Finite Group Databasebeta

← #13178201

Subgroups — #13178201

Order 1728.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64094C211yesmaximal, characteristic, complemented
2C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#64088C211yesmaximal, characteristic, complemented
4#11723727C211yesmaximal, characteristic
5#11723724C211yesmaximal, characteristic, complemented
6#11723723C211yesmaximal, characteristic, complemented
7#11723716C211yesmaximal, characteristic, complemented
8#11723694C211yesmaximal, characteristic, complemented
9#11723690C211yesmaximal, characteristic, complemented
10#11723688C211yesmaximal, characteristic, complemented
11#11723685C211yesmaximal, characteristic, complemented
12#11723684C211yesmaximal, characteristic, complemented
13#11723683C211yesmaximal, characteristic, complemented
14#11723674C211yesmaximal, characteristic, complemented
15#11723673C211yesmaximal, characteristic, complemented
16#10594153—31nomaximal
17#10594094—31nomaximal
18#10594092—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×#634C2211yescharacteristic, complemented
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C2×#6294C2211yescharacteristic, complemented
29C33×C22⋊C4C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic, complemented
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88815C2211yescharacteristic, complemented
47#88815C2211yescharacteristic, complemented
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88813C2211yescharacteristic, complemented
54#64094D311yescharacteristic, complemented
55C22⋊C4×C3⋊D3D311yescharacteristic, complemented
56#64088D311yescharacteristic, complemented
57C3×#885—31no—
58C3×#885—31no—
59C3×#885—61no—
60C3×D3×C22⋊C4—31no—
61C3×D3×C22⋊C4—31no—
62C3×D3×C22⋊C4—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#63969—31no—
72#63969—31no—
73D3×#217—31no—
74D3×#217—31no—
75#63956—31no—
76#63956—31no—
77#63956—31no—
78#63905—31no—
79#63904—31no—
80#63902—31no—
81#63896—31no—
82#63891—31no—
83#63890—31no—
84#63888—31no—
85#63887—31no—
86#63881—31no—
87#63880—31no—
88#63880—31no—
89#63879—31no—
90#63878—31no—
91#63877—31no—
92#63874—31no—
93#63871—31no—
94#63857—31no—
95#63856—31no—
96#63855—31no—
97#63855—31no—
98#63854—31no—
99#63853—31no—
100#63850—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C2×C33×C4C2311yescharacteristic
110C2×C33×C4C2311yescharacteristic
111C3×#638—41no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
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
121C3×C4×C3⋊D3—22no—
122C3×C4×C3⋊D3—41no—
123C3×#634—41no—
124#6295—22no—
125#6295—22no—
126#6294—22no—
127#6294—41no—
128#6294—41no—
129#5705—91no—
130#5679—91no—
131#5495—91no—
132C23×C3⋊D3C2×D311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×#638C2×D311yescharacteristic
137C2×C4×C3⋊D3C2×D311yescharacteristic
138C2×C4×C3⋊D3C2×D311yescharacteristic
139C2×#634C2×D311yescharacteristic, complemented
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—61no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—61no—
148C2×C3×C4×D3—61no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—61no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#625—31no—
157C2×#625—31no—
158C2×#624—31no—
159C2×#624—31no—
160C2×#624—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C32×C22⋊C4—21no—
168C32×C22⋊C4—21no—
169C32×C22⋊C4—21no—
170C32×C22⋊C4—41no—
171C32×C22⋊C4C2×D311yescharacteristic
172C32×C22⋊C4C2×D311yescharacteristic
173C32×C22⋊C4C2×D311yescharacteristic
