Finite Group Databasebeta

← #10716828

Subgroups — #10716828

Order 768.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5213C211yesmaximal, characteristic
2C2×#4956C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C3×C22⋊#95C211yesmaximal, characteristic, complemented
5#72127C211yesmaximal, characteristic, complemented
6#71545C211yesmaximal, characteristic, complemented
7#71545C211yesmaximal, characteristic, complemented
8(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
9(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
10#69408C211yesmaximal, characteristic, complemented
11#69408C211yesmaximal, characteristic, complemented
12#69406C211yesmaximal, characteristic, complemented
13#69405C211yesmaximal, characteristic, complemented
14#69403C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#13832—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×C4×Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38#5213C418yescomplemented
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53#4957C418yescomplemented
54#4956C418yescomplemented
55C2×#390—31no—
56C2×#386—31no—
57C2×#386—31no—
58#1437—31no—
59#1437—31no—
60#1437—31no—
61#1437—31no—
62#1436—31no—
63#1436—31no—
64#1434—31no—
65#1434—31no—
66C22⋊#95—31no—
67C22⋊#95—31no—
68C22⋊#95—31no—
69C22⋊#95D311yescharacteristic, complemented
70C25×C3C2311yescharacteristic
71C24×D3C2311yescharacteristic
72C23×C3×C4—41no—
73C23×C3×C4—41no—
74C23×C3×C4—41no—
75C23×C3×C4—41no—
76C23×C3×C4—41no—
77C23×C3×C4—41no—
78C23×C3×C4C2×C414yescomplemented
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—41no—
86C22×#67—41no—
87C22×#67—41no—
88C22×#67—41no—
89C22×#67C2×C414yes—
90C22×#67C2×C414yes—
91C22×#67C2×C414yes—
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C22×C4×D3—41no—
100C22×C4×D3—41no—
101C22×C4×D3—41no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3C2×C414yescomplemented
106C2×C3×C22⋊C4—41no—
107C2×C3×C22⋊C4—41no—
108C2×C3×C22⋊C4—41no—
109C2×C3×C22⋊C4—41no—
110C2×C3×C22⋊C4C2×C414yes—
111C2×C3×C22⋊C4C2×C414yescomplemented
112C2×#217—41no—
113C2×#217—41no—
114C2×#217—41no—
115C2×#217—41no—
116C2×#217—41no—
117C2×#217—41no—
118C2×#217C2×C414yes—
119C2×#217C2×C414yescomplemented
120C2×#217C2×C414yescomplemented
121C2×(C2×D3)⋊C4—41no—
122C2×(C2×D3)⋊C4—41no—
123C2×(C2×D3)⋊C4—41no—
124C2×(C2×D3)⋊C4—41no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4—41no—
129C2×(C2×D3)⋊C4—41no—
130C2×(C2×D3)⋊C4—41no—
131C2×(C2×D3)⋊C4C2×C414yes—
132C2×(C2×D3)⋊C4C2×C414yes—
133C2×(C2×D3)⋊C4C2×C414yescomplemented
134C2×(C2×D3)⋊C4C2×C414yescomplemented
135C2×(C2×D3)⋊C4C2×C414yescomplemented
136C2×Dic3⋊C4—41no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4C2×C414yescomplemented
139C2×C4×Dic3—41no—
140C2×C4×Dic3—41no—
141C2×C4×Dic3—41no—
142C2×C4×Dic3—41no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
147C2×C4×Dic3C2×C414yescomplemented
148C3×#95—41no—
149C3×#95—41no—
150C3×#95—41no—
151C3×#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C3⋊#95—41no—
157C3⋊#95—41no—
158C3⋊#95—41no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95C2×C414yescomplemented
163C3⋊#95C2×C414yescomplemented
164C3⋊#95C2×C414yescomplemented
165C3⋊#95C2×C414yescomplemented
166C23×D4—31no—
167C24×C4—31no—
168C24×C4C2×D311yescharacteristic
169C22×C4⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C42—31no—
181C22×C42—31no—
182C22×C42—31no—
183#390—38no—
184#386—38no—
185#386—38no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C2×#95C2×D311yescharacteristic
