Finite Group Databasebeta

← #13178678

Subgroups — #13178678

Order 1728.

1296 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64148C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4#11723728C211yesmaximal, characteristic, complemented
5#11723726C211yesmaximal, characteristic, complemented
6#11723725C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723724C211yesmaximal, characteristic, complemented
9#11723720C211yesmaximal, characteristic, complemented
10#11723717C211yesmaximal, characteristic, complemented
11#11723715C211yesmaximal, characteristic, complemented
12#11723694C211yesmaximal, characteristic, complemented
13#11723690C211yesmaximal, characteristic, complemented
14#11723684C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10595250—31nomaximal
17#10595205—31nomaximal
18#10595197—31nomaximal
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic
26C22×C3×C3⋊Dic3C2211yescharacteristic
27C22×C3×C3⋊Dic3C2211yescharacteristic
28C2×C3×C4×C3⋊D3C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6295C2211yescharacteristic
32C2×#6294C2211yescharacteristic
33C2×#6294C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64148D311yescharacteristic, complemented
55#64148D311yescharacteristic, complemented
56#64147D311yescharacteristic, complemented
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#939—61no—
62C3×#939—61no—
63C3×#938—31no—
64C3×#938—31no—
65C3×#938—61no—
66#63980—31no—
67#63979—31no—
68#63979—31no—
69#63979—31no—
70#63978—31no—
71#63978—31no—
72#63975—31no—
73#67⋊Dic3—31no—
74Dic3×#67—31no—
75#63971—31no—
76#63971—31no—
77#63970—31no—
78#63970—31no—
79#63969—31no—
80#63969—31no—
81#63966—31no—
82#63962—31no—
83#63961—31no—
84#63958—31no—
85#63958—31no—
86#63957—31no—
87#63955—31no—
88#63955—31no—
89#63952—31no—
90#63905—31no—
91#63904—31no—
92#63891—31no—
93#63890—31no—
94#63881—31no—
95#63879—31no—
96#63854—31no—
97#63853—31no—
98#63850—31no—
99#63847—31no—
100#63846—31no—
101#63845—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C33×D4—41no—
108C2×C33×C4C2311yescharacteristic
109C3×#638—22no—
110C3×#638—41no—
111C3×#638—41no—
112C3×#638—41no—
113C3×#638—41no—
114C3×#638—41no—
115C2×C3×C3⋊Dic3—22no—
116C2×C3×C3⋊Dic3—41no—
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C3×C4×C3⋊D3—41no—
127#6295—22no—
128#6295—41no—
129#6295—41no—
130#6294—41no—
131#6294—41no—
132#5619—91no—
133#5615—91no—
134#5615—91no—
135C2×C32×D4—21no—
136C2×C32×D4—21no—
137C2×C32×D4—21no—
138C2×C32×D4—41no—
139C2×C32×D4C2×D311yescharacteristic
140C2×C32×D4C2×D311yescharacteristic
141C2×C32×D4C2×D311yescharacteristic
142C2×#638C2×D311yescharacteristic
143C2×#638C2×D311yescharacteristic
144C2×#638C2×D311yescharacteristic
145C2×#638C2×D311yescharacteristic
146C2×#638C2×D311yescharacteristic
147C2×#638C2×D311yescharacteristic
148C22×C3⋊Dic3C2×D311yescharacteristic
149C22×C3⋊Dic3C2×D311yescharacteristic
150C2×C4×C3⋊D3C2×D311yescharacteristic
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—61no—
164C2×C3×#67—61no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×#67—61no—
168C2×C3×#67—61no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3—61no—
174C22×C3×Dic3—61no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—61no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#625—31no—
185C2×#625—31no—
186C2×#625—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193#3757C2×D311yescharacteristic
194#3757C2×D311yescharacteristic
195#3757C2×D311yescharacteristic
196#3757C2×D311yescharacteristic
197#3752C2×D311yescharacteristic
