Finite Group Databasebeta

← #13169179

Subgroups — #13169179

Order 1728.

1270 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723696C211yesmaximal, characteristic, complemented
2#11723532C211yesmaximal, characteristic, complemented
3C4×#6292C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic, complemented
7C3×#63869C211yesmaximal, characteristic, complemented
8#11723027C212yesmaximal, complemented
9#11722993C212yesmaximal, complemented
10#11722961C212yesmaximal, complemented
11#11722931C212yesmaximal, complemented
12#10594562—31nomaximal
13#10594561—31nomaximal
14#10593982—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6295C2212yes—
19C2×#6292C2211yescharacteristic
20C2×#6292C2212yes—
21C2×C3×#624C2212yes—
22C2×C3×#624C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4×Dic3C2211yescharacteristic
27#88814C2212yes—
28Dic3⋊(C3⋊Dic3)C2211yescharacteristic
29#88804C2212yes—
30#88804C2211yescharacteristic
31#88803C2212yes—
32#88803C2211yescharacteristic
33Dic3×C3⋊Dic3C2212yes—
34C3×#3724C2212yes—
35C3×#3724C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2212yes—
38#64104—31no—
39#64101—31no—
40C4×C4⋊(C3⋊D3)—31no—
41C3×#893—31no—
42C3×D3×C4⋊C4—31no—
43C3×D3×C4⋊C4—31no—
44C3×#890—31no—
45C3×C4×D12—31no—
46C3×#870—31no—
47#63916—31no—
48#63916—31no—
49#63916—31no—
50#63916—61no—
51#63910—32no—
52#63909—31no—
53#63909—32no—
54#63908—31no—
55#63906—32no—
56#63904—32no—
57#63904—32no—
58C4×#626—31no—
59C4×#626—31no—
60C4×#626—61no—
61C4×#625—32no—
62#63900D311yescharacteristic, complemented
63#63897—32no—
64#63894D311yescharacteristic, complemented
65#63869D311yescharacteristic, complemented
66#63862—32no—
67#63861—32no—
68#63850—32no—
69#63850—32no—
70#63849—31no—
71#63849—31no—
72#63849—61no—
73#63848—32no—
74C22×C3⋊(C3⋊D3)C2311yescharacteristic
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C4×C3⋊(C3⋊D3)—22no—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4⋊(C3⋊D3)—22no—
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88#6295—24no—
89#6292—22no—
90#6292—42no—
91C3×#624—42no—
92C3×#624—42no—
93#5695—91no—
94#5558—91no—
95#5514—91no—
96C2×C4⋊(C3⋊D3)—31no—
97C2×C4⋊(C3⋊D3)—32no—
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
99C2×C4×C3⋊D3—31no—
100C2×C4×C3⋊D3—31no—
101C2×C4×C3⋊D3—31no—
102C2×C4×C3⋊D3—61no—
103C2×C4×C3⋊D3—61no—
104C2×C4×C3⋊D3—61no—
105C2×C4×C3⋊D3—121no—
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×C3×D12—31no—
108C2×C3×D12—31no—
109C2×C3×D12—61no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—61no—
117C2×#626—32no—
118C2×#626—32no—
119C2×#626—31no—
120C2×#626—31no—
121C2×#626—32no—
122C2×#626—32no—
123C2×#626—61no—
124C2×#626—62no—
125C2×#625—32no—
126C2×#624C2×D312yes—
127C2×#624C2×D312yes—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C42—31no—
131#3752—31no—
132#3752—32no—
133#3752—31no—
134#3752—32no—
135C4⋊(C3⋊Dic3)—31no—
136C4⋊(C3⋊Dic3)C2×D311yescharacteristic
137C4×C3⋊Dic3—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—32no—
145C3×C4⋊Dic3—61no—
