Finite Group Databasebeta

← #13172144

Subgroups — #13172144

Order 1728.

1356 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#11723628C211yesmaximal, characteristic, complemented
4#11723616C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63959C211yesmaximal, characteristic, complemented
7C3×#63956C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11722990C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722963C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722928C211yesmaximal, characteristic, complemented
16#10595184—31nomaximal
17#10594162—31nomaximal
18#10594127—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6291C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic, complemented
28C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38#88807C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88804C2211yescharacteristic, complemented
42#88804C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64148—31no—
55#64092—31no—
56#64091—31no—
57C3×#937—31no—
58C3×#936—31no—
59C3×#885—31no—
60C3×#882—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63981D311yescharacteristic, complemented
64#63977—31no—
65#63977—31no—
66#63977—61no—
67#63975—31no—
68#63975—31no—
69#63975—61no—
70#63974—31no—
71#67⋊Dic3—31no—
72#63971—31no—
73#63971—31no—
74#63971—31no—
75#63971—61no—
76D3×#217—31no—
77D3×#217—31no—
78#63962—31no—
79#63959D311yescharacteristic, complemented
80#63958—31no—
81#63956D311yescharacteristic, complemented
82#63916—31no—
83#63910—31no—
84#63910—31no—
85#63907—31no—
86#63899—31no—
87#63894—31no—
88Dic3×D12—31no—
89#63890—31no—
90#63888—31no—
91#63887—31no—
92#63886—31no—
93#63884—31no—
94#63881—31no—
95#63880—31no—
96#63880—31no—
97#63868—31no—
98#63864—31no—
99#63861—31no—
100#63859—31no—
101#63852—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#6292—22no—
125#6292—41no—
126#6291—41no—
127#6289—41no—
128D3×C3⋊Dic3—41no—
129C3×#627—41no—
130C3×#626—22no—
131C3×#626—41no—
132#5704—91no—
133#5678—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—
148C22×C3⋊Dic3—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C3×#67—21no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67C2×D311yescharacteristic
156C2×C3×#67C2×D311yescharacteristic
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×Dic6—31no—
160C2×C3×Dic6—31no—
161C2×#627C2×D311yescharacteristic, complemented
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—61no—
169C2×#626—61no—
170C2×#626—61no—
171C2×#626C2×D311yescharacteristic
172C2×#626C2×D311yescharacteristic
173C2×#624—31no—
174C2×#624—31no—
175C2×#624—31no—
176C2×#624—31no—
177C2×#624—61no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—61no—
185C32×C22⋊C4—31no—
186C32×C22⋊C4—31no—
187#3757C2×D311yescharacteristic
188#3757C2×D311yescharacteristic
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193C4⋊(C3⋊Dic3)—31no—
194#3750—31no—
195#3750—31no—
196C3×#217—21no—
197C3×#217—21no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—61no—
205C3×#217—61no—
206C3×#217C2×D311yescharacteristic
207C3×#217C2×D311yescharacteristic
208C3×#217C2×D311yescharacteristic
209C3×#217C2×D311yescharacteristic
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—31no—
226#3724—31no—
227#3724—31no—
228#3724—61no—
229#3724C2×D311yescharacteristic, complemented
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237Dic3⋊Dic3C2×D311yescharacteristic, complemented
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—61no—
245#3722—61no—
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic
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—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
259(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
260Dic32C2×D311yescharacteristic, complemented
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×#124—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#947—91no—
295#946—91no—
296#939—91no—
297#939—91no—
298#939—91no—
299#939—181no—
300#938—91no—
301#937—31no—
302#936—31no—
303#935—91no—
304D4×Dic3—91no—
305#898—91no—
306#896—91no—
307#895—91no—
308#895—91no—
309#894—91no—
310#893—91no—
311#886—91no—
312#885—31no—
313#885—91no—
314#884—91no—
315#884—91no—
316#884—91no—
317#883—91no—
318#883—91no—
319#883—91no—
320#883—181no—
321#882—31no—
322#882—91no—
323#882—91no—
324#882—181no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327D3×C22⋊C4—91no—
328D3×C22⋊C4—91no—
329#879—31no—
330#879—31no—
331#879—91no—
332#878—91no—
333#876—91no—
334#875—91no—
335C4×D12—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⋊Dic3—121no—
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C4⋊(C3⋊D3)—62no—
402C4⋊(C3⋊D3)—121no—
403C4×C3⋊D3—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×Dic3C22×D311yescharacteristic
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
436C3×D12—62no—
437C3×D12—121no—
438C3×Dic6—121no—
439C3×Dic6—121no—
440#627—41no—
441#626—22no—
442#626—41no—
443#626—62no—
444#626—62no—
445#626—122no—
446#626—121no—
447#626—121no—
448#626—122no—
449#626—121no—
450#626—121no—
451#626—122no—
452#624—121no—
453#624—121no—
454#624—122no—
455#624—121no—
456#624—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459D3×Dic3—121no—
460D3×Dic3—121no—
461D3×Dic3—121no—
462D3×Dic3—121no—
463D3×Dic3—122no—
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×Q8—91no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—61no—
481C2×C3×D4—91no—
482C2×C3×D4—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—91no—