198#3752C2×D311yescharacteristic
199C4⋊(C3⋊Dic3)C2×D311yescharacteristic
200#3750C2×D311yescharacteristic
201#3750C2×D311yescharacteristic
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—61no—
211C3×#217—61no—
212C3×#217—61no—
213C3×#217—61no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—61no—
219C3×(C2×D3)⋊C4—61no—
220C3×C4⋊Dic3—31no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—61no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—61no—
228C3×Dic3⋊C4—61no—
229#3724—31no—
230#3724—31no—
231#3724—31no—
232#3724—31no—
233#3724—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—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—31no—
255(C2×D3)⋊Dic3—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—31no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
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—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C33×C4—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3#4112yes—
288C3×#121—91no—
289C3×#121—91no—
290C3×#121—91no—
291#940—91no—
292#940—91no—
293#940—91no—
294#939—31no—
295#939—31no—
296#939—31no—
297#939—31no—
298#939—61no—
299#939—61no—
300#939—91no—
301#939—91no—
302#939—91no—
303#939—91no—
304#938—31no—
305#938—31no—
306#938—61no—
307#938—91no—
308#938—91no—
309#935—91no—
310#935—91no—
311D4×Dic3—91no—
312#930—91no—
313#929—91no—
314#929—91no—
315C4×#67—91no—
316C4×#67—91no—
317#926—91no—
318#894—91no—
319#894—91no—
320#893—91no—
321#890—91no—
322#889—91no—
323#889—91no—
324#886—91no—
325#886—91no—
326#884—91no—
327#884—91no—
328#883—91no—
329#883—91no—
330#883—91no—
331#883—91no—
332#67⋊C4—91no—
333#67⋊C4—91no—
334#877—91no—
335#877—91no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—21no—
341C23×C32—21no—
342C23×C32—41no—
343C23×C32—41no—
344C23×C32C22×D311yescharacteristic
345C23×C32C22×D311yescharacteristic
346C23×C32C22×D311yescharacteristic
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—61no—
360C22×C3×D3—61no—
361C22×C3×D3—61no—
362C32×D4—41no—
363C32×D4—41no—
364C32×D4—41no—
365C32×D4—42no—
366C32×D4—42no—
367C32×D4—42no—
368C32×D4—44no—
369C2×C32×C4—21no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—41no—
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376#638—22no—
377#638—41no—
378#638—41no—
379#638—41no—
380#638—41no—
381#638—41no—
382C2×C3⋊Dic3—22no—
383C2×C3⋊Dic3—41no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C4×C3⋊D3—41no—
394C3×#67—62no—
395C3×#67—62no—
396C3×#67—122no—
397C3×#67—121no—
398C3×#67—121no—
399C3×#67—121no—
400C3×#67—121no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—121no—
404C3×#67—121no—
405C3×#67—121no—
406C3×#67—121no—
407C3×#67—122no—
408C3×#67—122no—
409C3×#67—122no—
410C3×#67—122no—
411C3×#67—122no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—62no—
440C2×C3×Dic3—62no—
441C2×C3×Dic3—122no—
442C2×C3×Dic3—121no—
443C2×C3×Dic3—121no—
444C2×C3×Dic3—122no—
445C3×C4×D3—121no—
446C3×C4×D3—121no—
447C3×C4×D3—122no—
448#626—62no—
449#626—62no—
450#626—121no—
451#626—121no—
452#626—121no—
453#626—121no—
454#625—62no—
455#625—121no—
456#625—121no—
457#624—121no—
458#624—121no—
459D3×Dic3—121no—
460D3×Dic3—121no—
461D3×Dic3—121no—
462D3×Dic3—121no—
463#540—271noSylow
464C2×C33—41no—
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3×C3⋊D3—41no—
470C3×C3⋊D3—41no—
471C3×C3⋊D3—41no—
472C2×C3×D4—21no—
473C2×C3×D4—21no—
474C2×C3×D4—21no—
475C2×C3×D4—41no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C2×C3×D4D3211yescharacteristic
483C2×C3×D4D3211yescharacteristic
484C2×C3×D4D3211yescharacteristic