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3C2×D311yescharacteristic
157C3×C4×Dic3C2×D311yescharacteristic
158#3724C2×D312yes—
159#3724C2×D312yes—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—61no—
163Dic3⋊Dic3C2×D312yes—
164#3722—32no—
165#3722—32no—
166#3722—32no—
167#3722—31no—
168#3722—31no—
169#3722—62no—
170#3722—61no—
171#3722C2×D312yes—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—61no—
179(C2×D3)⋊Dic3—62no—
180Dic32—32no—
181Dic32—32no—
182Dic32—62no—
183C22×C33C2411yescharacteristic
184C2×C3⋊(C3⋊D3)—21no—
185C2×C3⋊(C3⋊D3)—21no—
186C2×C3⋊(C3⋊D3)—21no—
187C2×C3×C3⋊D3—21no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3—22no—
191C2×C3×C3⋊D3—22no—
192C2×C3×C3⋊D3#4112yes—
193C33×C4#4112yes—
194C3⋊(C3⋊Dic3)—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3—22no—
200C32×Dic3—22no—
201C3×#125—91no—
202C3×C4×D4—91no—
203C2×C3×C4⋊C4—91no—
204#938—91no—
205#938—91no—
206#930—92no—
207#930—91no—
208#929—92no—
209C4×#67—92no—
210C4×#67—92no—
211C4×#67—91no—
212#898—92no—
213#898—92no—
214#895—92no—
215#895—91no—
216#895—91no—
217#895—91no—
218#895—181no—
219#894—92no—
220#894—92no—
221#893—31no—
222#893—92no—
223#892—91no—
224#892—91no—
225#892—91no—
226#892—181no—
227D3×C4⋊C4—31no—
228D3×C4⋊C4—31no—
229#890—31no—
230#884—92no—
231#879—92no—
232C4×D12—31no—
233C4×D12—91no—
234C4×D12—91no—
235C4×D12—181no—
236#870—31no—
237C22×C3⋊D3—31no—
238C22×C3⋊D3—31no—
239C22×C3⋊D3—31no—
240C22×C3⋊D3—61no—
241C22×C3⋊D3—61no—
242C22×C3⋊D3—61no—
243C22×C3⋊D3—121no—
244C22×C3⋊D3C22×D312yes—
245C22×C3⋊D3C22×D311yescharacteristic
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—32no—
249C22×C3×D3—32no—
250C22×C3×D3—61no—
251C22×C3×D3—62no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—32no—
256C2×C32×C4—31no—
257C2×C32×C4—31no—
258C2×C32×C4—32no—
259C2×C32×C4—41no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—61no—
267C2×C3⋊Dic3—61no—
268C2×C3⋊Dic3—61no—
269C2×C3⋊Dic3—121no—
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D312yes—
272C4⋊(C3⋊D3)—22no—
273C4⋊(C3⋊D3)—62no—
274C4⋊(C3⋊D3)—122no—
275C4×C3⋊D3—22no—
276C4×C3⋊D3—62no—
277C4×C3⋊D3—64no—
278C4×C3⋊D3—62no—
279C4×C3⋊D3—62no—
280C4×C3⋊D3—122no—
281C4×C3⋊D3—122no—
282C4×C3⋊D3—124no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—61no—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D312yes—
298C2×C3×Dic3C22×D312yes—
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D311yescharacteristic
301C3×D12—62no—
302C3×D12—62no—
303C3×D12—122no—
304C3×C4×D3—62no—
305C3×C4×D3—62no—
306C3×C4×D3—122no—
307C3×C4×D3—122no—
308C3×C4×D3—122no—
309C3×C4×D3—122no—
310C3×C4×D3—122no—
311#626—62no—
312#626—62no—
313#626—64no—
314#626—64no—
315#626—64no—
316#626—122no—
317#626—122no—
318#626—124no—
319#625—64no—
320#624—42no—
321#624—42no—
322#553—271noSylow
323C2×C33C2×#4111yescharacteristic
324C2×C33C2×#4111yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C3⋊(C3⋊D3)—41no—
327C3×C3⋊D3—22no—
328C3×C3⋊D3—42no—
329C2×C3×D4—91no—
330C22×C3×C4—92no—
331C22×C3×C4—92no—
332C22×C3×C4—91no—
