Finite Group Databasebeta

← #11773263

Subgroups — #11773263

Order 1152.

1821 conjugacy classes of subgroups.

The subgroup lattice has 1145 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C22×Dic32C211yesmaximal, characteristic, complemented
5C2×#63658C211yesmaximal, characteristic, complemented
6C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#71545—31nomaximal
9#69408—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—22no—
18C2×C3×(C2×D3)⋊C4—22no—
19C2×C3×(C2×D3)⋊C4C414yescomplemented
20C2×(C2×D3)⋊Dic3—22no—
21C2×(C2×D3)⋊Dic3—22no—
22C2×(C2×D3)⋊Dic3—22no—
23C2×(C2×D3)⋊Dic3—22no—
24C2×(C2×D3)⋊Dic3C414yescomplemented
25C2×(C2×D3)⋊Dic3C414yescomplemented
26C2×Dic32—22no—
27C2×Dic32—22no—
28C2×Dic32—22no—
29#63658—22no—
30C3×C3⋊#95—22no—
31#63579—22no—
32C22×C3×C22⋊C4—31no—
33C22×#217—31no—
34C22×#217—31no—
35C22×(C2×D3)⋊C4—31no—
36C22×(C2×D3)⋊C4—31no—
37C22×(C2×D3)⋊C4D311yescharacteristic
38C22×C4×Dic3—31no—
39C22×C4×Dic3—31no—
40C2×C3×#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—61no—
46C2×C3⋊#95D311yescharacteristic, complemented
47C24×C32C2311yescharacteristic
48C23×C3×D3—21no—
49C23×C3×D3—21no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C23×C3×D3—21no—
57C23×C3×D3—21no—
58C23×C3×D3—21no—
59C23×C3×D3—21no—
60C23×C3×D3C2×C412yes—
61C23×C3×D3C2×C412yes—
62C23×C3×D3C2×C412yes—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4C2×C412yes—
70C22×C3⋊Dic3—21no—
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3—21no—
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3—21no—
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3C2×C412yes—
81C22×C3⋊Dic3C2×C412yes—
82C22×C3⋊Dic3D412yes—
83C22×C3⋊Dic3D412yes—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3C2×C412yes—
99C22×C3×Dic3C2×C412yes—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105C3×(C2×D3)⋊C4—28no—
106(C2×D3)⋊Dic3—28no—
107(C2×D3)⋊Dic3—28no—
108Dic32—28no—
109#1437—91noSylow
110C25×C3—31no—
111C24×D3C2×D311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C23×C3×C4—31no—
116C23×C3×C4C2×D311yescharacteristic
117C23×C3×C4C2×D311yescharacteristic
118C23×Dic3—31no—
119C23×Dic3—31no—
120C23×Dic3—31no—
121C23×Dic3—31no—
122C23×Dic3—61no—
123C23×Dic3—61no—
124C23×Dic3C2×D311yescharacteristic
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C2×C3×C22⋊C4—34no—
128C2×C3×C22⋊C4—62no—
129C2×C3×C22⋊C4—62no—
130C2×#217—34no—
131C2×#217—34no—
132C2×#217—62no—
133C2×#217—62no—
134C2×#217—62no—
135C2×#217—62no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—34no—
139C2×(C2×D3)⋊C4—34no—
140C2×(C2×D3)⋊C4—62no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4—62no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4Dic314yescomplemented
145C2×C4×Dic3—62no—
146C2×C4×Dic3—62no—
147C2×C4×Dic3—62no—
148C2×C4×Dic3—62no—
149C2×C4×Dic3—62no—
150C2×C4×Dic3—62no—
151C3×#95—62no—
152C3⋊#95—22no—
153C3⋊#95—62no—
154C3⋊#95—62no—
155C3⋊#95—62no—
156C3⋊#95—64no—
157C3⋊#95—62no—
158C23×C32C22×C411yescharacteristic
159C23×C32C22×C411yescharacteristic
160C23×C32C22×C411yescharacteristic
161C23×C32C2×D411yescharacteristic
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C23×C32C2×D411yescharacteristic
166C23×C32C2×D411yescharacteristic
167C23×C32#4111yescharacteristic
