Finite Group Databasebeta

← #13169187

Subgroups — #13169187

Order 1728.

1302 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723696C211yesmaximal, characteristic, complemented
2#11723541C211yesmaximal, characteristic, complemented
3#11723417C211yesmaximal, characteristic, complemented
4#11723403C211yesmaximal, characteristic, complemented
5C3×#63897C211yesmaximal, characteristic, complemented
6C3×#63893C211yesmaximal, characteristic, complemented
7C3×#63881C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723007C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11722961C211yesmaximal, characteristic, complemented
12#11722960C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722930C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10594650—31nomaximal
17#10594639—31nomaximal
18#10594243—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic
23C2×#6295C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32#88859C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic, complemented
36C32×Dic3⋊C4C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic, complemented
39#88807C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64107—31no—
55#64103—31no—
56#64091—31no—
57C3×#897—31no—
58C3×#894—31no—
59C3×#894—31no—
60C3×#893—31no—
61C3×#67⋊C4—31no—
62C3×#878—31no—
63#63981—31no—
64#63978—31no—
65C2×#3722—31no—
66#63952—31no—
67#63923—31no—
68#63922—31no—
69#63922—31no—
70#63922—31no—
71#63922—61no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63916—31no—
75#63915—31no—
76#63910—31no—
77#63909—31no—
78#63909—31no—
79#63908—31no—
80#63907—31no—
81#63907—31no—
82#63907—31no—
83#63906—31no—
84#63906—31no—
85C4×#625—31no—
86#63897D311yescharacteristic, complemented
87#63893D311yescharacteristic, complemented
88#63885—31no—
89#63881D311yescharacteristic, complemented
90#63879—31no—
91#63868—31no—
92#63864—31no—
93#63859—31no—
94#63858—31no—
95#63852—31no—
96#63850—31no—
97#63850—31no—
98#63850—61no—
99#63848—31no—
100#63848—31no—
101#63848—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C3×C4⋊(C3⋊D3)—41no—
116C3×C4×C3⋊D3—41no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6295—41no—
123#6295—41no—
124#6292—41no—
125#6292—41no—
126#6290—22no—
127C3×#627—41no—
128C3×#626—22no—
129C3×#624—41no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5644—91no—
134#5560—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×#638—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
144C2×C3×#67—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—61no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
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×Dic6—31no—
159C2×C3×Dic6—31no—
160C2×#627C2×D311yescharacteristic, complemented
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—61no—
170C2×#626—61no—
171C2×#626C2×D311yescharacteristic
172C2×#625—31no—
173C2×#625—31no—
174C2×#625—31no—
175C2×#625—31no—
176C2×#625—61no—
177C2×#624C2×D311yescharacteristic, complemented
178C2×D3×Dic3C2×D311yescharacteristic
179C2×D3×Dic3C2×D311yescharacteristic
180C32×C4⋊C4—31no—
181C32×C4⋊C4—31no—
182C32×C22⋊C4—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—61no—
192#3752—61no—
193#3752—61no—
194#3752—121no—
195C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
196#3750—31no—
197#3750—31no—
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×(C2×D3)⋊C4—21no—
201C3×(C2×D3)⋊C4—31no—
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—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4C2×D311yescharacteristic
211C3×(C2×D3)⋊C4C2×D311yescharacteristic
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—61no—
216C3×Dic3⋊C4—21no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4C2×D311yescharacteristic, complemented
