Finite Group Databasebeta

← #13168589

Subgroups — #13168589

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#11723669C211yesmaximal, characteristic, complemented
2#11723510C211yesmaximal, characteristic, complemented
3#11723479C211yesmaximal, characteristic, complemented
4#11723475C211yesmaximal, characteristic, complemented
5C3×#63908C211yesmaximal, characteristic, complemented
6C3×#63905C211yesmaximal, characteristic, complemented
7C3×#63885C211yesmaximal, characteristic, complemented
8#11723031C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722989C211yesmaximal, characteristic, complemented
11#11722964C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722953C211yesmaximal, characteristic, complemented
14#11722925C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595250—31nomaximal
17#10595031—31nomaximal
18#10594220—31nomaximal
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×C3×#625C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32C2×C3×#625C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34#88859C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39#88815C2211yescharacteristic
40#88815C2211yescharacteristic
41#88815C2211yescharacteristic
42#88813C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44#88804C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64148—31no—
55C4×#638—31no—
56#64095—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#930—31no—
60C3×#929—31no—
61C3×#884—31no—
62C3×#883—31no—
63#63980—31no—
64#63979—31no—
65#63979—31no—
66#63979—31no—
67#63978—31no—
68#63975—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—31no—
71#63971—31no—
72#63970—31no—
73#63970—31no—
74#63969—31no—
75#63962—31no—
76#63958—31no—
77#63958—31no—
78#63955—31no—
79#63912—31no—
80#63908D311yescharacteristic, complemented
81#63906—31no—
82#63905D311yescharacteristic, complemented
83#63904—31no—
84#63904—31no—
85#63904—61no—
86#63902—31no—
87#63891—31no—
88#63890—31no—
89#63890—31no—
90#63890—61no—
91#63886—31no—
92#63886—31no—
93#63886—61no—
94#63885D311yescharacteristic, complemented
95#63878—31no—
96#63854—31no—
97#63853—31no—
98#63847—31no—
99#63846—31no—
100#63845—31no—
101#63841—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—41no—
118C32×C4×D3—41no—
119#6291—22no—
120#6291—41no—
121#6291—41no—
122#6291—41no—
123#6289—41no—
124D3×C3⋊Dic3—41no—
125D3×C3⋊Dic3—41no—
126C3×#625—22no—
127C3×#625—41no—
128C3×#625—41no—
129C3×#625—41no—
130C3×#625—41no—
131C3×D3×Dic3—22no—
132#5663—91no—
133#5619—91no—
134#5615—91no—
135C2×C32×D4—31no—
136C22×C32×C4—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638—31no—
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—31no—
143C2×C4×C3⋊D3—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
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—
154C22×C3×Dic3—31no—
155C2×C3×D12—21no—
156C2×C3×D12C2×D311yescharacteristic
157C2×C3×D12C2×D311yescharacteristic
158C2×C3×C4×D3—21no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3C2×D311yescharacteristic
161C2×C3×C4×D3C2×D311yescharacteristic
162C2×#626—31no—
163C2×#626—31no—
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×#626—61no—
174C2×#625C2×D311yescharacteristic
175C2×#625C2×D311yescharacteristic
176C2×#625C2×D311yescharacteristic
177C2×#625C2×D311yescharacteristic
178C2×#625C2×D311yescharacteristic
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—61no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—61no—
187C2×D3×Dic3—61no—
188C2×D3×Dic3C2×D311yescharacteristic
189C32×C22⋊C4—31no—
