Finite Group Databasebeta

← C3×#71547 #11773295

Subgroups — C3×#71547 #11773295

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic
3C22×C3×#217C211yesmaximal, characteristic
4C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#1439—31nomaximal
9#71547C311yesmaximal, characteristic, direct product factor
10C25×C32C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4—22no—
18C2×C32×C22⋊C4—22no—
19C2×C32×C22⋊C4—22no—
20C2×C3×#217—22no—
21C2×C3×#217—22no—
22C2×C3×#217—22no—
23C2×C3×#217—22no—
24C2×C3×#217—22no—
25C2×C3×#217C414yescomplemented
26C2×C3×Dic3⋊C4—22no—
27C2×C3×Dic3⋊C4—22no—
28C2×C3×Dic3⋊C4—22no—
29C3×C3⋊#95—22no—
30C3×C3⋊#95—22no—
31C3×C3⋊#95—22no—
32C22×C3×C4⋊C4—31no—
33C22×C3×C22⋊C4—21no—
34C22×C3×C22⋊C4—31no—
35C22×C3×C22⋊C4—31no—
36C22×C3×C22⋊C4D311yescharacteristic
37C22×C3×C22⋊C4C2×C311yescharacteristic
38C22×#217C2×C311yescharacteristic
39C22×#217C2×C311yescharacteristic
40C22×Dic3⋊C4C2×C311yescharacteristic, complemented
41C2×C3×#95—31no—
42C2×C3×#95—31no—
43C2×C3×#95—31no—
44C2×C3⋊#95C2×C311yescharacteristic, complemented
45C2×C3⋊#95C2×C311yescharacteristic, complemented
46C2×C3⋊#95C2×C311yescharacteristic, complemented
47C24×C32—21no—
48C24×C32—21no—
49C24×C32—21no—
50C24×C32—21no—
51C24×C32—21no—
52C24×C32—21no—
53C24×C32—21no—
54C24×C32—21no—
55C24×C32—21no—
56C24×C32—21no—
57C24×C32—21no—
58C24×C32—21no—
59C24×C32C2×C412yes—
60C24×C32D412yes—
61C24×C32Q812yes—
62C24×C32C2311yescharacteristic
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×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4D412yes—
76C22×C32×C4D412yes—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
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×Dic3C2×C412yes—
100C22×C3×Dic3C2×C412yes—
101C22×C3×Dic3D412yes—
102C22×C3×Dic3D412yes—
103C22×C3×Dic3D412yes—
104C22×C3×Dic3D412yes—
105C32×C22⋊C4—28no—
106C3×#217—28no—
107C3×#217—28no—
108C3×Dic3⋊C4—28no—
109#1439—31noSylow
110C25×C3—21no—
111C25×C3C2×D311yescharacteristic
112C25×C3C22×C311yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4—21no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×C3×C4—31no—
118C23×C3×C4—31no—
119C23×C3×C4C2×D311yescharacteristic
120C23×C3×C4C2×D311yescharacteristic
121C23×C3×C4C22×C311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C23×Dic3C22×C311yescharacteristic
124C23×Dic3C22×C311yescharacteristic
125C23×Dic3C22×C311yescharacteristic
126C23×Dic3C22×C311yescharacteristic
127C2×C3×C4⋊C4—62no—
128C2×C3×C4⋊C4—62no—
129C2×C3×C4⋊C4—62no—
130C2×C3×C22⋊C4—24no—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4—24no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—34no—
140C2×C3×C22⋊C4—62no—
141C2×C3×C22⋊C4—62no—
142C2×C3×C22⋊C4—62no—
143C2×C3×C22⋊C4—62no—
144C2×C3×C22⋊C4—62no—
145C2×#217—22no—
146C2×#217—22no—
147C2×#217—22no—
148C2×#217—22no—
149C2×#217—22no—
150C2×#217C3×C414yescomplemented
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C3×#95—62no—
155C3×#95—62no—
156C3×#95—62no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—22no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32—22no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—41no—
179C23×C32—41no—
180C23×C32—41no—
181C23×C32—41no—
182C23×C32—41no—
183C23×C32—41no—
184C23×C32—41no—
185C23×C32—41no—
186C23×C32—41no—
187C23×C32—41no—
188C23×C32—41no—
189C23×C32—41no—
