Finite Group Databasebeta

← #13178337

Subgroups — #13178337

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
1C3×#64104C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C3×#64098C211yesmaximal, characteristic, complemented
4#11723697C211yesmaximal, characteristic, complemented
5#11723696C211yesmaximal, characteristic, complemented
6#11723694C211yesmaximal, characteristic, complemented
7#11723690C211yesmaximal, characteristic, complemented
8#11723687C211yesmaximal, characteristic, complemented
9#11723687C211yesmaximal, characteristic, complemented
10#11723687C211yesmaximal, characteristic, complemented
11#11723687C211yesmaximal, characteristic, complemented
12#11723686C211yesmaximal, characteristic, complemented
13#11723684C211yesmaximal, characteristic, complemented
14#11723684C211yesmaximal, characteristic, complemented
15#11723683C211yesmaximal, characteristic, complemented
16#10594580—31nomaximal
17#10594563—31nomaximal
18#10594467—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6294C2211yescharacteristic
32C2×#6294C2211yescharacteristic
33C2×#6294C2211yescharacteristic
34C33×C4⋊C4C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45C3×#3750C2211yescharacteristic
46C3×C4×C3⋊Dic3C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic
53#88813C2211yescharacteristic
54#64104D311yescharacteristic, complemented
55#64103D311yescharacteristic, complemented
56#64098D311yescharacteristic, complemented
57C3×#895—31no—
58C3×#895—31no—
59C3×#895—61no—
60C3×#894—31no—
61C3×#894—31no—
62C3×#894—61no—
63C3×#889—31no—
64C3×#889—31no—
65C3×#889—61no—
66#63916—31no—
67#63914—31no—
68#63911—31no—
69#63911—31no—
70#63910—31no—
71#63910—31no—
72#63910—31no—
73#63910—31no—
74#63909—31no—
75#63908—31no—
76#63905—31no—
77#63904—31no—
78#63904—31no—
79#63897—31no—
80#63891—31no—
81#63890—31no—
82#63886—31no—
83#63886—31no—
84#63886—31no—
85#63886—31no—
86#63885—31no—
87#63885—31no—
88#63885—31no—
89#63885—31no—
90#63884—31no—
91#63884—31no—
92#63881—31no—
93#63881—31no—
94#63879—31no—
95#63879—31no—
96#63878—31no—
97#63877—31no—
98#63854—31no—
99#63853—31no—
100#63850—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C33×C4C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—41no—
118C3×C4⋊(C3⋊D3)—41no—
119C3×C4⋊(C3⋊D3)—41no—
120C3×C4⋊(C3⋊D3)—41no—
121C3×C4×C3⋊D3—41no—
122C3×C4×C3⋊D3—41no—
123#6295—22no—
124#6295—22no—
125#6295—41no—
126#6295—41no—
127#6295—41no—
128#6295—41no—
129#6294—22no—
130#6294—41no—
131#6294—41no—
132#5697—91no—
133#5663—91no—
134#5615—91no—
135C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
136C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
137C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
138C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
139C2×C4×C3⋊D3C2×D311yescharacteristic
140C2×C4×C3⋊D3C2×D311yescharacteristic
141C2×C3×D12—31no—
142C2×C3×D12—31no—
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—61no—
150C2×C3×D12—61no—
151C2×C3×D12—61no—
152C2×C3×D12—61no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—61no—
158C2×C3×C4×D3—61no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
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—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—31no—
174C2×#625—31no—
175C2×#625—31no—
176C2×#625—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C32×C4⋊C4—21no—
187C32×C4⋊C4—21no—
188C32×C4⋊C4—21no—
189C32×C4⋊C4—41no—