190#3757—31no—
191#3757—31no—
192#3752—31no—
193#3752—31no—
194#3752—31no—
195#3752—31no—
196#3752—61no—
197#3752—61no—
198#3752—61no—
199#3752—121no—
200C4⋊(C3⋊Dic3)—31no—
201C4⋊(C3⋊Dic3)C2×D311yescharacteristic
202#3750C2×D311yescharacteristic
203#3750C2×D311yescharacteristic
204C4×C3⋊Dic3—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×(C2×D3)⋊C4—21no—
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×(C2×D3)⋊C4C2×D311yescharacteristic
217C3×(C2×D3)⋊C4C2×D311yescharacteristic
218C3×C4⋊Dic3—31no—
219C3×C4⋊Dic3—31no—
220C3×C4⋊Dic3—31no—
221C3×C4⋊Dic3—61no—
222C3×Dic3⋊C4—31no—
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—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—61no—
241Dic3⋊Dic3C2×D311yescharacteristic
242#3722—31no—
243#3722—31no—
244#3722—61no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×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—
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#4112yes—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C3×#123—91no—
289C3×#121—91no—
290C3×#121—91no—
291#940—91no—
292#940—91no—
293#940—91no—
294#939—31no—
295#939—91no—
296#939—91no—
297#939—91no—
298#939—91no—
299#939—91no—
300#939—181no—
301#938—31no—
302#938—91no—
303#938—91no—
304#935—91no—
305D4×Dic3—91no—
306#930—31no—
307#930—91no—
308#929—31no—
309C4×#67—91no—
310C4×#67—91no—
311C4×#67—181no—
312#926—91no—
313#895—91no—
314#894—91no—
315#894—91no—
316#893—91no—
317#892—91no—
318#890—91no—
319#889—91no—
320#889—91no—
321#886—91no—
322#886—91no—
323#886—91no—
324#886—181no—
325#884—31no—
326#884—91no—
327#884—91no—
328#884—91no—
329#883—31no—
330#883—91no—
331#883—91no—
332#883—91no—
333#67⋊C4—91no—
334#67⋊C4—91no—
335#877—91no—
336C23×C32—31no—
337C23×C32—31no—
338C23×C32—31no—
339C23×C32—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—61no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—121no—
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—21no—
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
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—121no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—41no—
366C2×C32×C4—121no—
367C2×C32×C4C22×D311yescharacteristic
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370#638—62no—
371#638—121no—
372#638—121no—
373#638—121no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
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⋊Dic3C22×D311yescharacteristic
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—62no—
391C3×#67—62no—
392C3×#67—121no—
393C3×#67—121no—
394C3×#67—121no—
395C3×#67—121no—
396C3×#67—121no—
397C3×#67—121no—
398C3×#67—121no—
399C3×#67—121no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—62no—
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C3×D12—41no—
426C3×D12—41no—
427C3×D12—42no—
428C3×C4×D3—41no—
429C3×C4×D3—41no—
430C3×C4×D3—42no—
431C3×C4×D3—62no—
432#626—62no—
433#626—62no—
434#626—64no—
435#626—121no—
436#626—121no—
437#626—121no—
438#626—121no—
439#626—121no—
440#626—121no—
441#626—122no—
442#626—122no—
443#626—122no—
444#625—22no—
445#625—41no—
446#625—41no—
447#625—41no—
448#625—41no—
449#624—121no—
450#624—121no—
451#624—122no—
452D3×Dic3—22no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—122no—
458D3×Dic3—122no—
459#540—271noSylow
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3⋊(C3⋊D3)—41no—
464C32×D3—41no—
465C32×D3—41no—
466C32×D3—41no—
467C32×D3—41no—
468C2×C3×D4—31no—
469C2×C3×D4—31no—
470C2×C3×D4—61no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C2×C3×D4—91no—
