Finite Group Databasebeta

← #13168537

Subgroups — #13168537

Order 1728.

1286 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723531C211yesmaximal, characteristic, complemented
3#11723472C211yesmaximal, characteristic, complemented
4#11723470C211yesmaximal, characteristic, complemented
5C3×#63886C211yesmaximal, characteristic, complemented
6C3×#63884C211yesmaximal, characteristic, complemented
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11722991C211yesmaximal, characteristic, complemented
10#11722963C211yesmaximal, characteristic, complemented
11#11722963C211yesmaximal, characteristic, complemented
12#11722935C211yesmaximal, characteristic, complemented
13#11722932C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595195—31nomaximal
17#10594489—31nomaximal
18#10594461—31nomaximal
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6292C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36#88815C2211yescharacteristic
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88813C2211yescharacteristic
40#88807C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42#88804C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64102—31no—
56C4⋊C4×C3⋊D3—31no—
57C3×#939—31no—
58C3×#935—31no—
59C3×#895—31no—
60C3×#894—31no—
61C3×#890—31no—
62C3×#889—31no—
63Dic3×#67—31no—
64#63969—31no—
65#63958—31no—
66#63958—31no—
67#63956—31no—
68#63955—31no—
69#63952—31no—
70#63952—31no—
71#63916—31no—
72#63916—31no—
73#63916—31no—
74#63916—31no—
75#63916—61no—
76#63910—31no—
77#63910—31no—
78#63904—31no—
79C4×#626—31no—
80C4×#626—31no—
81Dic3×D12—31no—
82#63886D311yescharacteristic, complemented
83#63884—31no—
84#63884D311yescharacteristic, complemented
85#63883—31no—
86#63883—31no—
87#63883—61no—
88#63881—31no—
89#63881—31no—
90#63881—31no—
91#63881—61no—
92#63880—31no—
93#63878—31no—
94#63862—31no—
95#63861—31no—
96#63858—31no—
97#63858—31no—
98#63853—31no—
99#63848—31no—
100#63845D311yescharacteristic, complemented
101#63841—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊(C3⋊D3)—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—41no—
119#6292—22no—
120#6291—22no—
121#6291—22no—
122#6289—22no—
123#6289—41no—
124Dic3×C3⋊D3—41no—
125C3×#626—22no—
126C3×#626—41no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5695—91no—
130#5661—91no—
131#5614—91no—
132C2×C32×D4—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—61no—
143C2×C4×C3⋊D3—61no—
144C2×C4×C3⋊D3—61no—
145C2×C4×C3⋊D3—121no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C2×C3×D12—21no—
151C2×C3×D12—31no—
152C2×C3×D12—31no—
153C2×C3×D12C2×D311yescharacteristic
154C2×C3×D12C2×D311yescharacteristic
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—61no—
164C2×#626—61no—
165C2×#626—61no—
166C2×#626C2×D311yescharacteristic
167C2×#626C2×D311yescharacteristic
168C2×#624—31no—
169C2×#624—31no—
170C2×#624—31no—
171C2×#624—31no—
172C2×#624—61no—
173C2×#624—61no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—61no—
177C2×D3×Dic3C2×D311yescharacteristic
178C2×D3×Dic3C2×D311yescharacteristic
179C32×C4⋊C4—31no—
180C32×C4⋊C4—31no—
181#3757—31no—
182#3757—31no—
183#3752—31no—
184#3752C2×D311yescharacteristic
185C4⋊(C3⋊Dic3)—31no—
186C4⋊(C3⋊Dic3)C2×D311yescharacteristic
187#3750—31no—
188#3750C2×D311yescharacteristic
189C4×C3⋊Dic3—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—61no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×C4⋊Dic3—61no—
206C3×Dic3⋊C4—21no—
207C3×Dic3⋊C4—21no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—61no—
