Finite Group Databasebeta

← #13178225

Subgroups — #13178225

Order 1728.

1332 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64091C211yesmaximal, characteristic, complemented
2C3×#64090C211yesmaximal, characteristic, complemented
3C3×#64087C211yesmaximal, characteristic, complemented
4#11723727C211yesmaximal, characteristic, complemented
5#11723726C211yesmaximal, characteristic, complemented
6C2×#88814C211yesmaximal, characteristic, complemented
7#11723717C211yesmaximal, characteristic, complemented
8#11723696C211yesmaximal, characteristic, complemented
9#11723694C211yesmaximal, characteristic, complemented
10#11723687C211yesmaximal, characteristic, complemented
11#11723686C211yesmaximal, characteristic, complemented
12#11723677C211yesmaximal, characteristic, complemented
13#11723676C211yesmaximal, characteristic, complemented
14#11723675C211yesmaximal, characteristic, complemented
15#11723670C211yesmaximal, characteristic, complemented
16#10594243—31nomaximal
17#10594238—31nomaximal
18#10594173—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×#634C2211yescharacteristic, complemented
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic, complemented
31C2×#6294C2211yescharacteristic, complemented
32C33×C22⋊C4C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3750C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88814C2211yescharacteristic
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic, complemented
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88813C2211yescharacteristic, complemented
54#64091D311yescharacteristic, complemented
55#64090D311yescharacteristic, complemented
56#64087D311yescharacteristic, complemented
57C3×#882—31no—
58C3×#882—31no—
59C3×#882—61no—
60C3×#67⋊C4—31no—
61C3×#67⋊C4—31no—
62C3×#67⋊C4—61no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#878—61no—
66#63981—31no—
67#63980—31no—
68#63978—31no—
69#63978—31no—
70#63977—31no—
71#63976—31no—
72#67⋊Dic3—31no—
73Dic3×#67—31no—
74C2×#3722—31no—
75C2×(C2×D3)⋊Dic3—31no—
76C2×(C2×D3)⋊Dic3—31no—
77#63952—31no—
78#63916—31no—
79#63913—31no—
80#63910—31no—
81#63909—31no—
82#63908—31no—
83#63907—31no—
84#63907—31no—
85#63905—31no—
86#63897—31no—
87#63886—31no—
88#63885—31no—
89#63884—31no—
90#63884—31no—
91#63868—31no—
92#63864—31no—
93#63863—31no—
94#63862—31no—
95#63861—31no—
96#63860—31no—
97#63859—31no—
98#63858—31no—
99#63853—31no—
100#63850—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C2×C33×C4C2311yescharacteristic
111C2×C33×C4C2311yescharacteristic
112C3×#638—22no—
113C3×#638—22no—
114C2×C3×C3⋊Dic3—41no—
115C2×C3×C3⋊Dic3—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C3×C4⋊(C3⋊D3)—41no—
125C3×C4⋊(C3⋊D3)—41no—
126C3×C4×C3⋊D3—41no—
127C3×#634—41no—
128#6295—41no—
129#6295—41no—
130#6295—41no—
131#6294—41no—
132#5644—91no—
133#5593—91no—
134#5560—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C22×C3⋊Dic3C2×D311yescharacteristic
142C22×C3⋊Dic3C2×D311yescharacteristic
143C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
144C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
145C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
146C2×#634C2×D311yescharacteristic, complemented
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—61no—
