Finite Group Databasebeta

← #13171928

Subgroups — #13171928

Order 1728.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723720C211yesmaximal, characteristic, complemented
2#11723631C211yesmaximal, characteristic, complemented
3#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723614C211yesmaximal, characteristic, complemented
5C3×#63980C211yesmaximal, characteristic, complemented
6C3×#63979C211yesmaximal, characteristic, complemented
7C3×#63970C211yesmaximal, characteristic, complemented
8#11723011C211yesmaximal, characteristic, complemented
9#11722991C211yesmaximal, characteristic, complemented
10#11722989C211yesmaximal, characteristic, complemented
11#11722956C211yesmaximal, characteristic, complemented
12#11722954C211yesmaximal, characteristic, complemented
13#11722953C211yesmaximal, characteristic, complemented
14#11722929C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595217—31nomaximal
17#10595197—31nomaximal
18#10595188—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32C2×C3×#625C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34#88864C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36#88815C2211yescharacteristic
37#88815C2211yescharacteristic
38#88814C2211yescharacteristic
39#88814C2211yescharacteristic
40#88807C2211yescharacteristic
41#88806C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64144—31no—
56D4×C3⋊Dic3—31no—
57C3×#940—31no—
58C3×#940—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#939—31no—
62C3×#938—31no—
63#63980—31no—
64#63980—31no—
65#63980D311yescharacteristic, complemented
66#63979D311yescharacteristic, complemented
67#63978—31no—
68#67⋊Dic3—31no—
69Dic3×#67—31no—
70Dic3×#67—31no—
71Dic3×#67—61no—
72#63971—31no—
73#63970—31no—
74#63970—31no—
75#63970—31no—
76#63970—31no—
77#63970—31no—
78#63970—61no—
79#63970D311yescharacteristic, complemented
80#63969—31no—
81#63969—31no—
82#63969—31no—
83#63969—31no—
84#63969—61no—
85#63966—31no—
86#63962—31no—
87#63962—31no—
88#63961—31no—
89#63955—31no—
90#63908—31no—
91#63898—31no—
92#63891—31no—
93#63885—31no—
94#63884—31no—
95#63881—31no—
96#63877—31no—
97#63869—31no—
98#63867—31no—
99#63855—31no—
100#63853—31no—
101#63845—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C3×#638—41no—
110C2×C3×C3⋊Dic3—41no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—22no—
117C32×#67—41no—
118C32×#67—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6290—41no—
123Dic3×C3⋊D3—41no—
124D3×C3⋊Dic3—41no—
125D3×C3⋊Dic3—41no—
126C3×#626—22no—
127C3×#626—41no—
128C3×#625—41no—
129C3×#625—41no—
130C3×#625—41no—
131C3×D3×Dic3—22no—
132#5719—91no—
133#5619—91no—
134#5615—91no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×C32×D4—31no—
138C2×#638—31no—
139C2×#638C2×D311yescharacteristic
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3C2×D311yescharacteristic
143C2×C4×C3⋊D3—31no—
144C2×C3×#67—21no—
145C2×C3×#67—21no—
146C2×C3×#67—21no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
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—61no—
158C2×C3×#67C2×D311yescharacteristic
159C2×C3×#67C2×D311yescharacteristic
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic
163C2×C3×#67C2×D311yescharacteristic
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C22×C3×Dic3—61no—
168C2×C3×D12—31no—
169C2×C3×D12—31no—
170C2×C3×C4×D3—31no—
171C2×#626C2×D311yescharacteristic
172C2×#626C2×D311yescharacteristic
173C2×#625—31no—
174C2×#625—31no—
175C2×#625—61no—
176C2×#625C2×D311yescharacteristic
177C2×#625C2×D311yescharacteristic
178C2×#625C2×D311yescharacteristic
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—61no—
186C2×D3×Dic3—61no—
187C2×D3×Dic3—61no—
188C2×D3×Dic3C2×D311yescharacteristic
