Finite Group Databasebeta

← #13169146

Subgroups — #13169146

Order 1728.

1518 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89021C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3#11723406C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63855C211yesmaximal, characteristic, complemented
8#11722936C212yesmaximal, complemented
9#11722930C212yesmaximal, complemented
10#11722921C212yesmaximal, complemented
11#11722911C212yesmaximal, complemented
12#10594990—31nomaximal
13#10594359—31nomaximal
14#10593887—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6294C2212yes—
19C2×#6290C2212yes—
20C2×Dic3×C3⋊D3C2212yes—
21#89021C418yescomplemented
22C2×C3×#624C2212yes—
23C2×C3×D3×Dic3C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88814C2212yes—
29#88806C2212yes—
30#88806C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×#3722C2212yes—
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×#3828—31no—
40C2×#3795—31no—
41C2×#3795—31no—
42C2×#3795—61no—
43#64096—31no—
44C4×#634—31no—
45C3×#926—31no—
46C2×C3×C4⋊Dic3—31no—
47C3×#893—31no—
48C3×D3×C4⋊C4—31no—
49C3×C4×D12—31no—
50C3×#872—31no—
51#63952—32no—
52#63952—32no—
53#63902—32no—
54C4×#625—32no—
55#63900—32no—
56#63898—31no—
57#63894—31no—
58#63894D311yescharacteristic, complemented
59Dic3×D12—31no—
60D3×C4⋊Dic3D311yescharacteristic, complemented
61#63879—32no—
62#63879—32no—
63#63878—32no—
64#63878—32no—
65D3×Dic3⋊C4—32no—
66D3×Dic3⋊C4—32no—
67#63855D311yescharacteristic, complemented
68#63849—32no—
69#63844—31no—
70#63844—31no—
71#63844—31no—
72#63844—31no—
73#63844—61no—
74#63844—61no—
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79#6308C2×C414yescomplemented
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4⋊(C3⋊D3)C2×C414yescomplemented
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C32×C4×D3C2×C414yescomplemented
89#6294—42no—
90#6290C2×C418yescomplemented
91Dic3×C3⋊D3C2×C418yescomplemented
92C3×#624—42no—
93C3×D3×Dic3—42no—
94#5546—91no—
95#5523—91no—
96#5504—91no—
97C22×C32×C4—31no—
98C2×#638—32no—
99#3828—38no—
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×C4×C3⋊D3—32no—
102C2×#634—31no—
103C2×#634—31no—
104C2×#634—31no—
105C2×#634—61no—
106C2×#634—61no—
107C2×#634—61no—
108C2×#634—121no—
109C22×C3×Dic3—32no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—61no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3C2×D311yescharacteristic
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×#625—32no—
120C2×#625—32no—
121C2×#625—62no—
122C2×#624—32no—
123C2×#624C2×D312yes—
124C2×D3×Dic3—32no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—62no—
129C2×D3×Dic3C2×D312yes—
130#3795—38no—
131#3795—38no—
132#3795—68no—
133C32×C4⋊C4—31no—
134C32×C42—31no—
135C4⋊(C3⋊Dic3)C2×D311yescharacteristic
136#3750—32no—
137#3750—32no—
138C4×C3⋊Dic3—32no—
139C4×C3⋊Dic3—32no—
140C4×C3⋊Dic3C2×D311yescharacteristic
141C3×#217—31no—
142C3×#217—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×C4⋊Dic3—21no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—32no—
151C3×C4⋊Dic3—31no—
152C3×C4⋊Dic3—31no—
153C3×C4⋊Dic3—61no—
154C3×C4⋊Dic3C2×D311yescharacteristic
155C3×C4⋊Dic3C2×D311yescharacteristic
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—31no—
158C3×Dic3⋊C4—31no—
159C3×C4×Dic3—21no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—61no—
163C3×C4×Dic3C2×D311yescharacteristic
164C3×C4×Dic3C2×D311yescharacteristic
165#3724—32no—
166#3724—32no—
167#3724—32no—
168#3724—32no—
169#3724—62no—
170#3724—62no—
171Dic3⋊Dic3C2×D311yescharacteristic
172Dic3⋊Dic3C2×D311yescharacteristic
173Dic3⋊Dic3C2×D312yes—
174#3722—32no—
175#3722C2×D312yes—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3C2×D311yescharacteristic
179(C2×D3)⋊Dic3C2×D311yescharacteristic
180Dic32—32no—
181Dic32—32no—
182Dic32—32no—
183Dic32—32no—
