Finite Group Databasebeta

← #13168427

Subgroups — #13168427

Order 1728.

1214 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic, complemented
2#11723523C211yesmaximal, characteristic, complemented
3#11723522C211yesmaximal, characteristic, complemented
4#11723400C211yesmaximal, characteristic, complemented
5C3×#63886C211yesmaximal, characteristic, complemented
6C3×#63885C211yesmaximal, characteristic, complemented
7C3×#63881C211yesmaximal, characteristic, complemented
8#11723029C211yesmaximal, characteristic, complemented
9#11722988C211yesmaximal, characteristic, complemented
10#11722985C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic, complemented
12#11722956C211yesmaximal, characteristic, complemented
13#11722956C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595197—31nomaximal
17#10594496—31nomaximal
18#10594100—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6290C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39#88815C2211yescharacteristic
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42#88807C2211yescharacteristic
43#88806C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49Dic3×C3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64099—31no—
56#64092—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#895—31no—
60C3×#893—31no—
61C3×#884—31no—
62C3×#67⋊C4—31no—
63#63979—31no—
64#63979—31no—
65#63978—31no—
66#63978—31no—
67Dic3×#67—31no—
68#63971—31no—
69#63970—31no—
70#63970—31no—
71#63969—31no—
72#63966—31no—
73#63961—31no—
74#63955—31no—
75#63914—31no—
76#63912—31no—
77#63908—31no—
78#63908—31no—
79#63908—31no—
80#63908—31no—
81#63908—61no—
82#63905—31no—
83#63905—31no—
84#63905—31no—
85C4×#626—31no—
86Dic3×D12—31no—
87#63891—31no—
88#63891—31no—
89#63891—31no—
90#63891—61no—
91#63886D311yescharacteristic, complemented
92#63885—31no—
93#63885D311yescharacteristic, complemented
94#63881D311yescharacteristic, complemented
95#63877—31no—
96#63855—31no—
97#63853—31no—
98#63850—31no—
99#63845—31no—
100#63845—31no—
101#63845—61no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4×C3⋊D3—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—41no—
119#6295—41no—
120#6290—41no—
121#6290—41no—
122#6290—41no—
123Dic3×C3⋊D3—41no—
124C3×#626—22no—
125C3×#626—22no—
126C3×#626—41no—
127C3×#625—41no—
128C3×#625—41no—
129C3×D3×Dic3—22no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5619—91no—
133#5615—91no—
134#5562—91no—
135C2×C32×D4—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3C2×D311yescharacteristic
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C2×C3×D12—21no—
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×D12C2×D311yescharacteristic
156C2×C3×D12C2×D311yescharacteristic
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—61no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626C2×D311yescharacteristic
166C2×#626C2×D311yescharacteristic
167C2×#626C2×D311yescharacteristic
168C2×#625—31no—
169C2×#625—31no—
170C2×#625—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—31no—
174C2×#625—31no—
175C2×#625—61no—
176C2×#625—61no—
177C2×#625—61no—
178C2×#625C2×D311yescharacteristic
179C2×#625C2×D311yescharacteristic
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3C2×D311yescharacteristic
184C2×D3×Dic3C2×D311yescharacteristic
185C2×D3×Dic3C2×D311yescharacteristic
186C32×C4⋊C4—31no—
187C32×C22⋊C4—31no—
188#3757—31no—
189#3757—31no—
190#3757—31no—
191#3752C2×D311yescharacteristic
192C4⋊(C3⋊Dic3)—31no—
193C4⋊(C3⋊Dic3)—31no—
194C4⋊(C3⋊Dic3)—31no—
195C4⋊(C3⋊Dic3)—31no—
196C4⋊(C3⋊Dic3)—31no—
197C4⋊(C3⋊Dic3)—61no—