190C32×C4⋊C4C2×D311yescharacteristic
191C32×C4⋊C4C2×D311yescharacteristic
192C32×C4⋊C4C2×D311yescharacteristic
193#3752C2×D311yescharacteristic
194#3752C2×D311yescharacteristic
195#3752C2×D311yescharacteristic
196#3752C2×D311yescharacteristic
197#3752C2×D311yescharacteristic
198C4⋊(C3⋊Dic3)C2×D311yescharacteristic
199#3750C2×D311yescharacteristic
200#3750C2×D311yescharacteristic
201#3750C2×D311yescharacteristic
202#3750C2×D311yescharacteristic
203#3750C2×D311yescharacteristic
204C4×C3⋊Dic3C2×D311yescharacteristic
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
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—31no—
215C3×(C2×D3)⋊C4—61no—
216C3×(C2×D3)⋊C4—61no—
217C3×(C2×D3)⋊C4—61no—
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—31no—
228C3×Dic3⋊C4—31no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—61no—
234C3×Dic3⋊C4—61no—
235C3×Dic3⋊C4—61no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4—61no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—61no—
241#3724—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—31no—
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×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—
279C33×C4—21no—
280C33×C4—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×#125—91no—
289C3×#123—91no—
290C3×#121—91no—
291#940—91no—
292#940—91no—
293#939—91no—
294#939—91no—
295#939—91no—
296#939—91no—
297#938—91no—
298#935—91no—
299#930—91no—
300#929—91no—
301C4×#67—91no—
302C4×#67—91no—
303#895—31no—
304#895—31no—
305#895—61no—
306#895—91no—
307#895—91no—
308#895—91no—
309#895—91no—
310#895—91no—
311#894—31no—
312#894—31no—
313#894—61no—
314#894—91no—
315#894—91no—
316#894—91no—
317#894—91no—
318#893—91no—
319#893—91no—
320#892—91no—
321#889—31no—
322#889—31no—
323#889—61no—
324#886—91no—
325#884—91no—
326#884—91no—
327#884—91no—
328#884—91no—
329#883—91no—
330#883—91no—
331#67⋊C4—91no—
332#67⋊C4—91no—
333#877—91no—
334#874—91no—
335#872—91no—
336C22×C3⋊D3C22×D311yescharacteristic
337C22×C3⋊D3C22×D311yescharacteristic
338C22×C3⋊D3C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C22×C3×D3—61no—
354C22×C3×D3—61no—
355C22×C3×D3—61no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—41no—
366C2×C32×C4—41no—
367C2×C32×C4—41no—
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370C2×C32×C4C22×D311yescharacteristic
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C4⋊(C3⋊D3)—41no—
385C4⋊(C3⋊D3)—41no—
386C4⋊(C3⋊D3)—41no—
387C4⋊(C3⋊D3)—41no—
388C4×C3⋊D3—41no—
389C4×C3⋊D3—41no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C3×D12—121no—
412C3×D12—121no—
413C3×D12—121no—
414C3×D12—121no—
415C3×D12—121no—
416C3×D12—121no—
417C3×D12—121no—
418C3×D12—121no—
419C3×D12—122no—
420C3×D12—122no—
421C3×D12—122no—
422C3×D12—122no—
423C3×C4×D3—121no—
424C3×C4×D3—121no—
425C3×C4×D3—121no—
426C3×C4×D3—121no—
427C3×C4×D3—122no—
428C3×C4×D3—122no—
429#626—62no—
430#626—62no—
431#626—62no—
432#626—62no—
433#626—121no—
434#626—121no—
435#626—121no—
436#626—121no—
437#626—121no—
438#626—121no—
439#626—121no—
440#626—121no—
441#625—62no—
442#625—62no—
443#625—121no—
444#625—121no—
445#625—121no—
446#625—121no—
447#624—62no—
448#624—121no—
449#624—121no—
450D3×Dic3—62no—
451D3×Dic3—62no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456#540—271noSylow
457C2×C33C2×#4111yescharacteristic
458C2×C33H(5,𝔽2)11yescharacteristic
459C2×C33H(5,𝔽2)11yescharacteristic
460C3×C3⋊D3—41no—
461C3×C3⋊D3—41no—
462C3×C3⋊D3—41no—