184Dic32—62no—
185Dic32—62no—
186C22×C33C2411yescharacteristic
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3C22×C414yes—
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C2×C32×D3C22×C412yes—
193C33×C4C22×C412yes—
194C3⋊(C3⋊Dic3)C22×C414yes—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3—21no—
198C32×Dic3—22no—
199C32×Dic3—21no—
200C32×Dic3—21no—
201C32×Dic3C22×C412yes—
202C2×#237—91no—
203C2×#235—91no—
204C2×#235—91no—
205C2×#235—181no—
206C3×C4×D4—91no—
207C3×#117—91no—
208C2×C3×C4⋊C4—91no—
209D4×Dic3—91no—
210C4×#67—92no—
211C4×#67—92no—
212C4×#67—92no—
213#926—31no—
214C2×C4⋊Dic3—31no—
215C2×Dic3⋊C4—92no—
216#893—31no—
217#893—91no—
218#892—92no—
219#892—92no—
220D3×C4⋊C4—31no—
221D3×C4⋊C4—92no—
222D3×C4⋊C4—92no—
223#887—91no—
224#887—91no—
225#887—91no—
226#887—181no—
227#67⋊C4—92no—
228#67⋊C4—92no—
229#67⋊C4—92no—
230#877—92no—
231C4×D12—31no—
232C4×D12—91no—
233#872—31no—
234C4×Dic6—91no—
235C4×Dic6—91no—
236C4×Dic6—91no—
237C4×Dic6—181no—
238C23×C32—31no—
239C22×C3⋊D3C22×D312yes—
240C22×C3×D3—21no—
241C22×C3×D3—32no—
242C22×C3×D3—32no—
243C22×C3×D3—62no—
244C22×C3×D3C22×D311yescharacteristic
245C22×C3×D3C22×D311yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—31no—
250C2×C32×C4—34no—
251C2×C32×C4—31no—
252C2×C32×C4—32no—
253C2×C32×C4—31no—
254C2×C32×C4—41no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258#638—38no—
259C2×C3⋊Dic3—32no—
260C2×C3⋊Dic3—32no—
261C2×C3⋊Dic3—32no—
262C2×C3⋊Dic3—62no—
263C2×C3⋊Dic3—62no—
264C2×C3⋊Dic3—62no—
265C2×C3⋊Dic3—122no—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4⋊(C3⋊D3)C4×D314yescomplemented
270C4×C3⋊D3—38no—
271#634—34no—
272#634—34no—
273#634—34no—
274#634—64no—
275#634—64no—
276#634—64no—
277#634—124no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3—122no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C22×D312yes—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C2×C3×Dic3C22×D311yescharacteristic
300C3×D12—34no—
301C3×D12—34no—
302C3×D12—64no—
303C3×C4×D3—24no—
304C3×C4×D3—122no—
305C3×C4×D3—122no—
306C3×C4×D3—122no—
307C3×C4×D3C4×D314yescomplemented
308C3×C4×D3C4×D314yescomplemented
309#625—38no—
310#625—38no—
311#625—68no—
312#624—42no—
313#624—122no—
314D3×Dic3—38no—
315D3×Dic3—38no—
316D3×Dic3—42no—
317D3×Dic3—68no—
318D3×Dic3—122no—
319D3×Dic3—122no—
320#520—271noSylow
321C2×C33C23×C411yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C2×C332−1+411yescharacteristic
324C3×C3⋊D3—24no—
325C32×D3—22no—
326C2×C3×D4—91no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—92no—
331C22×C3×C4—92no—
332C2×#67—92no—
333C2×#67—92no—
334C2×#67—92no—
335C2×#67—182no—
336C22×Dic3—32no—
337C22×Dic3—92no—
338C22×Dic3—92no—
339#237—98no—
340#235—98no—
341#235—98no—
342#235—188no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—32no—
349C2×C4×D3—92no—
350C2×C4×D3—92no—
351C2×C4×D3—92no—
352C2×C4×D3—92no—
353C2×C4×D3—182no—
354C2×C4×D3D3211yescharacteristic
355C2×Dic6—91no—
356C2×Dic6—91no—
357C2×Dic6—91no—
358C2×Dic6—181no—
359C2×Dic6—181no—
360C2×Dic6—181no—
361C2×Dic6—361no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—92no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C22⋊C4—92no—
370C3×C22⋊C4—91no—
371C3×C22⋊C4—91no—
372C3×C42—31no—
373C3×C42—31no—
374C3×C42—61no—
375C3×C42—91no—
376#217—31no—
377#217—31no—
378#217—92no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—32no—
382(C2×D3)⋊C4—32no—
383(C2×D3)⋊C4—92no—
384(C2×D3)⋊C4—92no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—32no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3D3211yescharacteristic
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—32no—
395Dic3⋊C4—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—92no—
398Dic3⋊C4—92no—
399Dic3⋊C4—92no—
400Dic3⋊C4—92no—
401Dic3⋊C4—182no—