152C2×C3×#67—61no—
153C22×C3×Dic3—31no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—61no—
158C22×C3×Dic3—61no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×D12—61no—
164C2×C3×D12—61no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—61no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—31no—
170C2×C3×Dic6—61no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#625—31no—
178C2×#625—31no—
179C2×#625—31no—
180C2×#624—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C32×C22⋊C4—21no—
184C32×C22⋊C4—21no—
185C32×C22⋊C4—21no—
186C32×C22⋊C4—41no—
187C32×C22⋊C4C2×D311yescharacteristic
188C32×C22⋊C4C2×D311yescharacteristic
189C32×C22⋊C4C2×D311yescharacteristic
190#3757C2×D311yescharacteristic
191#3752C2×D311yescharacteristic
192#3752C2×D311yescharacteristic
193#3752C2×D311yescharacteristic, complemented
194C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
195#3750C2×D311yescharacteristic, complemented
196#3750C2×D311yescharacteristic, complemented
197#3750C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—61no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—61no—
209C3×(C2×D3)⋊C4—61no—
210C3×(C2×D3)⋊C4—61no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—61no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—61no—
221C3×Dic3⋊C4—61no—
222C3×Dic3⋊C4—61no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—61no—
226#3724—31no—
227#3724—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241(C2×D3)⋊Dic3—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—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×C33—21no—
263C22×C33—21no—
264C22×C33#4112yes—
265C22×C33C2411yescharacteristic
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—
278C2×C3×C3⋊D3—44no—
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—21no—
288C3×C3⋊Dic3—21no—
289C3×C22⋊Q8—91no—
290C3×#120—91no—
291C3×C4×D4—91no—
292#953—91no—
293C2×#217—91no—
294#947—91no—
295#947—91no—
296#939—91no—
297#939—91no—
298#939—91no—
299#938—91no—
300#937—91no—
301#936—91no—
302#935—91no—
303D4×Dic3—91no—
304#930—91no—
305#930—91no—
306#929—91no—
307C4×#67—91no—
308C2×(C2×D3)⋊C4—91no—
309C2×(C2×D3)⋊C4—91no—
310#898—91no—
311#898—91no—
312#898—91no—
313#895—91no—
314#895—91no—
315#894—91no—
316#894—91no—
317#894—91no—
318#885—91no—
319#885—91no—
320#884—91no—
321#883—91no—
322#882—31no—
323#882—31no—
324#882—61no—
325#882—91no—
326#67⋊C4—31no—
327#67⋊C4—31no—
328#67⋊C4—61no—
329#67⋊C4—91no—
330#879—91no—
331#879—91no—
332#878—31no—
333#878—31no—
334#878—61no—
335#876—91no—
336#875—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—41no—
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C22×C3⋊D3—22no—
345C22×C3⋊D3—41no—
346C22×C3⋊D3—41no—
347C22×C3⋊D3C22×D311yescharacteristic
348C22×C3⋊D3C22×D311yescharacteristic
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—61no—
360C22×C3×D3—61no—
361C22×C3×D3—61no—
362C22×C3×D3—61no—
363C22×C3×D3—62no—
364C22×C3×D3—62no—
365C22×C3×D3—122no—
366C22×C3×D3—121no—
367C22×C3×D3—121no—
368C22×C3×D3—121no—
369C22×C3×D3—121no—
370C22×C3×D3—122no—
371C22×C3×D3—122no—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—21no—
377C2×C32×C4—21no—
378C2×C32×C4—41no—
379C2×C32×C4—41no—
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383C2×C32×C4C22×D311yescharacteristic