168C23×C32#4111yescharacteristic
169C23×C32#4111yescharacteristic
170C23×C32#4111yescharacteristic
171C23×C32#4111yescharacteristic
172C23×C32#4111yescharacteristic
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3—41no—
192C22×C3×D3—41no—
193C22×C3×D3—41no—
194C22×C3×D3—41no—
195C22×C3×D3—41no—
196C22×C3×D3—41no—
197C22×C3×D3—41no—
198C22×C3×D3—41no—
199C22×C3×D3—41no—
200C22×C3×D3—41no—
201C22×C3×D3—41no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3—41no—
206C22×C3×D3—41no—
207C22×C3×D3C4214yescomplemented
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3—22no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—41no—
225C2×C3⋊Dic3—41no—
226C2×C3⋊Dic3—41no—
227C2×C3⋊Dic3—41no—
228C2×C3⋊Dic3C22⋊C414yescomplemented
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—41no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3C22⋊C414yescomplemented
249C2×C3×Dic3C22⋊C414yescomplemented
250C22×C22⋊C4—31no—
251C22×C22⋊C4—91no—
252C22×C22⋊C4—91no—
253C22×C42—91no—
254C2×#95—31no—
255C2×#95—91no—
256C2×#95—91no—
257C24×C3—21no—
258C24×C3—32no—
259C24×C3—32no—
260C24×C3—32no—
261C24×C3—61no—
262C24×C3—61no—
263C24×C3—61no—
264C24×C3—61no—
265C24×C3—61no—
266C24×C3—61no—
267C24×C3—61no—
268C24×C3—61no—
269C24×C3—61no—
270C24×C3—61no—
271C24×C3—61no—
272C24×C3—61no—
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3C4×D312yes—
288C23×D3C4×D312yes—
289C23×D3C2×Dic312yes—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—22no—
305C22×C3×C4—32no—
306C22×C3×C4—32no—
307C22×C3×C4—32no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—32no—
311C22×C3×C4—32no—
312C22×C3×C4—41no—
313C22×C3×C4—41no—
314C22×C3×C4—41no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C4×D312yes—
331C22×C3×C4C2×Dic312yes—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—32no—
347C22×Dic3—32no—
348C22×Dic3—32no—
349C22×Dic3—32no—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—32no—
353C22×Dic3—32no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—62no—
367C22×Dic3—62no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—121no—
381C22×Dic3—121no—
382C22×Dic3—121no—
383C22×Dic3—121no—
384C22×Dic3—121no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3C4×D312yes—
389C22×Dic3C4×D312yes—
390C22×Dic3D1212yes—
391C22×Dic3C2×Dic312yes—
392C22×Dic3#6712yes—
393C22×Dic3#6712yes—
394C22×Dic3#6712yes—
395C3×C22⋊C4—68no—
396#217—68no—
397#217—68no—
398(C2×D3)⋊C4—28no—
399(C2×D3)⋊C4—68no—
400(C2×D3)⋊C4—68no—
401C4×Dic3—68no—
402C4×Dic3—68no—
403C22×C32C2×C4211yescharacteristic
404C22×C32C2×C22⋊C411yescharacteristic
405C22×C32C2×C22⋊C411yescharacteristic
406C22×C32C2×C22⋊C411yescharacteristic
407C22×C32#11711yescharacteristic
408C22×C32#11711yescharacteristic
409C22×C32#11711yescharacteristic
410C22×C32C4×D411yescharacteristic
411C22×C32C4×D411yescharacteristic
412C22×C32C4×D411yescharacteristic
413C22×C32C4×D411yescharacteristic
414C22×C32C4×D411yescharacteristic
415C22×C32C4×D411yescharacteristic
416C22×C32C4×D411yescharacteristic
417C22×C32C4×D411yescharacteristic
418C22×C32C4×D411yescharacteristic
419C22×C32C4×D411yescharacteristic
420C22×C32C4×D411yescharacteristic
421C22×C32C4×D411yescharacteristic
422C22×C32#12011yescharacteristic
423C22×C32#12111yescharacteristic