174#3757C2×D311yescharacteristic
175#3757C2×D311yescharacteristic
176#3757C2×D311yescharacteristic
177#3757C2×D311yescharacteristic
178#3752C2×D311yescharacteristic
179#3752C2×D311yescharacteristic
180#3752C2×D311yescharacteristic, complemented
181#3752C2×D311yescharacteristic, complemented
182C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
183#3750C2×D311yescharacteristic, complemented
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3C2×D311yescharacteristic, complemented
186C4×C3⋊Dic3C2×D311yescharacteristic, complemented
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—61no—
196C3×#217—61no—
197C3×#217—61no—
198C3×#217—61no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
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—61no—
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—61no—
219C3×Dic3⋊C4—61no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—61no—
225C3×C4×Dic3—61no—
226#3724—31no—
227#3724—31no—
228#3724—31no—
229#3724—31no—
230#3724—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—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—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
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—44no—
271C2×C3×C3⋊D3#4112yes—
272C2×C3×C3⋊D3#4112yes—
273C33×C4—21no—
274C33×C4—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×#126—91no—
285C3×#124—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#946—91no—
290#946—91no—
291#937—91no—
292#935—91no—
293#929—91no—
294C4×#67—91no—
295#926—91no—
296#924—91no—
297#897—91no—
298#896—91no—
299#894—91no—
300#894—91no—
301#893—91no—
302#892—91no—
303#886—91no—
304#885—31no—
305#885—31no—
306#885—61no—
307#883—91no—
308#883—91no—
309#883—91no—
310#883—91no—
311#882—91no—
312#67⋊C4—91no—
313#67⋊C4—91no—
314#67⋊C4—91no—
315D3×C22⋊C4—31no—
316D3×C22⋊C4—31no—
317D3×C22⋊C4—61no—
318D3×C22⋊C4—91no—
319D3×C22⋊C4—91no—
320#879—31no—
321#879—31no—
322#879—61no—
323#879—91no—
324#879—91no—
325#879—91no—
326#878—91no—
327#877—91no—
328C4×D12—91no—
329#872—91no—
330#872—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3—22no—
340C22×C3⋊D3—22no—
341C22×C3⋊D3—41no—
342C22×C3⋊D3C22×D311yescharacteristic
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—62no—
357C22×C3×D3—62no—
358C22×C3×D3—64no—
359C22×C3×D3—122no—
360C22×C3×D3—121no—
361C22×C3×D3—121no—
362C22×C3×D3—122no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—41no—
370C2×C32×C4—41no—
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377#638—41no—
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C4×C3⋊D3—22no—
388C4×C3⋊D3—41no—
389#634—41no—
390C3×#67—121no—
391C3×#67—121no—
392C3×#67—122no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
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—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C3×C4×D3—62no—
421C3×C4×D3—62no—
422C3×C4×D3—122no—
423C3×C4×D3—121no—
424C3×C4×D3—121no—
425C3×C4×D3—122no—
426C3×Dic6—121no—
427C3×Dic6—121no—
428C3×Dic6—122no—
429#626—62no—
430#626—62no—
431#626—62no—
432#626—62no—
433#625—62no—
434#625—62no—
435#624—62no—
436#624—121no—
437#624—121no—
438D3×Dic3—62no—
439D3×Dic3—62no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443D3×Dic3—121no—
444#551—271noSylow
445C2×C33—41no—
446C2×C33C2×#4111yescharacteristic
447C2×C33C2×#4111yescharacteristic
448C2×C33H(5,𝔽2)11yescharacteristic
449C3×C3⋊D3—22no—
450C3×C3⋊D3—22no—
451C3×C3⋊D3—41no—
452C24×C3—91no—
453C23×D3—31no—
454C23×D3—31no—
455C23×D3—61no—
456C2×C3×Q8—91no—
457C2×C3×D4—91no—
