Finite Group Databasebeta

← #13169166

Subgroups — #13169166

Order 1728.

1562 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89020C211yesmaximal, characteristic
2#11723667C211yesmaximal, characteristic, complemented
3#11723503C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11722943C212yesmaximal, complemented
9#11722935C212yesmaximal, complemented
10#11722933C212yesmaximal, complemented
11#11722930C212yesmaximal, complemented
12#10594990—31nomaximal
13#10594510—31nomaximal
14#10594509—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6293C2211yescharacteristic
19C2×#6292C2211yescharacteristic
20C2×#6291C2211yescharacteristic
21C2×#6290C2211yescharacteristic
22C2×#6289C2212yes—
23#89020C418yescomplemented
24C2×C3×#624C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30#88814C2212yes—
31#88813C2212yes—
32#88806C2212yes—
33#88804C2212yes—
34Dic3×C3⋊Dic3C2212yes—
35C3×#3724C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×#3828—31no—
40C2×#3798—31no—
41C2×#3798—31no—
42C2×#3798—61no—
43#64101—31no—
44C4⋊C4×C3⋊D3—31no—
45C3×#926—31no—
46C2×C3×C4⋊Dic3—31no—
47C3×#892—31no—
48C3×D3×C4⋊C4—31no—
49C3×D3×C4⋊C4—31no—
50C3×D3×C4⋊C4—31no—
51#63952—32no—
52#63952—32no—
53#63904—32no—
54#63904—32no—
55C4×#626—32no—
56C4×#625—32no—
57#63900—31no—
58#63900—31no—
59#63900—61no—
60#63900D311yescharacteristic, complemented
61#63894—32no—
62D3×C4⋊Dic3D311yescharacteristic, complemented
63#63881—32no—
64#63879—32no—
65#63849—31no—
66#63849—31no—
67#63849—31no—
68#63849—61no—
69#63844—32no—
70#63841—31no—
71#63841—31no—
72#63841D311yescharacteristic, complemented
73#63838—32no—
74#63837—32no—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C4×C3⋊(C3⋊D3)C2×C414yescomplemented
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3C2×C414yescomplemented
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C32×C4×D3C2×C414yescomplemented
89#6293C2×C414yescomplemented
90#6292C2×C414yescomplemented
91#6291C2×C414yescomplemented
92#6290C2×C414yescomplemented
93#6289—42no—
94C3×#624—42no—
95C3×D3×Dic3—42no—
96#5523—91no—
97#5504—91no—
98#5504—91no—
99C22×C32×C4—31no—
100C2×#638—31no—
101C2×#638—31no—
102#3828—38no—
103C2×C4⋊(C3⋊D3)—31no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—31no—
106C2×C4×C3⋊D3—31no—
107C2×C4×C3⋊D3—32no—
108C2×C4×C3⋊D3—61no—
109C2×C4×C3⋊D3—61no—
110C2×C4×C3⋊D3—61no—
111C2×C4×C3⋊D3—121no—
112C2×C4×C3⋊D3C2×D311yescharacteristic
113C2×#634—31no—
114C22×C3×Dic3—32no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—32no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3—61no—
122C2×C3×C4×D3C2×D311yescharacteristic
123C2×C3×C4×D3C2×D311yescharacteristic
124C2×#627—31no—
125C2×#627—31no—
126C2×#627—61no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—61no—
132C2×#626—61no—
133C2×#625—31no—
134C2×#625—31no—
135C2×#625—61no—
136C2×#624—32no—
137C2×#624—32no—
138C2×#624—62no—
139C2×#624C2×D312yes—
140C2×D3×Dic3C2×D312yes—
141#3798—38no—
142#3798—38no—
143#3798—68no—
144C32×C4⋊C4—31no—
145C32×C4⋊C4—31no—
146#3752—32no—
147C4⋊(C3⋊Dic3)C2×D311yescharacteristic
148C4⋊(C3⋊Dic3)C2×D311yescharacteristic
149#3750—32no—
150C4×C3⋊Dic3—32no—
151C3×#217—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3—21no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—32no—
160C3×C4⋊Dic3—61no—
161C3×C4⋊Dic3—61no—
162C3×C4⋊Dic3C2×D311yescharacteristic