189#3757—31no—
190#3757—31no—
191#3757—31no—
192#3757—31no—
193#3757—31no—
194#3757—31no—
195#3757—61no—
196#3757—61no—
197#3757—61no—
198#3757—121no—
199#3757C2×D311yescharacteristic
200C4⋊(C3⋊Dic3)—31no—
201C4⋊(C3⋊Dic3)—31no—
202#3750—31no—
203#3750—31no—
204C4×C3⋊Dic3—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—61no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×C4⋊Dic3—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
224#3724—61no—
225#3724C2×D311yescharacteristic
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3C2×D311yescharacteristic
240#3722—31no—
241#3722—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
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—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic
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×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C3⋊(C3⋊Dic3)—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—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3#4112yes—
288C3×#127—91no—
289C3×#121—91no—
290C3×#121—91no—
291#940—31no—
292#940—31no—
293#939—31no—
294#939—31no—
295#939—31no—
296#939—91no—
297#939—91no—
298#939—91no—
299#939—91no—
300#939—91no—
301#939—91no—
302#938—31no—
303#938—91no—
304#938—91no—
305#938—91no—
306#938—91no—
307#938—181no—
308#935—91no—
309#935—91no—
310#935—91no—
311#935—91no—
312#935—91no—
313#935—181no—
314D4×Dic3—91no—
315D4×Dic3—91no—
316D4×Dic3—91no—
317D4×Dic3—181no—
318#930—91no—
319#929—91no—
320C4×#67—91no—
321#926—91no—
322#894—91no—
323#893—91no—
324#890—91no—
325#889—91no—
326#886—91no—
327#886—91no—
328#884—91no—
329#883—91no—
330#883—91no—
331#883—91no—
332#67⋊C4—91no—
333#877—91no—
334#872—91no—
335#870—91no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—31no—
340C23×C32—31no—
341C23×C32—31no—
342C23×C32—41no—
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C23×C32C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—61no—
353C22×C3×D3C22×D311yescharacteristic
354C22×C3×D3C22×D311yescharacteristic
355C22×C3×D3C22×D311yescharacteristic
356C22×C3×D3C22×D311yescharacteristic
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C32×D4—62no—
360C32×D4—121no—
361C32×D4—121no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365#638—41no—
366#638—121no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—41no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—121no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C4×C3⋊D3—121no—
390C3×#67—24no—
391C3×#67—22no—
392C3×#67—22no—
393C3×#67—41no—
394C3×#67—41no—
395C3×#67—41no—
396C3×#67—41no—
397C3×#67—42no—
398C3×#67—42no—
399C3×#67—62no—
400C3×#67—121no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—121no—
404C3×#67—121no—
405C3×#67—121no—
406C3×#67—121no—
407C3×#67—121no—
408C3×#67—121no—
409C3×#67—122no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
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—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—62no—
429C2×C3×Dic3—121no—
430C2×C3×Dic3—121no—
431C2×C3×Dic3—122no—
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C3×D12—62no—
439C3×D12—121no—
440C3×C4×D3—62no—
441#626—22no—
442#626—41no—
443#625—41no—
444#625—41no—
445#625—41no—
446#625—121no—
447#625—121no—
448#625—122no—
449D3×Dic3—22no—
450D3×Dic3—121no—
451D3×Dic3—121no—
452D3×Dic3—122no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—122no—
458D3×Dic3—122no—
459#540—271noSylow
460C2×C33—41no—
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3×C3⋊D3—41no—
465C32×D3—41no—
466C32×D3—41no—
467C32×D3—41no—
468C2×C3×D4—31no—
469C2×C3×D4—31no—
470C2×C3×D4—31no—
471C2×C3×D4—31no—
472C2×C3×D4—31no—
473C2×C3×D4—31no—
474C2×C3×D4—61no—