190C23×C32—41no—
191C23×C32—41no—
192C23×C32—41no—
193C23×C32—41no—
194C23×C32C4⋊C414yescomplemented
195C23×C32C22×C411yescharacteristic
196C23×C32C2×D411yescharacteristic
197C23×C32C2×D411yescharacteristic
198C23×C32C2×D411yescharacteristic
199C23×C32C2×D411yescharacteristic
200C23×C32C2×D411yescharacteristic
201C23×C32C2×D411yescharacteristic
202C23×C32C2×D411yescharacteristic
203C23×C32C2×Q811yescharacteristic
204C23×C32#4111yescharacteristic
205C23×C32#4111yescharacteristic
206C23×C32#4111yescharacteristic
207C23×C32#4111yescharacteristic
208C23×C32#4111yescharacteristic
209C23×C32#4111yescharacteristic
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—41no—
217C2×C32×C4—41no—
218C2×C32×C4—41no—
219C2×C32×C4—41no—
220C2×C32×C4—41no—
221C2×C32×C4—41no—
222C2×C32×C4—41no—
223C2×C32×C4—41no—
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—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—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—41no—
243C2×C3×Dic3—41no—
244C2×C3×Dic3—41no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—41no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3—41no—
250C2×C3×Dic3—41no—
251C2×C3×Dic3C22⋊C414yescomplemented
252C22×C4⋊C4—31no—
253C22×C22⋊C4—31no—
254C22×C22⋊C4—31no—
255C22×C22⋊C4C3×D311yescharacteristic
256C2×#95—31no—
257C2×#95—31no—
258C2×#95—31no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3—22no—
263C24×C3—21no—
264C24×C3—21no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—21no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—21no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3—21no—
276C24×C3—21no—
277C24×C3—21no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3—21no—
281C24×C3—21no—
282C24×C3—21no—
283C24×C3—21no—
284C24×C3—21no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3—22no—
288C24×C3—22no—
289C24×C3—22no—
290C24×C3—21no—
291C24×C3—41no—
292C24×C3—41no—
293C24×C3—41no—
294C24×C3—41no—
295C24×C3—41no—
296C24×C3—41no—
297C24×C3—41no—
298C24×C3—41no—
299C24×C3Dic612yes—
300C24×C3C4×D312yes—
301C24×C3#6712yes—
302C24×C3C2×C3×C412yes—
303C24×C3C3×D412yes—
304C24×C3C3×Q812yes—
305C24×C3C22×D311yescharacteristic
306C24×C3C23×C311yescharacteristic
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—22no—
336C22×C3×C4—22no—
337C22×C3×C4—32no—
338C22×C3×C4—32no—
339C22×C3×C4—32no—
340C22×C3×C4—32no—
341C22×C3×C4—32no—
342C22×C3×C4—32no—
343C22×C3×C4—41no—
344C22×C3×C4—41no—
345C22×C3×C4—41no—
346C22×C3×C4—41no—
347C22×C3×C4—41no—
348C22×C3×C4—41no—
349C22×C3×C4—41no—
350C22×C3×C4—41no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4—61no—
361C22×C3×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C22×C3×C4—61no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4#6712yes—
374C22×C3×C4#6712yes—
375C22×C3×C4C3×D412yes—
376C22×C3×C4C3×D412yes—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—21no—
384C22×Dic3—21no—
385C22×Dic3—21no—
386C22×Dic3—21no—
387C22×Dic3—21no—
388C22×Dic3—21no—
389C22×Dic3—21no—
390C22×Dic3—21no—
391C22×Dic3—21no—
392C22×Dic3—21no—
393C22×Dic3—21no—
394C22×Dic3—21no—
395C22×Dic3—21no—
396C22×Dic3—21no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3C2×C3×C412yes—
400C22×Dic3C2×C3×C412yes—
401C22×Dic3C3×D412yes—
402C22×Dic3C3×D412yes—
403C22×Dic3C3×D412yes—
404C22×Dic3C3×D412yes—
405C3×C4⋊C4—68no—