198C4⋊(C3⋊Dic3)—61no—
199C4⋊(C3⋊Dic3)—61no—
200C4⋊(C3⋊Dic3)—121no—
201#3750—31no—
202#3750—31no—
203#3750C2×D311yescharacteristic
204C4×C3⋊Dic3—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×(C2×D3)⋊C4—21no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—61no—
215C3×(C2×D3)⋊C4C2×D311yescharacteristic
216C3×(C2×D3)⋊C4C2×D311yescharacteristic
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—61no—
221C3×Dic3⋊C4C2×D311yescharacteristic
222C3×Dic3⋊C4C2×D311yescharacteristic
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225#3724—31no—
226#3724—31no—
227#3724—31no—
228#3724—61no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3—61no—
240#3722—31no—
241#3722—31no—
242#3722C2×D311yescharacteristic
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—31no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
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—
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—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3#4112yes—
288C3×#121—91no—
289C3×#121—91no—
290C3×C4×D4—91no—
291#940—91no—
292#940—91no—
293#940—91no—
294#939—31no—
295#939—31no—
296#939—91no—
297#939—91no—
298#939—91no—
299#938—91no—
300#938—91no—
301#938—91no—
302#938—91no—
303#938—181no—
304#935—91no—
305D4×Dic3—91no—
306#930—91no—
307#930—91no—
308#930—91no—
309#929—91no—
310#929—91no—
311#929—91no—
312C4×#67—91no—
313#926—91no—
314#895—31no—
315#894—91no—
316#893—31no—
317#890—91no—
318#890—91no—
319#890—181no—
320#889—91no—
321#886—91no—
322#886—91no—
323#884—31no—
324#884—91no—
325#884—91no—
326#883—91no—
327#883—91no—
328#883—91no—
329#883—91no—
330#883—91no—
331#883—181no—
332#67⋊C4—31no—
333#877—91no—
334C4×D12—91no—
335#872—91no—
336C23×C32—31no—
337C23×C32—31no—
338C23×C32—31no—
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—61no—
349C22×C3×D3—61no—
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C22×C3×D3C22×D311yescharacteristic
355C22×C3×D3C22×D311yescharacteristic
356C32×D4—121no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—41no—
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367#638—121no—
368#638—121no—
369#638—121no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C4×C3⋊D3—41no—
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—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
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—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—62no—
413C2×C3×Dic3—121no—
414C2×C3×Dic3—121no—
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C3×D12—41no—
422C3×D12—41no—
423C3×D12—42no—
424C3×D12—62no—
425C3×D12—62no—
426C3×D12—121no—
427C3×C4×D3—62no—
428C3×C4×D3—121no—
429C3×C4×D3—121no—
430C3×C4×D3—121no—
431C3×C4×D3—121no—
432C3×C4×D3—122no—
433#626—22no—
434#626—22no—
435#626—41no—
436#626—121no—
437#626—121no—
438#625—41no—
439#625—41no—
440#625—121no—
441#625—121no—
442#625—121no—
443#625—121no—
444#625—121no—
445#625—121no—
446#625—121no—
447#625—122no—
448#625—122no—
449#625—122no—
450D3×Dic3—22no—
451D3×Dic3—41no—
452D3×Dic3—41no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—122no—
456#540—271noSylow
457C2×C33C2×#4111yescharacteristic
458C2×C33H(5,𝔽2)11yescharacteristic
459C2×C33H(5,𝔽2)11yescharacteristic
460C3×C3⋊D3—41no—
461C3×C3⋊D3—41no—
462C32×D3—41no—
463C32×D3—41no—
464C32×D3—41no—
465C2×C3×D4—31no—
466C2×C3×D4—31no—
467C2×C3×D4—61no—
468C2×C3×D4—91no—
469C2×C3×D4—91no—
470C2×C3×D4—91no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C22×C3×C4—91no—
474C22×C3×C4—91no—
475C22×C3×C4—91no—
476C22×C3×C4—91no—
