Finite Group Databasebeta

← #13168096

Subgroups — #13168096

Order 1728.

1258 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723687C211yesmaximal, characteristic, complemented
2#11723523C211yesmaximal, characteristic, complemented
3Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#11723430C211yesmaximal, characteristic, complemented
5C3×#63923C211yesmaximal, characteristic, complemented
6C3×#63859C211yesmaximal, characteristic, complemented
7C3×#63852C211yesmaximal, characteristic, complemented
8#11723001C211yesmaximal, characteristic, complemented
9#11722991C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722947C211yesmaximal, characteristic, complemented
14#11722938C211yesmaximal, characteristic, complemented
15#11722902C211yesmaximal, characteristic, complemented
16#10594127—31nomaximal
17#10594122—31nomaximal
18#10594019—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6290C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
27C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic, complemented
34C3×#3750C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×C4×Dic3C2211yescharacteristic, complemented
38#88814C2211yescharacteristic, complemented
39#88807C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic, complemented
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64092—31no—
55#64088—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×#885—31no—
58C3×#882—31no—
59C3×#882—31no—
60C3×#879—31no—
61C3×#876—31no—
62C3×#875—31no—
63#63977—31no—
64#63976—31no—
65#63971—31no—
66#63970—31no—
67#63969—31no—
68D3×#217—31no—
69D3×#217—31no—
70#63959—31no—
71#63923D311yescharacteristic, complemented
72#63922—31no—
73#63921—31no—
74#63916—31no—
75#63912—31no—
76#63910—31no—
77#63907—31no—
78#63902—31no—
79#63899—31no—
80Dic3×D12—31no—
81Dic3×D12—31no—
82Dic3×D12—61no—
83#63891—31no—
84#63891—31no—
85#63891—61no—
86#63888—31no—
87#63887—31no—
88#63886—31no—
89#63886—31no—
90#63885—31no—
91#63885—31no—
92#63884—31no—
93#63881—31no—
94#63881—31no—
95#63863—31no—
96#63861—31no—
97#63861—31no—
98#63861—61no—
99#63859D311yescharacteristic, complemented
100#63853—31no—
101#63852D311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×C4⋊(C3⋊D3)—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—22no—
122#6295—41no—
123#6294—41no—
124#6290—41no—
125Dic3×C3⋊D3—41no—
126Dic3×C3⋊D3—41no—
127Dic3×C3⋊D3—41no—
128C3×#627—41no—
129C3×#626—41no—
130C3×#626—41no—
131C3×#626—41no—
132#5704—91no—
133#5678—91no—
134#5593—91no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C2×D311yescharacteristic
138C2×#638—31no—
139C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—31no—
151C2×C3×D12—61no—
152C2×C3×Dic6—31no—
153C2×C3×Dic6—31no—
154C2×#627C2×D311yescharacteristic, complemented
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626C2×D311yescharacteristic
160C2×#626C2×D311yescharacteristic
161C2×#626C2×D311yescharacteristic
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—61no—
167C2×#624—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—61no—
177C2×D3×Dic3—61no—
178C2×D3×Dic3—61no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C42—31no—
182#3757—31no—
183#3757—31no—
184#3757—31no—
185#3752—31no—
186#3752—31no—
187#3752C2×D311yescharacteristic, complemented
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)—31no—
190C4⋊(C3⋊Dic3)—31no—
191C4⋊(C3⋊Dic3)—61no—
192C4⋊(C3⋊Dic3)—61no—
193C4⋊(C3⋊Dic3)—61no—
194C4⋊(C3⋊Dic3)—121no—
195#3750—31no—
196#3750—31no—
197#3750C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×(C2×D3)⋊C4—21no—
203C3×(C2×D3)⋊C4—21no—
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)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—61no—
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×(C2×D3)⋊C4C2×D311yescharacteristic