406C3×C22⋊C4—216no—
407C3×C22⋊C4—28no—
408C3×C22⋊C4—28no—
409C3×C22⋊C4—68no—
410C3×C22⋊C4—68no—
411#217—28no—
412#217—28no—
413Dic3⋊C4—28no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—42no—
418C22×C32—42no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—42no—
426C22×C32—42no—
427C22×C32—42no—
428C22×C32—42no—
429C22×C32C2×C22⋊C411yescharacteristic
430C22×C32C2×C4⋊C411yescharacteristic
431C22×C32#11711yescharacteristic
432C22×C32C4×D411yescharacteristic
433C22×C32C4×D411yescharacteristic
434C22×C32C4×D411yescharacteristic
435C22×C32C4×D411yescharacteristic
436C22×C32#12011yescharacteristic
437C22×C32#12011yescharacteristic
438C22×C32#12011yescharacteristic
439C22×C32#12111yescharacteristic
440C22×C32#12111yescharacteristic
441C22×C32#12111yescharacteristic
442C22×C32#12111yescharacteristic
443C22×C32#12111yescharacteristic
444C22×C32#12111yescharacteristic
445C22×C32#12111yescharacteristic
446C22×C32#12111yescharacteristic
447C22×C32C22⋊Q811yescharacteristic
448C22×C32C22⋊Q811yescharacteristic
449C22×C32C22⋊Q811yescharacteristic
450C22×C32C22⋊Q811yescharacteristic
451C22×C32C22⋊Q811yescharacteristic
452C22×C32C22⋊Q811yescharacteristic
453C22×C32#12311yescharacteristic
454C22×C32#12311yescharacteristic
455C22×C32#12311yescharacteristic
456C22×C32#12311yescharacteristic
457C22×C32#12311yescharacteristic
458C22×C32#12411yescharacteristic
459C22×C32#12411yescharacteristic
460C22×C32#12411yescharacteristic
461C22×C32#12611yescharacteristic
462C22×C32#12611yescharacteristic
463C22×C32#12711yescharacteristic
464C32×C4—42no—
465C32×C4—42no—
466C3×Dic3—24no—
467C3×Dic3—42no—
468C3×Dic3—42no—
469C3×Dic3—42no—
470C25C2×C3×D311yescharacteristic
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—31no—
474C23×C4—31no—
475C23×C4C2×C3×D311yescharacteristic
476C23×C4C2×C3×D311yescharacteristic
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—34no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—24no—
495C23×C3—24no—
496C23×C3—24no—
497C23×C3—24no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—24no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—42no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—42no—
558C23×C3—42no—
559C23×C3—42no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—42no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—42no—
569C23×C3—42no—
570C23×C3—42no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—41no—
599C23×C3—41no—
600C23×C3—41no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—41no—
609C23×C3—41no—
610C23×C3Dic3⋊C414yescomplemented
611C23×C3C3×C4⋊C414yescomplemented
612C23×C3C2×Dic611yescharacteristic
613C23×C3C2×C4×D311yescharacteristic
614C23×C3#23511yescharacteristic
615C23×C3#23511yescharacteristic
616C23×C3D3×D411yescharacteristic
617C23×C3D3×D411yescharacteristic
618C23×C3D3×D411yescharacteristic
619C23×C3D3×D411yescharacteristic
620C23×C3#23711yescharacteristic
621C23×C3#23711yescharacteristic
622C23×C3#23711yescharacteristic
623C23×C3#23711yescharacteristic
624C23×C3C2×#6711yescharacteristic
625C23×C3C2×#6711yescharacteristic
626C23×C3C2×#6711yescharacteristic
627C23×C3C22×C3×C411yescharacteristic
628C23×C3C2×C3×D411yescharacteristic
629C23×C3C2×C3×D411yescharacteristic
630C23×C3C2×C3×D411yescharacteristic
631C23×C3C2×C3×D411yescharacteristic
632C23×C3C2×C3×D411yescharacteristic