384C2×C32×C4C22×D311yescharacteristic
385C2×C32×C4C22×D311yescharacteristic
386#638—22no—
387#638—22no—
388C2×C3⋊Dic3—41no—
389C2×C3⋊Dic3—41no—
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C4⋊(C3⋊D3)—41no—
399C4⋊(C3⋊D3)—41no—
400C4×C3⋊D3—41no—
401#634—41no—
402C3×#67—64no—
403C3×#67—62no—
404C3×#67—62no—
405C3×#67—62no—
406C3×#67—62no—
407C3×#67—122no—
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—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—121no—
433C2×C3×Dic3—121no—
434C2×C3×Dic3—121no—
435C2×C3×Dic3—121no—
436C2×C3×Dic3—122no—
437C2×C3×Dic3—122no—
438C3×D12—121no—
439C3×D12—121no—
440C3×D12—121no—
441C3×D12—121no—
442C3×D12—122no—
443C3×D12—122no—
444C3×C4×D3—121no—
445C3×C4×D3—121no—
446C3×C4×D3—122no—
447C3×Dic6—121no—
448C3×Dic6—121no—
449C3×Dic6—122no—
450#626—121no—
451#626—121no—
452#626—121no—
453#626—121no—
454#626—121no—
455#626—121no—
456#625—121no—
457#625—121no—
458#625—121no—
459#624—121no—
460D3×Dic3—121no—
461D3×Dic3—121no—
462#538—271noSylow
463C2×C33—22no—
464C2×C33C2×#4111yescharacteristic
465C2×C33H(5,𝔽2)11yescharacteristic
466C2×C33H(5,𝔽2)11yescharacteristic
467C3×C3⋊D3—41no—
468C3×C3⋊D3—41no—
469C3×C3⋊D3—41no—
470C3×C3⋊D3—41no—
471C24×C3—91no—
472C23×D3—31no—
473C23×D3—31no—
474C23×D3—61no—
475C2×C3×Q8—91no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C22×C3×C4—91no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—61no—
488C2×#67—61no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—91no—
495C22×Dic3—31no—
496C22×Dic3—31no—
497C22×Dic3—31no—
498C22×Dic3—31no—
499C22×Dic3—61no—
500C22×Dic3—61no—
501C22×Dic3—91no—
502C2×D12—31no—
503C2×D12—31no—
504C2×D12—31no—
505C2×D12—31no—
506C2×D12—61no—
507C2×D12—61no—
508C2×D12—91no—
509C2×D12—91no—
510C2×D12—91no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—61no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×Dic6—31no—
517C2×Dic6—31no—
518C2×Dic6—61no—
519C3×C4⋊C4—91no—
520C3×C4⋊C4—91no—
521C3×C4⋊C4—91no—
522C3×C4⋊C4—91no—
523C3×C22⋊C4—21no—
524C3×C22⋊C4—21no—
525C3×C22⋊C4—21no—
526C3×C22⋊C4—41no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4D3211yescharacteristic
532C3×C22⋊C4D3211yescharacteristic
533C3×C22⋊C4D3211yescharacteristic
534C3×C42—91no—
535#217—31no—
536#217—31no—
537#217—61no—
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—91no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—61no—
554(C2×D3)⋊C4—61no—
555(C2×D3)⋊C4—61no—
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—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574C4⋊Dic3—31no—
575C4⋊Dic3—31no—
576C4⋊Dic3—61no—
577C4⋊Dic3—91no—
578C4⋊Dic3—91no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—61no—
586Dic3⋊C4—61no—
587Dic3⋊C4—61no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3—61no—
595C4×Dic3—91no—
596C4×Dic3—91no—
597C4×Dic3—91no—
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—22no—
608C22×C32—22no—
609C22×C32—22no—
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—81no—
619C22×C32—81no—
620C22×C32#23512yes—
621C22×C32#23712yes—
622C22×C32#23912yes—
623C22×C32C23×D311yescharacteristic
624C22×C32C23×D311yescharacteristic
625C22×C32C23×D311yescharacteristic
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—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—44no—
