—41no—
668C2×C3×D3—41no—
669C2×C3×D3—41no—
670C2×C3×D3—62no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—62no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686C2×C3×D3—124no—
687C2×C3×D3—124no—
688C2×C3×D3—128no—
689C32×C4—61no—
690C32×C4—61no—
691C32×C4—61no—
692C32×C4—61no—
693C32×C4—61no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—61no—
699C3⋊Dic3—62no—
700C3⋊Dic3—61no—
701C3⋊Dic3—61no—
702C3⋊Dic3—121no—
703C3⋊Dic3—121no—
704C3⋊Dic3—122no—
705C3×Dic3—22no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—21no—
715C3×Dic3—21no—
716C3×Dic3—41no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—41no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732#126—91no—
733#126—271no—
734#124—271no—
735#124—271no—
736#123—91no—
737#123—271no—
738C22⋊Q8—271no—
739#121—271no—
740#121—271no—
741#121—271no—
742#120—91no—
743#120—271no—
744C4×D4—271no—
745C4×D4—271no—
746C2×C22⋊C4—271no—
747C33#53811yescharacteristic, complemented, Sylow
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—31no—
752C23×C3—31no—
753C23×C3—41no—
754C23×C3—61no—
755C23×C3—91no—
756C23×C3—91no—
757C23×C3—182no—
758C23×C3—361no—
759C23×C3—361no—
760C23×C3C2×D3211yescharacteristic
761C23×C3C2×D3211yescharacteristic
762C23×C3C2×D3211yescharacteristic
763C22×D3—31no—
764C22×D3—31no—
765C22×D3—31no—
766C22×D3—31no—
767C22×D3—61no—
768C22×D3—61no—
769C22×D3—62no—
770C22×D3—62no—
771C22×D3—91no—
772C22×D3—91no—
773C22×D3—91no—
774C22×D3—122no—
775C22×D3—121no—
776C22×D3—121no—
777C22×D3—121no—
778C22×D3—121no—
779C22×D3—122no—
780C22×D3—122no—
781C22×D3—181no—
782C22×D3—181no—
783C22×D3—181no—
784C22×D3—361no—
785C22×D3C2×D3211yescharacteristic
786C3×D4—121no—
787C3×D4—121no—
788C3×D4—122no—
789C3×D4—182no—
790C3×D4—361no—
791C2×C3×C4—31no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—61no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—91no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—361no—
811#67—41no—
812#67—62no—
813#67—121no—
814#67—182no—
815#67—361no—
816#67—361no—
817#67—361no—
818#67—362no—
819#67—361no—
820#67—361no—
821#67—361no—
822#67—362no—
823#67—362no—
824#67—362no—
825#67—364no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—61no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—91no—
839C2×Dic3—91no—
840C2×Dic3—91no—
841C2×Dic3—121no—
842C2×Dic3—181no—
843C2×Dic3—181no—
844C2×Dic3—181no—
845C2×Dic3—361no—
846C2×Dic3—361no—
847C2×Dic3—361no—
848C2×Dic3C2×D3211yescharacteristic
849C2×Dic3C2×D3211yescharacteristic
850C2×Dic3C2×D3211yescharacteristic
851C2×Dic3C2×D3211yescharacteristic
852C2×Dic3C2×D3211yescharacteristic
853D12—62no—
854D12—121no—
855D12—182no—
856D12—182no—
857D12—362no—
858D12—361no—
859D12—361no—
860D12—362no—
861D12—361no—
862C4×D3—121no—
863C4×D3—361no—
864C4×D3—361no—
865C4×D3—361no—
866C4×D3—361no—
867C4×D3—361no—
868C4×D3—361no—
869C4×D3—361no—
870C4×D3—362no—
871Dic6—361no—
872Dic6—361no—
873Dic6—361no—
874Dic6—362no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—41no—
885C2×C32—41no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—42no—
889C2×C32—41no—
890C2×C32—41no—
891C2×C32—81no—
892C2×C32—81no—
893C2×C32—82no—
894C2×C32—121no—
895C2×C32C2×#23711yescharacteristic
896C2×C32#100411yescharacteristic
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32D3×#4111yescharacteristic
900C2×C32D3×#4111yescharacteristic
901C2×C32#100911yescharacteristic
902C2×C32#100911yescharacteristic
903C2×C32#100911yescharacteristic
904C3⋊D3—22no—
905C3⋊D3—41no—
906C3⋊D3—121no—
907C3⋊D3—122no—
908C3⋊D3—121no—
909C3⋊D3—121no—
910C3⋊D3—241no—
911C3⋊D3—241no—
912C3⋊D3—242no—
913C3×D3—41no—
914C3×D3—41no—
915C3×D3—62no—
916C3×D3—62no—
917C3×D3—81no—
918C3×D3—122no—
919C3×D3—122no—
920C3×D3—121no—
921C3×D3—121no—
922C24—91no—
923C2×Q8—271no—
924C2×D4—31no—
925C2×D4—91no—
926C2×D4—91no—
927C2×D4—271no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4—271no—
931C22×C4—91no—
932C22×C4—271no—
933C22×C4—271no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—271no—
941C22⋊C4—31no—
942C22⋊C4—31no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—271no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—91no—
956C42—271no—
957C22×C3—22no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—42no—
979C22×C3—41no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—81no—
987C22×C3—81no—
988C22×C3—92no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—121no—
992C22×C3—181no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3—364no—
998C22×C3C22×D3211yescharacteristic