216C3×(C2×D3)⋊C4C2×D311yescharacteristic
217C3×(C2×D3)⋊C4C2×D311yescharacteristic
218C3×C4⋊Dic3—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—61no—
225C3×C4×Dic3—21no—
226C3×C4×Dic3C2×D311yescharacteristic, complemented
227C3×C4×Dic3C2×D311yescharacteristic, complemented
228#3724—31no—
229#3724—31no—
230#3724—61no—
231#3724C2×D311yescharacteristic, complemented
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3C2×D311yescharacteristic, complemented
236#3722—31no—
237#3722C2×D311yescharacteristic
238#3722C2×D311yescharacteristic, complemented
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—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—61no—
252(C2×D3)⋊Dic3—61no—
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
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
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#4112yes—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C3×D32—44no—
279C33×C4—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—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#124—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#947—91no—
295#946—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#898—91no—
305#896—91no—
306#895—91no—
307#895—91no—
308#894—91no—
309#893—91no—
310#886—91no—
311#885—31no—
312#885—91no—
313#884—91no—
314#884—91no—
315#884—91no—
316#883—91no—
317#883—91no—
318#883—91no—
319#883—181no—
320#882—31no—
321#882—31no—
322#882—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325D3×C22⋊C4—91no—
326D3×C22⋊C4—91no—
327#879—31no—
328#879—91no—
329#879—91no—
330#879—181no—
331#878—91no—
332#876—31no—
333#875—31no—
334C4×D12—91no—
335C4×D12—91no—
336C4×D12—181no—
337C23×C32—31no—
338C23×C32—31no—
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3⋊D3C22×D311yescharacteristic
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—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C22×C3×D3—62no—
354C22×C3×D3—62no—
355C22×C3×D3—121no—
356C22×C3×D3—121no—
357C22×C3×D3—121no—
358C22×C3×D3—121no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C2×D32—22no—
364C2×D32—41no—
365C2×D32—41no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—41no—
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377#638—121no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C4⋊(C3⋊D3)—22no—
396C4×C3⋊D3—121no—
397C4×C3⋊D3—121no—
398C4×C3⋊D3—121no—
399C3×#67—121no—
400C3×#67—121no—
401C3×#67—121no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3C22×D311yescharacteristic
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
423C3×D12—62no—
424C3×D12—62no—
425C3×D12—64no—
426C3×D12—121no—
427C3×D12—121no—
428C3×D12—121no—
429C3×Dic6—121no—
430C3×Dic6—121no—
431#627—41no—
432#626—41no—
433#626—41no—
434#626—41no—
435#626—62no—
436#626—62no—
437#626—121no—
438#626—121no—
439#625—62no—
440#625—121no—
441#625—121no—
442#625—121no—
443#625—122no—
444#624—121no—
445D3×Dic3—121no—
446D3×Dic3—121no—
447D3×Dic3—121no—
448D3×Dic3—121no—
449D3×Dic3—121no—
450D3×Dic3—121no—
451D3×Dic3—122no—
452D3×Dic3—122no—
453D3×Dic3—122no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456#538—271noSylow
457C2×C33C2×#4111yescharacteristic
458C2×C33H(5,𝔽2)11yescharacteristic
459C2×C33H(5,𝔽2)11yescharacteristic
460C3×C3⋊D3—22no—
461C3×C3⋊D3—41no—
462C3×C3⋊D3—41no—
463C32×D3—41no—
464C32×D3—41no—
465C24×C3—91no—
466C23×D3—31no—
467C23×D3—31no—
468C2×C3×Q8—91no—
469C2×C3×D4—91no—
470C2×C3×D4—91no—
471C2×C3×D4—91no—
472C2×C3×D4—91no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—181no—
484C22×Dic3—91no—
485C22×Dic3—91no—
486C22×Dic3—91no—
487C22×Dic3—91no—
488C2×D12—31no—
489C2×D12—31no—
490C2×D12—31no—
491C2×D12—31no—
492C2×D12—31no—
493C2×D12—61no—
494C2×D12—91no—
495C2×D12—91no—
496C2×C4×D3—91no—