639C2×C3×D3—62no—
640C2×C3×D3—62no—
641C2×C3×D3—62no—
642C2×C3×D3—61no—
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—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673C2×C3×D3—121no—
674C2×C3×D3—121no—
675C2×C3×D3—124no—
676C2×C3×D3—124no—
677C2×C3×D3—128no—
678C32×C4—21no—
679C32×C4—21no—
680C32×C4—21no—
681C32×C4—21no—
682C32×C4—21no—
683C32×C4—21no—
684C32×C4—41no—
685C32×C4—41no—
686C32×C4—41no—
687C32×C4—41no—
688C32×C4—41no—
689C32×C4—41no—
690C32×C4—81no—
691C32×C4—81no—
692C3⋊Dic3—21no—
693C3⋊Dic3—21no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—21no—
699C3⋊Dic3—21no—
700C3×Dic3—62no—
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—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722C3×Dic3—121no—
723C3×Dic3—121no—
724#126—271no—
725#126—271no—
726#124—271no—
727#124—271no—
728#123—271no—
729#123—271no—
730C22⋊Q8—91no—
731#121—271no—
732#121—271no—
733#121—271no—
734#120—91no—
735#120—271no—
736C4×D4—91no—
737C4×D4—271no—
738C2×C22⋊C4—271no—
739C33#53811yescharacteristic, complemented, Sylow
740C23×C3—21no—
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—41no—
744C23×C3—91no—
745C23×C3—91no—
746C23×C3—91no—
747C23×C3—91no—
748C23×C3—182no—
749C23×C3—361no—
750C23×C3—361no—
751C23×C3C2×D3211yescharacteristic
752C23×C3C2×D3211yescharacteristic
753C23×C3C2×D3211yescharacteristic
754C22×D3—31no—
755C22×D3—31no—
756C22×D3—31no—
757C22×D3—31no—
758C22×D3—31no—
759C22×D3—31no—
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—61no—
763C22×D3—61no—
764C22×D3—61no—
765C22×D3—61no—
766C22×D3—62no—
767C22×D3—62no—
768C22×D3—122no—
769C22×D3—121no—
770C22×D3—121no—
771C22×D3—121no—
772C22×D3—121no—
773C22×D3—122no—
774C22×D3—122no—
775C3×Q8—361no—
776C3×D4—182no—
777C3×D4—182no—
778C3×D4—361no—
779C3×D4—361no—
780C2×C3×C4—21no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—21no—
784C2×C3×C4—21no—
785C2×C3×C4—21no—
786C2×C3×C4—41no—
787C2×C3×C4—41no—
788C2×C3×C4—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—361no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799C2×C3×C4C2×D3211yescharacteristic
800C2×C3×C4C2×D3211yescharacteristic
801C2×C3×C4C2×D3211yescharacteristic
802C2×C3×C4C2×D3211yescharacteristic
803C2×C3×C4C2×D3211yescharacteristic
804C2×C3×C4C2×D3211yescharacteristic
805#67—64no—
806#67—62no—
807#67—62no—
808#67—62no—
809#67—62no—
810#67—122no—
811#67—361no—
812#67—361no—
813#67—361no—
814#67—361no—
815#67—361no—
816#67—361no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—61no—
834C2×Dic3—61no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—61no—
839C2×Dic3—61no—
840C2×Dic3—61no—
841C2×Dic3—121no—
842C2×Dic3—121no—
843C2×Dic3—121no—
844C2×Dic3—121no—
845C2×Dic3—122no—
846C2×Dic3—122no—
847C2×Dic3—361no—
848D12—121no—
849D12—121no—
850D12—121no—
851D12—121no—
852D12—122no—
853D12—122no—
854D12—361no—
855D12—361no—
856D12—361no—
857C4×D3—121no—
858C4×D3—121no—
859C4×D3—122no—
860C4×D3—361no—
861C4×D3—361no—
862Dic6—121no—
863Dic6—121no—
864Dic6—122no—
865C2×C32—22no—
866C2×C32—22no—
867C2×C32—22no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—41no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—42no—
881C2×C32—42no—
882C2×C32—42no—
883C2×C32—82no—