499C22×Dic3—91no—
500C22×Dic3—91no—
501C22×Dic3—91no—
502C22×Dic3—181no—
503C2×D12—31no—
504C2×D12—31no—
505C2×D12—91no—
506C2×D12—91no—
507C2×D12—91no—
508C2×D12—91no—
509C2×D12—91no—
510C2×D12—181no—
511C2×D12—181no—
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—91no—
519C2×C4×D3—91no—
520C2×C4×D3—181no—
521C2×Dic6—31no—
522C2×Dic6—31no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—61no—
531C3×C22⋊C4—61no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C42—91no—
539C3×C42—91no—
540#217—31no—
541#217—31no—
542#217—31no—
543#217—31no—
544#217—31no—
545#217—31no—
546#217—61no—
547#217—61no—
548#217—91no—
549#217—91no—
550#217—91no—
551#217—91no—
552#217D3211yescharacteristic
553#217D3211yescharacteristic
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—91no—
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—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578C4⋊Dic3—31no—
579C4⋊Dic3—31no—
580C4⋊Dic3—91no—
581C4⋊Dic3—91no—
582C4⋊Dic3—91no—
583C4⋊Dic3—181no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594Dic3⋊C4—181no—
595Dic3⋊C4—181no—
596C4×Dic3—31no—
597C4×Dic3—31no—
598C4×Dic3—31no—
599C4×Dic3—31no—
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—22no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—32no—
667C2×C3×D3—32no—
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—21no—
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—41no—
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—91no—
735#124—271no—
736#123—271no—
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×Q8—361no—
787C3×D4—121no—
788C3×D4—121no—
789C3×D4—122no—
790C3×D4—182no—
791C3×D4—361no—
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—31no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
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—181no—
842C2×Dic3—181no—
843C2×Dic3—181no—
844C2×Dic3—361no—
845C2×Dic3—361no—
846C2×Dic3—361no—
847C2×Dic3—361no—
848C2×Dic3—361no—
849C2×Dic3—362no—
850C2×Dic3C2×D3211yescharacteristic
851C2×Dic3C2×D3211yescharacteristic
852C2×Dic3C2×D3211yescharacteristic
853C2×Dic3C2×D3211yescharacteristic
854C2×Dic3C2×D3211yescharacteristic
855D12—62no—
856D12—121no—
857D12—182no—
858D12—182no—
859D12—362no—
860D12—361no—
861D12—361no—
862D12—362no—
863D12—361no—
864C4×D3—361no—
865C4×D3—361no—
866C4×D3—361no—
867C4×D3—361no—
868C4×D3—361no—
869C4×D3—361no—
870C4×D3—361no—
871C4×D3—362no—
872C4×D3—361no—
873Dic6—121no—
874Dic6—121no—
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—42no—
914C3×D3—41no—
915C3×D3—41no—
916C3×D3—62no—
917C3×D3—62no—
918C3×D3—122no—
919C3×D3—122no—
920C3×D3—121no—
921C3×D3—121no—
922C24—91no—
923C2×Q8—91no—
924C2×D4—31no—
925C2×D4—91no—
926C2×D4—91no—
927C2×D4—271no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4—271no—
931C22×C4—271no—
932C22×C4—271no—
933C22×C4—271no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—271no—
939C4⋊C4—271no—
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—91no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—91no—
956C42—91no—
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—62no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—81no—
988C22×C3—81no—
989C22×C3—92no—
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—61no—
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—121no—
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#567811yescharacteristic, complemented
1095C32#570411yescharacteristic, complemented
1096C23—31no—
1097C23—91no—
1098C23—91no—
1099C23—182no—
1100C23—271no—
1101C23—361no—
1102C23—361no—
1103C23D3311yescharacteristic
1104Q8—361no—
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—1081no—
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—122no—
1146C2×C3—121no—
1147C2×C3—121no—
1148C2×C3—182no—
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#1059412711yescharacteristic, complemented
1205C3#1059416211yescharacteristic, complemented
1206C3#1059518411yescharacteristic, 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. #11723628C2semidirect
4. #11723616C2semidirect
5. C3×#63981C2semidirect
6. C3×#63959C2semidirect
7. C3×#63956C2semidirect
8. #11723023C2semidirect
9. #11723003C2semidirect
10. #11722990C2semidirect
11. #11722979C2semidirect
12. #11722966C2semidirect
13. #11722963C2semidirect
14. #11722937C2semidirect
15. #11722928C2semidirect
26. C2×#6291C22semidirect
27. C2×#6289C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
29. C2×C3×#627C22semidirect
38. #88807C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. #88804C22semidirect
42. #88804C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
63. #63981D3semidirect
79. #63959D3semidirect
81. #63956D3semidirect
161. C2×#627C2×D3semidirect
229. #3724C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
237. Dic3⋊Dic3C2×D3semidirect
258. (C2×D3)⋊Dic3C2×D3semidirect
259. (C2×D3)⋊Dic3C2×D3semidirect
260. Dic32C2×D3semidirect
261. Dic32C2×D3semidirect
747. C33#538semidirect
1093. C32#5593semidirect
1094. C32#5678semidirect
1095. C32#5704semidirect
1204. C3#10594127semidirect
1205. C3#10594162semidirect
1206. C3#10595184semidirect

Maximal subgroups

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

subgroupindex
#117237232
#117236362
#117236282
#117236162
C3×#639812
C3×#639592
C3×#639562
#117230232
#117230032
#117229902
#117229792
#117229662
#117229632
#117229372
#117229282
#105951843
#105941623
#105941273