402Dic3⋊C4—182no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—92no—
407C4×Dic3—92no—
408C4×Dic3—92no—
409C4×Dic3—92no—
410C4×Dic3—92no—
411C4×Dic3—92no—
412C4×Dic3—182no—
413C4×Dic3—182no—
414C4×Dic3D3211yescharacteristic
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—32no—
419C22×C32—41no—
420C22×C32—61no—
421C22×C32—61no—
422C22×C32C23×D311yescharacteristic
423C22×C32C23×D311yescharacteristic
424C22×C32C23×D311yescharacteristic
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3C2×C4×D314yes—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—22no—
433C2×C3×D3—34no—
434C2×C3×D3—34no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—64no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—122no—
443C2×C3×D3—122no—
444C2×C3×D3C2×C4×D312yes—
445C2×C3×D3C2×C4×D312yes—
446C32×C4—22no—
447C32×C4—22no—
448C32×C4—22no—
449C32×C4—32no—
450C32×C4—42no—
451C32×C4—61no—
452C32×C4—61no—
453C32×C4—62no—
454C32×C4C2×C4×D312yes—
455C32×C4C2×C4×D312yes—
456C32×C4C2×C4×D312yes—
457C3⋊Dic3—21no—
458C3⋊Dic3—22no—
459C3⋊Dic3—21no—
460C3⋊Dic3—34no—
461C3⋊Dic3—34no—
462C3⋊Dic3—34no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—64no—
466C3⋊Dic3—124no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—21no—
470C3×Dic3—22no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—42no—
477C3×Dic3—62no—
478C3×Dic3—61no—
479C3×Dic3—61no—
480C3×Dic3—62no—
481C3×Dic3—61no—
482C3×Dic3—62no—
483C3×Dic3—61no—
484C3×Dic3—122no—
485C3×Dic3—121no—
486C3×Dic3C2×C4×D312yes—
487C3×Dic3C2×C4×D312yes—
488C2×#41—271no—
489C4×Q8—271no—
490C4×Q8—271no—
491C4×D4—91no—
492C4×D4—271no—
493C4×D4—272no—
494C4×D4—272no—
495#117—91no—
496#117—272no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—272no—
499C33#52011yescharacteristic, complemented, Sylow
500C23×C3—31no—
501C23×C3—31no—
502C23×C3—61no—
503C23×C3—92no—
504C22×D3—32no—
505C22×D3—32no—
506C22×D3—62no—
507C22×D3C2×D3211yescharacteristic
508C3×D4—94no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—64no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—62no—
527C2×C3×C4—61no—
528C2×C3×C4—91no—
529C2×C3×C4—92no—
530C2×C3×C4—91no—
531C2×C3×C4—362no—
532C2×C3×C4—362no—
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536#67—98no—
537#67—98no—
538#67—98no—
539#67—188no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—62no—
549C2×Dic3—92no—
550C2×Dic3—92no—
551C2×Dic3—92no—
552C2×Dic3—98no—
553C2×Dic3—122no—
554C2×Dic3—182no—
555C2×Dic3—182no—
556C2×Dic3—182no—
557C2×Dic3—362no—
558C2×Dic3—362no—
559C2×Dic3C2×D3211yescharacteristic
560C2×Dic3C2×D3212yes—
561C2×Dic3C2×D3211yescharacteristic
562C2×Dic3C2×D3211yescharacteristic
563D12—34no—
564D12—34no—
565D12—64no—
566C4×D3—98no—
567C4×D3—98no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—188no—
572C4×D3—362no—
573C4×D3—362no—
574C4×D3#62414yescomplemented
575Dic6—94no—
576Dic6—94no—
577Dic6—94no—
578Dic6—184no—
579Dic6—184no—
580Dic6—184no—
581Dic6—364no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—62no—
595C2×C32C22×C4×D311yescharacteristic
596C2×C32C22×C4×D311yescharacteristic
597C2×C32C22×C4×D311yescharacteristic
598C2×C32#100411yescharacteristic
599C2×C32#100411yescharacteristic
600C2×C32#100711yescharacteristic
601C2×C32#100911yescharacteristic
602C2×C32#101011yescharacteristic
603C2×C32#101011yescharacteristic
604C3⋊D3—24no—
605C3×D3—22no—
606C3×D3—22no—
607C3×D3—42no—
608C3×D3—64no—
609C3×D3—64no—
610C3×D3—124no—
611#41—278no—
612C2×Q8—271no—
613C2×D4—91no—
614C2×D4—272no—
615C22×C4—31no—
616C22×C4—92no—
617C22×C4—92no—
618C22×C4—272no—
619C22×C4—272no—
620C4⋊C4—31no—
621C4⋊C4—92no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—272no—
626C4⋊C4—272no—
627C22⋊C4—92no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4—272no—
631C42—31no—
632C42—91no—
633C42—272no—
634C42—272no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—32no—