485C22×C3×C4—91no—
486C22×C3×C4—91no—
487C22×C3×C4—91no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—31no—
493C2×#67—31no—
494C2×#67—31no—
495C2×#67—31no—
496C2×#67—31no—
497C2×#67—31no—
498C2×#67—31no—
499C2×#67—31no—
500C2×#67—61no—
501C2×#67—61no—
502C2×#67—61no—
503C2×#67—61no—
504C2×#67—61no—
505C2×#67—61no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C22×Dic3—31no—
513C22×Dic3—31no—
514C22×Dic3—31no—
515C22×Dic3—31no—
516C22×Dic3—61no—
517C22×Dic3—61no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520C2×D12—91no—
521C2×D12—91no—
522C2×D12—91no—
523C2×C4×D3—31no—
524C2×C4×D3—31no—
525C2×C4×D3—61no—
526C2×C4×D3—91no—
527C2×C4×D3—91no—
528C2×C4×D3—91no—
529C2×C4×D3—91no—
530C3×C4⋊C4—91no—
531C3×C4⋊C4—91no—
532C3×C4⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C22⋊C4—91no—
539#217—31no—
540#217—31no—
541#217—31no—
542#217—31no—
543#217—31no—
544#217—31no—
545#217—31no—
546#217—31no—
547#217—61no—
548#217—61no—
549#217—61no—
550#217—61no—
551#217—91no—
552#217—91no—
553#217—91no—
554#217—91no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—61no—
560(C2×D3)⋊C4—61no—
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—
569C4⋊Dic3—31no—
570C4⋊Dic3—31no—
571C4⋊Dic3—61no—
572C4⋊Dic3—91no—
573C4⋊Dic3—91no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—61no—
582Dic3⋊C4—61no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—91no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—22no—
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—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—41no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—42no—
628C22×C32—42no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—41no—
641C22×C32—81no—
642C22×C32—81no—
643C22×C32—81no—
644C22×C32—81no—
645C22×C32C23×D311yescharacteristic
646C22×C32C23×D311yescharacteristic
647C22×C32C23×D311yescharacteristic
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3⋊D3—21no—
657C2×C3×D3—62no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—121no—
677C2×C3×D3—121no—
678C2×C3×D3—121no—
679C2×C3×D3—121no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C32×C4—21no—
685C32×C4—22no—
686C32×C4—21no—
687C32×C4—21no—
688C32×C4—41no—
689C32×C4—41no—
690C32×C4—42no—
691C3⋊Dic3—21no—
692C3⋊Dic3—21no—
693C3⋊Dic3—21no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—21no—
699C3⋊Dic3#23712yes—
700C3×Dic3—32no—
701C3×Dic3—32no—
702C3×Dic3—62no—
703C3×Dic3—62no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722C3×Dic3—121no—
723C3×Dic3—121no—
724C3×Dic3—121no—
725C3×Dic3—121no—
726C3×Dic3—121no—
727#127—271no—
728#125—271no—
729#123—271no—
730#123—271no—
731#123—271no—
732#123—271no—
733#121—91no—
734#121—91no—
735#121—91no—
736#121—271no—
737#121—271no—
738#121—271no—
739C4×D4—271no—
740C4×D4—271no—
741#117—271no—
742C33#54011yescharacteristic, complemented, Sylow
743C23×C3—21no—
744C23×C3—21no—
745C23×C3—21no—
746C23×C3—21no—
747C23×C3—21no—
748C23×C3—21no—
749C23×C3—41no—
750C23×C3—41no—
751C23×C3—91no—
752C23×C3—91no—
753C23×C3—91no—
754C23×C3C2×D3211yescharacteristic
755C23×C3C2×D3211yescharacteristic
756C23×C3C2×D3211yescharacteristic
757C23×C3C2×D3211yescharacteristic
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—31no—
765C22×D3—31no—
766C22×D3—61no—
767C22×D3—61no—
768C22×D3—61no—
769C3×D4—41no—
770C3×D4—41no—
771C3×D4—41no—
772C3×D4—42no—
773C3×D4—42no—
774C3×D4—42no—
775C3×D4—44no—
776C3×D4—182no—
777C3×D4—361no—
778C3×D4—361no—
779C3×D4—361no—
780C3×D4—361no—
781C3×D4—361no—
782C2×C3×C4—21no—
783C2×C3×C4—21no—
784C2×C3×C4—21no—
