Finite Group Databasebeta

← #13178254

Subgroups — #13178254

Order 1728.

1300 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
1C3×#64094C211yesmaximal, characteristic, complemented
2C3×#64091C211yesmaximal, characteristic, complemented
3C3×#64088C211yesmaximal, characteristic, complemented
4#11723727C211yesmaximal, characteristic, complemented
5#11723725C211yesmaximal, characteristic, complemented
6#11723724C211yesmaximal, characteristic, complemented
7#11723723C211yesmaximal, characteristic, complemented
8#11723691C211yesmaximal, characteristic, complemented
9#11723690C211yesmaximal, characteristic, complemented
10#11723688C211yesmaximal, characteristic, complemented
11#11723687C211yesmaximal, characteristic, complemented
12#11723687C211yesmaximal, characteristic, complemented
13#11723685C211yesmaximal, characteristic, complemented
14#11723677C211yesmaximal, characteristic, complemented
15#11723676C211yesmaximal, characteristic, complemented
16#10594162—31nomaximal
17#10594126—31nomaximal
18#10594122—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic, complemented
25C2×#6295C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6295C2211yescharacteristic, complemented
28C2×#6294C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6294C2211yescharacteristic, complemented
31C2×#6294C2211yescharacteristic, complemented
32C33×C22⋊C4C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic, complemented
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88815C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#64094D311yescharacteristic, complemented
55#64091D311yescharacteristic, complemented
56#64088D311yescharacteristic, complemented
57C3×#885—31no—
58C3×#885—31no—
59C3×#885—61no—
60C3×#882—31no—
61C3×#882—31no—
62C3×#882—61no—
63C3×#879—31no—
64C3×#879—31no—
65C3×#879—61no—
66#63981—31no—
67#63977—31no—
68#63976—31no—
69#63975—31no—
70#63974—31no—
71#63971—31no—
72#63970—31no—
73#63969—31no—
74#63969—31no—
75D3×#217—31no—
76D3×#217—31no—
77#63958—31no—
78#63910—31no—
79#63910—31no—
80#63902—31no—
81#63898—31no—
82#63896—31no—
83#63894—31no—
84Dic3×D12—31no—
85#63891—31no—
86#63890—31no—
87#63888—31no—
88#63887—31no—
89#63886—31no—
90#63886—31no—
91#63885—31no—
92#63885—31no—
93#63880—31no—
94#63880—31no—
95#63868—31no—
96#63864—31no—
97#63863—31no—
98#63862—31no—
99#63860—31no—
100#63859—31no—
101#63854—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—41no—
113C3×#638—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C3×C4⋊(C3⋊D3)—22no—
123C3×C4⋊(C3⋊D3)—41no—
124C3×#634—41no—
125#6295—22no—
126#6295—41no—
127#6295—41no—
128#6294—41no—
129#6294—41no—
130#6294—41no—
131#6294—41no—
132#5704—91no—
133#5678—91no—
134#5593—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×#634C2×D311yescharacteristic, complemented
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—61no—
149C2×C3×#67—61no—
150C2×C3×D12—31no—
151C2×C3×D12—31no—
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12—61no—
155C2×C3×D12—61no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—31no—
158C2×C3×Dic6—61no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#624—31no—
169C2×#624—31no—
170C2×#624—31no—
171C2×#624—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C32×C22⋊C4—21no—
181C32×C22⋊C4—21no—
182C32×C22⋊C4—21no—
183C32×C22⋊C4—41no—
184C32×C22⋊C4C2×D311yescharacteristic
185C32×C22⋊C4C2×D311yescharacteristic
186C32×C22⋊C4C2×D311yescharacteristic
187#3757C2×D311yescharacteristic
188#3757C2×D311yescharacteristic
189#3757C2×D311yescharacteristic
190#3752C2×D311yescharacteristic
191#3752C2×D311yescharacteristic
192#3752C2×D311yescharacteristic, complemented
193#3752C2×D311yescharacteristic, complemented
194C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
195#3750C2×D311yescharacteristic, complemented
196#3750C2×D311yescharacteristic, complemented
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C4×C3⋊Dic3C2×D311yescharacteristic, complemented
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—61no—
206C3×#217—61no—
207C3×#217—61no—
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—31no—
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—61no—
228C3×Dic3⋊C4—61no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—31no—
232C3×C4×Dic3—31no—
233C3×C4×Dic3—61no—
234C3×C4×Dic3—61no—
235#3724—31no—