463C3×C3⋊D3—41no—
464C3×C3⋊D3—41no—
465C2×C3×D4—91no—
466C2×C3×D4—91no—
467C2×C3×D4—91no—
468C2×C3×D4—91no—
469C22×C3×C4—91no—
470C22×C3×C4—91no—
471C2×#67—91no—
472C2×#67—91no—
473C2×#67—91no—
474C2×#67—91no—
475C2×#67—91no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C22×Dic3—91no—
484C22×Dic3—91no—
485C22×Dic3—91no—
486C2×D12—31no—
487C2×D12—31no—
488C2×D12—31no—
489C2×D12—31no—
490C2×D12—31no—
491C2×D12—31no—
492C2×D12—31no—
493C2×D12—31no—
494C2×D12—61no—
495C2×D12—61no—
496C2×D12—61no—
497C2×D12—61no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×C4×D3—31no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—31no—
508C2×C4×D3—61no—
509C2×C4×D3—61no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C3×C4⋊C4—21no—
517C3×C4⋊C4—21no—
518C3×C4⋊C4—21no—
519C3×C4⋊C4—41no—
520C3×C4⋊C4—91no—
521C3×C4⋊C4—91no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4D3211yescharacteristic
527C3×C4⋊C4D3211yescharacteristic
528C3×C4⋊C4D3211yescharacteristic
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C42—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540(C2×D3)⋊C4—31no—
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—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—61no—
551(C2×D3)⋊C4—61no—
552(C2×D3)⋊C4—61no—
553(C2×D3)⋊C4—61no—
554(C2×D3)⋊C4—61no—
555(C2×D3)⋊C4—91no—
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—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565C4⋊Dic3—31no—
566C4⋊Dic3—31no—
567C4⋊Dic3—61no—
568C4⋊Dic3—91no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—61no—
580Dic3⋊C4—61no—
581Dic3⋊C4—61no—
582Dic3⋊C4—61no—
583Dic3⋊C4—61no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586C4×Dic3—31no—
587C4×Dic3—31no—
588C4×Dic3—61no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—41no—
596C22×C32C23×D311yescharacteristic
597C22×C32C23×D311yescharacteristic
598C22×C32C23×D311yescharacteristic
599C2×C3⋊D3—21no—
600C2×C3⋊D3—21no—
601C2×C3⋊D3—21no—
602C2×C3⋊D3—21no—
603C2×C3⋊D3—21no—
604C2×C3⋊D3—21no—
605C2×C3⋊D3—21no—
606C2×C3⋊D3—21no—
607C2×C3⋊D3—21no—
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—62no—
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—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—121no—
647C2×C3×D3—121no—
648C2×C3×D3—121no—
649C2×C3×D3—121no—
650C2×C3×D3—121no—
651C2×C3×D3—121no—
652C2×C3×D3—121no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658C2×C3×D3—121no—
659C32×C4—21no—
660C32×C4—22no—
661C32×C4—21no—
662C32×C4—21no—
663C32×C4—21no—
664C32×C4—21no—
665C32×C4—21no—
666C32×C4—21no—
667C32×C4—21no—
668C32×C4—21no—
669C32×C4—41no—
670C32×C4—41no—
671C32×C4—42no—
672C32×C4—41no—
673C32×C4—41no—
674C32×C4—41no—
675C32×C4—41no—
676C32×C4—41no—
677C32×C4—41no—
678C32×C4—81no—
679C32×C4—81no—
680C3⋊Dic3—21no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3#23912yes—
687C3×Dic3—32no—
688C3×Dic3—32no—
689C3×Dic3—62no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
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—121no—
707C3×Dic3—121no—
708#127—271no—
709#125—91no—
710#123—91no—
711#123—271no—
712#123—271no—
713#123—271no—
714#121—91no—
715#121—271no—
716#121—271no—
717#121—271no—
718#121—271no—
719#121—271no—
720C4×D4—271no—
721C4×D4—271no—
722#117—271no—
723C33#54011yescharacteristic, complemented, Sylow
724C23×C3—91no—
725C23×C3—91no—
726C23×C3—91no—
727C23×C3—91no—
728C23×C3—91no—
729C22×D3—31no—
730C22×D3—31no—
731C22×D3—31no—