477C2×#67—31no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—181no—
496C2×#67—181no—
497C2×#67—181no—
498C22×Dic3—31no—
499C22×Dic3—31no—
500C22×Dic3—31no—
501C22×Dic3—91no—
502C2×D12—31no—
503C2×D12—31no—
504C2×D12—31no—
505C2×D12—91no—
506C2×D12D3211yescharacteristic
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×C4×D3—31no—
510C2×C4×D3—31no—
511C2×C4×D3—31no—
512C2×C4×D3—61no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—181no—
516C3×C4⋊C4—31no—
517C3×C4⋊C4—31no—
518C3×C4⋊C4—61no—
519C3×C4⋊C4—91no—
520C3×C22⋊C4—31no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C42—91no—
528#217—31no—
529#217—31no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—181no—
539#217—181no—
540#217—181no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—61no—
548(C2×D3)⋊C4—91no—
549(C2×D3)⋊C4—91no—
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)⋊C4D3211yescharacteristic
556C4⋊Dic3—91no—
557C4⋊Dic3—91no—
558C4⋊Dic3—91no—
559C4⋊Dic3—91no—
560C4⋊Dic3—91no—
561C4⋊Dic3—91no—
562C4⋊Dic3—91no—
563C4⋊Dic3—91no—
564C4⋊Dic3—91no—
565C4⋊Dic3—181no—
566C4⋊Dic3—181no—
567C4⋊Dic3—181no—
568C4⋊Dic3—181no—
569C4⋊Dic3—181no—
570C4⋊Dic3—361no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—61no—
574Dic3⋊C4—91no—
575Dic3⋊C4—91no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—181no—
584Dic3⋊C4—181no—
585Dic3⋊C4D3211yescharacteristic
586C4×Dic3—31no—
587C4×Dic3—31no—
588C4×Dic3—91no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—181no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—41no—
596C22×C32—61no—
597C22×C32—61no—
598C22×C32—61no—
599C22×C32—61no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32C23×D311yescharacteristic
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C2×C3⋊D3—21no—
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3×D3—21no—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—41no—
637C2×C3×D3—41no—
638C2×C3×D3—41no—
639C2×C3×D3—41no—
640C2×C3×D3—41no—
641C2×C3×D3—62no—
642C2×C3×D3—62no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658C2×C3×D3—121no—
659C32×C4—21no—
660C32×C4—22no—
661C32×C4—21no—
662C32×C4—21no—
663C32×C4—32no—
664C32×C4—41no—
665C32×C4—41no—
666C32×C4—42no—
667C32×C4—61no—
668C32×C4—61no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3⋊Dic3—21no—
672C3⋊Dic3—21no—
673C3⋊Dic3—61no—
674C3⋊Dic3—61no—
675C3⋊Dic3—61no—
676C3⋊Dic3—61no—
677C3⋊Dic3—61no—
678C3⋊Dic3—61no—
679C3⋊Dic3—121no—
680C3⋊Dic3—121no—
681C3⋊Dic3—121no—
682C3⋊Dic3—121no—
683C3⋊Dic3—121no—
684C3⋊Dic3—121no—
685C3⋊Dic3—241no—
686C3⋊Dic3—241no—
687C3×Dic3—21no—
688C3×Dic3—21no—
689C3×Dic3—21no—
690C3×Dic3—21no—
691C3×Dic3—22no—
692C3×Dic3—41no—
693C3×Dic3—41no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—121no—
703C3×Dic3—121no—
704C3×Dic3—121no—
705C3×Dic3—121no—
706C3×Dic3#23512yes—
707C3×Dic3#23712yes—
708#127—271no—
709#125—271no—
710#123—271no—
711#123—271no—
712#123—271no—
713#123—271no—
714#121—91no—
715#121—91no—
716#121—271no—
717#121—271no—
718#121—271no—
719#121—271no—
720C4×D4—91no—
721C4×D4—271no—
722#117—271no—
723C33#54011yescharacteristic, complemented, Sylow
724C23×C3—31no—
725C23×C3—31no—
726C23×C3—31no—
727C23×C3—31no—
728C23×C3—31no—
729C23×C3—31no—
730C23×C3—61no—
731C23×C3—61no—
732C23×C3—61no—
733C23×C3—91no—
734C23×C3—91no—
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—61no—
740C22×D3—61no—
741C22×D3C2×D3211yescharacteristic
742C22×D3C2×D3211yescharacteristic
743C22×D3C2×D3211yescharacteristic
744C3×D4—121no—
745C3×D4—121no—
746C3×D4—122no—
747C3×D4—182no—
748C3×D4—182no—
749C3×D4—361no—
750C3×D4—361no—