424C22×C32#12111yescharacteristic
425C22×C32#12111yescharacteristic
426C22×C32#12111yescharacteristic
427C22×C32#12111yescharacteristic
428C22×C32#12111yescharacteristic
429C22×C32#12311yescharacteristic
430C22×C32#12311yescharacteristic
431C22×C32#12311yescharacteristic
432C22×C32#12411yescharacteristic
433C22×C32#12411yescharacteristic
434C22×C32#12411yescharacteristic
435C22×C32#12611yescharacteristic
436C22×C32#12611yescharacteristic
437C22×C32#12711yescharacteristic
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C2×C3×D3—42no—
445C2×C3×D3—42no—
446C2×C3×D3—42no—
447C2×C3×D3—42no—
448C2×C3×D3—42no—
449C2×C3×D3—42no—
450C2×C3×D3—42no—
451C2×C3×D3—42no—
452C2×C3×D3—42no—
453C32×C4—42no—
454C3⋊Dic3—24no—
455C3⋊Dic3—42no—
456C3×Dic3—24no—
457C3×Dic3—24no—
458C3×Dic3—42no—
459C25—31no—
460C23×C4—31no—
461C23×C4—31no—
462C23×C4—31no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4D3211yescharacteristic
466C2×C22⋊C4—34no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—94no—
470C2×C22⋊C4—94no—
471C2×C22⋊C4—182no—
472C2×C22⋊C4—182no—
473C2×C22⋊C4—182no—
474C2×C22⋊C4—182no—
475C2×C42—182no—
476C2×C42—182no—
477C2×C42—182no—
478#95—62no—
479#95—182no—
480#95—182no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—34no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—62no—
505C23×C3—62no—
506C23×C3—62no—
507C23×C3—62no—
508C23×C3—62no—
509C23×C3—62no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3—62no—
514C23×C3—62no—
515C23×C3—121no—
516C23×C3—121no—
517C23×C3—121no—
518C23×C3—121no—
519C23×C3—121no—
520C23×C3—121no—
521C23×C3—121no—
522C23×C3—121no—
523C23×C3—121no—
524C23×C3—121no—
525C23×C3—121no—
526C23×C3—121no—
527C23×C3—121no—
528C23×C3—121no—
529C23×C3—121no—
530C23×C3—121no—
531C23×C3C2×C4×D311yescharacteristic
532C23×C3C2×C4×D311yescharacteristic
533C23×C3C2×C4×D311yescharacteristic
534C23×C3C2×C4×D311yescharacteristic
535C23×C3C2×C4×D311yescharacteristic
536C23×C3C2×D1211yescharacteristic
537C23×C3#23511yescharacteristic
538C23×C3#23511yescharacteristic
539C23×C3#23511yescharacteristic
540C23×C3#23511yescharacteristic
541C23×C3D3×D411yescharacteristic
542C23×C3D3×D411yescharacteristic
543C23×C3D3×D411yescharacteristic
544C23×C3D3×D411yescharacteristic
545C23×C3D3×D411yescharacteristic
546C23×C3D3×D411yescharacteristic
547C23×C3D3×D411yescharacteristic
548C23×C3D3×D411yescharacteristic
549C23×C3#23711yescharacteristic
550C23×C3#23711yescharacteristic
551C23×C3#23711yescharacteristic
552C23×C3#23711yescharacteristic
553C23×C3#23711yescharacteristic
554C23×C3#23711yescharacteristic
555C23×C3#23911yescharacteristic
556C23×C3#23911yescharacteristic
557C23×C3C22×Dic311yescharacteristic
558C23×C3C2×#6711yescharacteristic
559C23×C3C2×#6711yescharacteristic
560C23×C3C2×#6711yescharacteristic
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3C4×Dic314yescomplemented
596C2×C3×C4—24no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—34no—
604C2×C3×C4—34no—
605C2×C3×C4—42no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—121no—
635C2×C3×C4—121no—
636C2×C3×C4—121no—
637C2×C3×C4—121no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—34no—
654C2×Dic3—34no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—64no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—122no—