236#3724—31no—
237#3724—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—31no—
249#3722—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—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
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—44no—
278C2×C3×C3⋊D3#4112yes—
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×#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—31no—
313#885—61no—
314#884—91no—
315#884—91no—
316#884—91no—
317#883—91no—
318#883—91no—
319#883—91no—
320#882—31no—
321#882—31no—
322#882—61no—
323#882—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326D3×C22⋊C4—91no—
327D3×C22⋊C4—91no—
328#879—31no—
329#879—31no—
330#879—61no—
331#879—91no—
332#878—91no—
333#876—91no—
334#875—91no—
335C4×D12—91no—
336C4×D12—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—41no—
387#638—41no—
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C4⋊(C3⋊D3)—22no—
397C4⋊(C3⋊D3)—41no—
398#634—41no—
399C3×#67—121no—
400C3×#67—121no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—122no—
404C3×#67—122no—
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—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—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C3×D12—62no—
430C3×D12—62no—
431C3×D12—122no—
432C3×D12—121no—
433C3×D12—121no—
434C3×D12—122no—
435C3×Dic6—121no—
436C3×Dic6—121no—
437C3×Dic6—122no—
438#626—62no—
439#626—62no—
440#626—121no—
441#626—121no—
442#626—121no—
443#626—121no—
444#625—62no—
445#625—121no—
446#625—121no—
447#624—121no—
448#624—121no—
449#624—121no—
450#624—121no—
451D3×Dic3—121no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459#538—271noSylow
460C2×C33—41no—
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3×C3⋊D3—22no—
465C3×C3⋊D3—41no—
466C3×C3⋊D3—41no—
467C3×C3⋊D3—41no—
468C24×C3—91no—
469C23×D3—31no—
470C23×D3—31no—
471C23×D3—61no—
472C2×C3×Q8—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C2×C3×D4—91no—
476C2×C3×D4—91no—
477C2×#67—31no—
478C2×#67—31no—
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—61no—
482C2×#67—61no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C22×Dic3—91no—
490C22×Dic3—91no—
491C22×Dic3—91no—
492C22×Dic3—91no—
493C2×D12—31no—
494C2×D12—31no—
495C2×D12—31no—
496C2×D12—31no—
497C2×D12—61no—
498C2×D12—61no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×Dic6—31no—
511C2×Dic6—31no—
512C2×Dic6—61no—
513C3×C4⋊C4—91no—
514C3×C4⋊C4—91no—
515C3×C4⋊C4—91no—
516C3×C22⋊C4—21no—
517C3×C22⋊C4—21no—
518C3×C22⋊C4—21no—
519C3×C22⋊C4—41no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4D3211yescharacteristic
528C3×C22⋊C4D3211yescharacteristic
529C3×C22⋊C4D3211yescharacteristic
530C3×C42—91no—
531C3×C42—91no—
532#217—31no—
533#217—31no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—61no—
539#217—61no—
540#217—61no—
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—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—61no—
556(C2×D3)⋊C4—61no—
557(C2×D3)⋊C4—61no—
558(C2×D3)⋊C4—61no—
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—
571C4⋊Dic3—31no—
572C4⋊Dic3—31no—
573C4⋊Dic3—61no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—91no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—61no—
582Dic3⋊C4—61no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—61no—
594C4×Dic3—61no—
595C22×C32—21no—
596C22×C32—22no—
597C22×C32—21no—
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—21no—
608C22×C32—41no—
609C22×C32—41no—
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×C32C23×D311yescharacteristic
621C22×C32C23×D311yescharacteristic
622C22×C32C23×D311yescharacteristic
623C2×C3⋊D3—21no—
624C2×C3⋊D3—21no—
625C2×C3⋊D3—21no—
626C2×C3⋊D3—21no—
627C2×C3⋊D3—21no—
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—44no—
635C2×C3⋊D3#23712yes—
636C2×C3×D3—32no—
637C2×C3×D3—32no—
638C2×C3×D3—62no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—62no—
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—121no—
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—121no—
671C2×C3×D3—121no—
672C2×C3×D3—124no—
673C2×C3×D3—124no—
674C2×C3×D3—128no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—21no—
679C32×C4—21no—
680C32×C4—21no—
681C32×C4—41no—
682C32×C4—41no—
683C32×C4—41no—
684C32×C4—41no—
685C32×C4—41no—
686C32×C4—41no—
687C32×C4—81no—