333C2×#67—92no—
334C2×#67—92no—
335C2×#67—91no—
336C2×#67—92no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—91no—
341C2×D12—91no—
342C2×D12—92no—
343C2×D12—92no—
344C2×D12—92no—
345C2×D12—181no—
346C2×D12—182no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—32no—
350C2×C4×D3—32no—
351C2×C4×D3—32no—
352C2×C4×D3—32no—
353C2×C4×D3—61no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—181no—
358C2×C4×D3—181no—
359C2×C4×D3—181no—
360C2×C4×D3—361no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—92no—
368C3×C4⋊C4—92no—
369C3×C4⋊C4—92no—
370C3×C4⋊C4—91no—
371C3×C22⋊C4—92no—
372C3×C42—31no—
373C3×C42—31no—
374C3×C42—61no—
375#217—92no—
376#217—92no—
377#217—91no—
378(C2×D3)⋊C4—32no—
379(C2×D3)⋊C4—32no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—92no—
383(C2×D3)⋊C4—92no—
384(C2×D3)⋊C4—92no—
385(C2×D3)⋊C4—92no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—92no—
389(C2×D3)⋊C4—92no—
390(C2×D3)⋊C4—92no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—181no—
393(C2×D3)⋊C4—182no—
394(C2×D3)⋊C4—181no—
395(C2×D3)⋊C4—182no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—32no—
399C4⋊Dic3—61no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3—181no—
403C4⋊Dic3D3211yescharacteristic
404C4⋊Dic3D3211yescharacteristic
405Dic3⋊C4—32no—
406Dic3⋊C4—32no—
407Dic3⋊C4—32no—
408Dic3⋊C4—32no—
409Dic3⋊C4—32no—
410Dic3⋊C4—91no—
411C4×Dic3—92no—
412C4×Dic3—92no—
413C4×Dic3—92no—
414C4×Dic3—182no—
415C4×Dic3D3211yescharacteristic
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—41no—
420C22×C32C23×D311yescharacteristic
421C22×C32C23×D311yescharacteristic
422C22×C32C23×D311yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—62no—
432C2×C3⋊D3—62no—
433C2×C3⋊D3—62no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—121no—
441C2×C3⋊D3—121no—
442C2×C3⋊D3—121no—
443C2×C3⋊D3—121no—
444C2×C3⋊D3—121no—
445C2×C3⋊D3—121no—
446C2×C3⋊D3—122no—
447C2×C3⋊D3—122no—
448C2×C3⋊D3—122no—
449C2×C3⋊D3#23912yes—
450C2×C3×D3—32no—
451C2×C3×D3—32no—
452C2×C3×D3—62no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—62no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—62no—
462C2×C3×D3—62no—
463C2×C3×D3—121no—
464C2×C3×D3—121no—
465C2×C3×D3—122no—
466C2×C3×D3—122no—
467C2×C3×D3—122no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4—42no—
472C32×C4—61no—
473C32×C4—61no—
474C32×C4—62no—
475C32×C4—62no—
476C32×C4#23512yes—
477C32×C4#23512yes—
478C32×C4#23912yes—
479C3⋊Dic3—21no—
480C3⋊Dic3—22no—
481C3⋊Dic3—61no—
482C3⋊Dic3—62no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3⋊Dic3—121no—
486C3⋊Dic3—121no—
487C3⋊Dic3—122no—
488C3×Dic3—22no—
489C3×Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—22no—
496C3×Dic3—21no—
497C3×Dic3—42no—
498C3×Dic3—41no—
499C3×Dic3—42no—
500C3×Dic3—61no—
501C3×Dic3—62no—
502C3×Dic3—61no—
503C3×Dic3—62no—
504C3×Dic3—121no—
505C3×Dic3—122no—
506#126—272no—
507#125—91no—
508#123—272no—
509#121—272no—
510#121—271no—
511#121—271no—
512C4×D4—91no—
513C4×D4—271no—
514C4×D4—272no—
515#117—271no—
516C2×C4⋊C4—91no—