639C22×C3—32no—
640C22×C3—41no—
641C22×C3—62no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—94no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—182no—
650C22×C3—182no—
651C22×C3C22×D3211yescharacteristic
652C22×C3C22×D3211yescharacteristic
653C22×C3C22×D3211yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—34no—
657C2×D3—34no—
658C2×D3—64no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—122no—
664C2×D3—122no—
665C2×D3C2×#62412yes—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—32no—
670C3×C4—32no—
671C3×C4—42no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—61no—
675C3×C4—62no—
676C3×C4—62no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—121no—
681C3×C4—122no—
682C3×C4—182no—
683C3×C4—181no—
684C3×C4—181no—
685C3×C4C4×D3212yes—
686C3×C4C4×D3212yes—
687C3×C4C2×#62412yes—
688Dic3—21no—
689Dic3—21no—
690Dic3—22no—
691Dic3—62no—
692Dic3—61no—
693Dic3—61no—
694Dic3—62no—
695Dic3—61no—
696Dic3—61no—
697Dic3—62no—
698Dic3—94no—
699Dic3—94no—
700Dic3—94no—
701Dic3—122no—
702Dic3—121no—
703Dic3—184no—
704Dic3—184no—
705Dic3—184no—
706Dic3—364no—
707Dic3C2×#62412yes—
708C32—21no—
709C32—21no—
710C32—21no—
711C32—41no—
712C32#550411yescharacteristic, complemented
713C32#552311yescharacteristic, complemented
714C32#554611yescharacteristic, complemented
715C23—31no—
716C23—92no—
717Q8—274no—
718D4—94no—
719D4—278no—
720C2×C4—31no—
721C2×C4—34no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—32no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—92no—
728C2×C4—278no—
729C2×C4—272no—
730C2×C4—362no—
731C2×C4—362no—
732C2×C4—1082no—
733C2×C4D3311yescharacteristic
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—62no—
747C2×C3—62no—
748C2×C3—122no—
749C2×C3—184no—
750C2×C3#6429711yescharacteristic
751C2×C3#6429811yescharacteristic
752C2×C3C2×C4×D3211yescharacteristic
753C2×C3C2×C4×D3211yescharacteristic
754C2×C3#6430711yescharacteristic
755C2×C3#6430711yescharacteristic
756C2×C3#6431311yescharacteristic
757C2×C3#6431511yescharacteristic
758C2×C3C22×#62411yescharacteristic
759D3—22no—
760D3—64no—
761D3—64no—
762D3—124no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—94no—
767C22—182no—
768C22—182no—
769C22C2×D3311yescharacteristic
770C4—32no—
771C4—61no—
772C4—62no—
773C4—61no—
774C4—182no—
775C4—181no—
776C4—181no—
777C4—274no—
778C4D3×#62412yes—
779C3—21no—
780C3—21no—
781C3—21no—
782C3—41no—
783C3#1059388711yescharacteristic, complemented
784C3#1059435911yescharacteristic, complemented
785C3#1059499011yescharacteristic, complemented
786C2—62no—
787C2—184no—
788C2#1172438011yescharacteristic
789C2#1172439611yescharacteristic
790C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89021C2
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. #11723406C2semidirect
4. #11723399C2semidirect
5. C3×#63894C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63855C2semidirect
8. #11722936C2semidirect
9. #11722930C2semidirect
10. #11722921C2semidirect
11. #11722911C2semidirect
21. #89021C4semidirect
58. #63894D3semidirect
60. D3×C4⋊Dic3D3semidirect
67. #63855D3semidirect
79. #6308C2×C4semidirect
83. C3×C4⋊(C3⋊D3)C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
90. #6290C2×C4semidirect
91. Dic3×C3⋊D3C2×C4semidirect
269. C4⋊(C3⋊D3)C4×D3semidirect
307. C3×C4×D3C4×D3semidirect
308. C3×C4×D3C4×D3semidirect
499. C33#520semidirect
574. C4×D3#624semidirect
712. C32#5504semidirect
713. C32#5523semidirect
714. C32#5546semidirect
783. C3#10593887semidirect
784. C3#10594359semidirect
785. C3#10594990semidirect

Maximal subgroups

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

subgroupindex
C2×#890212
#117236912
#117234062
#117233992
C3×#638942
C3×D3×C4⋊Dic32
C3×#638552
#117229362
#117229302
#117229212
#117229112
#105949903
#105943593
#105938873