203C2×#95C2×D311yescharacteristic
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—21no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C22×C412yes—
217C24×C3C22×C412yes—
218C24×C3C22×C412yes—
219C24×C3C2411yescharacteristic
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3C22×C412yes—
233C23×D3C22×C412yes—
234C23×D3C22×C412yes—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—44no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4—44no—
275C22×C3×C4—44no—
276C22×C3×C4—44no—
277C22×C3×C4—44no—
278C22×C3×C4C22×C412yes—
279C22×C3×C4C22×C412yes—
280C22×C3×C4C22×C412yes—
281C22×C3×C4C22×C412yes—
282C22×C3×C4C22×C412yes—
283C22×C3×C4C22×C412yes—
284C2×#67—44no—
285C2×#67—44no—
286C2×#67—44no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67C42116yescomplemented
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3C22×C412yes—
332C22×Dic3C22×C412yes—
333C22×Dic3C22×C412yes—
334C22×Dic3C22×C412yes—
335C22×Dic3C22×C412yes—
336C22×Dic3C22×C412yes—
337C22×Dic3C22×C412yes—
338C22×Dic3C22×C412yes—
339C22×Dic3C22×C412yes—
340C2×C4×D3—44no—
341C2×C4×D3—44no—
342C2×C4×D3—44no—
343C2×C4×D3—44no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C3×C22⋊C4—44no—
348C3×C22⋊C4—44no—
349#217—44no—
350#217—44no—
351#217—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—44no—
359C4×Dic3—44no—
360C4×Dic3—44no—
361C25—31no—
362C25C22×D311yescharacteristic
363C22×D4—34no—
364C22×D4—34no—
365C22×D4—34no—
366C22×D4—121no—
367C22×D4—121no—
368C22×D4—121no—
369C22×D4—121no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—34no—
378C23×C4—41no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4—41no—
382C23×C4—41no—
383C23×C4—41no—
384C23×C4—121no—
385C23×C4—121no—
386C23×C4—121no—
387C23×C4—121no—
388C23×C4—121no—
389C23×C4—121no—
390C23×C4C4×D314yescomplemented
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C2×C4⋊C4—34no—
398C2×C4⋊C4—121no—
399C2×C4⋊C4—121no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4C4×D314yes—
429C2×C22⋊C4C4×D314yescomplemented
430C2×C42—34no—
431C2×C42—121no—
432C2×C42—121no—
433C2×C42—121no—
434C2×C42—121no—
435C2×C42—121no—
436C2×C42—121no—
437C2×C42—121no—
438C2×C42—121no—
439#95—34no—
440#95—34no—
441#95—34no—
442#95—34no—
443#95—41no—
444#95—41no—
445#95—41no—
446#95—41no—
447#95—121no—
448#95—121no—
449#95—121no—
450#95—121no—
451#95—121no—
452#95—121no—
453#95—121no—
454#95—121no—
455#95—121no—
456#95—121no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3C2×C4214yes—
492C23×C3C23×C411yescharacteristic
493C23×C3C23×C411yescharacteristic
494C23×C3C23×C411yescharacteristic
495C23×C3H(5,𝔽2)11yescharacteristic
496C23×C3H(5,𝔽2)11yescharacteristic
497C23×C3H(5,𝔽2)11yescharacteristic
498C23×C3H(5,𝔽2)11yescharacteristic
499C23×C3H(5,𝔽2)11yescharacteristic
500C23×C3H(5,𝔽2)11yescharacteristic
501C23×C3H(5,𝔽2)11yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C32−1+411yescharacteristic
506C23×C32−1+411yescharacteristic
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3C2×C4214yes—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—416no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585#67—416no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
619C2×Dic3—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3C2×C4214yes—
635C4×D3—416no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—32no—
649C24—32no—
650C24—32no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24C2×C4×D312yes—