680C2×Dic3—122no—
681C2×Dic3—122no—
682C2×Dic3—122no—
683C2×Dic3—122no—
684C2×Dic3—122no—
685C2×Dic3—122no—
686C2×Dic3—122no—
687C2×Dic3—122no—
688C2×Dic3—122no—
689C2×Dic3—122no—
690C2×Dic3—122no—
691C2×Dic3—121no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3(C2×D3)⋊C414yescomplemented
700C2×Dic3#21714yescomplemented
701C2×C32C4×C22⋊C411yescharacteristic
702C2×C32C4×C22⋊C411yescharacteristic
703C2×C32C4×C22⋊C411yescharacteristic
704C2×C32#38611yescharacteristic
705C2×C32#38611yescharacteristic
706C2×C32#38611yescharacteristic
707C2×C32#38811yescharacteristic
708C2×C32#38811yescharacteristic
709C2×C32#38811yescharacteristic
710C2×C32#38811yescharacteristic
711C2×C32#38811yescharacteristic
712C2×C32#38811yescharacteristic
713C2×C32#39011yescharacteristic
714C2×C32#39011yescharacteristic
715C2×C32#39011yescharacteristic
716C3×D3—44no—
717C24—32no—
718C24—32no—
719C24—32no—
720C24—61no—
721C24—61no—
722C24—61no—
723C24—61no—
724C24—61no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24C2×D3211yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—92no—
761C22×C4—92no—
762C22×C4—92no—
763C22×C4—92no—
764C22×C4—181no—
765C22×C4—181no—
766C22×C4—181no—
767C22×C4—181no—
768C22×C4—181no—
769C22×C4—181no—
770C22×C4—181no—
771C22×C4—181no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4D3×Dic312yes—
775C22⋊C4—68no—
776C22⋊C4—188no—
777C22⋊C4—188no—
778C42—188no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—64no—
815C22×C3—64no—
816C22×C3—64no—
817C22×C3—122no—
818C22×C3—122no—
819C22×C3—122no—
820C22×C3—122no—
821C22×C3—122no—
822C22×C3—122no—
823C22×C3—122no—
824C22×C3—122no—
825C22×C3—122no—
826C22×C3—122no—
827C22×C3—122no—
828C22×C3—122no—
829C22×C3C42×D311yescharacteristic
830C22×C3#87211yescharacteristic
831C22×C3C4×D1211yescharacteristic
832C22×C3C4×D1211yescharacteristic
833C22×C3#87711yescharacteristic
834C22×C3#87711yescharacteristic
835C22×C3#87911yescharacteristic
836C22×C3#87911yescharacteristic
837C22×C3D3×C22⋊C411yescharacteristic
838C22×C3D3×C22⋊C411yescharacteristic
839C22×C3D3×C22⋊C411yescharacteristic
840C22×C3D3×C22⋊C411yescharacteristic
841C22×C3#67⋊C411yescharacteristic
842C22×C3#67⋊C411yescharacteristic
843C22×C3#67⋊C411yescharacteristic
844C22×C3#67⋊C411yescharacteristic
845C22×C3#67⋊C411yescharacteristic
846C22×C3#67⋊C411yescharacteristic
847C22×C3#67⋊C411yescharacteristic
848C22×C3#67⋊C411yescharacteristic
849C22×C3#88211yescharacteristic
850C22×C3#88311yescharacteristic
851C22×C3#88311yescharacteristic
852C22×C3#88411yescharacteristic
853C22×C3#88411yescharacteristic
854C22×C3#88411yescharacteristic
855C22×C3#88411yescharacteristic
856C22×C3#88511yescharacteristic
857C22×C3#88511yescharacteristic
858C22×C3#88511yescharacteristic
859C22×C3#88511yescharacteristic
860C22×C3#88611yescharacteristic
861C22×C3#89211yescharacteristic
862C22×C3#89211yescharacteristic
863C22×C3#89311yescharacteristic
864C22×C3#89311yescharacteristic
865C22×C3#89311yescharacteristic
866C22×C3#89311yescharacteristic
867C22×C3#89411yescharacteristic
868C22×C3#89411yescharacteristic
869C22×C3#89511yescharacteristic
870C22×C3#89511yescharacteristic
871C22×C3#89811yescharacteristic