220C3×Dic3⋊C4C2×D311yescharacteristic, complemented
221C3×Dic3⋊C4C2×D311yescharacteristic, complemented
222C3×Dic3⋊C4C2×D311yescharacteristic, complemented
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225#3724—31no—
226#3724—31no—
227#3724—61no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic, complemented
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—61no—
241#3722—61no—
242#3722—61no—
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic
245#3722C2×D311yescharacteristic, complemented
246#3722C2×D311yescharacteristic, complemented
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—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
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×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3#4112yes—
278D3×C3⋊D3—44no—
279C33×C4—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#123—91no—
290C3×C22⋊Q8—91no—
291C3×C4×D4—91no—
292#947—91no—
293#947—91no—
294#939—91no—
295#938—91no—
296#937—91no—
297#937—91no—
298#930—91no—
299#930—91no—
300#930—91no—
301#929—91no—
302C4×#67—91no—
303C4×#67—91no—
304C2×(C2×D3)⋊C4—91no—
305C2×(C2×D3)⋊C4—91no—
306#898—91no—
307#898—91no—
308#898—91no—
309#898—91no—
310#898—181no—
311#897—31no—
312#895—91no—
313#895—91no—
314#894—31no—
315#894—31no—
316#894—91no—
317#894—91no—
318#894—181no—
319#893—31no—
320#885—91no—
321#885—91no—
322#885—91no—
323#884—91no—
324#884—91no—
325#882—91no—
326#882—91no—
327#882—91no—
328#882—91no—
329#882—181no—
330#67⋊C4—31no—
331#67⋊C4—91no—
332D3×C22⋊C4—91no—
333#879—91no—
334#878—31no—
335#876—91no—
336#875—91no—
337C23×C32—31no—
338C22×C3⋊D3—31no—
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—61no—
342C22×C3⋊D3—61no—
343C22×C3⋊D3—61no—
344C22×C3⋊D3—62no—
345C22×C3⋊D3—121no—
346C22×C3⋊D3—121no—
347C22×C3⋊D3—121no—
348C22×C3⋊D3C22×D311yescharacteristic
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
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—61no—
359C22×C3×D3—61no—
360C22×C3×D3—61no—
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×D32—62no—
364C2×D32—62no—
365C2×D32—122no—
366C2×D32—121no—
367C2×D32—121no—
368C2×D32—121no—
369C2×D32—121no—
370C2×D32—122no—
371C2×D32—122no—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—41no—
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383C2×C32×C4C22×D311yescharacteristic
384#638—62no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—31no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C4⋊(C3⋊D3)—41no—
396C4⋊(C3⋊D3)—121no—
397C4⋊(C3⋊D3)—121no—
398C4×C3⋊D3—41no—
399C3×#67—62no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
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—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—121no—
415C2×C3×Dic3—121no—
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C3×D12—62no—
427C3×D12—121no—
428C3×D12—121no—
429C3×D12—122no—
430C3×C4×D3—121no—
431C3×C4×D3—121no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434C3×C4×D3—121no—
435C3×C4×D3—121no—
436C3×C4×D3—122no—
437C3×Dic6—121no—
438C3×Dic6—121no—
439#627—41no—
440#626—22no—
441#626—121no—
442#626—121no—
443#626—121no—
444#626—121no—
445#626—122no—
446#626—122no—
447#626—121no—
448#626—121no—
449#626—121no—
450#626—121no—
451#625—62no—
452#625—62no—
453#625—122no—
454#625—121no—
455#625—121no—
456#624—41no—
457D3×Dic3—41no—
458D3×Dic3—41no—
459#538—271noSylow
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3⋊(C3⋊D3)—41no—
464C3×C3⋊D3—41no—
465C3×C3⋊D3—41no—
466C3×C3⋊D3—41no—
467C32×D3—22no—
468C23×D3—91no—
469C23×D3—91no—
470C23×D3—91no—
471C23×D3—181no—
472C2×C3×Q8—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C22×C3×C4—91no—