751C3×D4—361no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—41no—
762C2×C3×C4—61no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—91no—
768C2×C3×C4—91no—
769C2×C3×C4—182no—
770C2×C3×C4—361no—
771C2×C3×C4—361no—
772C2×C3×C4—361no—
773C2×C3×C4C2×D3211yescharacteristic
774C2×C3×C4C2×D3211yescharacteristic
775C2×C3×C4C2×D3211yescharacteristic
776#67—62no—
777#67—62no—
778#67—121no—
779#67—121no—
780#67—121no—
781#67—121no—
782#67—121no—
783#67—361no—
784#67—361no—
785#67—361no—
786#67—361no—
787#67—361no—
788#67—361no—
789#67—361no—
790#67—361no—
791#67—361no—
792#67—361no—
793#67—361no—
794#67—362no—
795#67—362no—
796#67—362no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—62no—
810C2×Dic3—91no—
811C2×Dic3—91no—
812C2×Dic3—91no—
813C2×Dic3—91no—
814C2×Dic3—91no—
815C2×Dic3—91no—
816C2×Dic3—121no—
817C2×Dic3—121no—
818C2×Dic3—181no—
819C2×Dic3—181no—
820C2×Dic3—181no—
821C2×Dic3—181no—
822C2×Dic3—181no—
823C2×Dic3—181no—
824C2×Dic3—361no—
825C2×Dic3—361no—
826C2×Dic3—361no—
827C2×Dic3C2×D3211yescharacteristic
828C2×Dic3C2×D3211yescharacteristic
829C2×Dic3C2×D3211yescharacteristic
830D12—41no—
831D12—62no—
832D12—62no—
833D12—121no—
834D12—361no—
835C4×D3—62no—
836C4×D3—121no—
837C4×D3—121no—
838C4×D3—121no—
839C4×D3—121no—
840C4×D3—122no—
841C4×D3—361no—
842C4×D3—361no—
843C4×D3—362no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—41no—
854C2×C32—41no—
855C2×C32—41no—
856C2×C32—121no—
857C2×C32—121no—
858C2×C32—121no—
859C2×C32C2×#23511yescharacteristic
860C2×C32C2×#23711yescharacteristic
861C2×C32#100411yescharacteristic
862C2×C32#100411yescharacteristic
863C2×C32#100411yescharacteristic
864C2×C32#100411yescharacteristic
865C2×C32D3×#4111yescharacteristic
866C2×C32#100911yescharacteristic
867C2×C32#100911yescharacteristic
868C3⋊D3—41no—
869C3⋊D3—41no—
870C3×D3—41no—
871C3×D3—41no—
872C3×D3—41no—
873C3×D3—41no—
874C3×D3—41no—
875C3×D3—41no—
876C3×D3—81no—
877C3×D3—81no—
878C3×D3—81no—
879C3×D3—122no—
880C3×D3—122no—
881C3×D3—121no—
882C3×D3—121no—
883C3×D3—121no—
884C3×D3—121no—
885C2×D4—31no—
886C2×D4—91no—
887C2×D4—91no—
888C2×D4—91no—
889C2×D4—91no—
890C2×D4—91no—
891C2×D4—271no—
892C2×D4—271no—
893C2×D4—271no—
894C2×D4—271no—
895C22×C4—91no—
896C22×C4—91no—
897C22×C4—91no—
898C22×C4—91no—
899C22×C4—271no—
900C4⋊C4—31no—
901C4⋊C4—91no—
902C4⋊C4—271no—
903C4⋊C4—271no—
904C4⋊C4—271no—
905C4⋊C4—271no—
906C4⋊C4—271no—
907C4⋊C4—271no—
908C22⋊C4—31no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—91no—
913C22⋊C4—271no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C22⋊C4—271no—
917C22⋊C4—271no—
918C42—91no—
919C42—271no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—41no—
924C22×C3—61no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—121no—
943C22×C3—121no—
944C22×C3—121no—
945C22×C3—121no—
946C22×C3—121no—
947C22×C3—121no—
948C22×C3—121no—
949C22×C3—121no—
950C22×C3—121no—
951C22×C3—181no—
952C22×C3—181no—
953C22×C3—181no—
954C22×C3—181no—
955C22×C3—181no—
956C22×C3—181no—
957C22×C3C22×D3211yescharacteristic
958C22×C3C22×D3211yescharacteristic
959C22×C3C22×D3211yescharacteristic
960C2×D3—21no—
961C2×D3—21no—
962C2×D3—21no—
963C2×D3—21no—
964C2×D3—21no—
965C2×D3—21no—
966C2×D3—21no—
967C2×D3—21no—
968C2×D3—21no—
969C2×D3—62no—
970C2×D3—62no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—121no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C3×C4—22no—
988C3×C4—21no—
989C3×C4—21no—
990C3×C4—21no—
991C3×C4—32no—
992C3×C4—32no—
993C3×C4—41no—
994C3×C4—41no—
995C3×C4—42no—
996C3×C4—62no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—61no—
1000C3×C4—61no—