884C2×C32C2×#23511yescharacteristic
885C2×C32C2×#23711yescharacteristic
886C2×C32#100411yescharacteristic
887C2×C32#100411yescharacteristic
888C2×C32#100411yescharacteristic
889C2×C32#100411yescharacteristic
890C2×C32C2×#23911yescharacteristic
891C2×C32#100911yescharacteristic
892C2×C32#100911yescharacteristic
893C3⋊D3—41no—
894C3⋊D3—41no—
895C3⋊D3—41no—
896C3⋊D3—41no—
897C3×D3—122no—
898C3×D3—122no—
899C3×D3—122no—
900C3×D3—121no—
901C3×D3—121no—
902C3×D3—121no—
903C3×D3—121no—
904C3×D3—121no—
905C3×D3—121no—
906C3×D3—121no—
907C3×D3—121no—
908C3×D3—241no—
909C24—91no—
910C2×Q8—91no—
911C2×D4—91no—
912C2×D4—91no—
913C2×D4—91no—
914C2×D4—91no—
915C2×D4—271no—
916C2×D4—271no—
917C2×D4—271no—
918C22×C4—91no—
919C22×C4—91no—
920C22×C4—91no—
921C22×C4—271no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C4⋊C4—91no—
926C4⋊C4—271no—
927C4⋊C4—271no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C22⋊C4—271no—
940C22⋊C4—271no—
941C22⋊C4#111311yescharacteristic
942C42—91no—
943C42—271no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—22no—
954C22×C3—22no—
955C22×C3—22no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3—42no—
964C22×C3—81no—
965C22×C3—81no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—181no—
969C22×C3—181no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3—181no—
973C22×C3—181no—
974C22×C3—181no—
975C22×C3—181no—
976C22×C3—181no—
977C22×C3—181no—
978C22×C3—364no—
979C22×C3#379512yes—
980C22×C3#379612yes—
981C22×C3#379912yes—
982C22×C3C22×D3211yescharacteristic
983C22×C3C22×D3211yescharacteristic
984C22×C3C22×D3211yescharacteristic
985C2×D3—62no—
986C2×D3—62no—
987C2×D3—62no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—121no—
1013C2×D3—121no—
1014C2×D3—121no—
1015C2×D3—121no—
1016C2×D3—121no—
1017C2×D3—121no—
1018C2×D3—121no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C2×D3—124no—
1022C2×D3—124no—
1023C2×D3—128no—
1024C3×C4—21no—
1025C3×C4—21no—
1026C3×C4—21no—
1027C3×C4—21no—
1028C3×C4—21no—
1029C3×C4—21no—
1030C3×C4—41no—
1031C3×C4—41no—
1032C3×C4—41no—
1033C3×C4—41no—
1034C3×C4—41no—
1035C3×C4—41no—
1036C3×C4—81no—
1037C3×C4—81no—
1038C3×C4—181no—
1039C3×C4—181no—
1040C3×C4—181no—
1041C3×C4—181no—
1042C3×C4—181no—
1043C3×C4—181no—
1044C3×C4—181no—
1045C3×C4—181no—
1046Dic3—62no—
1047Dic3—62no—
1048Dic3—62no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—61no—
1056Dic3—61no—
1057Dic3—61no—
1058Dic3—61no—
1059Dic3—61no—
1060Dic3—61no—
1061Dic3—61no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—121no—
1066Dic3—121no—
1067Dic3—121no—
1068Dic3—121no—
1069Dic3—121no—
1070C32—21no—
1071C32—21no—
1072C32—21no—
1073C32—41no—
1074C32#556011yescharacteristic, complemented
1075C32#559311yescharacteristic, complemented
1076C32#564411yescharacteristic, complemented
1077C23—91no—
1078C23—91no—
1079C23—91no—
1080C23—91no—
1081C23—182no—
1082C23—361no—
1083C23—361no—
1084C23C2×#111311yescharacteristic
1085Q8—361no—
1086D4—182no—
1087D4—182no—
1088D4—361no—
1089D4—361no—
1090D4—1081no—
1091D4—1081no—
1092D4—1081no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—91no—
1098C2×C4—91no—
1099C2×C4—91no—
1100C2×C4—91no—
1101C2×C4—361no—
1102C2×C4—361no—
1103C2×C4—361no—
1104C2×C4—1081no—
1105C2×C4C2×#111311yescharacteristic