215C3×Dic3⋊C4C2×D311yescharacteristic
216C3×Dic3⋊C4C2×D311yescharacteristic
217C3×Dic3⋊C4C2×D311yescharacteristic
218C3×Dic3⋊C4C2×D311yescharacteristic
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221#3724—31no—
222#3724C2×D311yescharacteristic
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—61no—
238(C2×D3)⋊Dic3—31no—
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—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)#4112yes—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C33×C4—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#125—91no—
284C3×#123—91no—
285C3×#121—91no—
286#939—31no—
287#938—91no—
288#938—91no—
289#938—91no—
290#938—91no—
291#938—181no—
292#935—31no—
293#935—91no—
294D4×Dic3—91no—
295C4×#67—91no—
296C4×#67—91no—
297C4×#67—91no—
298#926—91no—
299#898—91no—
300#898—91no—
301#898—91no—
302#895—31no—
303#895—91no—
304#895—91no—
305#895—91no—
306#894—31no—
307#894—91no—
308#893—91no—
309#893—91no—
310#893—91no—
311#893—181no—
312#892—91no—
313D3×C4⋊C4—91no—
314D3×C4⋊C4—91no—
315D3×C4⋊C4—91no—
316D3×C4⋊C4—181no—
317#890—31no—
318#889—31no—
319#884—91no—
320#884—91no—
321#883—91no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#879—91no—
326#879—91no—
327#879—91no—
328#877—91no—
329C4×D12—91no—
330C4×D12—91no—
331C23×C32—31no—
332C23×C32—31no—
333C22×C3⋊D3—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—61no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—121no—
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—21no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—61no—
346C22×C3×D3C22×D311yescharacteristic
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C32×D4—121no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—31no—
357C2×C32×C4—31no—
358C2×C32×C4—41no—
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362#638—62no—
363#638—62no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—121no—
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C4⋊(C3⋊D3)—62no—
377C4×C3⋊D3—62no—
378C4×C3⋊D3—121no—
379C4×C3⋊D3—121no—
380C4×C3⋊D3—121no—
381C4×C3⋊D3—121no—
382C4×C3⋊D3—122no—
383C4×C3⋊D3—121no—
384C4×C3⋊D3—122no—
385C4×C3⋊D3—122no—
386C4×C3⋊D3—124no—
387C3×#67—62no—
388C3×#67—121no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
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—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3—121no—
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C3×D12—41no—
419C3×D12—41no—
420C3×D12—42no—
421C3×D12—62no—
422C3×D12—121no—
423C3×C4×D3—62no—
424C3×C4×D3—121no—
425#626—22no—
426#626—41no—
427#626—62no—
428#626—62no—
429#626—64no—
430#626—62no—
431#626—62no—
432#626—62no—
433#626—62no—
434#626—122no—
435#626—122no—
436#624—64no—
437#624—62no—
438#624—62no—
439#624—121no—
440#624—121no—
441#624—122no—
442D3×Dic3—22no—
443D3×Dic3—41no—
444D3×Dic3—121no—
445D3×Dic3—121no—
446D3×Dic3—122no—
447#553—271noSylow
448C2×C33C2×#4111yescharacteristic
449C2×C33C2×#4111yescharacteristic
450C2×C33H(5,𝔽2)11yescharacteristic
451C3⋊(C3⋊D3)—22no—
452C3×C3⋊D3—41no—
453C32×D3—41no—
454C32×D3—41no—
455C2×C3×D4—31no—
456C2×C3×D4—31no—
457C2×C3×D4—61no—
458C2×C3×D4—91no—
459C2×C3×D4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—91no—
465C2×#67—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—181no—
470C2×#67—181no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—91no—
474C2×D12—31no—
475C2×D12—31no—
476C2×D12—91no—
477C2×D12—91no—
478C2×D12—91no—
479C2×D12—91no—
480C2×D12—181no—
481C2×D12D3211yescharacteristic