163C3×C4⋊Dic3C2×D311yescharacteristic
164C3×C4⋊Dic3C2×D311yescharacteristic
165C3×C4⋊Dic3C2×D311yescharacteristic
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—32no—
168C3×Dic3⋊C4—32no—
169C3×C4×Dic3—32no—
170C3×C4×Dic3—32no—
171#3724—32no—
172#3724—32no—
173#3724—62no—
174#3724C2×D312yes—
175Dic3⋊Dic3C2×D312yes—
176#3722—32no—
177#3722—32no—
178#3722—32no—
179#3722—62no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3C2×D312yes—
183Dic32—32no—
184Dic32—32no—
185Dic32—32no—
186Dic32—32no—
187Dic32—32no—
188Dic32—62no—
189Dic32C2×D312yes—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)C22×C412yes—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3C22×C412yes—
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3C22×C412yes—
200C33×C4C22×C412yes—
201C3⋊(C3⋊Dic3)C22×C412yes—
202C3×C3⋊Dic3—22no—
203C3×C3⋊Dic3—22no—
204C3×C3⋊Dic3C22×C412yes—
205C32×Dic3—22no—
206C32×Dic3—22no—
207C32×Dic3C22×C412yes—
208C2×#235—91no—
209C2×#235—91no—
210C2×#235—91no—
211C2×#235—181no—
212C3×#117—91no—
213C2×C3×C4⋊C4—91no—
214C2×C3×C4⋊C4—91no—
215C4×#67—92no—
216C4×#67—92no—
217C4×#67—92no—
218C4×#67—92no—
219#926—31no—
220#926—91no—
221C2×C4⋊Dic3—31no—
222#893—92no—
223#893—92no—
224#892—31no—
225#892—91no—
226#892—91no—
227#892—91no—
228#892—91no—
229#892—91no—
230#892—181no—
231D3×C4⋊C4—31no—
232D3×C4⋊C4—31no—
233D3×C4⋊C4—31no—
234D3×C4⋊C4—91no—
235D3×C4⋊C4—91no—
236D3×C4⋊C4—91no—
237D3×C4⋊C4—181no—
238#887—92no—
239#887—92no—
240#67⋊C4—92no—
241#67⋊C4—92no—
242C4×D12—92no—
243C4×Dic6—92no—
244C23×C32—31no—
245C22×C3⋊D3—31no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—61no—
249C22×C3⋊D3—61no—
250C22×C3⋊D3—61no—
251C22×C3⋊D3—121no—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—21no—
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—61no—
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—31no—
263C2×C32×C4—34no—
264C2×C32×C4—32no—
265C2×C32×C4—32no—
266C2×C32×C4—41no—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270#638—34no—
271#638—34no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—61no—
276C2×C3⋊Dic3—61no—
277C2×C3⋊Dic3—61no—
278C2×C3⋊Dic3—121no—
279C2×C3⋊Dic3C22×D312yes—
280C2×C3⋊Dic3C22×D312yes—
281C2×C3⋊Dic3C22×D311yescharacteristic
282C4⋊(C3⋊D3)—34no—
283C4×C3⋊D3—34no—
284C4×C3⋊D3—34no—
285C4×C3⋊D3—34no—
286C4×C3⋊D3—64no—
287C4×C3⋊D3—64no—
288C4×C3⋊D3—64no—
289C4×C3⋊D3—124no—
290C4×C3⋊D3—122no—
291C4×C3⋊D3C4×D314yescomplemented
292#634—34no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—61no—
303C2×C3×Dic3—62no—
304C2×C3×Dic3—62no—
305C2×C3×Dic3—122no—
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C22×D312yes—
308C2×C3×Dic3C22×D312yes—
309C2×C3×Dic3C22×D312yes—
310C2×C3×Dic3C22×D311yescharacteristic
311C2×C3×Dic3C22×D311yescharacteristic
312C3×C4×D3—24no—
313C3×C4×D3—34no—
314C3×C4×D3—34no—
315C3×C4×D3—64no—
316C3×C4×D3—122no—
317C3×C4×D3—122no—
318C3×C4×D3—122no—
319C3×C4×D3C4×D314yescomplemented
320C3×C4×D3C4×D314yescomplemented
321#627—34no—
322#627—34no—
323#627—64no—
324#626—34no—
325#626—34no—
326#626—34no—
327#626—34no—
328#626—64no—
329#626—64no—
330#625—34no—
331#625—34no—
332#625—64no—
333#624—42no—
334#624—122no—
335#624—122no—
336#624—124no—
337D3×Dic3—42no—
338#520—271noSylow
339C2×C33C23×C411yescharacteristic
340C2×C33H(5,𝔽2)11yescharacteristic
341C2×C332−1+411yescharacteristic
342C3⋊(C3⋊D3)—22no—
343C3×C3⋊D3—22no—