476C22×C3×C4—31no—
477C22×C3×C4—31no—
478C22×C3×C4—61no—
479C22×C3×C4—91no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—181no—
499C2×#67—181no—
500C2×#67—181no—
501C2×#67—181no—
502C22×Dic3—31no—
503C22×Dic3—91no—
504C22×Dic3—91no—
505C22×Dic3—91no—
506C22×Dic3—91no—
507C22×Dic3—181no—
508C22×Dic3—181no—
509C2×D12—91no—
510C2×D12—91no—
511C2×D12—91no—
512C2×D12—91no—
513C2×D12D3211yescharacteristic
514C2×C4×D3—31no—
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×C4×D3D3211yescharacteristic
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—61no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—181no—
544#217—181no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—91no—
551(C2×D3)⋊C4—91no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—181no—
559(C2×D3)⋊C4—181no—
560(C2×D3)⋊C4—181no—
561(C2×D3)⋊C4—181no—
562(C2×D3)⋊C4—361no—
563(C2×D3)⋊C4D3211yescharacteristic
564C4⋊Dic3—31no—
565C4⋊Dic3—31no—
566C4⋊Dic3—31no—
567C4⋊Dic3—61no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571C4⋊Dic3—91no—
572C4⋊Dic3—91no—
573C4⋊Dic3—181no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—61no—
580Dic3⋊C4—61no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588C4×Dic3—91no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—41no—
599C22×C32—61no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C2×C3⋊D3—61no—
615C2×C3⋊D3—62no—
616C2×C3⋊D3—61no—
617C2×C3⋊D3—61no—
618C2×C3⋊D3—61no—
619C2×C3⋊D3—61no—
620C2×C3⋊D3—61no—
621C2×C3⋊D3—61no—
622C2×C3⋊D3—61no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—121no—
625C2×C3⋊D3—121no—
626C2×C3⋊D3—122no—
627C2×C3⋊D3—121no—
628C2×C3⋊D3—121no—
629C2×C3⋊D3—121no—
630C2×C3⋊D3—121no—
631C2×C3⋊D3—121no—
632C2×C3⋊D3—121no—
633C2×C3⋊D3—241no—
634C2×C3⋊D3—241no—
635C2×C3×D3—22no—
636C2×C3×D3—22no—
637C2×C3×D3—22no—
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—21no—
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—41no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—41no—
667C2×C3×D3—41no—
668C2×C3×D3—41no—
669C2×C3×D3—41no—
670C2×C3×D3—41no—
671C32×C4—21no—
672C32×C4—21no—
673C32×C4—21no—
674C32×C4—41no—
675C32×C4—41no—
676C32×C4—41no—
677C32×C4—61no—
678C32×C4—61no—
679C32×C4—81no—
680C3⋊Dic3—21no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—21no—
685C3⋊Dic3—61no—
686C3⋊Dic3—61no—
687C3⋊Dic3—61no—
688C3⋊Dic3—121no—
689C3⋊Dic3—121no—
690C3⋊Dic3—121no—
691C3⋊Dic3—241no—
692C3⋊Dic3#23712yes—
693C3×Dic3—22no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—32no—
699C3×Dic3—32no—
700C3×Dic3—41no—
701C3×Dic3—62no—
702C3×Dic3—62no—
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—61no—
712C3×Dic3—61no—
713C3×Dic3—121no—
714C3×Dic3—121no—
715C3×Dic3—121no—
716C3×Dic3—121no—
717#127—271no—
718#125—271no—
719#123—91no—
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—31no—
734C23×C3—31no—
735C23×C3—31no—
736C23×C3—31no—
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—31no—
741C23×C3—61no—
742C23×C3—61no—
743C23×C3—61no—
744C23×C3—61no—
745C22×D3—91no—
746C22×D3—91no—
747C22×D3—91no—
748C22×D3—181no—
749C22×D3—181no—
750C22×D3—181no—
751C22×D3—361no—
752C22×D3C2×D3211yescharacteristic
753C22×D3C2×D3211yescharacteristic
754C22×D3C2×D3211yescharacteristic
755C22×D3C2×D3211yescharacteristic
756C3×D4—121no—
757C3×D4—121no—
758C3×D4—122no—
759C3×D4—182no—
760C3×D4—361no—
761C3×D4—361no—
762C3×D4—361no—
763C3×D4—361no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—41no—
772C2×C3×C4—61no—
773C2×C3×C4—61no—
774C2×C3×C4—91no—