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—91no—
493C2×C4×D3—91no—
494C2×C4×D3—91no—
495C2×C4×D3—181no—
496C2×C4×D3—181no—
497C2×C4×D3—181no—
498C2×C4×D3—181no—
499C2×C4×D3—181no—
500C2×C4×D3—181no—
501C2×C4×D3—361no—
502C3×C4⋊C4—31no—
503C3×C4⋊C4—31no—
504C3×C4⋊C4—31no—
505C3×C4⋊C4—31no—
506C3×C4⋊C4—61no—
507C3×C4⋊C4—61no—
508C3×C4⋊C4—91no—
509C3×C4⋊C4—91no—
510C3×C4⋊C4—91no—
511C3×C4⋊C4—91no—
512C3×C4⋊C4—91no—
513C3×C22⋊C4—91no—
514C3×C22⋊C4—91no—
515C3×C22⋊C4—91no—
516C3×C22⋊C4—91no—
517C3×C22⋊C4—91no—
518C3×C42—91no—
519#217—31no—
520#217—31no—
521#217—31no—
522#217—31no—
523#217—91no—
524#217—91no—
525#217—91no—
526#217—91no—
527#217—91no—
528#217—91no—
529#217—181no—
530#217—181no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—61no—
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—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—181no—
548C4⋊Dic3—31no—
549C4⋊Dic3—31no—
550C4⋊Dic3—31no—
551C4⋊Dic3—31no—
552C4⋊Dic3—61no—
553C4⋊Dic3—91no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—181no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—61no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—181no—
571Dic3⋊C4D3211yescharacteristic
572Dic3⋊C4D3211yescharacteristic
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—181no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—41no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32—61no—
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C22×C32C23×D311yescharacteristic
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3—21no—
598C2×C3⋊D3—32no—
599C2×C3⋊D3—32no—
600C2×C3⋊D3—32no—
601C2×C3⋊D3—62no—
602C2×C3⋊D3—62no—
603C2×C3⋊D3—62no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—61no—
606C2×C3⋊D3—62no—
607C2×C3⋊D3—62no—
608C2×C3⋊D3—61no—
609C2×C3⋊D3—61no—
610C2×C3⋊D3—61no—
611C2×C3⋊D3—61no—
612C2×C3⋊D3—122no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—121no—
615C2×C3⋊D3—121no—
616C2×C3⋊D3—121no—
617C2×C3⋊D3—122no—
618C2×C3⋊D3—122no—
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—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—41no—
637C2×C3×D3—62no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—121no—
645C2×C3×D3—121no—
646C32×C4—21no—
647C32×C4—22no—
648C32×C4—21no—
649C32×C4—21no—
650C32×C4—32no—
651C32×C4—41no—
652C32×C4—41no—
653C32×C4—42no—
654C32×C4—61no—
655C32×C4—61no—
656C32×C4—61no—
657C3⋊Dic3—21no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3⋊Dic3—21no—
661C3⋊Dic3—21no—
662C3⋊Dic3—61no—
663C3⋊Dic3—62no—
664C3⋊Dic3—61no—
665C3⋊Dic3—61no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
668C3⋊Dic3—122no—
669C3×Dic3—22no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—22no—
677C3×Dic3—41no—
678C3×Dic3—41no—
679C3×Dic3—62no—
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—61no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3#23712yes—
695C3×Dic3#23912yes—
696#126—271no—
697#126—271no—
698#125—91no—
699#123—91no—
700#123—271no—
701#121—91no—
702#121—271no—
703#121—271no—
704#121—271no—
705C4×D4—271no—
706C4×D4—271no—
707C4×D4—271no—
708C4×D4—271no—
709#117—271no—
710C2×C4⋊C4—271no—
711C33#55311yescharacteristic, complemented, Sylow
712C23×C3—31no—
713C23×C3—31no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—61no—
717C23×C3—61no—
718C23×C3—91no—
719C22×D3—31no—
720C22×D3—31no—
721C22×D3—61no—
722C22×D3—91no—
723C22×D3—91no—
724C22×D3—91no—
725C22×D3—181no—
726C22×D3—181no—
727C22×D3—181no—
728C22×D3—361no—
729C22×D3C2×D3211yescharacteristic
730C22×D3C2×D3211yescharacteristic