476C22×C3×C4—91no—
477C22×C3×C4—91no—
478C22×C3×C4—91no—
479C2×#67—31no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—181no—
490C22×Dic3—31no—
491C22×Dic3—31no—
492C2×D12—31no—
493C2×D12—31no—
494C2×D12—31no—
495C2×D12—61no—
496C2×D12—91no—
497C2×D12—91no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—181no—
503C2×D12—181no—
504C2×C4×D3—31no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×C4×D3—31no—
510C2×C4×D3—61no—
511C2×Dic6—31no—
512C2×Dic6—31no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—31no—
515C3×C4⋊C4—31no—
516C3×C4⋊C4—31no—
517C3×C4⋊C4—61no—
518C3×C4⋊C4—61no—
519C3×C4⋊C4—91no—
520C3×C4⋊C4—91no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—31no—
523C3×C22⋊C4—61no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C42—91no—
530#217—31no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—31no—
539(C2×D3)⋊C4—31no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
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)⋊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—181no—
565(C2×D3)⋊C4—181no—
566(C2×D3)⋊C4—181no—
567(C2×D3)⋊C4—181no—
568(C2×D3)⋊C4—181no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4—181no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—361no—
573(C2×D3)⋊C4D3211yescharacteristic
574C4⋊Dic3—31no—
575C4⋊Dic3—31no—
576C4⋊Dic3—31no—
577C4⋊Dic3—61no—
578C4⋊Dic3—91no—
579Dic3⋊C4—31no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—181no—
586Dic3⋊C4—181no—
587Dic3⋊C4D3211yescharacteristic, complemented
588Dic3⋊C4D3211yescharacteristic, complemented
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—32no—
599C22×C32—41no—
600C22×C32—61no—
601C22×C32—61no—
602C22×C32C23×D311yescharacteristic
603C22×C32C23×D311yescharacteristic
604C22×C32C23×D311yescharacteristic
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—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—124no—
634C2×C3⋊D3—241no—
635C2×C3⋊D3—241no—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—22no—
641C2×C3×D3—41no—
642C2×C3×D3—41no—
643C2×C3×D3—62no—
644C2×C3×D3—62no—
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—121no—
664C2×C3×D3—121no—
665C2×C3×D3—121no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3#23512yes—
671C2×C3×D3#23912yes—
672D32—124no—
673D32—124no—
674D32—128no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—41no—
679C32×C4—41no—
680C32×C4—41no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C32×C4—81no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—61no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—241no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—271no—
722#126—271no—
723#124—271no—
724#124—271no—
725#123—91no—
726#123—271no—
727C22⋊Q8—91no—
728#121—271no—
729#121—271no—
730#121—271no—
731#120—271no—
732#120—271no—
733C4×D4—91no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—61no—
740C23×C3—91no—
741C23×C3—91no—
742C23×C3—91no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—31no—
749C22×D3—61no—
750C22×D3—61no—
751C22×D3—61no—
752C22×D3—91no—
753C22×D3—91no—
754C22×D3—91no—
755C22×D3—181no—
756C22×D3—181no—
757C22×D3—181no—
758C22×D3—182no—
759C22×D3—182no—
760C22×D3—182no—
761C22×D3—361no—
762C22×D3—362no—
763C22×D3—361no—
764C22×D3—361no—
765C22×D3—361no—
766C22×D3—361no—
767C22×D3—361no—
768C22×D3—361no—
769C22×D3—362no—
770C22×D3—362no—
771C22×D3C2×D3211yescharacteristic
772C3×Q8—361no—
773C3×D4—182no—
774C3×D4—361no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—41no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—91no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799C2×C3×C4—361no—
800C2×C3×C4—361no—
801C2×C3×C4C2×D3211yescharacteristic