517C33#55311yescharacteristic, complemented, Sylow
518C23×C3—91no—
519C23×C3—92no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—61no—
525C22×D3—62no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—181no—
532C22×D3—361no—
533C3×D4—182no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—41no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—61no—
549C2×C3×C4—62no—
550C2×C3×C4—92no—
551C2×C3×C4—91no—
552C2×C3×C4—182no—
553C2×C3×C4—362no—
554C2×C3×C4—362no—
555C2×C3×C4C2×D3211yescharacteristic
556C2×C3×C4C2×D3211yescharacteristic
557C2×C3×C4C2×D3211yescharacteristic
558#67—182no—
559#67—184no—
560#67—184no—
561#67—362no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—62no—
567C2×Dic3—61no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—181no—
572C2×Dic3—181no—
573C2×Dic3—181no—
574C2×Dic3—361no—
575C2×Dic3C2×D3212yes—
576C2×Dic3C2×D3211yescharacteristic
577C2×Dic3C2×D3211yescharacteristic
578C2×Dic3C2×D3212yes—
579D12—62no—
580D12—62no—
581D12—122no—
582D12—182no—
583D12—182no—
584D12—184no—
585D12—184no—
586D12—362no—
587D12—362no—
588D12—364no—
589C4×D3—62no—
590C4×D3—62no—
591C4×D3—122no—
592C4×D3—122no—
593C4×D3—122no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—184no—
597C4×D3—182no—
598C4×D3—182no—
599C4×D3—182no—
600C4×D3—362no—
601C4×D3—362no—
602C4×D3—364no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32—41no—
615C2×C32C2×#23511yescharacteristic
616C2×C32C2×#23511yescharacteristic
617C2×C32#100411yescharacteristic
618C2×C32#100411yescharacteristic
619C2×C32C2×#23911yescharacteristic
620C2×C32C2×#23911yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C2×C32D3×#4111yescharacteristic
623C2×C32#100911yescharacteristic
624C3⋊D3—22no—
625C3⋊D3—42no—
626C3⋊D3—122no—
627C3⋊D3—122no—
628C3⋊D3—122no—
629C3⋊D3—124no—
630C3⋊D3—121no—
631C3⋊D3—121no—
632C3⋊D3—121no—
633C3×D3—62no—
634C3×D3—62no—
635C3×D3—122no—
636C3×D3—122no—
637C3×D3—122no—
638C3×D3—242no—
639C2×D4—91no—
640C2×D4—271no—
641C2×D4—272no—
642C2×D4—272no—
643C22×C4—92no—
644C22×C4—92no—
645C22×C4—91no—
646C22×C4—271no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—92no—
650C4⋊C4—92no—
651C4⋊C4—92no—
652C4⋊C4—91no—
653C4⋊C4—271no—
654C22⋊C4—92no—
655C22⋊C4—272no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4—272no—
659C22⋊C4—272no—
660C42—31no—
661C42—272no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—41no—
666C22×C3—92no—
667C22×C3—181no—
668C22×C3—181no—
669C22×C3—182no—
670C22×C3—182no—
671C22×C3—182no—
672C22×C3C22×D3211yescharacteristic
673C22×C3C22×D3211yescharacteristic
674C22×C3C22×D3211yescharacteristic
675C2×D3—32no—
676C2×D3—32no—
677C2×D3—62no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—62no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—122no—
691C2×D3—122no—
692C2×D3—122no—
693C2×D3—182no—
694C2×D3—182no—
695C2×D3—182no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—361no—
706C2×D3—361no—
707C2×D3—361no—
708C2×D3—361no—
709C2×D3—361no—
710C2×D3—361no—
711C2×D3—362no—
712C2×D3—362no—