633C23×C3C2×C3×D411yescharacteristic
634C23×C3C2×C3×D411yescharacteristic
635C23×C3C2×C3×Q811yescharacteristic
636C23×C3C3×#4111yescharacteristic
637C23×C3C3×#4111yescharacteristic
638C23×C3C3×#4111yescharacteristic
639C23×C3C3×#4111yescharacteristic
640C23×C3C3×#4111yescharacteristic
641C23×C3C3×#4111yescharacteristic
642C2×C3×C4—24no—
643C2×C3×C4—24no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—34no—
657C2×C3×C4—42no—
658C2×C3×C4—42no—
659C2×C3×C4—42no—
660C2×C3×C4—42no—
661C2×C3×C4—42no—
662C2×C3×C4—42no—
663C2×C3×C4—42no—
664C2×C3×C4—42no—
665C2×C3×C4—42no—
666C2×C3×C4—42no—
667C2×C3×C4—42no—
668C2×C3×C4—42no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—62no—
693C2×C3×C4—62no—
694C2×C3×C4—62no—
695C2×C3×C4—62no—
696C2×C3×C4—62no—
697C2×C3×C4—62no—
698C2×C3×C4—62no—
699C2×C3×C4—62no—
700C2×C3×C4—121no—
701C2×C3×C4—121no—
702C2×C3×C4—121no—
703C2×C3×C4—121no—
704C2×C3×C4—121no—
705C2×C3×C4—121no—
706C2×C3×C4—121no—
707C2×C3×C4—121no—
708C2×C3×C4—121no—
709C2×C3×C4—121no—
710C2×C3×C4—121no—
711C2×C3×C4—121no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3C3×C22⋊C414yescomplemented
740C2×C32—44no—
741C2×C32#38011yescharacteristic
742C2×C32#38511yescharacteristic
743C2×C32#38511yescharacteristic
744C2×C32#38611yescharacteristic
745C2×C32#38811yescharacteristic
746C2×C32#38811yescharacteristic
747C2×C32#39011yescharacteristic
748C2×C32#39211yescharacteristic
749C2×C32#39311yescharacteristic
750C2×C32#39411yescharacteristic
751C2×C32#39411yescharacteristic
752C2×C32#39611yescharacteristic
753C2×C32#39611yescharacteristic
754C2×C32#39711yescharacteristic
755C2×C32#39911yescharacteristic
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24C3×Dic612yes—
769C24C3×C4×D312yes—
770C24C3×#6712yes—
771C24C22×C3×D311yescharacteristic
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—32no—
785C22×C4—32no—
786C22×C4—32no—
787C22×C4—32no—
788C22×C4—32no—
789C22×C4—32no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4C3×#6712yes—
813C22×C4C3×#6712yes—
814C4⋊C4—68no—
815C22⋊C4—28no—
816C22⋊C4—68no—
817C22⋊C4—68no—
818C22×C3—28no—
819C22×C3—24no—
820C22×C3—24no—
821C22×C3—24no—
822C22×C3—24no—
823C22×C3—24no—
824C22×C3—24no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—44no—
861C22×C3—44no—
862C22×C3—44no—
863C22×C3—44no—
864C22×C3—44no—
865C22×C3—44no—
866C22×C3—44no—
867C22×C3—44no—
868C22×C3—44no—
869C22×C3—44no—
870C22×C3—44no—
871C22×C3—44no—
872C22×C3—44no—
873C22×C3—44no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—42no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3#87711yescharacteristic
899C22×C3#87811yescharacteristic
900C22×C3#87811yescharacteristic
901C22×C3#87811yescharacteristic
902C22×C3#87811yescharacteristic
903C22×C3#87911yescharacteristic
904C22×C3#87911yescharacteristic
905C22×C3D3×C22⋊C411yescharacteristic
906C22×C3#67⋊C411yescharacteristic
907C22×C3#67⋊C411yescharacteristic
908C22×C3#88311yescharacteristic
909C22×C3#88311yescharacteristic
910C22×C3#88411yescharacteristic
911C22×C3#88411yescharacteristic
912C22×C3#88511yescharacteristic
913C22×C3#88511yescharacteristic
914C22×C3C2×Dic3⋊C411yescharacteristic
915C22×C3#92411yescharacteristic
916C22×C3#92411yescharacteristic
917C22×C3C4×#6711yescharacteristic
918C22×C3C4×#6711yescharacteristic
919C22×C3#92911yescharacteristic
920C22×C3#93511yescharacteristic