1106C2×C4C2×#111311yescharacteristic
1107C2×C3—22no—
1108C2×C3—22no—
1109C2×C3—22no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—21no—
1113C2×C3—21no—
1114C2×C3—21no—
1115C2×C3—21no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—42no—
1120C2×C3—42no—
1121C2×C3—42no—
1122C2×C3—41no—
1123C2×C3—41no—
1124C2×C3—41no—
1125C2×C3—82no—
1126C2×C3—361no—
1127C2×C3—361no—
1128C2×C3—361no—
1129C2×C3—361no—
1130C2×C3C2×#379511yescharacteristic
1131C2×C3C2×#379611yescharacteristic
1132C2×C3C2×#379911yescharacteristic
1133C2×C3#6431311yescharacteristic
1134C2×C3#6431311yescharacteristic
1135C2×C3#6431411yescharacteristic
1136C2×C3#6431411yescharacteristic
1137C2×C3#6431411yescharacteristic
1138C2×C3#6431411yescharacteristic
1139D3—122no—
1140D3—122no—
1141D3—122no—
1142D3—121no—
1143D3—121no—
1144D3—121no—
1145D3—121no—
1146D3—121no—
1147D3—121no—
1148D3—121no—
1149D3—121no—
1150D3—241no—
1151C22—21no—
1152C22—21no—
1153C22—181no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—181no—
1158C22—181no—
1159C22—181no—
1160C22—181no—
1161C22—181no—
1162C22—181no—
1163C22—181no—
1164C22—181no—
1165C22—364no—
1166C22#8904112yes—
1167C22C22×#111311yescharacteristic
1168C4—21no—
1169C4—21no—
1170C4—181no—
1171C4—181no—
1172C4—181no—
1173C4—181no—
1174C4—181no—
1175C4—181no—
1176C4—181no—
1177C4—181no—
1178C3—21no—
1179C3—21no—
1180C3—21no—
1181C3—41no—
1182C3#1059417311yescharacteristic, complemented
1183C3#1059423811yescharacteristic, complemented
1184C3#1059424311yescharacteristic, complemented
1185C2—22no—
1186C2—361no—
1187C2—361no—
1188C2—361no—
1189C2—361no—
1190C2C2×#8904111yescharacteristic
1191C2#1172462311yescharacteristic
1192C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64091C2semidirect
2. C3×#64090C2semidirect
3. C3×#64087C2semidirect
4. #11723727C2semidirect
5. #11723726C2semidirect
6. C2×#88814C2semidirect
7. #11723717C2semidirect
8. #11723696C2semidirect
9. #11723694C2semidirect
10. #11723687C2semidirect
11. #11723686C2semidirect
12. #11723677C2semidirect
13. #11723676C2semidirect
14. #11723675C2semidirect
15. #11723670C2semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×#634C22semidirect
30. C2×#6295C22semidirect
31. C2×#6294C22semidirect
36. C3×#3752C22semidirect
37. C3×C4⋊(C3⋊Dic3)C22semidirect
38. C3×#3750C22semidirect
39. C3×#3750C22semidirect
40. C3×#3750C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
50. #88814C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88813C22semidirect
54. #64091D3semidirect
55. #64090D3semidirect
56. #64087D3semidirect
145. C2×C4×C3⋊D3C2×D3semidirect
146. C2×#634C2×D3semidirect
193. #3752C2×D3semidirect
194. C4⋊(C3⋊Dic3)C2×D3semidirect
195. #3750C2×D3semidirect
196. #3750C2×D3semidirect
197. #3750C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
739. C33#538semidirect
1074. C32#5560semidirect
1075. C32#5593semidirect
1076. C32#5644semidirect
1182. C3#10594173semidirect
1183. C3#10594238semidirect
1184. C3#10594243semidirect

Maximal subgroups

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

subgroupindex
C3×#640912
C3×#640902
C3×#640872
#117237272
#117237262
C2×#888142
#117237172
#117236962
#117236942
#117236872
#117236862
#117236772
#117236762
#117236752
#117236702
#105942433
#105942383
#105941733