475C2×C3×D4—61no—
476C2×C3×D4—61no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C2×C3×D4—91no—
483C22×C3×C4—91no—
484C22×C3×C4—91no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—31no—
493C2×#67—31no—
494C2×#67—31no—
495C2×#67—61no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—181no—
500C2×#67D3211yescharacteristic
501C2×#67D3211yescharacteristic
502C2×#67D3211yescharacteristic
503C22×Dic3—31no—
504C22×Dic3—31no—
505C22×Dic3—31no—
506C22×Dic3—61no—
507C22×Dic3—91no—
508C22×Dic3—91no—
509C22×Dic3—91no—
510C22×Dic3—91no—
511C22×Dic3—91no—
512C22×Dic3—181no—
513C22×Dic3—181no—
514C2×D12—31no—
515C2×D12—31no—
516C2×C4×D3—31no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—91no—
521C2×C4×D3—181no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C42—91no—
529#217—31no—
530#217—31no—
531#217—31no—
532#217—31no—
533#217—31no—
534#217—61no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—181no—
547#217—181no—
548#217—181no—
549#217—181no—
550#217—181no—
551#217—181no—
552#217—361no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563C4⋊Dic3—31no—
564C4⋊Dic3—91no—
565C4⋊Dic3—91no—
566C4⋊Dic3—91no—
567C4⋊Dic3—91no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571C4⋊Dic3—181no—
572C4⋊Dic3—181no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—181no—
588Dic3⋊C4—181no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—22no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—42no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—61no—
619C22×C32—61no—
620C22×C32—61no—
621C22×C32—61no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32—81no—
628C22×C32—81no—
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C22×C32C23×D311yescharacteristic
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3×D3—22no—
636C2×C3×D3—22no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—21no—
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—41no—
656C2×C3×D3—41no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—62no—
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—121no—
670C2×C3×D3—121no—
671C32×C4—32no—
672C32×C4—61no—
673C32×C4—61no—
674C3⋊Dic3—21no—
675C3⋊Dic3—21no—
676C3⋊Dic3—21no—
677C3⋊Dic3—21no—
678C3⋊Dic3—21no—
679C3⋊Dic3—61no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—61no—
683C3⋊Dic3—61no—
684C3⋊Dic3—61no—
685C3⋊Dic3—121no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—121no—
689C3⋊Dic3—121no—
690C3⋊Dic3—121no—
691C3⋊Dic3—241no—
692C3⋊Dic3—241no—
693C3×Dic3—22no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—22no—
699C3×Dic3—41no—
700C3×Dic3—62no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—121no—
712C3×Dic3—121no—
713C3×Dic3—121no—
714C3×Dic3—121no—
715C3×Dic3#23712yes—
716C3×Dic3#23712yes—
717#127—91no—
718#125—271no—
719#123—271no—
720#123—271no—
721#123—271no—
722#123—271no—
723#121—91no—
724#121—91no—
725#121—271no—
726#121—271no—
727#121—271no—
728#121—271no—
729C4×D4—271no—
730C4×D4—271no—
731#117—271no—
732C33#54011yescharacteristic, complemented, Sylow
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—21no—
736C23×C3—31no—
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—41no—
743C23×C3—61no—
744C23×C3—61no—
745C23×C3—61no—
746C23×C3—91no—
747C23×C3C2×D3211yescharacteristic
748C23×C3C2×D3211yescharacteristic
749C23×C3C2×D3211yescharacteristic
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—61no—
753C22×D3C2×D3211yescharacteristic
754C22×D3C2×D3211yescharacteristic
755C22×D3C2×D3211yescharacteristic
756C3×D4—62no—
757C3×D4—62no—
758C3×D4—64no—
759C3×D4—121no—
760C3×D4—121no—
761C3×D4—121no—
762C3×D4—121no—
763C3×D4—122no—
764C3×D4—122no—
765C3×D4—182no—
766C3×D4—361no—
767C3×D4—361no—