802C2×C3×C4C2×D3211yescharacteristic
803C2×C3×C4C2×D3211yescharacteristic
804#67—62no—
805#67—182no—
806#67—182no—
807#67—182no—
808#67—362no—
809#67—361no—
810#67—361no—
811#67—361no—
812#67—361no—
813#67—361no—
814#67—361no—
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—91no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—121no—
828C2×Dic3—121no—
829C2×Dic3—181no—
830C2×Dic3—181no—
831C2×Dic3—181no—
832C2×Dic3—361no—
833C2×Dic3C2×D3211yescharacteristic
834C2×Dic3C2×D3211yescharacteristic
835C2×Dic3C2×D3211yescharacteristic
836C2×Dic3C2×D3211yescharacteristic
837C2×Dic3C2×D3211yescharacteristic
838D12—62no—
839D12—121no—
840D12—121no—
841D12—122no—
842D12—361no—
843D12—361no—
844D12—361no—
845D12—361no—
846D12—362no—
847D12—362no—
848D12—361no—
849D12—361no—
850C4×D3—121no—
851C4×D3—121no—
852C4×D3—121no—
853C4×D3—121no—
854C4×D3—121no—
855C4×D3—121no—
856C4×D3—122no—
857Dic6—121no—
858Dic6—121no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—62no—
872C2×C32C2×#23511yescharacteristic
873C2×C32#100411yescharacteristic
874C2×C32#100411yescharacteristic
875C2×C32#100411yescharacteristic
876C2×C32C2×#23911yescharacteristic
877C2×C32D3×#4111yescharacteristic
878C2×C32#100911yescharacteristic
879C2×C32#100911yescharacteristic
880C2×C32#100911yescharacteristic
881C3⋊D3—41no—
882C3⋊D3—41no—
883C3⋊D3—41no—
884C3⋊D3—121no—
885C3⋊D3—122no—
886C3⋊D3—121no—
887C3⋊D3—121no—
888C3⋊D3—241no—
889C3⋊D3—241no—
890C3⋊D3—242no—
891C3×D3—22no—
892C3×D3—22no—
893C3×D3—42no—
894C3×D3—122no—
895C3×D3—122no—
896C3×D3—121no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—121no—
902C3×D3—241no—
903C24—271no—
904C2×Q8—91no—
905C2×D4—91no—
906C2×D4—91no—
907C2×D4—271no—
908C2×D4—271no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—91no—
915C22×C4—91no—
916C4⋊C4—31no—
917C4⋊C4—31no—
918C4⋊C4—91no—
919C4⋊C4—91no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C22⋊C4—31no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C42—91no—
937C42—271no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—32no—
942C22×C3—32no—
943C22×C3—41no—
944C22×C3—62no—
945C22×C3—61no—
946C22×C3—61no—
947C22×C3—61no—
948C22×C3—61no—
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×C3—181no—
958C22×C3—181no—
959C22×C3—181no—
960C22×C3C22×D3211yescharacteristic
961C22×C3C22×D3211yescharacteristic
962C22×C3C22×D3211yescharacteristic
963C2×D3—21no—
964C2×D3—21no—
965C2×D3—62no—
966C2×D3—62no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—61no—
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—61no—
984C2×D3—61no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—182no—
993C2×D3—181no—
994C2×D3—181no—
995C2×D3—181no—
996C2×D3—181no—
997C2×D3—181no—
998C2×D3—181no—
999C2×D3—181no—
1000C2×D3—181no—
1001C2×D3—181no—
1002C2×D3—361no—
1003C2×D3—361no—
1004C2×D3—361no—
1005C2×D3—361no—
1006C2×D3—361no—
1007C2×D3—361no—
1008C2×D3—361no—
1009C2×D3—361no—
1010C2×D3—362no—
1011C2×D3—364no—
1012C2×D3—364no—
1013C2×D3—364no—
1014C2×D3—368no—
1015C2×D3—721no—
1016C2×D3—721no—
1017C2×D3#379912yes—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—41no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—61no—
1033C3×C4—61no—
1034C3×C4—81no—
1035C3×C4—121no—
1036C3×C4—121no—
1037C3×C4—121no—
1038C3×C4—121no—
1039C3×C4—121no—
1040C3×C4—181no—
1041C3×C4—181no—
1042C3×C4—181no—
1043Dic3—21no—
1044Dic3—21no—
1045Dic3—21no—
1046Dic3—21no—
1047Dic3—21no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—121no—
1055Dic3—121no—
1056Dic3—121no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—721no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#556011yescharacteristic, complemented
1069C32#564411yescharacteristic, complemented