775C2×C3×C4—91no—
776C2×C3×C4—91no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—121no—
781C2×C3×C4—121no—
782C2×C3×C4—122no—
783C2×C3×C4—182no—
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787#67—62no—
788#67—62no—
789#67—121no—
790#67—121no—
791#67—121no—
792#67—121no—
793#67—121no—
794#67—121no—
795#67—121no—
796#67—121no—
797#67—182no—
798#67—182no—
799#67—184no—
800#67—361no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—361no—
805#67—361no—
806#67—362no—
807#67—362no—
808#67—362no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—61no—
827C2×Dic3—62no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—91no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—361no—
835C2×Dic3—361no—
836C2×Dic3—361no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839C2×Dic3—362no—
840C2×Dic3—362no—
841C2×Dic3C2×D3211yescharacteristic
842C2×Dic3C2×D3211yescharacteristic
843D12—41no—
844D12—182no—
845D12—361no—
846D12—361no—
847D12—361no—
848C4×D3—41no—
849C4×D3—62no—
850C4×D3—361no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—362no—
854C4×D3—361no—
855C4×D3—361no—
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—121no—
869C2×C32—121no—
870C2×C32—121no—
871C2×C32—121no—
872C2×C32C2×#23711yescharacteristic
873C2×C32#100411yescharacteristic
874C2×C32#100411yescharacteristic
875C2×C32#100411yescharacteristic
876C2×C32#100411yescharacteristic
877C2×C32D3×#4111yescharacteristic
878C2×C32D3×#4111yescharacteristic
879C2×C32#100911yescharacteristic
880C2×C32#100911yescharacteristic
881C3⋊D3—121no—
882C3⋊D3—122no—
883C3⋊D3—121no—
884C3⋊D3—121no—
885C3⋊D3—241no—
886C3⋊D3—241no—
887C3⋊D3—242no—
888C3×D3—42no—
889C3×D3—42no—
890C3×D3—42no—
891C3×D3—41no—
892C3×D3—41no—
893C3×D3—41no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—81no—
900C2×D4—31no—
901C2×D4—91no—
902C2×D4—91no—
903C2×D4—91no—
904C2×D4—91no—
905C2×D4—91no—
906C2×D4—271no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C22×C4—31no—
911C22×C4—91no—
912C22×C4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C4⋊C4—91no—
916C4⋊C4—91no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C22⋊C4—31no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C42—271no—
934C42—271no—
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—41no—
939C22×C3—62no—
940C22×C3—62no—
941C22×C3—62no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—61no—
949C22×C3—61no—
950C22×C3—61no—
951C22×C3—61no—
952C22×C3—61no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—61no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—61no—
966C22×C3—121no—
967C22×C3—121no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—121no—
971C22×C3—121no—
972C22×C3—121no—
973C22×C3—121no—
974C22×C3—121no—
975C22×C3C22×D3211yescharacteristic
976C22×C3C22×D3211yescharacteristic
977C22×C3C22×D3211yescharacteristic
978C2×D3—21no—
979C2×D3—21no—
980C2×D3—21no—
981C2×D3—21no—
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—21no—
986C2×D3—21no—
987C2×D3—21no—
988C2×D3—21no—
989C2×D3—21no—
990C2×D3—182no—
991C2×D3—181no—
992C2×D3—181no—
993C2×D3—181no—
994C2×D3—181no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—361no—
1001C2×D3—361no—
1002C2×D3—361no—
1003C2×D3—361no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—362no—
1009C2×D3—721no—
1010C2×D3—721no—
1011C3×C4—21no—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—41no—
1015C3×C4—41no—
1016C3×C4—41no—
1017C3×C4—62no—
1018C3×C4—61no—
1019C3×C4—61no—
1020C3×C4—61no—
1021C3×C4—61no—
1022C3×C4—81no—
1023C3×C4—92no—
1024C3×C4—121no—