768C3×D4—361no—
769C3×D4—361no—
770C3×D4—361no—
771C2×C3×C4—31no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—31no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—61no—
780C2×C3×C4—91no—
781C2×C3×C4—91no—
782C2×C3×C4—91no—
783C2×C3×C4—91no—
784C2×C3×C4—91no—
785C2×C3×C4—182no—
786C2×C3×C4—361no—
787#67—22no—
788#67—41no—
789#67—41no—
790#67—62no—
791#67—121no—
792#67—121no—
793#67—121no—
794#67—121no—
795#67—121no—
796#67—121no—
797#67—121no—
798#67—121no—
799#67—121no—
800#67—122no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—362no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—61no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—62no—
821C2×Dic3—91no—
822C2×Dic3—91no—
823C2×Dic3—91no—
824C2×Dic3—91no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—121no—
828C2×Dic3—121no—
829C2×Dic3—122no—
830C2×Dic3—181no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—181no—
835C2×Dic3—181no—
836C2×Dic3—361no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839C2×Dic3—361no—
840C2×Dic3—361no—
841C2×Dic3—361no—
842C2×Dic3—361no—
843C2×Dic3—362no—
844C2×Dic3—362no—
845C2×Dic3C2×D3211yescharacteristic
846C2×Dic3C2×D3211yescharacteristic
847C2×Dic3C2×D3211yescharacteristic
848D12—62no—
849D12—121no—
850C4×D3—62no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—361no—
854C4×D3—361no—
855C4×D3—362no—
856C2×C32—21no—
857C2×C32—21no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—41no—
866C2×C32—41no—
867C2×C32—41no—
868C2×C32—41no—
869C2×C32—42no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—81no—
873C2×C32—81no—
874C2×C32—82no—
875C2×C32—121no—
876C2×C32—121no—
877C2×C32—121no—
878C2×C32C2×#23711yescharacteristic
879C2×C32C2×#23711yescharacteristic
880C2×C32#100411yescharacteristic
881C2×C32#100411yescharacteristic
882C2×C32#100411yescharacteristic
883C2×C32#100411yescharacteristic
884C2×C32#100411yescharacteristic
885C2×C32D3×#4111yescharacteristic
886C2×C32#100911yescharacteristic
887C3⋊D3—41no—
888C3×D3—42no—
889C3×D3—42no—
890C3×D3—41no—
891C3×D3—41no—
892C3×D3—41no—
893C3×D3—41no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—81no—
897C3×D3—122no—
898C3×D3—121no—
899C3×D3—121no—
900C2×D4—31no—
901C2×D4—31no—
902C2×D4—31no—
903C2×D4—91no—
904C2×D4—91no—
905C2×D4—91no—
906C2×D4—91no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—271no—
910C22×C4—91no—
911C22×C4—91no—
912C22×C4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C4⋊C4—91no—
916C4⋊C4—91no—
917C4⋊C4—271no—
918C4⋊C4—271no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—271no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C42—91no—
934C42—271no—
935C22×C3—22no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—41no—
949C22×C3—41no—
950C22×C3—41no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—42no—
957C22×C3—41no—
958C22×C3—62no—
959C22×C3—62no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—61no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—61no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—81no—
979C22×C3—81no—
980C22×C3—121no—
981C22×C3—121no—
982C22×C3—121no—
983C22×C3—121no—
984C22×C3—121no—
985C22×C3—121no—
986C22×C3—121no—
987C22×C3—181no—
988C22×C3—181no—
989C22×C3—181no—
990C22×C3C22×D3211yescharacteristic
991C22×C3C22×D3211yescharacteristic
992C22×C3C22×D3211yescharacteristic
993C2×D3—21no—
994C2×D3—21no—
995C2×D3—21no—
996C2×D3—21no—
997C2×D3—21no—
998C2×D3—21no—
999C2×D3—21no—
1000C2×D3—21no—
1001C2×D3—21no—
1002C2×D3—62no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—121no—
1010C2×D3—121no—
1011C3×C4—32no—
1012C3×C4—32no—
1013C3×C4—62no—
1014C3×C4—62no—
1015C3×C4—61no—
1016C3×C4—61no—
1017C3×C4—61no—
1018C3×C4—61no—