732C22×D3—31no—
733C22×D3—31no—
734C22×D3—31no—
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—61no—
740C22×D3—61no—
741C22×D3—61no—
742C22×D3—61no—
743C22×D3—61no—
744C3×D4—361no—
745C3×D4—361no—
746C3×D4—361no—
747C3×D4—361no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—21no—
756C2×C3×C4—21no—
757C2×C3×C4—41no—
758C2×C3×C4—41no—
759C2×C3×C4—41no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—361no—
768C2×C3×C4—361no—
769C2×C3×C4C2×D3211yescharacteristic
770C2×C3×C4C2×D3211yescharacteristic
771C2×C3×C4C2×D3211yescharacteristic
772C2×C3×C4C2×D3211yescharacteristic
773C2×C3×C4C2×D3211yescharacteristic
774C2×C3×C4C2×D3211yescharacteristic
775C2×C3×C4C2×D3211yescharacteristic
776C2×C3×C4C2×D3211yescharacteristic
777C2×C3×C4C2×D3211yescharacteristic
778#67—182no—
779#67—182no—
780#67—182no—
781#67—182no—
782#67—361no—
783#67—361no—
784#67—361no—
785#67—361no—
786#67—361no—
787#67—361no—
788#67—361no—
789#67—361no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—61no—
810C2×Dic3—61no—
811C2×Dic3—182no—
812C2×Dic3—361no—
813C2×Dic3—361no—
814D12—121no—
815D12—121no—
816D12—121no—
817D12—121no—
818D12—121no—
819D12—121no—
820D12—121no—
821D12—121no—
822D12—122no—
823D12—122no—
824D12—122no—
825D12—122no—
826D12—182no—
827D12—182no—
828D12—361no—
829D12—361no—
830D12—361no—
831D12—361no—
832C4×D3—121no—
833C4×D3—121no—
834C4×D3—121no—
835C4×D3—121no—
836C4×D3—122no—
837C4×D3—122no—
838C4×D3—182no—
839C4×D3—182no—
840C4×D3—361no—
841C4×D3—361no—
842C4×D3—361no—
843C4×D3—361no—
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#100411yescharacteristic
857C2×C32#100411yescharacteristic
858C2×C32#100411yescharacteristic
859C2×C32C2×#23911yescharacteristic
860C2×C32D3×#4111yescharacteristic
861C2×C32D3×#4111yescharacteristic
862C2×C32#100911yescharacteristic
863C2×C32#100911yescharacteristic
864C2×C32#100911yescharacteristic
865C3⋊D3—41no—
866C3⋊D3—41no—
867C3⋊D3—41no—
868C3⋊D3—41no—
869C3⋊D3—41no—
870C3×D3—122no—
871C3×D3—122no—
872C3×D3—121no—
873C3×D3—121no—
874C3×D3—121no—
875C3×D3—121no—
876C3×D3—121no—
877C3×D3—121no—
878C3×D3—121no—
879C3×D3—121no—
880C3×D3—121no—
881C3×D3—121no—
882C3×D3—241no—
883C3×D3—241no—
884C3×D3—241no—
885C2×D4—91no—
886C2×D4—91no—
887C2×D4—91no—
888C2×D4—91no—
889C2×D4—271no—
890C2×D4—271no—
891C2×D4—271no—
892C2×D4—271no—
893C2×D4—271no—
894C2×D4—271no—
895C22×C4—91no—
896C22×C4—91no—
897C22×C4—271no—
898C22×C4—271no—
899C22×C4—271no—
900C4⋊C4—91no—
901C4⋊C4—91no—
902C4⋊C4—91no—
903C4⋊C4—91no—
904C4⋊C4—91no—
905C4⋊C4—91no—
906C4⋊C4—271no—
907C4⋊C4#111311yescharacteristic
908C22⋊C4—91no—
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—181no—
925C22×C3—181no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3—181no—
933C22×C3—181no—
934C22×C3—181no—
935C22×C3—181no—
936C22×C3—181no—
937C22×C3—181no—
938C22×C3—181no—
939C22×C3C22×D3211yescharacteristic
940C22×C3C22×D3211yescharacteristic
941C22×C3C22×D3211yescharacteristic
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—121no—
975C2×D3—121no—
976C2×D3—121no—
977C2×D3—121no—
978C2×D3—121no—
979C2×D3—121no—
980C2×D3—121no—
981C2×D3—121no—
982C2×D3—121no—
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—21no—
992C3×C4—21no—
993C3×C4—21no—
994C3×C4—21no—
995C3×C4—21no—
996C3×C4—21no—
997C3×C4—41no—
998C3×C4—41no—
999C3×C4—41no—
1000C3×C4—41no—
1001C3×C4—41no—
1002C3×C4—41no—
1003C3×C4—41no—
1004C3×C4—41no—
1005C3×C4—42no—
1006C3×C4—81no—