999C22×C3C22×D3211yescharacteristic
1000C22×C3C22×D3211yescharacteristic
1001C2×D3—21no—
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—32no—
1005C2×D3—32no—
1006C2×D3—62no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—62no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—121no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C2×D3—121no—
1022C2×D3—124no—
1023C2×D3—124no—
1024C2×D3—128no—
1025C2×D3—182no—
1026C2×D3—181no—
1027C2×D3—181no—
1028C2×D3—181no—
1029C2×D3—181no—
1030C2×D3—181no—
1031C2×D3—181no—
1032C2×D3—181no—
1033C2×D3—181no—
1034C2×D3—181no—
1035C2×D3—361no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—361no—
1039C2×D3—361no—
1040C2×D3—361no—
1041C2×D3—361no—
1042C2×D3—361no—
1043C2×D3—362no—
1044C2×D3—721no—
1045C2×D3—721no—
1046C3×C4—62no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—121no—
1058C3×C4—121no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—181no—
1062C3×C4—181no—
1063C3×C4—181no—
1064C3×C4—181no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—182no—
1083Dic3—181no—
1084Dic3—181no—
1085Dic3—181no—
1086Dic3—361no—
1087Dic3—361no—
1088Dic3—362no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#559311yescharacteristic, complemented
1094C32#565711yescharacteristic, complemented
1095C32#570411yescharacteristic, complemented
1096C23—31no—
1097C23—91no—
1098C23—91no—
1099C23—182no—
1100C23—271no—
1101C23—361no—
1102C23—361no—
1103C23D3311yescharacteristic
1104Q8—1081no—
1105D4—121no—
1106D4—182no—
1107D4—361no—
1108D4—542no—
1109D4—1081no—
1110D4—1081no—
1111D4—1081no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—271no—
1122C2×C4—361no—
1123C2×C4—1081no—
1124C2×C4—1081no—
1125C2×C4—1081no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—42no—
1136C2×C3—41no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—81no—
1143C2×C3—81no—
1144C2×C3—82no—
1145C2×C3—121no—
1146C2×C3—121no—
1147C2×C3—182no—
1148C2×C3—241no—
1149C2×C3—361no—
1150C2×C3#6430711yescharacteristic
1151C2×C3#6430811yescharacteristic
1152C2×C3D3×#23711yescharacteristic
1153C2×C3D3×#23711yescharacteristic
1154C2×C3#6431211yescharacteristic
1155C2×C3#6431411yescharacteristic
1156C2×C3#6431411yescharacteristic
1157C2×C3#6431411yescharacteristic
1158C2×C3#6433011yescharacteristic
1159D3—41no—
1160D3—62no—
1161D3—62no—
1162D3—122no—
1163D3—122no—
1164D3—121no—
1165D3—121no—
1166D3—362no—
1167D3—361no—
1168D3—361no—
1169D3—361no—
1170D3—721no—
1171D3—721no—
1172D3—722no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—61no—
1177C22—61no—
1178C22—61no—
1179C22—92no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—364no—
1186C22—541no—
1187C22—541no—
1188C22—541no—
1189C22C2×D3311yescharacteristic
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—61no—
1195C4—181no—
1196C4—181no—
1197C4—181no—
1198C4—181no—
1199C4—541no—
1200C3—21no—
1201C3—21no—
1202C3—21no—
1203C3—41no—
1204C3#1059412611yescharacteristic, complemented
1205C3#1059423211yescharacteristic, complemented
1206C3#1059518511yescharacteristic, complemented
1207C2—41no—
1208C2—121no—
1209C2—182no—
1210C2—361no—
1211C2—1081no—
1212C2#1172440811yescharacteristic
1213C2#1172441811yescharacteristic
1214C2#1172442011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723723C2semidirect
2. #11723636C2semidirect
3. #11723599C2semidirect
4. #11723592C2semidirect
5. C3×#63981C2semidirect
6. C3×#63969C2semidirect
7. C3×#63956C2semidirect
8. #11723027C2semidirect
9. #11723002C2semidirect
10. #11723000C2semidirect
11. #11722984C2semidirect
12. #11722966C2semidirect
13. #11722959C2semidirect
14. #11722937C2semidirect
15. #11722927C2semidirect
24. C2×#6293C22semidirect
27. C2×#6291C22semidirect
28. C2×#6289C22semidirect
31. C2×C3×D3×Dic3C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
39. #88804C22semidirect
40. #88804C22semidirect
43. (C2×D3)⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
63. #63981D3semidirect
71. #63969D3semidirect
78. #63956D3semidirect
184. C2×D3×Dic3C2×D3semidirect
226. #3724C2×D3semidirect
227. #3724C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
747. C33#538semidirect
1093. C32#5593semidirect
1094. C32#5657semidirect
1095. C32#5704semidirect
1204. C3#10594126semidirect
1205. C3#10594232semidirect
1206. C3#10595185semidirect

Maximal subgroups

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

subgroupindex
#117237232
#117236362
#117235992
#117235922
C3×#639812
C3×#639692
C3×#639562
#117230272
#117230022
#117230002
#117229842
#117229662
#117229592
#117229372
#117229272
#105951853
#105942323
#105941263