458C22×C3×C4—91no—
459C22×C3×C4—91no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—61no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C22×Dic3—91no—
468C22×Dic3—91no—
469C22×Dic3—91no—
470C2×D12—91no—
471C2×D12—91no—
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×C4×D3—31no—
475C2×C4×D3—31no—
476C2×C4×D3—61no—
477C2×C4×D3—61no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×Dic6—31no—
485C2×Dic6—31no—
486C2×Dic6—61no—
487C3×C4⋊C4—91no—
488C3×C4⋊C4—91no—
489C3×C4⋊C4—91no—
490C3×C22⋊C4—21no—
491C3×C22⋊C4—21no—
492C3×C22⋊C4—21no—
493C3×C22⋊C4—41no—
494C3×C22⋊C4—91no—
495C3×C22⋊C4—91no—
496C3×C22⋊C4—91no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4D3211yescharacteristic
503C3×C22⋊C4D3211yescharacteristic
504C3×C22⋊C4D3211yescharacteristic
505C3×C42—91no—
506C3×C42—91no—
507#217—31no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—31no—
513#217—31no—
514#217—31no—
515#217—61no—
516#217—61no—
517#217—61no—
518#217—61no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—91no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—61no—
533(C2×D3)⋊C4—61no—
534(C2×D3)⋊C4—61no—
535(C2×D3)⋊C4—61no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546C4⋊Dic3—31no—
547C4⋊Dic3—31no—
548C4⋊Dic3—61no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—91no—
553C4⋊Dic3—91no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—61no—
559Dic3⋊C4—61no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—61no—
575C4×Dic3—61no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C22×C32—21no—
580C22×C32—22no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—41no—
593C22×C32—41no—
594C22×C32—41no—
595C22×C32—42no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—81no—
603C22×C32—81no—
604C22×C32C23×D311yescharacteristic
605C22×C32C23×D311yescharacteristic
606C22×C32C23×D311yescharacteristic
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—44no—
615C2×C3⋊D3#23512yes—
616C2×C3⋊D3#23712yes—
617C2×C3×D3—32no—
618C2×C3×D3—32no—
619C2×C3×D3—32no—
620C2×C3×D3—32no—
621C2×C3×D3—62no—
622C2×C3×D3—62no—
623C2×C3×D3—62no—
624C2×C3×D3—62no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3—124no—
645C2×C3×D3—124no—
646C2×C3×D3—128no—
647C32×C4—21no—
648C32×C4—21no—
649C32×C4—21no—
650C32×C4—21no—
651C32×C4—21no—
652C32×C4—21no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—41no—
656C32×C4—41no—
657C32×C4—41no—
658C32×C4—41no—
659C32×C4—81no—
660C32×C4—81no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—21no—
667C3⋊Dic3—21no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3×Dic3—62no—
671C3×Dic3—61no—
672C3×Dic3—61no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—121no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697#126—91no—
698#126—271no—
699#124—91no—
700#123—271no—
701#123—271no—
702#123—271no—
703C22⋊Q8—271no—
704C22⋊Q8—271no—
705#120—271no—
706C4×D4—271no—
707C4×D4—271no—
708#117—271no—
709#117—271no—
710C2×C22⋊C4—91no—
711C2×C22⋊C4—271no—
712C33#55111yescharacteristic, complemented, Sylow
713C23×C3—21no—
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—41no—
717C23×C3—91no—
718C23×C3—91no—
719C23×C3—91no—
720C23×C3—182no—
721C23×C3—182no—
722C23×C3—361no—
723C23×C3C2×D3211yescharacteristic
724C23×C3C2×D3211yescharacteristic
725C23×C3C2×D3211yescharacteristic
726C22×D3—31no—
727C22×D3—31no—
728C22×D3—31no—
729C22×D3—31no—
730C22×D3—31no—
731C22×D3—31no—
732C22×D3—61no—
733C22×D3—61no—
734C22×D3—61no—
735C22×D3—62no—
736C22×D3—62no—
737C22×D3—62no—
738C22×D3—62no—