688C32×C4—81no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—21no—
692C3⋊Dic3—21no—
693C3⋊Dic3—21no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3×Dic3—62no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—61no—
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—121no—
715C3×Dic3—121no—
716C3×Dic3—121no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721#126—91no—
722#126—271no—
723#124—91no—
724#124—271no—
725#123—271no—
726#123—271no—
727C22⋊Q8—271no—
728#121—271no—
729#121—271no—
730#121—271no—
731#120—91no—
732#120—271no—
733C4×D4—271no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—21no—
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—41no—
741C23×C3—91no—
742C23×C3—91no—
743C23×C3—91no—
744C23×C3—91no—
745C23×C3—182no—
746C23×C3—361no—
747C23×C3—361no—
748C23×C3C2×D3211yescharacteristic
749C23×C3C2×D3211yescharacteristic
750C23×C3C2×D3211yescharacteristic
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—31no—
754C22×D3—31no—
755C22×D3—31no—
756C22×D3—31no—
757C22×D3—31no—
758C22×D3—31no—
759C22×D3—61no—
760C22×D3—61no—
761C22×D3—61no—
762C22×D3—61no—
763C22×D3—62no—
764C22×D3—62no—
765C22×D3—122no—
766C22×D3—121no—
767C22×D3—121no—
768C22×D3—121no—
769C22×D3—121no—
770C22×D3—122no—
771C22×D3—122no—
772C3×Q8—361no—
773C3×D4—182no—
774C3×D4—361no—
775C3×D4—361no—
776C3×D4—361no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—41no—
784C2×C3×C4—41no—
785C2×C3×C4—91no—
786C2×C3×C4—91no—
787C2×C3×C4—91no—
788C2×C3×C4—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4C2×D3211yescharacteristic
794C2×C3×C4C2×D3211yescharacteristic
795C2×C3×C4C2×D3211yescharacteristic
796C2×C3×C4C2×D3211yescharacteristic
797C2×C3×C4C2×D3211yescharacteristic
798C2×C3×C4C2×D3211yescharacteristic
799#67—121no—
800#67—121no—
801#67—121no—
802#67—121no—
803#67—122no—
804#67—122no—
805#67—182no—
806#67—182no—
807#67—361no—
808#67—361no—
809#67—361no—
810#67—361no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
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—61no—
828C2×Dic3—61no—
829C2×Dic3—61no—
830C2×Dic3—61no—
831C2×Dic3—61no—
832C2×Dic3—61no—
833C2×Dic3—61no—
834C2×Dic3—61no—
835C2×Dic3—361no—
836C2×Dic3—361no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839D12—62no—
840D12—62no—
841D12—122no—
842D12—121no—
843D12—121no—
844D12—122no—
845D12—182no—
846D12—361no—
847D12—361no—
848C4×D3—361no—
849C4×D3—361no—
850C4×D3—361no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—361no—
854C4×D3—361no—
855C4×D3—361no—
856Dic6—121no—
857Dic6—121no—
858Dic6—122no—
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—41no—
872C2×C32—42no—
873C2×C32—41no—
874C2×C32—41no—
875C2×C32—81no—
876C2×C32—81no—
877C2×C32—82no—
878C2×C32C2×#23711yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32#100411yescharacteristic
881C2×C32#100411yescharacteristic
882C2×C32D3×#4111yescharacteristic
883C2×C32D3×#4111yescharacteristic
884C2×C32#100911yescharacteristic
885C2×C32#100911yescharacteristic
886C2×C32#100911yescharacteristic
887C3⋊D3—22no—
888C3⋊D3—41no—
889C3⋊D3—41no—
890C3⋊D3—41no—
891C3×D3—62no—
892C3×D3—62no—
893C3×D3—122no—
894C3×D3—122no—
895C3×D3—121no—
896C3×D3—121no—
897C3×D3—121no—
898C3×D3—121no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—241no—
902C3×D3—241no—
903C24—91no—
904C2×Q8—91no—
905C2×D4—91no—
906C2×D4—91no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—271no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C22×C4—271no—
916C4⋊C4—91no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C22⋊C4—91no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4#111311yescharacteristic
936C42—91no—
937C42—91no—
938C22×C3—22no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—42no—
960C22×C3—41no—
961C22×C3—81no—
962C22×C3—81no—
963C22×C3—92no—
964C22×C3—181no—
965C22×C3—181no—
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—364no—
976C22×C3C22×D3211yescharacteristic
977C22×C3C22×D3211yescharacteristic
978C22×C3C22×D3211yescharacteristic
979C2×D3—32no—
980C2×D3—32no—
981C2×D3—62no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—62no—
987C2×D3—61no—
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—121no—
1006C2×D3—121no—
1007C2×D3—121no—
1008C2×D3—121no—
1009C2×D3—121no—
1010C2×D3—121no—
1011C2×D3—121no—
1012C2×D3—121no—
1013C2×D3—121no—
1014C2×D3—121no—
1015C2×D3—124no—