497C2×C4×D3—91no—
498C2×C4×D3—91no—
499C2×C4×D3—91no—
500C2×C4×D3—91no—
501C2×C4×D3—91no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—181no—
505C2×C4×D3—181no—
506C2×C4×D3—181no—
507C2×Dic6—31no—
508C2×Dic6—31no—
509C3×C4⋊C4—91no—
510C3×C4⋊C4—91no—
511C3×C4⋊C4—91no—
512C3×C22⋊C4—31no—
513C3×C22⋊C4—31no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—61no—
517C3×C22⋊C4—61no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C42—31no—
525C3×C42—31no—
526C3×C42—61no—
527#217—31no—
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—91no—
539#217—181no—
540#217—181no—
541#217—181no—
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—31no—
551(C2×D3)⋊C4—61no—
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—181no—
562(C2×D3)⋊C4—181no—
563(C2×D3)⋊C4D3211yescharacteristic
564(C2×D3)⋊C4D3211yescharacteristic
565C4⋊Dic3—31no—
566C4⋊Dic3—91no—
567C4⋊Dic3—91no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—181no—
571C4⋊Dic3—181no—
572C4⋊Dic3—181no—
573C4⋊Dic3—361no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—61no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—181no—
586Dic3⋊C4—181no—
587C4×Dic3—91no—
588C4×Dic3—91no—
589C4×Dic3—91no—
590C4×Dic3—181no—
591C4×Dic3D3211yescharacteristic, complemented
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×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#23712yes—
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—32no—
627C2×C3×D3—32no—
628C2×C3×D3—41no—
629C2×C3×D3—41no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—62no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—62no—
640C2×C3×D3—62no—
641C2×C3×D3—61no—
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—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658C2×C3×D3—121no—
659C2×C3×D3—124no—
660C2×C3×D3—124no—
661D32—44no—
662C32×C4—21no—
663C32×C4—22no—
664C32×C4—21no—
665C32×C4—21no—
666C32×C4—41no—
667C32×C4—41no—
668C32×C4—42no—
669C32×C4—61no—
670C32×C4—61no—
671C32×C4—61no—
672C32×C4—61no—
673C3⋊Dic3—21no—
674C3⋊Dic3—21no—
675C3⋊Dic3—21no—
676C3⋊Dic3—61no—
677C3⋊Dic3—61no—
678C3⋊Dic3—61no—
679C3⋊Dic3—61no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—121no—
683C3⋊Dic3—121no—
684C3⋊Dic3—121no—
685C3⋊Dic3—121no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—241no—
689C3⋊Dic3—241no—
690C3×Dic3—22no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—41no—
700C3×Dic3—41no—
701C3×Dic3—41no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—121no—
709C3×Dic3—121no—
710C3×Dic3—121no—
711#126—91no—
712#126—271no—
713#124—91no—
714#124—271no—
715#123—271no—
716#123—271no—
717C22⋊Q8—271no—
718#121—271no—
719#121—271no—
720#121—271no—
721#120—91no—
722#120—271no—
723C4×D4—271no—
724C4×D4—271no—
725C2×C22⋊C4—271no—
726C33#53811yescharacteristic, complemented, Sylow
727C23×C3—31no—
728C23×C3—31no—
729C23×C3—31no—
730C23×C3—31no—
731C23×C3—61no—
732C23×C3—61no—
733C23×C3—91no—
734C23×C3—91no—
735C23×C3—91no—
736C23×C3—182no—
737C23×C3—361no—
738C23×C3—361no—
739C22×D3—31no—
740C22×D3—31no—
741C22×D3—31no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—61no—
746C22×D3—61no—
747C22×D3—61no—
748C22×D3—62no—
749C22×D3—62no—
750C22×D3—121no—
751C22×D3—121no—
752C22×D3—121no—
753C22×D3—121no—
754C22×D3C2×D3211yescharacteristic
755C22×D3C2×D3211yescharacteristic
756C3×Q8—361no—
757C3×D4—182no—
758C3×D4—361no—
759C3×D4—361no—
760C3×D4—361no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—41no—
773C2×C3×C4—61no—
774C2×C3×C4—61no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4C2×D3211yescharacteristic
781C2×C3×C4C2×D3211yescharacteristic
782C2×C3×C4C2×D3211yescharacteristic
783#67—121no—
784#67—121no—
785#67—121no—
786#67—182no—
787#67—182no—
788#67—361no—
789#67—361no—
790#67—361no—
791#67—361no—