344C32×D3—22no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—61no—
348C22×C3×C4—92no—
349C22×C3×C4—92no—
350C22×C3×C4—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—181no—
358C2×#67—181no—
359C22×Dic3—32no—
360#235—98no—
361#235—98no—
362#235—98no—
363#235—188no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—181no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—32no—
371C2×C4×D3—32no—
372C2×C4×D3—32no—
373C2×C4×D3—61no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—92no—
378C2×C4×D3—92no—
379C2×C4×D3—92no—
380C2×C4×D3—181no—
381C2×C4×D3—181no—
382C2×C4×D3—181no—
383C2×C4×D3—182no—
384C2×C4×D3—361no—
385C2×C4×D3D3211yescharacteristic
386C2×Dic6—91no—
387C2×Dic6—91no—
388C2×Dic6—91no—
389C2×Dic6—181no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4—92no—
397C3×C4⋊C4—92no—
398C3×C4⋊C4—91no—
399C3×C4⋊C4—91no—
400C3×C22⋊C4—92no—
401C3×C42—92no—
402#217—32no—
403#217—92no—
404(C2×D3)⋊C4—32no—
405(C2×D3)⋊C4—92no—
406(C2×D3)⋊C4—92no—
407(C2×D3)⋊C4—92no—
408(C2×D3)⋊C4—92no—
409(C2×D3)⋊C4—92no—
410(C2×D3)⋊C4—182no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—32no—
416C4⋊Dic3—61no—
417C4⋊Dic3—61no—
418C4⋊Dic3D3211yescharacteristic
419C4⋊Dic3D3211yescharacteristic
420Dic3⋊C4—32no—
421Dic3⋊C4—32no—
422Dic3⋊C4—32no—
423Dic3⋊C4—92no—
424Dic3⋊C4—92no—
425Dic3⋊C4—92no—
426Dic3⋊C4—182no—
427C4×Dic3—32no—
428C4×Dic3—32no—
429C4×Dic3—92no—
430C4×Dic3—92no—
431C4×Dic3—92no—
432C4×Dic3—92no—
433C4×Dic3—92no—
434C4×Dic3—92no—
435C4×Dic3—182no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—32no—
440C22×C32—41no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—32no—
449C2×C3⋊D3—32no—
450C2×C3⋊D3—32no—
451C2×C3⋊D3—62no—
452C2×C3⋊D3—62no—
453C2×C3⋊D3—62no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—62no—
457C2×C3⋊D3—62no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—61no—
460C2×C3⋊D3—61no—
461C2×C3⋊D3—61no—
462C2×C3⋊D3—122no—
463C2×C3⋊D3—121no—
464C2×C3⋊D3—121no—
465C2×C3⋊D3—121no—
466C2×C3⋊D3—121no—
467C2×C3⋊D3—122no—
468C2×C3⋊D3—122no—
469C2×C3⋊D3C2×C4×D312yes—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—22no—
475C2×C3×D3—32no—
476C2×C3×D3—32no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—62no—
480C2×C3×D3—61no—
481C2×C3×D3—61no—
482C2×C3×D3—61no—
483C2×C3×D3—61no—
484C2×C3×D3—121no—
485C2×C3×D3—121no—
486C2×C3×D3C2×C4×D312yes—
487C2×C3×D3C2×C4×D312yes—
488C32×C4—22no—
489C32×C4—22no—
490C32×C4—22no—
491C32×C4—32no—
492C32×C4—42no—
493C32×C4—62no—
494C32×C4—62no—
495C32×C4C2×C4×D312yes—
496C32×C4C2×C4×D312yes—
497C32×C4C2×C4×D312yes—
498C3⋊Dic3—22no—
499C3⋊Dic3—22no—
500C3⋊Dic3—32no—
501C3⋊Dic3—32no—
502C3⋊Dic3—32no—
503C3⋊Dic3—62no—
504C3⋊Dic3—62no—
505C3⋊Dic3—62no—
506C3⋊Dic3—122no—
507C3⋊Dic3C2×C4×D312yes—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—32no—
514C3×Dic3—32no—
515C3×Dic3—42no—
516C3×Dic3—42no—
517C3×Dic3—62no—
518C3×Dic3—62no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—62no—
522C3×Dic3—122no—
523C3×Dic3—122no—
524C3×Dic3C2×C4×D312yes—
525C3×Dic3C2×C4×D312yes—
526C2×#41—271no—
527C4×Q8—272no—
528C4×D4—272no—
529C4×D4—272no—
530C4×D4—272no—
531#117—91no—
532#117—271no—
533#117—271no—
534C2×C4⋊C4—91no—
535C2×C4⋊C4—91no—
536C2×C4⋊C4—271no—
537C33#52011yescharacteristic, complemented, Sylow
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—91no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—61no—