1016C2×D3—124no—
1017C2×D3—128no—
1018C3×C4—21no—
1019C3×C4—21no—
1020C3×C4—21no—
1021C3×C4—21no—
1022C3×C4—21no—
1023C3×C4—21no—
1024C3×C4—41no—
1025C3×C4—41no—
1026C3×C4—41no—
1027C3×C4—41no—
1028C3×C4—41no—
1029C3×C4—41no—
1030C3×C4—81no—
1031C3×C4—81no—
1032C3×C4—181no—
1033C3×C4—181no—
1034C3×C4—181no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039C3×C4—181no—
1040Dic3—62no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—61no—
1056Dic3—61no—
1057Dic3—121no—
1058Dic3—121no—
1059Dic3—121no—
1060Dic3—121no—
1061Dic3—121no—
1062Dic3—121no—
1063Dic3—121no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#559311yescharacteristic, complemented
1069C32#567811yescharacteristic, complemented
1070C32#570411yescharacteristic, complemented
1071C23—91no—
1072C23—91no—
1073C23—91no—
1074C23—91no—
1075C23—182no—
1076C23—361no—
1077C23—361no—
1078C23C2×#111311yescharacteristic
1079Q8—361no—
1080D4—182no—
1081D4—361no—
1082D4—361no—
1083D4—361no—
1084D4—542no—
1085D4—1081no—
1086D4—1081no—
1087C2×C4—91no—
1088C2×C4—91no—
1089C2×C4—91no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—1081no—
1096C2×C4—1081no—
1097C2×C4—1081no—
1098C2×C4—1081no—
1099C2×C4C2×#111311yescharacteristic
1100C2×C4C2×#111311yescharacteristic
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—42no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—41no—
1114C2×C3—41no—
1115C2×C3—41no—
1116C2×C3—41no—
1117C2×C3—81no—
1118C2×C3—81no—
1119C2×C3—82no—
1120C2×C3—182no—
1121C2×C3—361no—
1122C2×C3—361no—
1123C2×C3—361no—
1124C2×C3#6430711yescharacteristic
1125C2×C3#6430711yescharacteristic
1126C2×C3#6430811yescharacteristic
1127C2×C3D3×#23711yescharacteristic
1128C2×C3D3×#23711yescharacteristic
1129C2×C3#6431211yescharacteristic
1130C2×C3#6431311yescharacteristic
1131C2×C3#6431411yescharacteristic
1132C2×C3#6431411yescharacteristic
1133D3—62no—
1134D3—62no—
1135D3—122no—
1136D3—122no—
1137D3—121no—
1138D3—121no—
1139D3—121no—
1140D3—121no—
1141D3—121no—
1142D3—121no—
1143D3—241no—
1144D3—241no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—92no—
1149C22—181no—
1150C22—181no—
1151C22—181no—
1152C22—181no—
1153C22—181no—
1154C22—181no—
1155C22—181no—
1156C22—181no—
1157C22—181no—
1158C22—181no—
1159C22—181no—
1160C22—364no—
1161C22C22×#111311yescharacteristic
1162C4—21no—
1163C4—21no—
1164C4—181no—
1165C4—181no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059412211yescharacteristic, complemented
1177C3#1059412611yescharacteristic, complemented
1178C3#1059416211yescharacteristic, complemented
1179C2—41no—
1180C2—182no—
1181C2—361no—
1182C2—361no—
1183C2—361no—
1184C2#1172461911yescharacteristic
1185C2#1172462211yescharacteristic
1186C2#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×#64094C2semidirect
2. C3×#64091C2semidirect
3. C3×#64088C2semidirect
4. #11723727C2semidirect
5. #11723725C2semidirect
6. #11723724C2semidirect
7. #11723723C2semidirect
8. #11723691C2semidirect
9. #11723690C2semidirect
10. #11723688C2semidirect
11. #11723687C2semidirect
12. #11723687C2semidirect
13. #11723685C2semidirect
14. #11723677C2semidirect
15. #11723676C2semidirect
24. C2×C3×#634C22semidirect
27. C2×#6295C22semidirect
30. C2×#6294C22semidirect
31. C2×#6294C22semidirect
38. C3×#3752C22semidirect
39. C3×#3752C22semidirect
40. C3×C4⋊(C3⋊Dic3)C22semidirect
41. C3×#3750C22semidirect
42. C3×#3750C22semidirect
43. C3×C4×C3⋊Dic3C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
45. #88815C22semidirect
46. #88815C22semidirect
47. #88815C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #64094D3semidirect
55. #64091D3semidirect
56. #64088D3semidirect
143. C2×#634C2×D3semidirect
192. #3752C2×D3semidirect
193. #3752C2×D3semidirect
194. C4⋊(C3⋊Dic3)C2×D3semidirect
195. #3750C2×D3semidirect
196. #3750C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
198. C4×C3⋊Dic3C2×D3semidirect
736. C33#538semidirect
1068. C32#5593semidirect
1069. C32#5678semidirect
1070. C32#5704semidirect
1176. C3#10594122semidirect
1177. C3#10594126semidirect
1178. C3#10594162semidirect

Maximal subgroups

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

subgroupindex
C3×#640942
C3×#640912
C3×#640882
#117237272
#117237252
#117237242
#117237232
#117236912
#117236902
#117236882
#117236872
#117236852
#117236772
#117236762
#105941623
#105941263
#105941223