Finite Group Databasebeta

← #13169261

Subgroups — #13169261

Order 1728.

1562 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89017C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3#11723503C211yesmaximal, characteristic, complemented
4#11723452C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63843C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722937C212yesmaximal, complemented
9#11722933C212yesmaximal, complemented
10#11722919C212yesmaximal, complemented
11#11722911C212yesmaximal, complemented
12#10595353—31nomaximal
13#10594361—31nomaximal
14#10593889—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2212yes—
19C2×#6292C2212yes—
20C2×#6289C2212yes—
21C2×Dic3×C3⋊D3C2212yes—
22#89017C418yescomplemented
23C2×C3×#624C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88814C2212yes—
29#88806C2211yescharacteristic
30#88806C2212yes—
31#88806C2211yescharacteristic
32#88804C2211yescharacteristic
33#88804C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38C3×Dic32C2212yes—
39C2×#3832—31no—
40C2×#3796—31no—
41C2×#3796—31no—
42C2×#3796—61no—
43C4⋊C4×C3⋊D3—31no—
44#64081—31no—
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—31no—
47C3×#893—31no—
48C3×#887—31no—
49C3×C4×D12—31no—
50C3×C4×Dic6—31no—
51#63904—32no—
52C4×#626—32no—
53#63900—32no—
54#63900—31no—
55#63900—31no—
56#63900—61no—
57#63898—31no—
58#63894—31no—
59#63894—32no—
60#63894—32no—
61#63894D311yescharacteristic, complemented
62Dic3×D12—31no—
63#63881—32no—
64#63880—32no—
65#63877—32no—
66#63877—32no—
67D3×Dic3⋊C4—32no—
68D3×Dic3⋊C4—32no—
69#63874—31no—
70#63874—31no—
71#63874—32no—
72#63874—61no—
73#63843D311yescharacteristic, complemented
74Dic3×Dic6D311yescharacteristic, complemented
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊D3C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C4×C3⋊(C3⋊D3)C2×C414yescomplemented
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4⋊(C3⋊D3)C2×C414yescomplemented
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C32×Dic6C2×C414yescomplemented
89#6294—42no—
90#6292C2×C418yescomplemented
91#6289—42no—
92Dic3×C3⋊D3C2×C418yescomplemented
93C3×#624—42no—
94#5574—91no—
95#5574—91no—
96#5546—91no—
97C2×C32×Q8—31no—
98#3832—38no—
99C2×C4⋊(C3⋊D3)—32no—
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×C4×C3⋊D3—32no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3—31no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—32no—
106C2×C4×C3⋊D3—61no—
107C2×C4×C3⋊D3—61no—
108C2×C4×C3⋊D3—61no—
109C2×C4×C3⋊D3—121no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—61no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—32no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2×D311yescharacteristic
117C2×C3×Dic6C2×D311yescharacteristic
118C2×#626—32no—
119C2×#626—32no—
120C2×#626—62no—
121C2×#624—32no—
122C2×#624—32no—
123C2×#624—32no—
124C2×#624—62no—
125C2×#624C2×D312yes—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129C2×D3×Dic3—32no—
130C2×D3×Dic3—62no—
131#3796—38no—
132#3796—38no—
133#3796—68no—
134C32×C4⋊C4—31no—
135C32×C42—31no—
136#3752—31no—
137#3752—31no—
138C4⋊(C3⋊Dic3)C2×D311yescharacteristic
139#3750—31no—
140#3750—31no—
141#3750—32no—
142C4×C3⋊Dic3C2×D311yescharacteristic
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—32no—