921C22×C3#93511yescharacteristic
922C22×C3#93611yescharacteristic
923C22×C3#93711yescharacteristic
924C22×C3#93711yescharacteristic
925C22×C3#93811yescharacteristic
926C22×C3#93811yescharacteristic
927C22×C3#93911yescharacteristic
928C22×C3#93911yescharacteristic
929C22×C3#93911yescharacteristic
930C22×C3#93911yescharacteristic
931C22×C3#94011yescharacteristic
932C22×C3#95311yescharacteristic
933C22×C3C2×C3×C22⋊C411yescharacteristic
934C22×C3C2×C3×C4⋊C411yescharacteristic
935C22×C3C3×#11711yescharacteristic
936C22×C3C3×C4×D411yescharacteristic
937C22×C3C3×C4×D411yescharacteristic
938C22×C3C3×C4×D411yescharacteristic
939C22×C3C3×C4×D411yescharacteristic
940C22×C3C3×#12011yescharacteristic
941C22×C3C3×#12011yescharacteristic
942C22×C3C3×#12011yescharacteristic
943C22×C3C3×#12111yescharacteristic
944C22×C3C3×#12111yescharacteristic
945C22×C3C3×#12111yescharacteristic
946C22×C3C3×#12111yescharacteristic
947C22×C3C3×#12111yescharacteristic
948C22×C3C3×#12111yescharacteristic
949C22×C3C3×#12111yescharacteristic
950C22×C3C3×#12111yescharacteristic
951C22×C3C3×C22⋊Q811yescharacteristic
952C22×C3C3×C22⋊Q811yescharacteristic
953C22×C3C3×C22⋊Q811yescharacteristic
954C22×C3C3×C22⋊Q811yescharacteristic
955C22×C3C3×C22⋊Q811yescharacteristic
956C22×C3C3×C22⋊Q811yescharacteristic
957C22×C3C3×#12311yescharacteristic
958C22×C3C3×#12311yescharacteristic
959C22×C3C3×#12311yescharacteristic
960C22×C3C3×#12311yescharacteristic
961C22×C3C3×#12311yescharacteristic
962C22×C3C3×#12411yescharacteristic
963C22×C3C3×#12411yescharacteristic
964C22×C3C3×#12411yescharacteristic
965C22×C3C3×#12611yescharacteristic
966C22×C3C3×#12611yescharacteristic
967C22×C3C3×#12711yescharacteristic
968C3×C4—44no—
969C3×C4—44no—
970C3×C4—42no—
971C3×C4—42no—
972C3×C4—42no—
973C3×C4—42no—
974C3×C4—64no—
975C3×C4—122no—
976C3×C4—122no—
977C3×C4—122no—
978Dic3—24no—
979Dic3—42no—
980Dic3—42no—
981Dic3—42no—
982C32#143911yescharacteristic, complemented, Sylow
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23C3×Dic3⋊C414yescomplemented
1018C23C2×C3×Dic611yescharacteristic
1019C23C2×C3×C4×D311yescharacteristic
1020C23C3×#23511yescharacteristic
1021C23C3×#23511yescharacteristic
1022C23C3×D3×D411yescharacteristic
1023C23C3×D3×D411yescharacteristic
1024C23C3×D3×D411yescharacteristic
1025C23C3×D3×D411yescharacteristic
1026C23C3×#23711yescharacteristic
1027C23C3×#23711yescharacteristic
1028C23C3×#23711yescharacteristic
1029C23C3×#23711yescharacteristic
1030C23C2×C3×#6711yescharacteristic
1031C23C2×C3×#6711yescharacteristic
1032C23C2×C3×#6711yescharacteristic
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—34no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—21no—
1090C2×C3—48no—
1091C2×C3—44no—
1092C2×C3—44no—
1093C2×C3#494211yescharacteristic
1094C2×C3#494411yescharacteristic
1095C2×C3#494511yescharacteristic
1096C2×C3#494611yescharacteristic
1097C2×C3#494711yescharacteristic
1098C2×C3#494811yescharacteristic
1099C2×C3#494811yescharacteristic
1100C2×C3#494911yescharacteristic
1101C2×C3#495211yescharacteristic
1102C2×C3#495611yescharacteristic
1103C2×C3#495711yescharacteristic
1104C2×C3#495911yescharacteristic
1105C2×C3#521011yescharacteristic
1106C2×C3#522211yescharacteristic
1107C2×C3#522311yescharacteristic
1108C2×C3C3×#38011yescharacteristic
1109C2×C3C3×#38511yescharacteristic