1001C3×C4—121no—
1002C3×C4—121no—
1003C3×C4—181no—
1004C3×C4—181no—
1005C3×C4—181no—
1006C3×C4—181no—
1007Dic3—21no—
1008Dic3—21no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—121no—
1018Dic3—121no—
1019Dic3—121no—
1020Dic3—121no—
1021Dic3—181no—
1022Dic3—181no—
1023Dic3—181no—
1024Dic3—181no—
1025Dic3—181no—
1026Dic3—181no—
1027Dic3—361no—
1028Dic3—361no—
1029Dic3—361no—
1030Dic3—361no—
1031Dic3—361no—
1032Dic3—361no—
1033Dic3—721no—
1034Dic3—721no—
1035Dic3#379512yes—
1036C32—21no—
1037C32—21no—
1038C32—21no—
1039C32—41no—
1040C32#556211yescharacteristic, complemented
1041C32#561511yescharacteristic, complemented
1042C32#561911yescharacteristic, complemented
1043C23—31no—
1044C23—31no—
1045C23—31no—
1046C23—91no—
1047C23—91no—
1048D4—121no—
1049D4—182no—
1050D4—182no—
1051D4—361no—
1052D4—361no—
1053D4—361no—
1054D4—1081no—
1055D4—1081no—
1056D4—1081no—
1057D4—1081no—
1058C2×C4—31no—
1059C2×C4—31no—
1060C2×C4—31no—
1061C2×C4—91no—
1062C2×C4—91no—
1063C2×C4—91no—
1064C2×C4—91no—
1065C2×C4—182no—
1066C2×C4—271no—
1067C2×C4—271no—
1068C2×C4—361no—
1069C2×C4—361no—
1070C2×C4—361no—
1071C2×C4—1081no—
1072C2×C4D3311yescharacteristic
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—41no—
1083C2×C3—41no—
1084C2×C3—41no—
1085C2×C3—121no—
1086C2×C3—121no—
1087C2×C3—121no—
1088C2×C3—121no—
1089C2×C3—121no—
1090C2×C3—121no—
1091C2×C3—241no—
1092C2×C3—241no—
1093C2×C3—241no—
1094C2×C3—361no—
1095C2×C3—361no—
1096C2×C3C2×#379511yescharacteristic
1097C2×C3D3×#23511yescharacteristic
1098C2×C3D3×#23711yescharacteristic
1099C2×C3#6431311yescharacteristic
1100C2×C3#6431311yescharacteristic
1101C2×C3#6431411yescharacteristic
1102C2×C3#6431411yescharacteristic
1103C2×C3#6432011yescharacteristic
1104C2×C3#6433011yescharacteristic
1105D3—41no—
1106D3—41no—
1107D3—41no—
1108D3—122no—
1109D3—122no—
1110D3—121no—
1111D3—121no—
1112D3—121no—
1113D3—121no—
1114C22—61no—
1115C22—61no—
1116C22—61no—
1117C22—61no—
1118C22—61no—
1119C22—61no—
1120C22—61no—
1121C22—61no—
1122C22—61no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22C2×D3311yescharacteristic
1130C4—21no—
1131C4—32no—
1132C4—61no—
1133C4—61no—
1134C4—181no—
1135C4—181no—
1136C4—181no—
1137C4—181no—
1138C4—541no—
1139C4—541no—
1140C3—21no—
1141C3—21no—
1142C3—21no—
1143C3—41no—
1144C3#1059410011yescharacteristic, complemented
1145C3#1059449611yescharacteristic, complemented
1146C3#1059519711yescharacteristic, complemented
1147C2—121no—
1148C2—121no—
1149C2—121no—
1150C2—361no—
1151C2—361no—
1152C2D3×#379511yescharacteristic
1153C2#1172438611yescharacteristic
1154C2#1172441511yescharacteristic
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. #11723694C2semidirect
2. #11723523C2semidirect
3. #11723522C2semidirect
4. #11723400C2semidirect
5. C3×#63886C2semidirect
6. C3×#63885C2semidirect
7. C3×#63881C2semidirect
8. #11723029C2semidirect
9. #11722988C2semidirect
10. #11722985C2semidirect
11. #11722967C2semidirect
12. #11722956C2semidirect
13. #11722956C2semidirect
14. Dic3×#626C2semidirect
15. #11722913C2semidirect
91. #63886D3semidirect
93. #63885D3semidirect
94. #63881D3semidirect
723. C33#540semidirect
1040. C32#5562semidirect
1041. C32#5615semidirect
1042. C32#5619semidirect
1144. C3#10594100semidirect
1145. C3#10594496semidirect
1146. C3#10595197semidirect

Maximal subgroups

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

subgroupindex
#117236942
#117235232
#117235222
#117234002
C3×#638862
C3×#638852
C3×#638812
#117230292
#117229882
#117229852
#117229672
#117229562
Dic3×#6262
#117229132
#105951973
#105944963
#105941003