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—32no—
149C3×C4⋊Dic3—32no—
150C3×C4⋊Dic3—61no—
151C3×C4⋊Dic3C2×D311yescharacteristic
152C3×C4⋊Dic3C2×D311yescharacteristic
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—32no—
159C3×C4×Dic3—32no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3—61no—
163C3×C4×Dic3C2×D311yescharacteristic
164C3×C4×Dic3C2×D311yescharacteristic
165#3724—31no—
166#3724—31no—
167#3724—31no—
168#3724—31no—
169#3724—32no—
170#3724—32no—
171#3724—61no—
172#3724—61no—
173#3724—62no—
174Dic3⋊Dic3C2×D312yes—
175Dic3⋊Dic3C2×D312yes—
176#3722—32no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180#3722—31no—
181#3722—61no—
182#3722—61no—
183#3722C2×D312yes—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186Dic32C2×D312yes—
187Dic32C2×D312yes—
188C22×C33C2411yescharacteristic
189C2×C3⋊(C3⋊D3)—21no—
190C2×C3⋊(C3⋊D3)—21no—
191C2×C3⋊(C3⋊D3)C22×C412yes—
192C2×C3×C3⋊D3—22no—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3C22×C414yes—
195C33×C4C22×C412yes—
196C3⋊(C3⋊Dic3)C22×C412yes—
197C3×C3⋊Dic3—22no—
198C3×C3⋊Dic3—21no—
199C3×C3⋊Dic3—21no—
200C32×Dic3—21no—
201C32×Dic3—22no—
202C32×Dic3—21no—
203C32×Dic3C22×C414yes—
204C2×#239—91no—
205C2×#239—91no—
206C2×#239—181no—
207C2×#237—91no—
208C3×C4×Q8—91no—
209C3×C4×Q8—91no—
210C3×C4×D4—91no—
211Q8×Dic3—31no—
212Q8×Dic3—31no—
213D4×Dic3—91no—
214C4×#67—92no—
215C2×Dic3⋊C4—92no—
216#893—31no—
217#893—92no—
218#893—92no—
219#893—91no—
220D3×C4⋊C4—91no—
221D3×C4⋊C4—91no—
222D3×C4⋊C4—92no—
223D3×C4⋊C4—92no—
224D3×C4⋊C4—91no—
225D3×C4⋊C4—181no—
226#887—31no—
227#67⋊C4—92no—
228#877—92no—
229C4×D12—31no—
230C4×D12—92no—
231C4×D12—92no—
232C4×D12—91no—
233#872—92no—
234#872—92no—
235#872—91no—
236#872—91no—
237#872—91no—
238#872—181no—
239C4×Dic6—31no—
240C22×C3⋊D3—31no—
241C22×C3⋊D3—31no—
242C22×C3⋊D3—31no—
243C22×C3⋊D3—61no—
244C22×C3⋊D3—61no—
245C22×C3⋊D3—61no—
246C22×C3⋊D3—121no—
247C22×C3⋊D3C22×D312yes—
248C22×C3×D3—32no—
249C22×C3×D3—32no—
250C22×C3×D3—62no—
251C32×Q8—34no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—32no—
256C2×C32×C4—31no—
257C2×C32×C4—32no—
258C2×C32×C4—31no—
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—
272C2×C3⋊Dic3C22×D311yescharacteristic
273C4⋊(C3⋊D3)—38no—
274C4⋊(C3⋊D3)C4×D314yescomplemented
275C4×C3⋊D3—38no—
276C4×C3⋊D3—34no—
277C4×C3⋊D3—34no—
278C4×C3⋊D3—34no—
279C4×C3⋊D3—64no—
280C4×C3⋊D3—64no—
281C4×C3⋊D3—64no—
282C4×C3⋊D3—124no—
283C4×C3⋊D3—122no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—62no—
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D312yes—
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D311yescharacteristic
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D312yes—
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D312yes—
305C3×D12—34no—
306C3×D12—34no—
307C3×D12—64no—
308C3×C4×D3—122no—
309C3×C4×D3—122no—
310C3×Dic6—24no—
311C3×Dic6C4×D314yescomplemented
312C3×Dic6C4×D314yescomplemented
313#626—38no—
314#626—38no—
315#626—68no—
316#624—42no—
317#624—122no—
318#624—122no—
319#624—124no—
320#624—122no—
321D3×Dic3—38no—
322D3×Dic3—38no—
323D3×Dic3—68no—
324D3×Dic3—122no—
325D3×Dic3—122no—
326#520—271noSylow
327C2×C33C23×C411yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C2×C332−1+411yescharacteristic
330C3⋊(C3⋊D3)—22no—