1110C2×C3C3×#38511yescharacteristic
1111C2×C3C3×#38611yescharacteristic
1112C2×C3C3×#38811yescharacteristic
1113C2×C3C3×#38811yescharacteristic
1114C2×C3C3×#39011yescharacteristic
1115C2×C3C3×#39211yescharacteristic
1116C2×C3C3×#39311yescharacteristic
1117C2×C3C3×#39411yescharacteristic
1118C2×C3C3×#39411yescharacteristic
1119C2×C3C3×#39611yescharacteristic
1120C2×C3C3×#39611yescharacteristic
1121C2×C3C3×#39711yescharacteristic
1122C2×C3C3×#39911yescharacteristic
1123C22—24no—
1124C22—24no—
1125C22—24no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22C3×#87711yescharacteristic
1139C22C3×#87811yescharacteristic
1140C22C3×#87811yescharacteristic
1141C22C3×#87811yescharacteristic
1142C22C3×#87811yescharacteristic
1143C22C3×#87911yescharacteristic
1144C22C3×#87911yescharacteristic
1145C22C3×D3×C22⋊C411yescharacteristic
1146C22C3×#67⋊C411yescharacteristic
1147C22C3×#67⋊C411yescharacteristic
1148C22C3×#88311yescharacteristic
1149C22C3×#88311yescharacteristic
1150C22C3×#88411yescharacteristic
1151C22C3×#88411yescharacteristic
1152C22C3×#88511yescharacteristic
1153C22C3×#88511yescharacteristic
1154C22C2×C3×Dic3⋊C411yescharacteristic
1155C22C3×#92411yescharacteristic
1156C22C3×#92411yescharacteristic
1157C22C3×C4×#6711yescharacteristic
1158C22C3×C4×#6711yescharacteristic
1159C22C3×#92911yescharacteristic
1160C22C3×#93511yescharacteristic
1161C22C3×#93511yescharacteristic
1162C22C3×#93611yescharacteristic
1163C22C3×#93711yescharacteristic
1164C22C3×#93711yescharacteristic
1165C22C3×#93811yescharacteristic
1166C22C3×#93811yescharacteristic
1167C22C3×#93911yescharacteristic
1168C22C3×#93911yescharacteristic
1169C22C3×#93911yescharacteristic
1170C22C3×#93911yescharacteristic
1171C22C3×#94011yescharacteristic
1172C22C3×#95311yescharacteristic
1173C4—42no—
1174C4—42no—
1175C4—64no—
1176C4—122no—
1177C4—122no—
1178C4—122no—
1179C3—21no—
1180C3#7154711yescharacteristic, direct product factor
1181C3C3×#143911yescharacteristic, complemented
1182C2—44no—
1183C2C3×#494211yescharacteristic
1184C2C3×#494411yescharacteristic
1185C2C3×#494511yescharacteristic
1186C2C3×#494611yescharacteristic
1187C2C3×#494711yescharacteristic
1188C2C3×#494811yescharacteristic
1189C2C3×#494811yescharacteristic
1190C2C3×#494911yescharacteristic
1191C2C3×#495211yescharacteristic
1192C2C3×#495611yescharacteristic
1193C2C3×#495711yescharacteristic
1194C2C3×#495911yescharacteristic
1195C2C3×#521011yescharacteristic
1196C2C3×#522211yescharacteristic
1197C2C3×#522311yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC25×C32C22
cosocleC24×C3C23×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×C3×Dic3⋊C4C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C2×C3×C3⋊#95C2semidirect
7. C2×C3×C3⋊#95C2semidirect
9. #71547C3direct (N × H)
25. C2×C3×#217C4semidirect
40. C22×Dic3⋊C4C2×C3semidirect
44. C2×C3⋊#95C2×C3semidirect
45. C2×C3⋊#95C2×C3semidirect
46. C2×C3⋊#95C2×C3semidirect
150. C2×#217C3×C4semidirect
194. C23×C32C4⋊C4semidirect
251. C2×C3×Dic3C22⋊C4semidirect
610. C23×C3Dic3⋊C4semidirect
611. C23×C3C3×C4⋊C4semidirect
739. C2×Dic3C3×C22⋊C4semidirect
982. C32#1439semidirect
1017. C23C3×Dic3⋊C4semidirect
1180. C3#71547direct (N × H)
1181. C3C3×#1439semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C22×C3×#2172
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C3×#14393
#715473