739C22×D3—64no—
740C22×D3—122no—
741C22×D3—121no—
742C22×D3—121no—
743C22×D3—122no—
744C3×Q8—361no—
745C3×D4—361no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—41no—
753C2×C3×C4—41no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—91no—
758C2×C3×C4—91no—
759C2×C3×C4—91no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—182no—
764C2×C3×C4—361no—
765C2×C3×C4C2×D3211yescharacteristic
766C2×C3×C4C2×D3211yescharacteristic
767C2×C3×C4C2×D3211yescharacteristic
768C2×C3×C4C2×D3211yescharacteristic
769C2×C3×C4C2×D3211yescharacteristic
770C2×C3×C4C2×D3211yescharacteristic
771#67—121no—
772#67—121no—
773#67—122no—
774#67—182no—
775#67—182no—
776#67—182no—
777#67—182no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—61no—
797C2×Dic3—61no—
798C2×Dic3—61no—
799C2×Dic3—61no—
800C2×Dic3—61no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—182no—
806C2×Dic3—361no—
807C2×Dic3—361no—
808D12—182no—
809D12—182no—
810C4×D3—62no—
811C4×D3—62no—
812C4×D3—122no—
813C4×D3—121no—
814C4×D3—121no—
815C4×D3—122no—
816C4×D3—182no—
817C4×D3—182no—
818C4×D3—361no—
819C4×D3—361no—
820C4×D3—361no—
821C4×D3—361no—
822Dic6—121no—
823Dic6—121no—
824Dic6—122no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—41no—
837C2×C32—41no—
838C2×C32—42no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—81no—
842C2×C32—81no—
843C2×C32—82no—
844C2×C32C2×#23511yescharacteristic
845C2×C32C2×#23711yescharacteristic
846C2×C32#100411yescharacteristic
847C2×C32#100411yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32D3×#4111yescharacteristic
852C2×C32#100911yescharacteristic
853C3⋊D3—22no—
854C3⋊D3—22no—
855C3⋊D3—41no—
856C3×D3—64no—
857C3×D3—62no—
858C3×D3—62no—
859C3×D3—62no—
860C3×D3—62no—
861C3×D3—122no—
862C3×D3—121no—
863C3×D3—121no—
864C3×D3—241no—
865C24—91no—
866C2×Q8—91no—
867C2×D4—91no—
868C2×D4—271no—
869C2×D4—271no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—271no—
873C22×C4—271no—
874C22×C4—271no—
875C4⋊C4—91no—
876C4⋊C4—91no—
877C4⋊C4—91no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C4⋊C4—271no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4#111311yescharacteristic
897C42—91no—
898C42—91no—
899C42—271no—
900C22×C3—22no—
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—42no—
922C22×C3—41no—
923C22×C3—81no—
924C22×C3—81no—
925C22×C3—92no—
926C22×C3—92no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3—181no—
933C22×C3—181no—
934C22×C3—364no—
935C22×C3C22×D3211yescharacteristic
936C22×C3C22×D3211yescharacteristic
937C22×C3C22×D3211yescharacteristic
938C2×D3—32no—
939C2×D3—32no—
940C2×D3—32no—
941C2×D3—32no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3—121no—
963C2×D3—121no—
964C2×D3—121no—
965C2×D3—124no—
966C2×D3—124no—
967C2×D3—128no—
968C3×C4—21no—
969C3×C4—21no—
970C3×C4—21no—
971C3×C4—21no—
972C3×C4—21no—
973C3×C4—21no—
974C3×C4—41no—
975C3×C4—41no—
976C3×C4—41no—
977C3×C4—41no—
978C3×C4—41no—
979C3×C4—41no—
980C3×C4—81no—
981C3×C4—81no—
982C3×C4—181no—
983C3×C4—181no—
984C3×C4—181no—
985C3×C4—181no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989C3×C4—181no—
990C3×C4—181no—
991Dic3—62no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—121no—
1011Dic3—121no—
1012Dic3—121no—
1013Dic3—121no—
1014Dic3—121no—
1015Dic3—121no—
1016Dic3—121no—
1017Dic3—121no—
1018C32—21no—
1019C32—21no—
1020C32—21no—
1021C32—41no—
1022C32#549511yescharacteristic, complemented
1023C32#567911yescharacteristic, complemented
1024C32#570511yescharacteristic, complemented
1025C23—91no—