731C3×D4—121no—
732C3×D4—121no—
733C3×D4—122no—
734C3×D4—182no—
735C3×D4—361no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—41no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—61no—
751C2×C3×C4—61no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—182no—
758C2×C3×C4—361no—
759C2×C3×C4C2×D3211yescharacteristic
760C2×C3×C4C2×D3211yescharacteristic
761C2×C3×C4C2×D3211yescharacteristic
762#67—62no—
763#67—121no—
764#67—182no—
765#67—182no—
766#67—182no—
767#67—182no—
768#67—182no—
769#67—362no—
770#67—362no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—61no—
786C2×Dic3—62no—
787C2×Dic3—91no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—121no—
791C2×Dic3—181no—
792C2×Dic3—181no—
793C2×Dic3—181no—
794C2×Dic3—361no—
795C2×Dic3—361no—
796C2×Dic3C2×D3211yescharacteristic
797C2×Dic3C2×D3211yescharacteristic
798C2×Dic3C2×D3211yescharacteristic
799C2×Dic3C2×D3211yescharacteristic
800D12—41no—
801D12—62no—
802D12—121no—
803D12—182no—
804D12—182no—
805D12—184no—
806D12—182no—
807D12—182no—
808C4×D3—62no—
809C4×D3—121no—
810C4×D3—182no—
811C4×D3—182no—
812C4×D3—184no—
813C4×D3—182no—
814C4×D3—361no—
815C4×D3—361no—
816C4×D3—361no—
817C4×D3—362no—
818C4×D3—361no—
819C4×D3—361no—
820C4×D3—361no—
821C4×D3—362no—
822C4×D3—361no—
823C4×D3—361no—
824C4×D3—362no—
825C4×D3—362no—
826C4×D3—362no—
827C4×D3—364no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—41no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—121no—
841C2×C32—121no—
842C2×C32C2×#23711yescharacteristic
843C2×C32#100411yescharacteristic
844C2×C32#100411yescharacteristic
845C2×C32C2×#23911yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32#100911yescharacteristic
851C3⋊D3—41no—
852C3⋊D3—62no—
853C3⋊D3—64no—
854C3⋊D3—62no—
855C3⋊D3—62no—
856C3⋊D3—122no—
857C3⋊D3—122no—
858C3⋊D3—124no—
859C3×D3—41no—
860C3×D3—41no—
861C3×D3—41no—
862C3×D3—41no—
863C3×D3—81no—
864C3×D3—81no—
865C3×D3—122no—
866C3×D3—121no—
867C3×D3—121no—
868C2×D4—31no—
869C2×D4—91no—
870C2×D4—91no—
871C2×D4—271no—
872C2×D4—271no—
873C2×D4—271no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—271no—
877C22×C4—271no—
878C22×C4—271no—
879C22×C4—271no—
880C4⋊C4—31no—
881C4⋊C4—31no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C4⋊C4—91no—
886C4⋊C4—91no—
887C4⋊C4—271no—
888C4⋊C4—271no—
889C4⋊C4—271no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C42—91no—
901C42—271no—
902C42—271no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—41no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—61no—
910C22×C3—61no—
911C22×C3—61no—
912C22×C3—61no—
913C22×C3—61no—
914C22×C3—61no—
915C22×C3—61no—
916C22×C3—61no—
917C22×C3—61no—
918C22×C3—61no—
919C22×C3—121no—
920C22×C3—121no—
921C22×C3—121no—
922C22×C3—121no—
923C22×C3—121no—
924C22×C3—121no—
925C22×C3—181no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3C22×D3211yescharacteristic
929C22×C3C22×D3211yescharacteristic
930C22×C3C22×D3211yescharacteristic
931C2×D3—21no—
932C2×D3—21no—
933C2×D3—21no—
934C2×D3—21no—
935C2×D3—21no—
936C2×D3—21no—
937C2×D3—62no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—92no—
945C2×D3—92no—
946C2×D3—92no—
947C2×D3—121no—
948C2×D3—121no—
949C2×D3—182no—
950C2×D3—182no—
951C2×D3—182no—
952C2×D3—182no—
953C2×D3—182no—
954C2×D3—181no—
955C2×D3—181no—
956C2×D3—181no—
957C2×D3—181no—
958C2×D3—181no—
959C2×D3—181no—
960C2×D3—362no—
961C2×D3—361no—
962C2×D3—361no—
963C2×D3—361no—
964C2×D3—361no—
965C2×D3—362no—
966C2×D3—362no—
967C3×C4—22no—
968C3×C4—21no—
969C3×C4—21no—
970C3×C4—21no—