331C3×C3⋊D3—24no—
332C2×C3×Q8—31no—
333C2×C3×Q8—31no—
334C2×C3×Q8—61no—
335C2×C3×D4—91no—
336C22×C3×C4—92no—
337C2×#67—92no—
338C22×Dic3—92no—
339C22×Dic3—92no—
340#239—98no—
341#239—98no—
342#239—188no—
343#237—98no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—61no—
347C2×D12—92no—
348C2×D12—92no—
349C2×D12—182no—
350C2×C4×D3—32no—
351C2×C4×D3—32no—
352C2×C4×D3—92no—
353C2×C4×D3—92no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—92no—
358C2×C4×D3—92no—
359C2×C4×D3—92no—
360C2×C4×D3—92no—
361C2×C4×D3—92no—
362C2×C4×D3—181no—
363C2×C4×D3—181no—
364C2×C4×D3—181no—
365C2×C4×D3—182no—
366C2×C4×D3—182no—
367C2×C4×D3—361no—
368C2×Dic6D3211yescharacteristic
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—92no—
373C3×C4⋊C4—92no—
374C3×C4⋊C4—91no—
375C3×C22⋊C4—92no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—61no—
379C3×C42—92no—
380C3×C42—92no—
381C3×C42—91no—
382#217—92no—
383(C2×D3)⋊C4—32no—
384(C2×D3)⋊C4—32no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—92no—
390(C2×D3)⋊C4—92no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—181no—
394(C2×D3)⋊C4—181no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—32no—
398C4⋊Dic3—32no—
399C4⋊Dic3—61no—
400C4⋊Dic3D3211yescharacteristic
401Dic3⋊C4—32no—
402Dic3⋊C4—32no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—92no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—92no—
409Dic3⋊C4—91no—
410Dic3⋊C4—92no—
411Dic3⋊C4—91no—
412Dic3⋊C4—181no—
413Dic3⋊C4—181no—
414Dic3⋊C4—182no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—32no—
418C4×Dic3—32no—
419C4×Dic3—32no—
420C4×Dic3—32no—
421C4×Dic3—61no—
422C4×Dic3D3211yescharacteristic
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—41no—
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D311yescharacteristic
429C22×C32C23×D311yescharacteristic
430C2×C3⋊D3—22no—
431C2×C3⋊D3—22no—
432C2×C3⋊D3—32no—
433C2×C3⋊D3—32no—
434C2×C3⋊D3—32no—
435C2×C3⋊D3—62no—
436C2×C3⋊D3—62no—
437C2×C3⋊D3—62no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—62no—
441C2×C3⋊D3—62no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—122no—
447C2×C3⋊D3—121no—
448C2×C3⋊D3—121no—
449C2×C3⋊D3—121no—
450C2×C3⋊D3—121no—
451C2×C3⋊D3—122no—
452C2×C3⋊D3—122no—
453C2×C3⋊D3C2×C4×D314yes—
454C2×C3×D3—34no—
455C2×C3×D3—34no—
456C2×C3×D3—64no—
457C2×C3×D3—62no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—122no—
462C2×C3×D3—122no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—34no—
467C32×C4—42no—
468C32×C4—61no—
469C32×C4—61no—
470C32×C4—62no—
471C32×C4C2×C4×D312yes—
472C32×C4C2×C4×D312yes—
473C32×C4C2×C4×D312yes—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—22no—
477C3⋊Dic3—32no—
478C3⋊Dic3—32no—
479C3⋊Dic3—32no—
480C3⋊Dic3—62no—
481C3⋊Dic3—62no—
482C3⋊Dic3—62no—
483C3⋊Dic3—122no—
484C3×Dic3—21no—
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—22no—
488C3×Dic3—21no—
489C3×Dic3—21no—
490C3×Dic3—24no—
491C3×Dic3—42no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C3×Dic3—62no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—62no—
499C3×Dic3—61no—
500C3×Dic3—122no—
501C3×Dic3—121no—
502C3×Dic3—121no—
503C3×Dic3C2×C4×D314yes—
504C3×Dic3C2×C4×D314yes—
505C2×#41—271no—
506C4×Q8—91no—
507C4×Q8—91no—
508C4×D4—91no—
509C4×D4—272no—
510C4×D4—272no—