792#67—361no—
793#67—362no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—61no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—91no—
804C2×Dic3—91no—
805C2×Dic3—91no—
806C2×Dic3—91no—
807C2×Dic3—91no—
808C2×Dic3—91no—
809C2×Dic3—181no—
810C2×Dic3—181no—
811C2×Dic3—181no—
812C2×Dic3—181no—
813C2×Dic3—181no—
814C2×Dic3—181no—
815C2×Dic3—361no—
816C2×Dic3—361no—
817C2×Dic3—361no—
818C2×Dic3—361no—
819C2×Dic3—361no—
820C2×Dic3—361no—
821C2×Dic3C2×D3211yescharacteristic
822C2×Dic3C2×D3211yescharacteristic
823C2×Dic3C2×D3211yescharacteristic
824C2×Dic3C2×D3211yescharacteristic
825D12—62no—
826D12—62no—
827D12—64no—
828D12—121no—
829D12—121no—
830D12—121no—
831D12—182no—
832D12—361no—
833C4×D3—361no—
834C4×D3—361no—
835C4×D3—361no—
836C4×D3—361no—
837C4×D3—361no—
838C4×D3—361no—
839C4×D3—361no—
840C4×D3—361no—
841C4×D3—362no—
842C4×D3—362no—
843C4×D3—362no—
844Dic6—121no—
845Dic6—121no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—21no—
854C2×C32—21no—
855C2×C32—41no—
856C2×C32—41no—
857C2×C32—41no—
858C2×C32—121no—
859C2×C32—121no—
860C2×C32C2×#23711yescharacteristic
861C2×C32#100411yescharacteristic
862C2×C32#100411yescharacteristic
863C2×C32#100411yescharacteristic
864C2×C32D3×#4111yescharacteristic
865C2×C32D3×#4111yescharacteristic
866C2×C32#100911yescharacteristic
867C2×C32#100911yescharacteristic
868C2×C32#100911yescharacteristic
869C3⋊D3—22no—
870C3⋊D3—41no—
871C3⋊D3—41no—
872C3×D3—41no—
873C3×D3—41no—
874C3×D3—41no—
875C3×D3—41no—
876C3×D3—62no—
877C3×D3—62no—
878C3×D3—81no—
879C3×D3—81no—
880C3×D3—122no—
881C3×D3—122no—
882C3×D3—122no—
883C3×D3—121no—
884C3×D3—121no—
885C3×D3—121no—
886C3×D3—121no—
887C24—91no—
888C2×Q8—91no—
889C2×D4—91no—
890C2×D4—91no—
891C2×D4—91no—
892C2×D4—91no—
893C2×D4—271no—
894C2×D4—271no—
895C2×D4—271no—
896C22×C4—271no—
897C22×C4—271no—
898C22×C4—271no—
899C22×C4—271no—
900C4⋊C4—91no—
901C4⋊C4—91no—
902C4⋊C4—91no—
903C4⋊C4—271no—
904C4⋊C4—271no—
905C4⋊C4—271no—
906C22⋊C4—31no—
907C22⋊C4—31no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—91no—
913C22⋊C4—91no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C22⋊C4—271no—
917C22⋊C4—271no—
918C22⋊C4—271no—
919C22⋊C4—271no—
920C42—31no—
921C42—271no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—41no—
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—92no—
939C22×C3—121no—
940C22×C3—121no—
941C22×C3—121no—
942C22×C3—121no—
943C22×C3—121no—
944C22×C3—121no—
945C22×C3—181no—
946C22×C3—181no—
947C22×C3—181no—
948C22×C3—181no—
949C22×C3—181no—
950C22×C3—181no—
951C22×C3—181no—
952C22×C3—181no—
953C22×C3—364no—
954C22×C3C22×D3211yescharacteristic
955C22×C3C22×D3211yescharacteristic
956C22×C3C22×D3211yescharacteristic
957C2×D3—21no—
958C2×D3—21no—
959C2×D3—21no—
960C2×D3—21no—
961C2×D3—21no—
962C2×D3—21no—
963C2×D3—32no—
964C2×D3—32no—
965C2×D3—62no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—62no—
971C2×D3—62no—
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—121no—
985C2×D3—121no—
986C2×D3—121no—
987C2×D3—121no—
988C2×D3—121no—
989C2×D3—121no—
990C2×D3—124no—
991C2×D3—124no—
992C3×C4—22no—
993C3×C4—21no—
994C3×C4—21no—
995C3×C4—21no—
996C3×C4—41no—
997C3×C4—41no—
998C3×C4—42no—
999C3×C4—62no—
1000C3×C4—61no—
1001C3×C4—61no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—121no—
1009C3×C4—121no—
1010C3×C4—121no—
1011C3×C4—181no—
1012C3×C4—181no—
1013C3×C4—181no—
1014Dic3—21no—
1015Dic3—21no—
1016Dic3—21no—
1017Dic3—21no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—121no—
1025Dic3—121no—
1026Dic3—121no—
1027Dic3—181no—
1028Dic3—181no—
1029Dic3—181no—
1030Dic3—181no—
1031Dic3—181no—
1032Dic3—181no—
1033Dic3—361no—
1034Dic3—361no—
1035Dic3—361no—
1036Dic3—361no—
1037Dic3—361no—
1038Dic3—361no—
1039Dic3—721no—
1040Dic3—721no—
1041C32—21no—
