Finite Group Databasebeta

← #11773340

Subgroups — #11773340

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1133 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
4C2×#63658C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#71548—31nomaximal
9#69429—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)⋊Dic3—22no—
25C2×(C2×D3)⋊Dic3—22no—
26#63658—22no—
27C3×C3⋊#95—22no—
28#63579—22no—
29#63579—22no—
30C22×C3×C22⋊C4—31no—
31C22×#217—31no—
32C22×#217—31no—
33C22×(C2×D3)⋊C4—31no—
34C22×(C2×D3)⋊C4—31no—
35C22×(C2×D3)⋊C4D311yescharacteristic
36C2×C3×#95—31no—
37C2×C3⋊#95—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—61no—
44C2×C3⋊#95D311yescharacteristic, complemented
45C24×C32C2311yescharacteristic
46C23×C3×D3—21no—
47C23×C3×D3—21no—
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×D3C2×C412yes—
59C23×C3×D3D412yes—
60C23×C3×D3D412yes—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4C2×C412yes—
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—21no—
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⋊Dic3D412yes—
81C22×C3⋊Dic3D412yes—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
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×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C3×(C2×D3)⋊C4—28no—
104(C2×D3)⋊Dic3—28no—
105(C2×D3)⋊Dic3—28no—
106#1440—91noSylow
107C25×C3—31no—
108C24×D3C2×D311yescharacteristic
109C23×C3×C4—21no—
110C23×C3×C4—31no—
111C23×C3×C4—31no—
112C23×C3×C4—31no—
113C23×C3×C4C2×D311yescharacteristic
114C23×C3×C4C2×D311yescharacteristic
115C23×Dic3—31no—
116C23×Dic3—31no—
117C23×Dic3—31no—
118C23×Dic3—31no—
119C23×Dic3—61no—
120C23×Dic3—61no—
121C23×Dic3C2×D311yescharacteristic
122C23×Dic3C2×D311yescharacteristic
123C23×Dic3C2×D311yescharacteristic
124C2×C3×C22⋊C4—34no—
125C2×C3×C22⋊C4—62no—
126C2×C3×C22⋊C4—62no—
127C2×#217—62no—
128C2×#217—62no—
129C2×#217—62no—
130C2×#217—62no—
131C2×#217—62no—
132C2×#217—62no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—62no—
136C2×(C2×D3)⋊C4—62no—
137C2×(C2×D3)⋊C4—62no—
138C2×(C2×D3)⋊C4—62no—
139C2×(C2×D3)⋊C4—62no—
140C2×(C2×D3)⋊C4—62no—
141C2×(C2×D3)⋊C4Dic314yescomplemented
142C3×#95—62no—
143C3⋊#95—22no—
144C3⋊#95—62no—
145C3⋊#95—62no—
146C3⋊#95—62no—
147C3⋊#95—62no—
148C3⋊#95—62no—
149C3⋊#95—64no—
150C3⋊#95—62no—
151C23×C32C22×C411yescharacteristic
152C23×C32C2×D411yescharacteristic
153C23×C32C2×D411yescharacteristic
154C23×C32C2×D411yescharacteristic
155C23×C32C2×D411yescharacteristic
156C23×C32C2×D411yescharacteristic
157C23×C32C2×D411yescharacteristic
158C23×C32#4111yescharacteristic
159C23×C32#4111yescharacteristic
160C23×C32#4111yescharacteristic
161C23×C32#4111yescharacteristic
162C23×C32#4111yescharacteristic
163C23×C32#4111yescharacteristic
164C23×C32#4111yescharacteristic
165C23×C32#4111yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
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—41no—
185C22×C3×D3—41no—
186C22×C3×D3—41no—
187C22×C3×D3—41no—
188C22×C3×D3—41no—
189C22×C3×D3—41no—
190C22×C3×D3—41no—
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×D3C22⋊C414yes—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—41no—
205C2×C32×C4—41no—
206C2×C32×C4—41no—
207C2×C32×C4—41no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—22no—
210C2×C3⋊Dic3—22no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3—22no—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3—41no—
215C2×C3⋊Dic3—41no—
216C2×C3⋊Dic3—41no—
217C2×C3⋊Dic3—41no—
218C2×C3⋊Dic3—41no—
219C2×C3⋊Dic3—41no—
220C2×C3⋊Dic3—41no—
221C2×C3⋊Dic3—41no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—41no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—41no—
237C2×C3×Dic3—41no—
238C2×C3×Dic3—41no—
239C2×C3×Dic3—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C22×C22⋊C4—31no—