511C4×D4—271no—
512#117—271no—
513#117—272no—
514C2×C4⋊C4—271no—
515C2×C4⋊C4—272no—
516C33#52011yescharacteristic, complemented, Sylow
517C23×C3—92no—
518C22×D3—32no—
519C22×D3—32no—
520C22×D3—62no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—181no—
525C22×D3—181no—
526C22×D3—181no—
527C22×D3—361no—
528C3×Q8—34no—
529C3×Q8—34no—
530C3×Q8—64no—
531C3×D4—94no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—31no—
538C2×C3×C4—32no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—31no—
543C2×C3×C4—41no—
544C2×C3×C4—62no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—91no—
549C2×C3×C4—91no—
550C2×C3×C4—92no—
551C2×C3×C4—362no—
552C2×C3×C4C2×D3211yescharacteristic
553C2×C3×C4C2×D3211yescharacteristic
554C2×C3×C4C2×D3211yescharacteristic
555#67—98no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—31no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—62no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—98no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3—181no—
572C2×Dic3—361no—
573C2×Dic3—362no—
574C2×Dic3C2×D3211yescharacteristic
575C2×Dic3C2×D3212yes—
576C2×Dic3C2×D3211yescharacteristic
577C2×Dic3C2×D3212yes—
578D12—34no—
579D12—34no—
580D12—64no—
581D12—98no—
582D12—98no—
583D12—188no—
584C4×D3—98no—
585C4×D3—98no—
586C4×D3—94no—
587C4×D3—94no—
588C4×D3—94no—
589C4×D3—122no—
590C4×D3—122no—
591C4×D3—184no—
592C4×D3—184no—
593C4×D3—184no—
594C4×D3—188no—
595C4×D3—364no—
596C4×D3—362no—
597C4×D3—362no—
598C4×D3—362no—
599C4×D3—362no—
600C4×D3—362no—
601C4×D3—364no—
602Dic6#62414yescomplemented
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×C32C22×C4×D311yescharacteristic
616C2×C32C22×C4×D311yescharacteristic
617C2×C32C22×C4×D311yescharacteristic
618C2×C32#100411yescharacteristic
619C2×C32#100711yescharacteristic
620C2×C32#100711yescharacteristic
621C2×C32#100911yescharacteristic
622C2×C32#100911yescharacteristic
623C2×C32#101011yescharacteristic
624C3⋊D3—24no—
625C3⋊D3—62no—
626C3⋊D3—64no—
627C3⋊D3—62no—
628C3⋊D3—62no—
629C3⋊D3—122no—
630C3⋊D3—122no—
631C3⋊D3—124no—
632C3×D3—64no—
633C3×D3—64no—
634C3×D3—124no—
635#41—278no—
636C2×Q8—31no—
637C2×D4—91no—
638C2×D4—272no—
639C22×C4—92no—
640C22×C4—272no—
641C22×C4—272no—
642C22×C4—272no—
643C22×C4—271no—
644C4⋊C4—31no—
645C4⋊C4—92no—
646C4⋊C4—92no—
647C4⋊C4—91no—
648C4⋊C4—271no—
649C4⋊C4—272no—
650C4⋊C4—271no—
651C22⋊C4—92no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—272no—
655C42—31no—
656C42—92no—
657C42—92no—
658C42—91no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—41no—
663C22×C3—94no—
664C22×C3—182no—
665C22×C3—182no—
666C22×C3C22×D3211yescharacteristic
667C22×C3C22×D3211yescharacteristic
668C22×C3C22×D3211yescharacteristic
669C2×D3—34no—
670C2×D3—34no—
671C2×D3—64no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—92no—
677C2×D3—92no—
678C2×D3—92no—
679C2×D3—122no—
680C2×D3—122no—
681C2×D3—182no—
682C2×D3—182no—
683C2×D3—182no—
684C2×D3—182no—
685C2×D3—182no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—362no—
693C2×D3—361no—
694C2×D3—361no—
695C2×D3—361no—
696C2×D3—361no—
697C2×D3—362no—
698C2×D3—362no—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—34no—
703C3×C4—34no—
704C3×C4—42no—
705C3×C4—64no—
706C3×C4—62no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—62no—