1007C3×C4—81no—
1008C3×C4—92no—
1009C3×C4—181no—
1010C3×C4—181no—
1011C3×C4—181no—
1012C3×C4—181no—
1013C3×C4—181no—
1014C3×C4—181no—
1015Dic3—32no—
1016Dic3—32no—
1017Dic3—62no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—61no—
1025Dic3—61no—
1026Dic3—61no—
1027Dic3—61no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—121no—
1031Dic3—121no—
1032Dic3—121no—
1033Dic3—121no—
1034Dic3—121no—
1035Dic3—121no—
1036C32—21no—
1037C32—21no—
1038C32—21no—
1039C32—41no—
1040C32#561511yescharacteristic, complemented
1041C32#566311yescharacteristic, complemented
1042C32#569711yescharacteristic, complemented
1043C23—91no—
1044C23—91no—
1045C23—91no—
1046C23—91no—
1047C23—91no—
1048D4—361no—
1049D4—361no—
1050D4—361no—
1051D4—361no—
1052D4—542no—
1053D4—542no—
1054D4—1081no—
1055D4—1081no—
1056D4—1081no—
1057D4—1081no—
1058C2×C4—91no—
1059C2×C4—91no—
1060C2×C4—91no—
1061C2×C4—91no—
1062C2×C4—91no—
1063C2×C4—91no—
1064C2×C4—91no—
1065C2×C4—361no—
1066C2×C4—361no—
1067C2×C4—542no—
1068C2×C4—1081no—
1069C2×C4—1081no—
1070C2×C4C2×#111311yescharacteristic
1071C2×C4C2×#111311yescharacteristic
1072C2×C4C2×#111311yescharacteristic
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—361no—
1086C2×C3—361no—
1087C2×C3—361no—
1088C2×C3—361no—
1089C2×C3—361no—
1090C2×C3#6430711yescharacteristic
1091C2×C3#6430711yescharacteristic
1092C2×C3#6430811yescharacteristic
1093C2×C3#6431311yescharacteristic
1094C2×C3#6431411yescharacteristic
1095C2×C3#6431411yescharacteristic
1096C2×C3D3×#23911yescharacteristic
1097C2×C3D3×#23911yescharacteristic
1098C2×C3#6431911yescharacteristic
1099D3—122no—
1100D3—122no—
1101D3—121no—
1102D3—121no—
1103D3—121no—
1104D3—121no—
1105D3—121no—
1106D3—121no—
1107D3—121no—
1108D3—121no—
1109D3—121no—
1110D3—121no—
1111D3—241no—
1112D3—241no—
1113D3—241no—
1114C22—181no—
1115C22—181no—
1116C22—181no—
1117C22—181no—
1118C22—181no—
1119C22—181no—
1120C22—181no—
1121C22—181no—
1122C22—181no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22C22×#111311yescharacteristic
1130C4—21no—
1131C4—21no—
1132C4—21no—
1133C4—92no—
1134C4—181no—
1135C4—181no—
1136C4—181no—
1137C4—181no—
1138C4—181no—
1139C4—181no—
1140C3—21no—
1141C3—21no—
1142C3—21no—
1143C3—41no—
1144C3#1059446711yescharacteristic, complemented
1145C3#1059456311yescharacteristic, complemented
1146C3#1059458011yescharacteristic, complemented
1147C2—361no—
1148C2—361no—
1149C2—361no—
1150C2—361no—
1151C2—361no—
1152C2#1172461911yescharacteristic
1153C2#1172462311yescharacteristic
1154C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64104C2semidirect
2. C3×#64103C2semidirect
3. C3×#64098C2semidirect
4. #11723697C2semidirect
5. #11723696C2semidirect
6. #11723694C2semidirect
7. #11723690C2semidirect
8. #11723687C2semidirect
9. #11723687C2semidirect
10. #11723687C2semidirect
11. #11723687C2semidirect
12. #11723686C2semidirect
13. #11723684C2semidirect
14. #11723684C2semidirect
15. #11723683C2semidirect
54. #64104D3semidirect
55. #64103D3semidirect
56. #64098D3semidirect
723. C33#540semidirect
1040. C32#5615semidirect
1041. C32#5663semidirect
1042. C32#5697semidirect
1144. C3#10594467semidirect
1145. C3#10594563semidirect
1146. C3#10594580semidirect

Maximal subgroups

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

subgroupindex
C3×#641042
C3×#641032
C3×#640982
#117236972
#117236962
#117236942
#117236902
#117236872
#117236862
#117236842
#117236832
#105945803
#105945633
#105944673