1025C3×C4—181no—
1026C3×C4—181no—
1027C3×C4—181no—
1028C3×C4—181no—
1029C3×C4—181no—
1030Dic3—21no—
1031Dic3—21no—
1032Dic3—32no—
1033Dic3—32no—
1034Dic3—62no—
1035Dic3—62no—
1036Dic3—61no—
1037Dic3—61no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—121no—
1047Dic3—121no—
1048Dic3—121no—
1049Dic3—121no—
1050Dic3—181no—
1051Dic3—181no—
1052Dic3—181no—
1053Dic3—361no—
1054Dic3—361no—
1055Dic3—361no—
1056Dic3—721no—
1057C32—21no—
1058C32—21no—
1059C32—21no—
1060C32—41no—
1061C32#561511yescharacteristic, complemented
1062C32#561911yescharacteristic, complemented
1063C32#566311yescharacteristic, complemented
1064C23—31no—
1065C23—31no—
1066C23—31no—
1067C23—31no—
1068C23—271no—
1069D4—121no—
1070D4—182no—
1071D4—361no—
1072D4—361no—
1073D4—361no—
1074D4—361no—
1075D4—542no—
1076D4—1081no—
1077D4—1081no—
1078D4—1081no—
1079C2×C4—31no—
1080C2×C4—31no—
1081C2×C4—91no—
1082C2×C4—91no—
1083C2×C4—91no—
1084C2×C4—91no—
1085C2×C4—91no—
1086C2×C4—91no—
1087C2×C4—121no—
1088C2×C4—182no—
1089C2×C4—271no—
1090C2×C4—1081no—
1091C2×C4—1081no—
1092C2×C4—1081no—
1093C2×C4D3311yescharacteristic
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—41no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—122no—
1107C2×C3—122no—
1108C2×C3—122no—
1109C2×C3—121no—
1110C2×C3—121no—
1111C2×C3—121no—
1112C2×C3—121no—
1113C2×C3—121no—
1114C2×C3—121no—
1115C2×C3—121no—
1116C2×C3—121no—
1117C2×C3—241no—
1118C2×C3#6430611yescharacteristic
1119C2×C3#6430711yescharacteristic
1120C2×C3#6430811yescharacteristic
1121C2×C3D3×#23711yescharacteristic
1122C2×C3D3×#23711yescharacteristic
1123C2×C3#6431311yescharacteristic
1124C2×C3#6431411yescharacteristic
1125C2×C3#6433011yescharacteristic
1126C2×C3#6433011yescharacteristic
1127D3—41no—
1128D3—41no—
1129D3—41no—
1130D3—41no—
1131D3—362no—
1132D3—361no—
1133D3—361no—
1134D3—361no—
1135D3—721no—
1136D3—721no—
1137D3—722no—
1138C22—61no—
1139C22—61no—
1140C22—61no—
1141C22—61no—
1142C22—61no—
1143C22—61no—
1144C22—61no—
1145C22—61no—
1146C22—61no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—541no—
1151C22—541no—
1152C22—541no—
1153C22C2×D3311yescharacteristic
1154C4—21no—
1155C4—61no—
1156C4—61no—
1157C4—92no—
1158C4—181no—
1159C4—181no—
1160C4—181no—
1161C4—181no—
1162C4—181no—
1163C4—541no—
1164C3—21no—
1165C3—21no—
1166C3—21no—
1167C3—41no—
1168C3#1059422011yescharacteristic, complemented
1169C3#1059503111yescharacteristic, complemented
1170C3#1059525011yescharacteristic, complemented
1171C2—121no—
1172C2—121no—
1173C2—121no—
1174C2—121no—
1175C2—1081no—
1176C2#1172437311yescharacteristic
1177C2#1172438411yescharacteristic
1178C2#1172441411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
2. #11723510C2semidirect
3. #11723479C2semidirect
4. #11723475C2semidirect
5. C3×#63908C2semidirect
6. C3×#63905C2semidirect
7. C3×#63885C2semidirect
8. #11723031C2semidirect
9. #11722996C2semidirect
10. #11722989C2semidirect
11. #11722964C2semidirect
12. #11722958C2semidirect
13. #11722953C2semidirect
14. #11722925C2semidirect
15. #11722914C2semidirect
80. #63908D3semidirect
82. #63905D3semidirect
94. #63885D3semidirect
732. C33#540semidirect
1061. C32#5615semidirect
1062. C32#5619semidirect
1063. C32#5663semidirect
1168. C3#10594220semidirect
1169. C3#10595031semidirect
1170. C3#10595250semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117235102
#117234792
#117234752
C3×#639082
C3×#639052
C3×#638852
#117230312
#117229962
#117229892
#117229642
#117229582
#117229532
#117229252
#117229142
#105952503
#105950313
#105942203