244C22×C22⋊C4—91no—
245C22×C22⋊C4—91no—
246C2×#95—31no—
247C2×#95—91no—
248C2×#95—91no—
249C2×#95—91no—
250C24×C3—21no—
251C24×C3—32no—
252C24×C3—32no—
253C24×C3—32no—
254C24×C3—61no—
255C24×C3—61no—
256C24×C3—61no—
257C24×C3—61no—
258C24×C3—61no—
259C24×C3—61no—
260C24×C3—61no—
261C24×C3—61no—
262C24×C3—61no—
263C24×C3—61no—
264C24×C3—61no—
265C24×C3—61no—
266C24×C3C22×D311yescharacteristic
267C24×C3C22×D311yescharacteristic
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3C2×Dic312yes—
281C23×D3#6712yes—
282C23×D3#6712yes—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—22no—
298C22×C3×C4—32no—
299C22×C3×C4—32no—
300C22×C3×C4—32no—
301C22×C3×C4—41no—
302C22×C3×C4—41no—
303C22×C3×C4—41no—
304C22×C3×C4—41no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
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×C4C4×D312yes—
324C22×C3×C4C2×Dic312yes—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
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—32no—
344C22×Dic3—32no—
345C22×Dic3—32no—
346C22×Dic3—32no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3—62no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—61no—
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—61no—
367C22×Dic3—61no—
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—121no—
378C22×Dic3—121no—
379C22×Dic3—121no—
380C22×Dic3—121no—
381C22×Dic3—121no—
382C22×Dic3—121no—
383C22×Dic3—121no—
384C22×Dic3—121no—
385C22×Dic3D1212yes—
386C22×Dic3C2×Dic312yes—
387C22×Dic3#6712yes—
388C3×C22⋊C4—68no—
389#217—68no—
390#217—68no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—68no—
393(C2×D3)⋊C4—68no—
394C22×C32C2×C22⋊C411yescharacteristic
395C22×C32#11711yescharacteristic
396C22×C32#11711yescharacteristic
397C22×C32C4×D411yescharacteristic
398C22×C32C4×D411yescharacteristic
399C22×C32C4×D411yescharacteristic
400C22×C32C4×D411yescharacteristic
401C22×C32#12011yescharacteristic
402C22×C32#12011yescharacteristic
403C22×C32#12111yescharacteristic
404C22×C32#12111yescharacteristic
405C22×C32#12111yescharacteristic
406C22×C32#12111yescharacteristic
407C22×C32#12111yescharacteristic
408C22×C32#12111yescharacteristic
409C22×C32#12111yescharacteristic
410C22×C32#12111yescharacteristic
411C22×C32#12311yescharacteristic
412C22×C32#12311yescharacteristic
413C22×C32#12311yescharacteristic
414C22×C32#12311yescharacteristic
415C22×C32#12311yescharacteristic
416C22×C32#12311yescharacteristic
417C22×C32#12311yescharacteristic
418C22×C32#12311yescharacteristic
419C22×C32#12311yescharacteristic
420C22×C32#12311yescharacteristic
421C22×C32#12411yescharacteristic
422C22×C32#12411yescharacteristic
423C22×C32#12411yescharacteristic
424C22×C32#12411yescharacteristic
425C22×C32#12611yescharacteristic
426C22×C32#12611yescharacteristic
427C22×C32#12611yescharacteristic
428C22×C32#12611yescharacteristic
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431C2×C3×D3—24no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C2×C3×D3—42no—
435C2×C3×D3—42no—
436C2×C3×D3—42no—
437C2×C3×D3—42no—
438C2×C3×D3—42no—
439C2×C3×D3—42no—
440C2×C3×D3—42no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C32×C4—42no—
445C3⋊Dic3—42no—
446C3⋊Dic3—42no—
447C3×Dic3—42no—
448C3×Dic3—42no—
449C3×Dic3—42no—
450C25—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—91no—
455C23×C4—91no—
456C23×C4D3211yescharacteristic
457C2×C22⋊C4—34no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—182no—
461C2×C22⋊C4—182no—
462C2×C22⋊C4—182no—
463C2×C22⋊C4—182no—
464C2×C22⋊C4—182no—
465C2×C22⋊C4—182no—
466#95—62no—
467#95—182no—
468#95—182no—
469#95—182no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—34no—
486C23×C3—62no—
487C23×C3—62no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—62no—