1070C32#565711yescharacteristic, complemented
1071C23—31no—
1072C23—91no—
1073C23—91no—
1074C23—91no—
1075C23—271no—
1076C23—542no—
1077C23—1081no—
1078C23—1081no—
1079Q8—361no—
1080D4—182no—
1081D4—361no—
1082D4—542no—
1083D4—1081no—
1084D4—1081no—
1085D4—1081no—
1086D4—1081no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—271no—
1096C2×C4—361no—
1097C2×C4—361no—
1098C2×C4—361no—
1099C2×C4—361no—
1100C2×C4D3311yescharacteristic
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—41no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—62no—
1114C2×C3—62no—
1115C2×C3—122no—
1116C2×C3—361no—
1117C2×C3—361no—
1118C2×C3—361no—
1119C2×C3C2×#379911yescharacteristic
1120C2×C3D3×#23511yescharacteristic
1121C2×C3#6430711yescharacteristic
1122C2×C3#6431311yescharacteristic
1123C2×C3#6431411yescharacteristic
1124C2×C3#6431411yescharacteristic
1125C2×C3#6431411yescharacteristic
1126C2×C3D3×#23911yescharacteristic
1127C2×C3#6432011yescharacteristic
1128D3—22no—
1129D3—122no—
1130D3—122no—
1131D3—121no—
1132D3—121no—
1133D3—121no—
1134D3—121no—
1135D3—121no—
1136D3—121no—
1137D3—241no—
1138D3—362no—
1139D3—361no—
1140D3—361no—
1141D3—361no—
1142D3—721no—
1143D3—721no—
1144D3—722no—
1145C22—32no—
1146C22—61no—
1147C22—61no—
1148C22—181no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22—181no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—541no—
1158C22—541no—
1159C22—541no—
1160C22—1084no—
1161C22C2×D3311yescharacteristic
1162C4—21no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—61no—
1167C4—61no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—541no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059424311yescharacteristic, complemented
1177C3#1059463911yescharacteristic, complemented
1178C3#1059465011yescharacteristic, complemented
1179C2—62no—
1180C2—361no—
1181C2—361no—
1182C2—361no—
1183C2—1081no—
1184C2D3×#379911yescharacteristic
1185C2#1172438511yescharacteristic
1186C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723696C2semidirect
2. #11723541C2semidirect
3. #11723417C2semidirect
4. #11723403C2semidirect
5. C3×#63897C2semidirect
6. C3×#63893C2semidirect
7. C3×#63881C2semidirect
8. #11723024C2semidirect
9. #11723007C2semidirect
10. #11723003C2semidirect
11. #11722961C2semidirect
12. #11722960C2semidirect
13. #11722950C2semidirect
14. #11722930C2semidirect
15. D3×#3722C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
23. C2×#6295C22semidirect
27. C2×C3×#627C22semidirect
29. C2×C3×#624C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
35. C32×Dic3⋊C4C22semidirect
36. C32×Dic3⋊C4C22semidirect
38. #88814C22semidirect
39. #88807C22semidirect
40. #88806C22semidirect
45. #88803C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
86. #63897D3semidirect
87. #63893D3semidirect
89. #63881D3semidirect
143. C2×C4×C3⋊D3C2×D3semidirect
160. C2×#627C2×D3semidirect
177. C2×#624C2×D3semidirect
195. C4⋊(C3⋊Dic3)C2×D3semidirect
219. C3×Dic3⋊C4C2×D3semidirect
220. C3×Dic3⋊C4C2×D3semidirect
221. C3×Dic3⋊C4C2×D3semidirect
222. C3×Dic3⋊C4C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
245. #3722C2×D3semidirect
246. #3722C2×D3semidirect
261. Dic32C2×D3semidirect
587. Dic3⋊C4D32semidirect
588. Dic3⋊C4D32semidirect
736. C33#538semidirect
1068. C32#5560semidirect
1069. C32#5644semidirect
1070. C32#5657semidirect
1176. C3#10594243semidirect
1177. C3#10594639semidirect
1178. C3#10594650semidirect

Maximal subgroups

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

subgroupindex
#117236962
#117235412
#117234172
#117234032
C3×#638972
C3×#638932
C3×#638812
#117230242
#117230072
#117230032
#117229612
#117229602
#117229502
#117229302
D3×#37222
#105946503
#105946393
#105942433