872C22×C3#89811yescharacteristic
873C22×C3C2×C4×Dic311yescharacteristic
874C22×C3#92611yescharacteristic
875C22×C3C2×(C2×D3)⋊C411yescharacteristic
876C22×C3C4×#6711yescharacteristic
877C22×C3C4×#6711yescharacteristic
878C22×C3C4×#6711yescharacteristic
879C22×C3C4×#6711yescharacteristic
880C22×C3C4×#6711yescharacteristic
881C22×C3C4×#6711yescharacteristic
882C22×C3D4×Dic311yescharacteristic
883C22×C3D4×Dic311yescharacteristic
884C22×C3D4×Dic311yescharacteristic
885C22×C3D4×Dic311yescharacteristic
886C22×C3#93511yescharacteristic
887C22×C3#93611yescharacteristic
888C22×C3#93711yescharacteristic
889C22×C3#93811yescharacteristic
890C22×C3#93811yescharacteristic
891C22×C3#93911yescharacteristic
892C22×C3#93911yescharacteristic
893C22×C3#93911yescharacteristic
894C22×C3#93911yescharacteristic
895C22×C3#94011yescharacteristic
896C22×C3#94011yescharacteristic
897C22×C3#94711yescharacteristic
898C22×C3C2×#21711yescharacteristic
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—42no—
903C2×D3—42no—
904C2×D3—42no—
905C2×D3—42no—
906C2×D3—42no—
907C2×D3—42no—
908C2×D3—42no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3—42no—
912C2×D3—42no—
913C2×D3—42no—
914C3×C4—44no—
915C3×C4—42no—
916C3×C4—42no—
917C3×C4—64no—
918C3×C4—64no—
919C3×C4—122no—
920Dic3—24no—
921Dic3—24no—
922Dic3—42no—
923Dic3—64no—
924Dic3—64no—
925Dic3—124no—
926Dic3—124no—
927Dic3—122no—
928Dic3—122no—
929C32#143711yescharacteristic, complemented, Sylow
930C23—34no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23#379511yescharacteristic
966C23#379511yescharacteristic
967C23#379611yescharacteristic
968C23#379911yescharacteristic
969C23C4×D3211yescharacteristic
970C23C4×D3211yescharacteristic
971C23D3×D1211yescharacteristic
972C23#380211yescharacteristic
973C23C2×D3×Dic311yescharacteristic
974C23#380411yescharacteristic
975C23#380511yescharacteristic
976C23D3×#6711yescharacteristic
977C23D3×#6711yescharacteristic
978C23D3×#6711yescharacteristic
979C23#381111yescharacteristic
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—34no—
984C2×C4—34no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—94no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—182no—
1010C2×C4—182no—
1011C2×C4—182no—
1012C2×C4—182no—
1013C2×C4—182no—
1014C2×C4—182no—
1015C2×C4—182no—
1016C2×C4—182no—
1017C2×C4—182no—
1018C2×C4—361no—
1019C2×C4—361no—
1020C2×C4—361no—
1021C2×C4—361no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—124no—
1038C2×C3#466511yescharacteristic
1039C2×C3#466511yescharacteristic
1040C2×C3#466611yescharacteristic
1041C2×C3#466611yescharacteristic
1042C2×C3#466911yescharacteristic
1043C2×C3#466911yescharacteristic
1044C2×C3#467011yescharacteristic
1045C2×C3#467011yescharacteristic
1046C2×C3C4×(C2×D3)⋊C411yescharacteristic
1047C2×C3Dic3×C22⋊C411yescharacteristic
1048C2×C3Dic3×C22⋊C411yescharacteristic
1049C2×C3#494411yescharacteristic
1050C2×C3#494411yescharacteristic
1051C2×C3#494511yescharacteristic
1052C2×C3#494511yescharacteristic
1053C2×C3#495111yescharacteristic
1054C2×C3#495111yescharacteristic
1055C2×C3#495611yescharacteristic
1056C2×C3#495611yescharacteristic
1057C2×C3#495711yescharacteristic
1058C2×C3#495711yescharacteristic
1059C2×C3#495711yescharacteristic
1060C2×C3#495711yescharacteristic