1042C32—21no—
1043C32—21no—
1044C32—41no—
1045C32#559311yescharacteristic, complemented
1046C32#567811yescharacteristic, complemented
1047C32#570411yescharacteristic, complemented
1048C23—31no—
1049C23—31no—
1050C23—91no—
1051C23—91no—
1052C23—91no—
1053C23—182no—
1054C23—361no—
1055C23—361no—
1056Q8—361no—
1057D4—182no—
1058D4—361no—
1059D4—361no—
1060D4—361no—
1061D4—542no—
1062D4—1081no—
1063D4—1081no—
1064C2×C4—31no—
1065C2×C4—31no—
1066C2×C4—31no—
1067C2×C4—31no—
1068C2×C4—91no—
1069C2×C4—91no—
1070C2×C4—91no—
1071C2×C4—271no—
1072C2×C4—271no—
1073C2×C4—1081no—
1074C2×C4—1081no—
1075C2×C4—1081no—
1076C2×C4—1081no—
1077C2×C4D3311yescharacteristic
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—41no—
1088C2×C3—41no—
1089C2×C3—41no—
1090C2×C3—121no—
1091C2×C3—121no—
1092C2×C3—121no—
1093C2×C3—121no—
1094C2×C3—182no—
1095C2×C3—241no—
1096C2×C3—241no—
1097C2×C3—361no—
1098C2×C3—361no—
1099C2×C3#6430611yescharacteristic
1100C2×C3#6430711yescharacteristic
1101C2×C3#6430711yescharacteristic
1102C2×C3#6430711yescharacteristic
1103C2×C3#6430811yescharacteristic
1104C2×C3D3×#23711yescharacteristic
1105C2×C3D3×#23711yescharacteristic
1106C2×C3#6431311yescharacteristic
1107C2×C3#6431411yescharacteristic
1108D3—41no—
1109D3—41no—
1110D3—62no—
1111D3—62no—
1112D3—122no—
1113D3—122no—
1114D3—122no—
1115D3—121no—
1116D3—121no—
1117D3—121no—
1118D3—121no—
1119C22—61no—
1120C22—61no—
1121C22—61no—
1122C22—61no—
1123C22—61no—
1124C22—61no—
1125C22—92no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—181no—
1132C22—181no—
1133C22—181no—
1134C22—364no—
1135C22C2×D3311yescharacteristic
1136C4—21no—
1137C4—61no—
1138C4—61no—
1139C4—61no—
1140C4—61no—
1141C4—181no—
1142C4—181no—
1143C4—181no—
1144C4—541no—
1145C4—541no—
1146C3—21no—
1147C3—21no—
1148C3—21no—
1149C3—41no—
1150C3#1059401911yescharacteristic, complemented
1151C3#1059412211yescharacteristic, complemented
1152C3#1059412711yescharacteristic, complemented
1153C2—121no—
1154C2—121no—
1155C2—182no—
1156C2—361no—
1157C2—361no—
1158C2#1172438011yescharacteristic
1159C2#1172438411yescharacteristic
1160C2#1172440711yescharacteristic
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. #11723687C2semidirect
2. #11723523C2semidirect
3. Dic3×C4⋊(C3⋊D3)C2semidirect
4. #11723430C2semidirect
5. C3×#63923C2semidirect
6. C3×#63859C2semidirect
7. C3×#63852C2semidirect
8. #11723001C2semidirect
9. #11722991C2semidirect
10. #11722979C2semidirect
11. #11722967C2semidirect
12. #11722962C2semidirect
13. #11722947C2semidirect
14. #11722938C2semidirect
15. #11722902C2semidirect
22. C2×#6295C22semidirect
26. C2×Dic3×C3⋊D3C22semidirect
27. C2×Dic3×C3⋊D3C22semidirect
28. C2×C3×#627C22semidirect
32. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
33. C3×#3752C22semidirect
34. C3×#3750C22semidirect
37. C32×C4×Dic3C22semidirect
38. #88814C22semidirect
39. #88807C22semidirect
40. #88806C22semidirect
42. #88803C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
71. #63923D3semidirect
99. #63859D3semidirect
101. #63852D3semidirect
154. C2×#627C2×D3semidirect
187. #3752C2×D3semidirect
197. #3750C2×D3semidirect
226. C3×C4×Dic3C2×D3semidirect
227. C3×C4×Dic3C2×D3semidirect
231. #3724C2×D3semidirect
235. Dic3⋊Dic3C2×D3semidirect
238. #3722C2×D3semidirect
591. C4×Dic3D32semidirect
726. C33#538semidirect
1045. C32#5593semidirect
1046. C32#5678semidirect
1047. C32#5704semidirect
1150. C3#10594019semidirect
1151. C3#10594122semidirect
1152. C3#10594127semidirect

Maximal subgroups

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

subgroupindex
#117236872
#117235232
Dic3×C4⋊(C3⋊D3)2
#117234302
C3×#639232
C3×#638592
C3×#638522
#117230012
#117229912
#117229792
#117229672
#117229622
#117229472
#117229382
#117229022
#105941273
#105941223
#105940193