491C23×C3—62no—
492C23×C3—62no—
493C23×C3—62no—
494C23×C3—62no—
495C23×C3—62no—
496C23×C3—62no—
497C23×C3—62no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—62no—
504C23×C3—121no—
505C23×C3—121no—
506C23×C3—121no—
507C23×C3—121no—
508C23×C3—121no—
509C23×C3—121no—
510C23×C3—121no—
511C23×C3—121no—
512C23×C3—121no—
513C23×C3—121no—
514C23×C3—121no—
515C23×C3—121no—
516C23×C3—121no—
517C23×C3—121no—
518C23×C3—121no—
519C23×C3—121no—
520C23×C3C2×C4×D311yescharacteristic
521C23×C3C2×D1211yescharacteristic
522C23×C3#23511yescharacteristic
523C23×C3#23511yescharacteristic
524C23×C3#23511yescharacteristic
525C23×C3#23511yescharacteristic
526C23×C3#23511yescharacteristic
527C23×C3#23511yescharacteristic
528C23×C3#23511yescharacteristic
529C23×C3#23511yescharacteristic
530C23×C3D3×D411yescharacteristic
531C23×C3D3×D411yescharacteristic
532C23×C3D3×D411yescharacteristic
533C23×C3D3×D411yescharacteristic
534C23×C3D3×D411yescharacteristic
535C23×C3D3×D411yescharacteristic
536C23×C3D3×D411yescharacteristic
537C23×C3D3×D411yescharacteristic
538C23×C3#23711yescharacteristic
539C23×C3#23711yescharacteristic
540C23×C3#23711yescharacteristic
541C23×C3#23711yescharacteristic
542C23×C3#23711yescharacteristic
543C23×C3#23711yescharacteristic
544C23×C3#23911yescharacteristic
545C23×C3#23911yescharacteristic
546C23×C3C22×Dic311yescharacteristic
547C23×C3C2×#6711yescharacteristic
548C23×C3C2×#6711yescharacteristic
549C23×C3C2×#6711yescharacteristic
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3#21714yes—
585C2×C3×C4—24no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—42no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—62no—
607C2×C3×C4—62no—
608C2×C3×C4—62no—
609C2×C3×C4—62no—
610C2×C3×C4—62no—
611C2×C3×C4—62no—
612C2×C3×C4—62no—
613C2×C3×C4—62no—
614C2×C3×C4—62no—
615C2×C3×C4—121no—
616C2×C3×C4—121no—
617C2×C3×C4—121no—
618C2×C3×C4—121no—
619C2×C3×C4—121no—
620C2×C3×C4—121no—
621C2×C3×C4—121no—
622C2×C3×C4—121no—
623C2×C3×C4—121no—
624C2×C3×C4—121no—
625C2×C3×C4—121no—
626C2×C3×C4—121no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—64no—
649C2×Dic3—64no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—122no—
663C2×Dic3—122no—
664C2×Dic3—122no—
665C2×Dic3—122no—
666C2×Dic3—122no—
667C2×Dic3—122no—
668C2×Dic3—122no—
669C2×Dic3—122no—
670C2×Dic3—122no—
671C2×Dic3—122no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3—121no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3—121no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×C32#38111yescharacteristic
691C2×C32#38611yescharacteristic
692C2×C32#38611yescharacteristic
693C2×C32#38811yescharacteristic
694C2×C32#38811yescharacteristic
695C2×C32#38811yescharacteristic
696C2×C32#38811yescharacteristic
697C2×C32#39411yescharacteristic
698C2×C32#39411yescharacteristic
699C2×C32#39411yescharacteristic
700C2×C32#39411yescharacteristic
701C2×C32#39711yescharacteristic
702C2×C32#39711yescharacteristic
703C2×C32#39711yescharacteristic
704C2×C32#39711yescharacteristic
705C3×D3—44no—
706C24—32no—
707C24—32no—
708C24—32no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24—61no—
717C24—61no—
718C24—61no—
719C24—61no—
720C24—61no—
721C24C2×D3211yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—32no—
729C22×C4—32no—
730C22×C4—32no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—92no—
750C22×C4—92no—
751C22×C4—181no—
752C22×C4—181no—
753C22×C4—181no—
754C22×C4—181no—
755C22×C4—181no—
756C22×C4—181no—
757C22×C4—181no—
758C22×C4—181no—
759C22×C4—181no—
760C22×C4—181no—
761C22×C4—181no—
762C22×C4—181no—
763C22×C4D3×Dic312yes—
764C22⋊C4—68no—
765C22⋊C4—188no—
766C22⋊C4—188no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