971C3×C4—32no—
972C3×C4—32no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4—42no—
976C3×C4—62no—
977C3×C4—62no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—61no—
984C3×C4—121no—
985C3×C4—121no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989C3×C4—181no—
990C3×C4—181no—
991Dic3—21no—
992Dic3—21no—
993Dic3—21no—
994Dic3—62no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—121no—
1006Dic3—121no—
1007Dic3—121no—
1008Dic3—121no—
1009Dic3—182no—
1010Dic3—181no—
1011Dic3—181no—
1012Dic3—181no—
1013Dic3—361no—
1014Dic3—361no—
1015Dic3—362no—
1016Dic3#379612yes—
1017C32—21no—
1018C32—21no—
1019C32—21no—
1020C32—41no—
1021C32#561411yescharacteristic, complemented
1022C32#566111yescharacteristic, complemented
1023C32#569511yescharacteristic, complemented
1024C23—31no—
1025C23—31no—
1026C23—91no—
1027C23—271no—
1028D4—121no—
1029D4—182no—
1030D4—361no—
1031D4—542no—
1032D4—542no—
1033D4—542no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—31no—
1037C2×C4—31no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—182no—
1044C2×C4—271no—
1045C2×C4—361no—
1046C2×C4—542no—
1047C2×C4—1081no—
1048C2×C4—1081no—
1049C2×C4—1081no—
1050C2×C4D3311yescharacteristic
1051C2×C3—21no—
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—41no—
1061C2×C3—41no—
1062C2×C3—41no—
1063C2×C3—121no—
1064C2×C3—121no—
1065C2×C3—121no—
1066C2×C3—121no—
1067C2×C3—241no—
1068C2×C3—241no—
1069C2×C3—361no—
1070C2×C3C2×#379611yescharacteristic
1071C2×C3#6430611yescharacteristic
1072C2×C3D3×#23711yescharacteristic
1073C2×C3#6431211yescharacteristic
1074C2×C3#6431411yescharacteristic
1075C2×C3#6431411yescharacteristic
1076C2×C3D3×#23911yescharacteristic
1077C2×C3#6431911yescharacteristic
1078C2×C3#6433011yescharacteristic
1079D3—41no—
1080D3—41no—
1081D3—122no—
1082D3—121no—
1083D3—121no—
1084D3—184no—
1085D3—182no—
1086D3—182no—
1087D3—182no—
1088D3—362no—
1089D3—362no—
1090D3—364no—
1091C22—61no—
1092C22—61no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—61no—
1097C22—181no—
1098C22—181no—
1099C22—181no—
1100C22—272no—
1101C22—541no—
1102C22—541no—
1103C22C2×D3311yescharacteristic
1104C4—21no—
1105C4—32no—
1106C4—61no—
1107C4—61no—
1108C4—61no—
1109C4—181no—
1110C4—181no—
1111C4—181no—
1112C4—181no—
1113C4—181no—
1114C4—541no—
1115C3—21no—
1116C3—21no—
1117C3—21no—
1118C3—41no—
1119C3#1059446111yescharacteristic, complemented
1120C3#1059448911yescharacteristic, complemented
1121C3#1059519511yescharacteristic, complemented
1122C2—121no—
1123C2—121no—
1124C2—361no—
1125C2—542no—
1126C2D3×#379611yescharacteristic
1127C2#1172437611yescharacteristic
1128C2#1172441911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723675C2semidirect
2. #11723531C2semidirect
3. #11723472C2semidirect
4. #11723470C2semidirect
5. C3×#63886C2semidirect
6. C3×#63884C2semidirect
7. C3×#63845C2semidirect
8. #11723019C2semidirect
9. #11722991C2semidirect
10. #11722963C2semidirect
11. #11722963C2semidirect
12. #11722935C2semidirect
13. #11722932C2semidirect
14. Dic3×#626C2semidirect
15. #11722914C2semidirect
82. #63886D3semidirect
84. #63884D3semidirect
100. #63845D3semidirect
711. C33#553semidirect
1021. C32#5614semidirect
1022. C32#5661semidirect
1023. C32#5695semidirect
1119. C3#10594461semidirect
1120. C3#10594489semidirect
1121. C3#10595195semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117235312
#117234722
#117234702
C3×#638862
C3×#638842
C3×#638452
#117230192
#117229912
#117229632
#117229352
#117229322
Dic3×#6262
#117229142
#105951953
#105944893
#105944613