545C22×D3—91no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—181no—
549C22×D3—181no—
550C22×D3—181no—
551C22×D3—361no—
552C22×D3C2×D3211yescharacteristic
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—34no—
559C2×C3×C4—34no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—41no—
565C2×C3×C4—64no—
566C2×C3×C4—61no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4—91no—
570C2×C3×C4—94no—
571C2×C3×C4—92no—
572C2×C3×C4—92no—
573C2×C3×C4—362no—
574C2×C3×C4—362no—
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577C2×C3×C4C2×D3211yescharacteristic
578#67—94no—
579#67—94no—
580#67—94no—
581#67—94no—
582#67—94no—
583#67—94no—
584#67—184no—
585#67—184no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—61no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—122no—
599C2×Dic3—181no—
600C2×Dic3—181no—
601C2×Dic3—181no—
602C2×Dic3—361no—
603C2×Dic3C2×D3212yes—
604C2×Dic3C2×D3212yes—
605C2×Dic3C2×D3211yescharacteristic
606D12—94no—
607D12—94no—
608D12—94no—
609D12—184no—
610C4×D3—34no—
611C4×D3—34no—
612C4×D3—64no—
613C4×D3—94no—
614C4×D3—94no—
615C4×D3—94no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—122no—
619C4×D3—184no—
620C4×D3—184no—
621C4×D3—184no—
622C4×D3—364no—
623C4×D3—362no—
624C4×D3—362no—
625C4×D3—362no—
626C4×D3—364no—
627C4×D3#62414yescomplemented
628Dic6—94no—
629Dic6—94no—
630Dic6—94no—
631Dic6—184no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—41no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—62no—
645C2×C32C22×C4×D311yescharacteristic
646C2×C32C22×C4×D311yescharacteristic
647C2×C32C22×C4×D311yescharacteristic
648C2×C32#100411yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32#100711yescharacteristic
651C2×C32#100711yescharacteristic
652C2×C32#100911yescharacteristic
653C2×C32#101011yescharacteristic
654C3⋊D3—22no—
655C3⋊D3—62no—
656C3⋊D3—64no—
657C3⋊D3—62no—
658C3⋊D3—62no—
659C3⋊D3—122no—
660C3⋊D3—122no—
661C3⋊D3—124no—
662C3×D3—22no—
663C3×D3—22no—
664C3×D3—42no—
665C3×D3—62no—
666C3×D3—62no—
667C3×D3—122no—
668#41—278no—
669C2×Q8—271no—
670C2×D4—271no—
671C2×D4—271no—
672C2×D4—271no—
673C22×C4—31no—
674C22×C4—92no—
675C22×C4—92no—
676C22×C4—91no—
677C22×C4—272no—
678C22×C4—271no—
679C4⋊C4—31no—
680C4⋊C4—31no—
681C4⋊C4—92no—
682C4⋊C4—92no—
683C4⋊C4—91no—
684C4⋊C4—91no—
685C4⋊C4—272no—
686C22⋊C4—92no—
687C22⋊C4—272no—
688C22⋊C4—272no—
689C42—92no—
690C42—272no—
691C42—272no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—32no—
696C22×C3—32no—
697C22×C3—41no—
698C22×C3—62no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—92no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—181no—
707C22×C3—181no—
708C22×C3C22×D3211yescharacteristic
709C22×C3C22×D3211yescharacteristic
710C22×C3C22×D3211yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—32no—
714C2×D3—32no—
715C2×D3—62no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—92no—
721C2×D3—92no—
722C2×D3—92no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—182no—
726C2×D3—182no—
727C2×D3—182no—
728C2×D3—182no—
729C2×D3—182no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—181no—
734C2×D3—181no—
735C2×D3—181no—
736C2×D3—362no—
737C2×D3—361no—
738C2×D3—361no—
739C2×D3—361no—
740C2×D3—361no—
741C2×D3—362no—
742C2×D3—362no—
743C2×D3C2×#62412yes—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—32no—
748C3×C4—32no—