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—64no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—122no—
806C22×C3—122no—
807C22×C3—122no—
808C22×C3—122no—
809C22×C3—122no—
810C22×C3—122no—
811C22×C3—122no—
812C22×C3—122no—
813C22×C3—122no—
814C22×C3—122no—
815C22×C3—122no—
816C22×C3—122no—
817C22×C3#87211yescharacteristic
818C22×C3C4×D1211yescharacteristic
819C22×C3#87511yescharacteristic
820C22×C3#87611yescharacteristic
821C22×C3#87911yescharacteristic
822C22×C3#87911yescharacteristic
823C22×C3#87911yescharacteristic
824C22×C3#87911yescharacteristic
825C22×C3D3×C22⋊C411yescharacteristic
826C22×C3#67⋊C411yescharacteristic
827C22×C3#88211yescharacteristic
828C22×C3#88311yescharacteristic
829C22×C3#88311yescharacteristic
830C22×C3#88311yescharacteristic
831C22×C3#88311yescharacteristic
832C22×C3#88311yescharacteristic
833C22×C3#88311yescharacteristic
834C22×C3#88311yescharacteristic
835C22×C3#88411yescharacteristic
836C22×C3#88411yescharacteristic
837C22×C3#88411yescharacteristic
838C22×C3#88411yescharacteristic
839C22×C3#88411yescharacteristic
840C22×C3#88411yescharacteristic
841C22×C3#88411yescharacteristic
842C22×C3#88511yescharacteristic
843C22×C3#88511yescharacteristic
844C22×C3#88511yescharacteristic
845C22×C3#88511yescharacteristic
846C22×C3#88511yescharacteristic
847C22×C3#88511yescharacteristic
848C22×C3#88611yescharacteristic
849C22×C3#89211yescharacteristic
850C22×C3#89311yescharacteristic
851C22×C3#89411yescharacteristic
852C22×C3#89411yescharacteristic
853C22×C3#89411yescharacteristic
854C22×C3#89411yescharacteristic
855C22×C3#89411yescharacteristic
856C22×C3#89511yescharacteristic
857C22×C3#89511yescharacteristic
858C22×C3#89811yescharacteristic
859C22×C3#89811yescharacteristic
860C22×C3#89811yescharacteristic
861C22×C3#92611yescharacteristic
862C22×C3#92611yescharacteristic
863C22×C3C4×#6711yescharacteristic
864C22×C3#92911yescharacteristic
865C22×C3#92911yescharacteristic
866C22×C3#92911yescharacteristic
867C22×C3#92911yescharacteristic
868C22×C3#92911yescharacteristic
869C22×C3#93011yescharacteristic
870C22×C3D4×Dic311yescharacteristic
871C22×C3D4×Dic311yescharacteristic
872C22×C3D4×Dic311yescharacteristic
873C22×C3D4×Dic311yescharacteristic
874C22×C3#93511yescharacteristic
875C22×C3#93511yescharacteristic
876C22×C3#93711yescharacteristic
877C22×C3#93711yescharacteristic
878C22×C3#93711yescharacteristic
879C22×C3#93811yescharacteristic
880C22×C3#93911yescharacteristic
881C22×C3#93911yescharacteristic
882C22×C3#93911yescharacteristic
883C22×C3#93911yescharacteristic
884C22×C3#93911yescharacteristic
885C22×C3#94711yescharacteristic
886C22×C3C2×#21711yescharacteristic
887C2×D3—24no—
888C2×D3—24no—
889C2×D3—24no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C2×D3—42no—
895C2×D3—42no—
896C2×D3—42no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C3×C4—44no—
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—122no—
906C3×C4—122no—
907C3×C4—122no—
908Dic3—42no—
909Dic3—42no—
910Dic3—42no—
911Dic3—124no—
912Dic3—124no—
913Dic3—122no—
914Dic3—122no—
915Dic3—122no—
916Dic3—122no—
917C32#144011yescharacteristic, complemented, Sylow
918C23—34no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23#379511yescharacteristic
954C23#379511yescharacteristic
955C23#379611yescharacteristic
956C23#379811yescharacteristic
957C23#379811yescharacteristic
958C23#379911yescharacteristic
959C23D3×D1211yescharacteristic
960C23#380211yescharacteristic
961C23C2×D3×Dic311yescharacteristic
962C23#380411yescharacteristic
963C23#380511yescharacteristic
964C23D3×#6711yescharacteristic
965C23D3×#6711yescharacteristic
966C23D3×#6711yescharacteristic
967C23#381111yescharacteristic
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—182no—
997C2×C4—182no—
998C2×C4—182no—
999C2×C4—182no—