664C24C2×C4×D312yes—
665C24C2×C4×D312yes—
666C24C23×D311yescharacteristic
667C2×D4—316no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C2×D4—124no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—32no—
711C22×C4—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
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—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—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—124no—
767C22×C4—124no—
768C22×C4—124no—
769C22×C4—124no—
770C22×C4—124no—
771C22×C4—124no—
772C22×C4—124no—
773C22×C4C2×C4×D312yes—
774C22×C4C2×C4×D312yes—
775C22×C4C2×C4×D312yes—
776C22×C4C2×C4×D312yes—
777C22×C4C2×C4×D312yes—
778C22×C4C2×C4×D312yes—
779C4⋊C4—124no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4—124no—
786C22⋊C4—124no—
787C22⋊C4—124no—
788C22⋊C4—124no—
789C22⋊C4—124no—
790C42—124no—
791C42—124no—
792C42—124no—
793C22×C3—24no—
794C22×C3—24no—
795C22×C3—24no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3C22×C4211yescharacteristic
809C22×C3#51811yescharacteristic
810C22×C3#51811yescharacteristic
811C22×C3#51811yescharacteristic
812C22×C3#51811yescharacteristic
813C22×C3#51811yescharacteristic
814C22×C3#51811yescharacteristic
815C22×C3#51811yescharacteristic
816C22×C3#51811yescharacteristic
817C22×C3#51811yescharacteristic
818C22×C3#51811yescharacteristic
819C22×C3#51811yescharacteristic
820C22×C3#51811yescharacteristic
821C22×C3#52011yescharacteristic
822C22×C3#52011yescharacteristic
823C22×C3#52011yescharacteristic
824C22×C3#52011yescharacteristic
825C22×C3#52011yescharacteristic
826C22×C3#52011yescharacteristic
827C22×C3#56011yescharacteristic
828C22×C3#56011yescharacteristic
829C22×C3#56011yescharacteristic
830C22×C3#56011yescharacteristic
831C22×C3#56011yescharacteristic
832C22×C3#56011yescharacteristic
833C22×C3#56011yescharacteristic
834C22×C3#56011yescharacteristic
835C22×C3H(3,𝔽4)11yescharacteristic
836C22×C3#56211yescharacteristic
837C22×C3#56211yescharacteristic
838C22×C3#56211yescharacteristic
839C22×C3#56211yescharacteristic
840C22×C3#56211yescharacteristic
841C22×C3#56211yescharacteristic
842C22×C3#56311yescharacteristic
843C2×D3—24no—
844C2×D3—24no—
845C2×D3—24no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—42no—
863C3×C4—42no—
864Dic3—24no—
865Dic3—42no—
866Dic3—42no—
867Dic3—42no—
868Dic3—42no—
869Dic3—42no—
870Dic3—42no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—34no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23C42×D314yes—
941C23C22×C4×D311yescharacteristic
942C23C22×C4×D311yescharacteristic
943C23C22×C4×D311yescharacteristic
944C23#100411yescharacteristic
945C23#100411yescharacteristic
946C23#100411yescharacteristic
947C23#100411yescharacteristic
948C23#100411yescharacteristic
949C23#100411yescharacteristic
950C23#100411yescharacteristic
951C23#100711yescharacteristic
952C23#100911yescharacteristic
953C23#100911yescharacteristic
954C23#100911yescharacteristic
955C23#101011yescharacteristic
956D4—1216no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—34no—
976C2×C4—416no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—1216no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C3—44no—
1051C2×C3#227311yescharacteristic
1052C2×C3#227511yescharacteristic
1053C2×C3#227511yescharacteristic
1054C2×C3#237511yescharacteristic
1055C2×C3#237511yescharacteristic
1056C2×C3#237611yescharacteristic
1057C2×C3#237611yescharacteristic
1058C2×C3#237711yescharacteristic