1026C23—91no—
1027C23—91no—
1028C23—182no—
1029C23—182no—
1030C23—361no—
1031C23C2×#111311yescharacteristic
1032Q8—361no—
1033D4—361no—
1034D4—542no—
1035D4—542no—
1036C2×C4—91no—
1037C2×C4—91no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—91no—
1045C2×C4—182no—
1046C2×C4—361no—
1047C2×C4—542no—
1048C2×C4—1081no—
1049C2×C4—1081no—
1050C2×C4C2×#111311yescharacteristic
1051C2×C4C2×#111311yescharacteristic
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—42no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—41no—
1068C2×C3—81no—
1069C2×C3—81no—
1070C2×C3—82no—
1071C2×C3—182no—
1072C2×C3—182no—
1073C2×C3—361no—
1074C2×C3D3×#23511yescharacteristic
1075C2×C3D3×#23511yescharacteristic
1076C2×C3#6430611yescharacteristic
1077C2×C3D3×#23711yescharacteristic
1078C2×C3D3×#23711yescharacteristic
1079C2×C3#6431211yescharacteristic
1080C2×C3#6431311yescharacteristic
1081C2×C3#6431411yescharacteristic
1082C2×C3#6431411yescharacteristic
1083D3—64no—
1084D3—62no—
1085D3—62no—
1086D3—62no—
1087D3—62no—
1088D3—122no—
1089D3—121no—
1090D3—121no—
1091D3—241no—
1092C22—21no—
1093C22—21no—
1094C22—21no—
1095C22—92no—
1096C22—92no—
1097C22—181no—
1098C22—181no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22—181no—
1103C22—181no—
1104C22—364no—
1105C22C22×#111311yescharacteristic
1106C4—21no—
1107C4—21no—
1108C4—181no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—181no—
1114C4—181no—
1115C4—181no—
1116C4—181no—
1117C3—21no—
1118C3—21no—
1119C3—21no—
1120C3—41no—
1121C3#1059409211yescharacteristic, complemented
1122C3#1059409411yescharacteristic, complemented
1123C3#1059415311yescharacteristic, complemented
1124C2—41no—
1125C2—182no—
1126C2—182no—
1127C2—361no—
1128C2#1172461811yescharacteristic
1129C2#1172462211yescharacteristic
1130C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radical#11723727C2
hypercenterC22⋊C4#1113
hypocenterC33#551
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×C22⋊C4×C3⋊D3C2semidirect
3. C3×#64088C2semidirect
5. #11723724C2semidirect
6. #11723723C2semidirect
7. #11723716C2semidirect
8. #11723694C2semidirect
9. #11723690C2semidirect
10. #11723688C2semidirect
11. #11723685C2semidirect
12. #11723684C2semidirect
13. #11723683C2semidirect
14. #11723674C2semidirect
15. #11723673C2semidirect
23. C2×C3×#634C22semidirect
28. C2×#6294C22semidirect
36. C3×#3752C22semidirect
37. C3×#3752C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C3×#3750C22semidirect
40. C3×#3750C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
42. C3×C4×C3⋊Dic3C22semidirect
43. #88815C22semidirect
44. #88815C22semidirect
45. #88815C22semidirect
46. #88815C22semidirect
47. #88815C22semidirect
52. #88814C22semidirect
53. #88813C22semidirect
54. #64094D3semidirect
55. C22⋊C4×C3⋊D3D3semidirect
56. #64088D3semidirect
139. C2×#634C2×D3semidirect
180. #3752C2×D3semidirect
181. #3752C2×D3semidirect
182. C4⋊(C3⋊Dic3)C2×D3semidirect
183. #3750C2×D3semidirect
184. #3750C2×D3semidirect
185. C4×C3⋊Dic3C2×D3semidirect
186. C4×C3⋊Dic3C2×D3semidirect
712. C33#551semidirect
1022. C32#5495semidirect
1023. C32#5679semidirect
1024. C32#5705semidirect
1121. C3#10594092semidirect
1122. C3#10594094semidirect
1123. C3#10594153semidirect

Maximal subgroups

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

subgroupindex
C3×#640942
C3×C22⋊C4×C3⋊D32
C3×#640882
#117237272
#117237242
#117237232
#117237162
#117236942
#117236902
#117236882
#117236852
#117236842
#117236832
#117236742
#117236732
#105941533
#105940943
#105940923