749C3×C4—42no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—62no—
754C3×C4—62no—
755C3×C4—92no—
756C3×C4—122no—
757C3×C4—122no—
758C3×C4—182no—
759C3×C4—182no—
760C3×C4C4×D3212yes—
761C3×C4C4×D3212yes—
762C3×C4C2×#62412yes—
763Dic3—22no—
764Dic3—22no—
765Dic3—32no—
766Dic3—32no—
767Dic3—62no—
768Dic3—62no—
769Dic3—62no—
770Dic3—62no—
771Dic3—62no—
772Dic3—92no—
773Dic3—92no—
774Dic3—92no—
775Dic3—122no—
776Dic3—122no—
777Dic3—182no—
778Dic3—182no—
779Dic3—182no—
780Dic3—362no—
781Dic3C2×#62412yes—
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32#550411yescharacteristic, complemented
787C32#550411yescharacteristic, complemented
788C32#552311yescharacteristic, complemented
789C23—31no—
790C23—91no—
791C23—271no—
792Q8—274no—
793D4—274no—
794D4—274no—
795D4—274no—
796C2×C4—31no—
797C2×C4—34no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—91no—
801C2×C4—94no—
802C2×C4—92no—
803C2×C4—92no—
804C2×C4—271no—
805C2×C4—274no—
806C2×C4—362no—
807C2×C4—362no—
808C2×C4—1082no—
809C2×C4D3311yescharacteristic
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—62no—
823C2×C3—62no—
824C2×C3—122no—
825C2×C3—182no—
826C2×C3#6429711yescharacteristic
827C2×C3C2×C4×D3211yescharacteristic
828C2×C3C2×C4×D3211yescharacteristic
829C2×C3#6430711yescharacteristic
830C2×C3#6431311yescharacteristic
831C2×C3#6431411yescharacteristic
832C2×C3#6431511yescharacteristic
833C2×C3#6431611yescharacteristic
834C2×C3C22×#62411yescharacteristic
835D3—22no—
836D3—62no—
837D3—62no—
838D3—122no—
839D3—184no—
840D3—182no—
841D3—182no—
842D3—182no—
843D3—362no—
844D3—362no—
845D3—364no—
846C22—32no—
847C22—61no—
848C22—61no—
849C22—92no—
850C22—181no—
851C22—181no—
852C22—272no—
853C22—541no—
854C22—541no—
855C22C2×D3311yescharacteristic
856C4—32no—
857C4—62no—
858C4—62no—
859C4—92no—
860C4—182no—
861C4—182no—
862C4—272no—
863C4D3×#62412yes—
864C3—21no—
865C3—21no—
866C3—21no—
867C3—41no—
868C3#1059450911yescharacteristic, complemented
869C3#1059451011yescharacteristic, complemented
870C3#1059499011yescharacteristic, complemented
871C2—62no—
872C2—182no—
873C2—542no—
874C2#1172438111yescharacteristic
875C2#1172439711yescharacteristic
876C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89020C2
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. #11723667C2semidirect
3. #11723503C2semidirect
4. #11723413C2semidirect
5. C3×#63900C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63841C2semidirect
8. #11722943C2semidirect
9. #11722935C2semidirect
10. #11722933C2semidirect
11. #11722930C2semidirect
23. #89020C4semidirect
60. #63900D3semidirect
62. D3×C4⋊Dic3D3semidirect
72. #63841D3semidirect
80. C4×C3⋊(C3⋊D3)C2×C4semidirect
84. C3×C4×C3⋊D3C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
89. #6293C2×C4semidirect
90. #6292C2×C4semidirect
91. #6291C2×C4semidirect
92. #6290C2×C4semidirect
291. C4×C3⋊D3C4×D3semidirect
319. C3×C4×D3C4×D3semidirect
320. C3×C4×D3C4×D3semidirect
537. C33#520semidirect
627. C4×D3#624semidirect
786. C32#5504semidirect
787. C32#5504semidirect
788. C32#5523semidirect
868. C3#10594509semidirect
869. C3#10594510semidirect
870. C3#10594990semidirect

Maximal subgroups

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

subgroupindex
C2×#890202
#117236672
#117235032
#117234132
C3×#639002
C3×D3×C4⋊Dic32
C3×#638412
#117229432
#117229352
#117229332
#117229302
#105949903
#105945103
#105945093