713C2×D3—362no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—42no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—61no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—122no—
728C3×C4—122no—
729C3×C4—121no—
730C3×C4—181no—
731C3×C4—182no—
732C3×C4#379812yes—
733C3×C4#379912yes—
734C3×C4#379912yes—
735Dic3—21no—
736Dic3—21no—
737Dic3—22no—
738Dic3—22no—
739Dic3—61no—
740Dic3—61no—
741Dic3—62no—
742Dic3—62no—
743Dic3—121no—
744Dic3—122no—
745Dic3—182no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749Dic3—361no—
750Dic3—361no—
751Dic3—362no—
752C32—21no—
753C32—21no—
754C32—21no—
755C32—41no—
756C32#551411yescharacteristic, complemented
757C32#555811yescharacteristic, complemented
758C32#569511yescharacteristic, complemented
759C23—91no—
760C23—92no—
761C23—271no—
762D4—182no—
763D4—542no—
764D4—544no—
765D4—1082no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—92no—
771C2×C4—91no—
772C2×C4—182no—
773C2×C4—271no—
774C2×C4—362no—
775C2×C4—362no—
776C2×C4—542no—
777C2×C4D3311yescharacteristic
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—182no—
791C2×C3—362no—
792C2×C3C2×#379811yescharacteristic
793C2×C3C2×#379911yescharacteristic
794C2×C3C2×#379911yescharacteristic
795C2×C3#6430611yescharacteristic
796C2×C3#6430711yescharacteristic
797C2×C3#6431311yescharacteristic
798C2×C3#6431411yescharacteristic
799C2×C3D3×#23911yescharacteristic
800C2×C3D3×#23911yescharacteristic
801D3—62no—
802D3—62no—
803D3—122no—
804D3—122no—
805D3—122no—
806D3—242no—
807D3—362no—
808D3—362no—
809D3—362no—
810D3—364no—
811D3—361no—
812D3—361no—
813D3—361no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—182no—
818C22—182no—
819C22—182no—
820C22—541no—
821C22—541no—
822C22—541no—
823C22C2×D3311yescharacteristic
824C4—61no—
825C4—62no—
826C4—62no—
827C4—61no—
828C4—182no—
829C4—181no—
830C4—541no—
831C4#8896512yes—
832C3—21no—
833C3—21no—
834C3—21no—
835C3—41no—
836C3#1059398211yescharacteristic, complemented
837C3#1059456111yescharacteristic, complemented
838C3#1059456211yescharacteristic, complemented
839C2—182no—
840C2—362no—
841C2—1081no—
842C2#1172438111yescharacteristic
843C2#1172439111yescharacteristic
844C2C2×#8896511yescharacteristic
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. #11723696C2semidirect
2. #11723532C2semidirect
3. C4×#6292C2semidirect
4. #11723413C2semidirect
5. C3×#63900C2semidirect
6. C3×#63894C2semidirect
7. C3×#63869C2semidirect
8. #11723027C2semidirect
9. #11722993C2semidirect
10. #11722961C2semidirect
11. #11722931C2semidirect
62. #63900D3semidirect
64. #63894D3semidirect
65. #63869D3semidirect
517. C33#553semidirect
756. C32#5514semidirect
757. C32#5558semidirect
758. C32#5695semidirect
836. C3#10593982semidirect
837. C3#10594561semidirect
838. C3#10594562semidirect

Maximal subgroups

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

subgroupindex
#117236962
#117235322
C4×#62922
#117234132
C3×#639002
C3×#638942
C3×#638692
#117230272
#117229932
#117229612
#117229312
#105945623
#105945613
#105939823