1000C2×C4—182no—
1001C2×C4—182no—
1002C2×C4—361no—
1003C2×C4—361no—
1004C2×C4—361no—
1005C2×C4—361no—
1006C2×C4—361no—
1007C2×C4—361no—
1008C2×C4—361no—
1009C2×C4—361no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—124no—
1026C2×C3#466411yescharacteristic
1027C2×C3#466511yescharacteristic
1028C2×C3#466911yescharacteristic
1029C2×C3#467011yescharacteristic
1030C2×C3#467211yescharacteristic
1031C2×C3#467411yescharacteristic
1032C2×C3#467511yescharacteristic
1033C2×C3#467511yescharacteristic
1034C2×C3#494011yescharacteristic
1035C2×C3#495111yescharacteristic
1036C2×C3#495111yescharacteristic
1037C2×C3#495111yescharacteristic
1038C2×C3#495111yescharacteristic
1039C2×C3#495211yescharacteristic
1040C2×C3#495211yescharacteristic
1041C2×C3#495211yescharacteristic
1042C2×C3#495211yescharacteristic
1043C2×C3#495611yescharacteristic
1044C2×C3#495911yescharacteristic
1045C2×C3#495911yescharacteristic
1046C2×C3#495911yescharacteristic
1047C2×C3#495911yescharacteristic
1048C2×C3#495911yescharacteristic
1049C2×C3#496111yescharacteristic
1050C2×C3#499011yescharacteristic
1051C2×C3#499111yescharacteristic
1052C2×C3#499211yescharacteristic
1053C2×C3#521111yescharacteristic
1054C2×C3#522011yescharacteristic
1055C2×C3#522011yescharacteristic
1056D3—44no—
1057C22—64no—
1058C22—64no—
1059C22—64no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—122no—
1070C22—122no—
1071C22—122no—
1072C22#6384111yescharacteristic
1073C22#6385011yescharacteristic
1074C22#6385011yescharacteristic
1075C22#6385211yescharacteristic
1076C22#6385311yescharacteristic
1077C22#6385411yescharacteristic
1078C22#6385511yescharacteristic
1079C22#6385811yescharacteristic
1080C22#6385911yescharacteristic
1081C22#6386111yescharacteristic
1082C22#6386211yescharacteristic
1083C22#6388411yescharacteristic
1084C22#6388511yescharacteristic
1085C22#6388511yescharacteristic
1086C22#6388611yescharacteristic
1087C22#6389111yescharacteristic
1088C22Dic3×D1211yescharacteristic
1089C22#6389811yescharacteristic
1090C22#6390511yescharacteristic
1091C22#6390511yescharacteristic
1092C22#6390511yescharacteristic
1093C22#6390611yescharacteristic
1094C22#6390711yescharacteristic
1095C22#6391011yescharacteristic
1096C22#6391211yescharacteristic
1097C22#6391311yescharacteristic
1098C22#6391511yescharacteristic
1099C22#6392211yescharacteristic
1100C22D3×#21711yescharacteristic
1101C22#6396911yescharacteristic
1102C22#6397011yescharacteristic
1103C22#6397111yescharacteristic
1104C22Dic3×#6711yescharacteristic
1105C22#67⋊Dic311yescharacteristic
1106C22#6398311yescharacteristic
1107C4—42no—
1108C4—122no—
1109C4—122no—
1110C4—122no—
1111C4—362no—
1112C4—362no—
1113C3—21no—
1114C3#6942911yescharacteristic, complemented
1115C3#7154811yescharacteristic, complemented
1116C2—124no—
1117C2#1059128611yescharacteristic
1118C2#1059129111yescharacteristic
1119C2#1059129211yescharacteristic
1120C2#1059129411yescharacteristic
1121C2#1059129611yescharacteristic
1122C2#1059129811yescharacteristic
1123C2#1059129911yescharacteristic
1124C2#1059130111yescharacteristic
1125C2#1059130511yescharacteristic
1126C2#1059130711yescharacteristic
1127C2#1059131611yescharacteristic
1128C2#1059137611yescharacteristic
1129C2#1059138811yescharacteristic
1130C2#1059139011yescharacteristic
1131C2#1059172111yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32#1440
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63658C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
19. C2×C3×(C2×D3)⋊C4C4semidirect
44. C2×C3⋊#95D3semidirect
141. C2×(C2×D3)⋊C4Dic3semidirect
917. C32#1440semidirect
1114. C3#69429semidirect
1115. C3#71548semidirect

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
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#715483
#694293