1059C2×C3#237711yescharacteristic
1060C2×C3#237711yescharacteristic
1061C2×C3#237711yescharacteristic
1062C2×C3#237711yescharacteristic
1063C2×C3#237711yescharacteristic
1064C2×C3#237911yescharacteristic
1065C2×C3#238011yescharacteristic
1066D3—44no—
1067C22—24no—
1068C22—24no—
1069C22—24no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—64no—
1083C22—64no—
1084C22—64no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22C2×C42×D311yescharacteristic
1098C22#548611yescharacteristic
1099C22#548611yescharacteristic
1100C22#548611yescharacteristic
1101C22#548611yescharacteristic
1102C22#548611yescharacteristic
1103C22#550411yescharacteristic
1104C22#550411yescharacteristic
1105C22#550411yescharacteristic
1106C22#552111yescharacteristic
1107C22#552311yescharacteristic
1108C22#554511yescharacteristic
1109C22#554511yescharacteristic
1110C22#554511yescharacteristic
1111C22#554511yescharacteristic
1112C22#554511yescharacteristic
1113C22#554511yescharacteristic
1114C22#554611yescharacteristic
1115C22#554611yescharacteristic
1116C22#559411yescharacteristic
1117C22#559511yescharacteristic
1118C22#559511yescharacteristic
1119C22#559511yescharacteristic
1120C22#562011yescharacteristic
1121C22#562011yescharacteristic
1122C22#562011yescharacteristic
1123C22#562111yescharacteristic
1124C22#564611yescharacteristic
1125C22#564711yescharacteristic
1126C22#564711yescharacteristic
1127C22#564711yescharacteristic
1128C22#566611yescharacteristic
1129C22#566611yescharacteristic
1130C22#566711yescharacteristic
1131C22#566711yescharacteristic
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—64no—
1139C4—122no—
1140C4—122no—
1141C4—122no—
1142C4—122no—
1143C4—122no—
1144C4—122no—
1145C3#1383211yescharacteristic, complemented, Sylow
1146C2—44no—
1147C2—124no—
1148C2#7332211yescharacteristic
1149C2#7343611yescharacteristic
1150C2#7356011yescharacteristic
1151C2#7385111yescharacteristic
1152C2#7401311yescharacteristic
1153C2#7401411yescharacteristic
1154C2#7412411yescharacteristic
1155C2#7440111yescharacteristic
1156C2#7440111yescharacteristic
1157C2#7440211yescharacteristic
1158C2#7459811yescharacteristic
1159C2#7468311yescharacteristic
1160C2#7468511yescharacteristic
1161C2#7488211yescharacteristic
1162C2#7488311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC22×C3C22×C42
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#13832
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C3×C22⋊#95C2semidirect
5. #72127C2semidirect
6. #71545C2semidirect
7. #71545C2semidirect
8. (C2×D3)⋊#95C2semidirect
9. (C2×D3)⋊#95C2semidirect
10. #69408C2semidirect
11. #69408C2semidirect
12. #69406C2semidirect
13. #69405C2semidirect
14. #69403C2semidirect
15. #69402C2semidirect
38. #5213C4semidirect
53. #4957C4semidirect
54. #4956C4semidirect
69. C22⋊#95D3semidirect
78. C23×C3×C4C2×C4semidirect
105. C22×C4×D3C2×C4semidirect
111. C2×C3×C22⋊C4C2×C4semidirect
119. C2×#217C2×C4semidirect
120. C2×#217C2×C4semidirect
133. C2×(C2×D3)⋊C4C2×C4semidirect
134. C2×(C2×D3)⋊C4C2×C4semidirect
135. C2×(C2×D3)⋊C4C2×C4semidirect
138. C2×Dic3⋊C4C2×C4semidirect
147. C2×C4×Dic3C2×C4semidirect
162. C3⋊#95C2×C4semidirect
163. C3⋊#95C2×C4semidirect
164. C3⋊#95C2×C4semidirect
165. C3⋊#95C2×C4semidirect
290. C2×#67C42semidirect
390. C23×C4C4×D3semidirect
429. C2×C22⋊C4C4×D3semidirect
1145. C3#13832semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C2×#49562
C2×#49572
C3×C22⋊#952
#721272
#715452
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