711C3×C4—61no—
712C3×C4—122no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—181no—
716C3×C4—181no—
717C3×C4—182no—
718C3×C4C4×D3212yes—
719C3×C4C4×D3212yes—
720C3×C4C2×#62412yes—
721Dic3—21no—
722Dic3—21no—
723Dic3—22no—
724Dic3—62no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—62no—
729Dic3—61no—
730Dic3—92no—
731Dic3—92no—
732Dic3—92no—
733Dic3—122no—
734Dic3—121no—
735Dic3—121no—
736Dic3—182no—
737Dic3—182no—
738Dic3—182no—
739Dic3—362no—
740Dic3C2×#62414yes—
741C32—21no—
742C32—21no—
743C32—21no—
744C32—41no—
745C32#554611yescharacteristic, complemented
746C32#557411yescharacteristic, complemented
747C32#557411yescharacteristic, complemented
748C23—92no—
749C23—271no—
750Q8—34no—
751D4—94no—
752D4—278no—
753C2×C4—32no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—32no—
757C2×C4—91no—
758C2×C4—92no—
759C2×C4—91no—
760C2×C4—278no—
761C2×C4—271no—
762C2×C4—274no—
763C2×C4—362no—
764C2×C4—1082no—
765C2×C4—1082no—
766C2×C4D3311yescharacteristic
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—41no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—184no—
780C2×C3#6429711yescharacteristic
781C2×C3C2×C4×D3211yescharacteristic
782C2×C3C2×C4×D3211yescharacteristic
783C2×C3#6430711yescharacteristic
784C2×C3#6431411yescharacteristic
785C2×C3#6431511yescharacteristic
786C2×C3#6431611yescharacteristic
787C2×C3#6432011yescharacteristic
788C2×C3C22×#62411yescharacteristic
789D3—64no—
790D3—64no—
791D3—124no—
792D3—184no—
793D3—182no—
794D3—182no—
795D3—182no—
796D3—362no—
797D3—362no—
798D3—364no—
799C22—94no—
800C22—182no—
801C22—182no—
802C22—272no—
803C22—541no—
804C22—541no—
805C22C2×D3311yescharacteristic
806C4—34no—
807C4—61no—
808C4—62no—
809C4—61no—
810C4—182no—
811C4—181no—
812C4—181no—
813C4—272no—
814C4D3×#62412yes—
815C3—21no—
816C3—21no—
817C3—21no—
818C3—41no—
819C3#1059388911yescharacteristic, complemented
820C3#1059436111yescharacteristic, complemented
821C3#1059535311yescharacteristic, complemented
822C2—184no—
823C2—542no—
824C2#1172438511yescharacteristic
825C2#1172439711yescharacteristic
826C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89017C2
hypercenterC2×C4D33
hypocenterC33#520
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723691C2semidirect
3. #11723503C2semidirect
4. #11723452C2semidirect
5. C3×#63894C2semidirect
6. C3×#63843C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722937C2semidirect
9. #11722933C2semidirect
10. #11722919C2semidirect
11. #11722911C2semidirect
22. #89017C4semidirect
61. #63894D3semidirect
73. #63843D3semidirect
74. Dic3×Dic6D3semidirect
79. C4×C3⋊(C3⋊D3)C2×C4semidirect
83. C3×C4⋊(C3⋊D3)C2×C4semidirect
88. C32×Dic6C2×C4semidirect
90. #6292C2×C4semidirect
92. Dic3×C3⋊D3C2×C4semidirect
274. C4⋊(C3⋊D3)C4×D3semidirect
311. C3×Dic6C4×D3semidirect
312. C3×Dic6C4×D3semidirect
516. C33#520semidirect
602. Dic6#624semidirect
745. C32#5546semidirect
746. C32#5574semidirect
747. C32#5574semidirect
819. C3#10593889semidirect
820. C3#10594361semidirect
821. C3#10595353semidirect

Maximal subgroups

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

subgroupindex
C2×#890172
#117236912
#117235032
#117234522
C3×#638942
C3×#638432
C3×Dic3×Dic62
#117229372
#117229332
#117229192
#117229112
#105953533
#105943613
#105938893