785C2×C3×C4—41no—
786C2×C3×C4—91no—
787C2×C3×C4—91no—
788C2×C3×C4—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—182no—
796C2×C3×C4—361no—
797C2×C3×C4—361no—
798C2×C3×C4C2×D3211yescharacteristic
799C2×C3×C4C2×D3211yescharacteristic
800C2×C3×C4C2×D3211yescharacteristic
801#67—62no—
802#67—62no—
803#67—122no—
804#67—121no—
805#67—121no—
806#67—121no—
807#67—121no—
808#67—121no—
809#67—121no—
810#67—121no—
811#67—121no—
812#67—121no—
813#67—121no—
814#67—122no—
815#67—122no—
816#67—122no—
817#67—122no—
818#67—122no—
819#67—182no—
820#67—182no—
821#67—361no—
822#67—361no—
823#67—361no—
824#67—361no—
825C2×Dic3—31no—
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—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—61no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—61no—
852C2×Dic3—62no—
853C2×Dic3—62no—
854C2×Dic3—122no—
855C2×Dic3—121no—
856C2×Dic3—121no—
857C2×Dic3—122no—
858C2×Dic3—361no—
859C2×Dic3—361no—
860D12—182no—
861D12—361no—
862D12—361no—
863C4×D3—121no—
864C4×D3—121no—
865C4×D3—122no—
866C4×D3—361no—
867C4×D3—361no—
868C4×D3—361no—
869C4×D3—361no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—41no—
880C2×C32—41no—
881C2×C32—41no—
882C2×C32—41no—
883C2×C32—41no—
884C2×C32—42no—
885C2×C32—42no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—41no—
889C2×C32—41no—
890C2×C32—81no—
891C2×C32—81no—
892C2×C32—81no—
893C2×C32—81no—
894C2×C32—82no—
895C2×C32—82no—
896C2×C32C2×#23711yescharacteristic
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32#100411yescharacteristic
900C2×C32#100411yescharacteristic
901C2×C32#100411yescharacteristic
902C2×C32D3×#4111yescharacteristic
903C2×C32D3×#4111yescharacteristic
904C2×C32#100911yescharacteristic
905C3⋊D3—41no—
906C3⋊D3—41no—
907C3⋊D3—41no—
908C3×D3—122no—
909C3×D3—121no—
910C3×D3—121no—
911C3×D3—121no—
912C3×D3—121no—
913C3×D3—121no—
914C3×D3—121no—
915C3×D3—241no—
916C3×D3—241no—
917C2×D4—91no—
918C2×D4—91no—
919C2×D4—91no—
920C2×D4—91no—
921C2×D4—91no—
922C2×D4—91no—
923C2×D4—271no—
924C2×D4—271no—
925C2×D4—271no—
926C2×D4#111311yescharacteristic
927C22×C4—91no—
928C22×C4—91no—
929C22×C4—91no—
930C22×C4—271no—
931C22×C4—271no—
932C4⋊C4—91no—
933C4⋊C4—91no—
934C4⋊C4—91no—
935C4⋊C4—271no—
936C4⋊C4—271no—
937C4⋊C4—271no—
938C4⋊C4—271no—
939C4⋊C4—271no—
940C22⋊C4—91no—
941C22⋊C4—91no—
942C22⋊C4—91no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—271no—
947C22⋊C4—271no—
948C22⋊C4—271no—
949C22⋊C4—271no—
950C42—271no—
951C42—271no—
952C22×C3—22no—
953C22×C3—22no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—21no—
957C22×C3—21no—
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—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—42no—
992C22×C3—42no—
993C22×C3—41no—
994C22×C3—81no—
995C22×C3—81no—
996C22×C3—81no—
997C22×C3—81no—
998C22×C3—181no—
999C22×C3—181no—
1000C22×C3—181no—
1001C22×C3—181no—
1002C22×C3—181no—
1003C22×C3—181no—
1004C22×C3—181no—
1005C22×C3—181no—
1006C22×C3—181no—
1007C22×C3C22×D3211yescharacteristic
1008C22×C3C22×D3211yescharacteristic
1009C22×C3C22×D3211yescharacteristic
1010C2×D3—62no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—121no—
1030C2×D3—121no—
1031C2×D3—121no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C3×C4—22no—
1038C3×C4—21no—
1039C3×C4—21no—
1040C3×C4—21no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—92no—
1045C3×C4—181no—
1046C3×C4—181no—
1047C3×C4—181no—
1048C3×C4—181no—
1049C3×C4—181no—
1050C3×C4—181no—
1051C3×C4—181no—
1052C3×C4—181no—
1053Dic3—32no—
1054Dic3—32no—
1055Dic3—62no—
1056Dic3—62no—
1057Dic3—61no—