1061C2×C3#495811yescharacteristic
1062C2×C3#498811yescharacteristic
1063C2×C3#499011yescharacteristic
1064C2×C3#499011yescharacteristic
1065C2×C3C4×#21711yescharacteristic
1066C2×C3#522011yescharacteristic
1067C2×C3#522111yescharacteristic
1068D3—44no—
1069C22—64no—
1070C22—64no—
1071C22—64no—
1072C22—122no—
1073C22—122no—
1074C22—122no—
1075C22—122no—
1076C22—122no—
1077C22—122no—
1078C22—122no—
1079C22—122no—
1080C22—122no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22#6384111yescharacteristic
1085C22#6385411yescharacteristic
1086C22#6385811yescharacteristic
1087C22#6386111yescharacteristic
1088C22C4×D3×Dic311yescharacteristic
1089C22#6387711yescharacteristic
1090C22#6387811yescharacteristic
1091C22#6387911yescharacteristic
1092C22#6387911yescharacteristic
1093C22#6387911yescharacteristic
1094C22#6388011yescharacteristic
1095C22#6388111yescharacteristic
1096C22#6388411yescharacteristic
1097C22#6388511yescharacteristic
1098C22#6388511yescharacteristic
1099C22#6388611yescharacteristic
1100C22#6389111yescharacteristic
1101C22Dic3×D1211yescharacteristic
1102C22#6389811yescharacteristic
1103C22#6390211yescharacteristic
1104C22#6390411yescharacteristic
1105C22#6390411yescharacteristic
1106C22#6390711yescharacteristic
1107C22#6391011yescharacteristic
1108C22#6391311yescharacteristic
1109C22D3×(C2×D3)⋊C411yescharacteristic
1110C22#6392111yescharacteristic
1111C22#6392211yescharacteristic
1112C22#6395811yescharacteristic
1113C22#6395911yescharacteristic
1114C22D3×#21711yescharacteristic
1115C22#6397011yescharacteristic
1116C22Dic3×#6711yescharacteristic
1117C22#67⋊Dic311yescharacteristic
1118C22#6397911yescharacteristic
1119C4—42no—
1120C4—64no—
1121C4—64no—
1122C4—122no—
1123C4—184no—
1124C4—362no—
1125C3—21no—
1126C3#6940811yescharacteristic, complemented
1127C3#7154511yescharacteristic, complemented
1128C2—124no—
1129C2#1059123711yescharacteristic
1130C2#1059127511yescharacteristic
1131C2#1059128111yescharacteristic
1132C2#1059128211yescharacteristic
1133C2#1059128411yescharacteristic
1134C2#1059128511yescharacteristic
1135C2#1059130711yescharacteristic
1136C2#1059131611yescharacteristic
1137C2#1059136311yescharacteristic
1138C2Dic3×(C2×D3)⋊C411yescharacteristic
1139C2#1059136811yescharacteristic
1140C2#1059137611yescharacteristic
1141C2#1059138411yescharacteristic
1142C2#1059138611yescharacteristic
1143C2#1059170711yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC22×C32C2×C42
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32#1437
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C22×Dic32C2semidirect
5. C2×#63658C2semidirect
6. C2×C3×C3⋊#95C2semidirect
7. C2×#63579C2semidirect
19. C2×C3×(C2×D3)⋊C4C4semidirect
24. C2×(C2×D3)⋊Dic3C4semidirect
25. C2×(C2×D3)⋊Dic3C4semidirect
46. C2×C3⋊#95D3semidirect
144. C2×(C2×D3)⋊C4Dic3semidirect
207. C22×C3×D3C42semidirect
228. C2×C3⋊Dic3C22⋊C4semidirect
248. C2×C3×Dic3C22⋊C4semidirect
249. C2×C3×Dic3C22⋊C4semidirect
595. C22×D3C4×Dic3semidirect
699. C2×Dic3(C2×D3)⋊C4semidirect
700. C2×Dic3#217semidirect
929. C32#1437semidirect
1126. C3#69408semidirect
1127. C3#71545semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic32
C22×Dic322
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#715453
#694083