1019C3×C4—121no—
1020C3×C4—181no—
1021C3×C4—181no—
1022C3×C4—181no—
1023C3×C4—181no—
1024C3×C4—181no—
1025Dic3—21no—
1026Dic3—21no—
1027Dic3—62no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—61no—
1035Dic3—61no—
1036Dic3—61no—
1037Dic3—61no—
1038Dic3—121no—
1039Dic3—121no—
1040Dic3—121no—
1041Dic3—121no—
1042Dic3—181no—
1043Dic3—181no—
1044Dic3—181no—
1045Dic3—181no—
1046Dic3—181no—
1047Dic3—181no—
1048Dic3—361no—
1049Dic3—361no—
1050Dic3—361no—
1051Dic3—361no—
1052Dic3—361no—
1053Dic3—361no—
1054Dic3—721no—
1055Dic3—721no—
1056Dic3#380512yes—
1057C32—21no—
1058C32—21no—
1059C32—21no—
1060C32—41no—
1061C32#561511yescharacteristic, complemented
1062C32#561911yescharacteristic, complemented
1063C32#571911yescharacteristic, complemented
1064C23—31no—
1065C23—31no—
1066C23—31no—
1067C23—91no—
1068C23D3311yescharacteristic
1069D4—62no—
1070D4—121no—
1071D4—121no—
1072D4—182no—
1073D4—361no—
1074D4—361no—
1075D4—361no—
1076D4—361no—
1077D4—361no—
1078D4—1081no—
1079C2×C4—31no—
1080C2×C4—31no—
1081C2×C4—31no—
1082C2×C4—91no—
1083C2×C4—91no—
1084C2×C4—91no—
1085C2×C4—91no—
1086C2×C4—91no—
1087C2×C4—182no—
1088C2×C4—271no—
1089C2×C4—271no—
1090C2×C4—361no—
1091C2×C4—1081no—
1092C2×C4—1081no—
1093C2×C4—1081no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—42no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—41no—
1107C2×C3—41no—
1108C2×C3—41no—
1109C2×C3—41no—
1110C2×C3—81no—
1111C2×C3—81no—
1112C2×C3—82no—
1113C2×C3—122no—
1114C2×C3—122no—
1115C2×C3—121no—
1116C2×C3—121no—
1117C2×C3—121no—
1118C2×C3—121no—
1119C2×C3—121no—
1120C2×C3—121no—
1121C2×C3—241no—
1122C2×C3—361no—
1123C2×C3D3×#23711yescharacteristic
1124C2×C3D3×#23711yescharacteristic
1125C2×C3#6431311yescharacteristic
1126C2×C3#6431311yescharacteristic
1127C2×C3#6431411yescharacteristic
1128C2×C3#6431411yescharacteristic
1129C2×C3C2×#380511yescharacteristic
1130C2×C3#6433011yescharacteristic
1131C2×C3#6433011yescharacteristic
1132D3—41no—
1133D3—41no—
1134D3—41no—
1135D3—122no—
1136D3—121no—
1137D3—121no—
1138C22—21no—
1139C22—21no—
1140C22—21no—
1141C22—61no—
1142C22—61no—
1143C22—61no—
1144C22—61no—
1145C22—61no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22C2×D3311yescharacteristic
1154C4—32no—
1155C4—61no—
1156C4—61no—
1157C4—181no—
1158C4—181no—
1159C4—181no—
1160C4—181no—
1161C4—181no—
1162C4—541no—
1163C4—541no—
1164C3—21no—
1165C3—21no—
1166C3—21no—
1167C3—41no—
1168C3#1059518811yescharacteristic, complemented
1169C3#1059519711yescharacteristic, complemented
1170C3#1059521711yescharacteristic, complemented
1171C2—41no—
1172C2—121no—
1173C2—121no—
1174C2—121no—
1175C2—361no—
1176C2D3×#380511yescharacteristic
1177C2#1172441411yescharacteristic
1178C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723720C2semidirect
2. #11723631C2semidirect
3. #67×C3⋊Dic3C2semidirect
4. #11723614C2semidirect
5. C3×#63980C2semidirect
6. C3×#63979C2semidirect
7. C3×#63970C2semidirect
8. #11723011C2semidirect
9. #11722991C2semidirect
10. #11722989C2semidirect
11. #11722956C2semidirect
12. #11722954C2semidirect
13. #11722953C2semidirect
14. #11722929C2semidirect
15. #11722913C2semidirect
65. #63980D3semidirect
66. #63979D3semidirect
79. #63970D3semidirect
732. C33#540semidirect
1061. C32#5615semidirect
1062. C32#5619semidirect
1063. C32#5719semidirect
1168. C3#10595188semidirect
1169. C3#10595197semidirect
1170. C3#10595217semidirect

Maximal subgroups

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

subgroupindex
#117237202
#117236312
#67×C3⋊Dic32
#117236142
C3×#639802
C3×#639792
C3×#639702
#117230112
#117229912
#117229892
#117229562
#117229542
#117229532
#117229292
#117229132
#105952173
#105951973
#105951883