1058Dic3—61no—
1059Dic3—61no—
1060Dic3—61no—
1061Dic3—61no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—61no—
1066Dic3—61no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—121no—
1074Dic3—121no—
1075Dic3—121no—
1076Dic3—121no—
1077Dic3—121no—
1078Dic3—121no—
1079Dic3—121no—
1080C32—21no—
1081C32—21no—
1082C32—21no—
1083C32—41no—
1084C32#561511yescharacteristic, complemented
1085C32#561511yescharacteristic, complemented
1086C32#561911yescharacteristic, complemented
1087C23—91no—
1088C23—91no—
1089C23—91no—
1090C23C2×#111311yescharacteristic
1091C23C2×#111311yescharacteristic
1092D4—41no—
1093D4—182no—
1094D4—361no—
1095D4—361no—
1096D4—361no—
1097D4—361no—
1098D4—361no—
1099D4—542no—
1100D4—1081no—
1101D4—1081no—
1102C2×C4—91no—
1103C2×C4—91no—
1104C2×C4—91no—
1105C2×C4—91no—
1106C2×C4—91no—
1107C2×C4—91no—
1108C2×C4—91no—
1109C2×C4—91no—
1110C2×C4—91no—
1111C2×C4—182no—
1112C2×C4—361no—
1113C2×C4—361no—
1114C2×C4—1081no—
1115C2×C4—1081no—
1116C2×C4C2×#111311yescharacteristic
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—21no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—21no—
1123C2×C3—21no—
1124C2×C3—21no—
1125C2×C3—21no—
1126C2×C3—42no—
1127C2×C3—42no—
1128C2×C3—41no—
1129C2×C3—41no—
1130C2×C3—41no—
1131C2×C3—41no—
1132C2×C3—41no—
1133C2×C3—41no—
1134C2×C3—41no—
1135C2×C3—41no—
1136C2×C3—41no—
1137C2×C3—81no—
1138C2×C3—81no—
1139C2×C3—81no—
1140C2×C3—81no—
1141C2×C3—82no—
1142C2×C3—82no—
1143C2×C3—361no—
1144C2×C3—361no—
1145C2×C3—361no—
1146C2×C3D3×#23711yescharacteristic
1147C2×C3D3×#23711yescharacteristic
1148C2×C3#6431211yescharacteristic
1149C2×C3#6431311yescharacteristic
1150C2×C3#6431411yescharacteristic
1151C2×C3#6431411yescharacteristic
1152C2×C3#6433011yescharacteristic
1153C2×C3#6433011yescharacteristic
1154C2×C3#6433011yescharacteristic
1155D3—122no—
1156D3—121no—
1157D3—121no—
1158D3—121no—
1159D3—121no—
1160D3—121no—
1161D3—121no—
1162D3—241no—
1163D3—241no—
1164C22—21no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—181no—
1171C22—181no—
1172C22—181no—
1173C22—181no—
1174C22—181no—
1175C22—181no—
1176C22—181no—
1177C22—181no—
1178C22—181no—
1179C22C22×#111311yescharacteristic
1180C4—21no—
1181C4—92no—
1182C4—181no—
1183C4—181no—
1184C4—181no—
1185C4—181no—
1186C4—181no—
1187C4—181no—
1188C4—181no—
1189C4—181no—
1190C3—21no—
1191C3—21no—
1192C3—21no—
1193C3—41no—
1194C3#1059519711yescharacteristic, complemented
1195C3#1059520511yescharacteristic, complemented
1196C3#1059525011yescharacteristic, complemented
1197C2—41no—
1198C2—41no—
1199C2—361no—
1200C2—361no—
1201C2—361no—
1202C2#1172462211yescharacteristic
1203C2#1172462311yescharacteristic
1204C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64148C2semidirect
2. C3×#64148C2semidirect
3. C3×#64147C2semidirect
4. #11723728C2semidirect
5. #11723726C2semidirect
6. #11723725C2semidirect
7. #11723725C2semidirect
8. #11723724C2semidirect
9. #11723720C2semidirect
10. #11723717C2semidirect
11. #11723715C2semidirect
12. #11723694C2semidirect
13. #11723690C2semidirect
14. #11723684C2semidirect
15. #11723669C2semidirect
54. #64148D3semidirect
55. #64148D3semidirect
56. #64147D3semidirect
742. C33#540semidirect
1084. C32#5615semidirect
1085. C32#5615semidirect
1086. C32#5619semidirect
1194. C3#10595197semidirect
1195. C3#10595205semidirect
1196. C3#10595250semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C3×#641472
#117237282
#117237262
#117237252
#117237242
#117237202
#117237172
#117237152
#117236942
#117236902
#117236842
#117236692
#105952503
#105952053
#105951973