Finite Group Databasebeta

← C2×#82599 #11429972

Subgroups — C2×#82599 #11429972

Order 768.

4098 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#120C211yesmaximal, characteristic
2C22×#879C211yesmaximal, characteristic, complemented
3C2×#5247C211yesmaximal, characteristic, complemented
4C2×#5247C211yesmaximal, characteristic, complemented
5C2×#5222C211yesmaximal, characteristic, complemented
6C2×#5222C211yesmaximal, characteristic, complemented
7C2×#5222C211yesmaximal, characteristic, complemented
8C2×#5222C211yesmaximal, characteristic, complemented
9C2×#5221C211yesmaximal, characteristic, complemented
10C2×#5221C211yesmaximal, characteristic, complemented
11#82599C2116yesmaximal, direct product factor
12C2×#4949C211yesmaximal, characteristic, complemented
13C2×#4948C211yesmaximal, characteristic, complemented
14C2×#4945C211yesmaximal, characteristic, complemented
15C2×#4944C211yesmaximal, characteristic, complemented
16C2×#4951C211yesmaximal, characteristic, complemented
17C2×#2685—31nomaximal, Sylow
18C26×C3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic
22C2×C3×#120—28no—
23C2×C3×#120C2218yes—
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×#217C2211yescharacteristic, complemented
40C22×#217C2211yescharacteristic, complemented
41C22×#217C2211yescharacteristic, complemented
42C22×#217C2211yescharacteristic, complemented
43C22×C4⋊Dic3C2211yescharacteristic, complemented
44C22×C4⋊Dic3C2211yescharacteristic, complemented
45C22×Dic3⋊C4C2211yescharacteristic, complemented
46C22×Dic3⋊C4C2211yescharacteristic, complemented
47C22×Dic3⋊C4C2211yescharacteristic, complemented
48C22×Dic3⋊C4C2211yescharacteristic, complemented
49C22×C4×Dic3C2211yescharacteristic, complemented
50C22×C4×Dic3C2211yescharacteristic, complemented
51C2×#879—28no—
52C2×#879C2218yescomplemented
53#5247C2218yescomplemented
54#5247C2218yescomplemented
55#5222C2218yescomplemented
56#5222C2218yescomplemented
57#5222C2218yescomplemented
58#5222C2218yescomplemented
59#5221C2218yescomplemented
60#5221C2218yescomplemented
61C2×C3⋊#95C2211yescharacteristic, complemented
62C2×C3⋊#95C2211yescharacteristic, complemented
63C2×C3⋊#95C2211yescharacteristic, complemented
64C2×C3⋊#95C2211yescharacteristic, complemented
65#4951C2218yescomplemented
66#4949C2218yescomplemented
67#4948C2218yescomplemented
68#4945C2218yescomplemented
69#4944C2218yescomplemented
70C22×#126—31no—
71C22×#120D311yescharacteristic
72#2685—316no—
73C2×#399—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#390—31no—
80C2×#390—31no—
81C2×#388—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#379—31no—
85C2×#379—31no—
86C25×C3—24no—
87C25×C3—24no—
88C25×C3—24no—
89C25×C3—42no—
90C25×C3—42no—
91C25×C3—42no—
92C25×C3—42no—
93C25×C3C2311yescharacteristic
94C25×C3C2311yescharacteristic
95C25×C3C2311yescharacteristic
96C25×C3C2311yescharacteristic
97C25×C3C2314yes—
98C22×C3×D4—24no—
99C22×C3×D4—24no—
100C22×C3×D4—24no—
101C22×C3×D4—24no—
102C22×C3×D4—24no—
103C22×C3×D4—42no—
104C22×C3×D4—42no—
105C22×C3×D4—42no—
106C22×C3×D4—42no—
107C22×C3×D4C2314yes—
108C22×C3×D4C2314yes—
109C22×C3×D4C2314yes—
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C3×#120—232no—
122C2×C3×C22⋊C4—24no—
123C2×C3×C22⋊C4—24no—
124C2×C3×C22⋊C4D418yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C22⋊C4C2314yes—
128C2×#217—24no—
129C2×#217—24no—
130C2×#217—24no—
131C2×#217—24no—
132C2×#217—42no—
133C2×#217—42no—
134C2×#217—42no—
135C2×#217—42no—
136C2×#217—42no—
137C2×#217—42no—
138C2×#217—42no—
139C2×#217—42no—
140C2×#217—42no—
141C2×#217—42no—
142C2×#217—42no—
143C2×#217—42no—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153C2×#217C2314yes—
154C2×#217C2314yes—
155C2×#217C2314yes—
156C2×#217C2314yescomplemented
157C2×#217C2314yescomplemented
158C2×#217C2314yescomplemented
159C2×#217C2314yescomplemented
160C2×C4⋊Dic3—24no—
161C2×C4⋊Dic3—42no—
162C2×C4⋊Dic3C2314yescomplemented
163C2×C4⋊Dic3C2314yescomplemented
164C2×Dic3⋊C4—24no—
165C2×Dic3⋊C4—24no—
166C2×Dic3⋊C4—42no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4C2314yescomplemented
169C2×Dic3⋊C4C2314yescomplemented
170C2×Dic3⋊C4C2314yescomplemented
171C2×Dic3⋊C4C2314yescomplemented
172C2×C4×Dic3—24no—
173C2×C4×Dic3—42no—
174C2×C4×Dic3C2314yescomplemented
175C2×C4×Dic3C2314yescomplemented
176#879—232no—
177C3⋊#95C2314yescomplemented
178C3⋊#95C2314yescomplemented
179C3⋊#95C2314yescomplemented
180C3⋊#95C2314yescomplemented
181C26C2×D311yescharacteristic
182C23×D4C2×D311yescharacteristic
183C23×D4C2×D311yescharacteristic
184C23×D4C2×D311yescharacteristic
185C2×#126—38no—
186C2×#126—68no—
187C2×#120—28no—
188C2×#120C2×D318yes—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic
214C22×C42—31no—
215C22×C42—31no—
216#399—38no—
217#396—38no—
218#394—38no—
219#394—38no—
220#394—38no—
221#394—38no—
222#390—38no—
223#390—38no—
224#388—38no—
225#388—38no—
226#388—38no—
227#379—38no—
228#379—38no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—28no—
252C24×C3—22no—
253C24×C3—28no—
254C24×C3—28no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—44no—
262C24×C3—44no—
263C24×C3—44no—
264C24×C3—44no—
265C24×C3—416no—
266C24×C3—416no—
267C24×C3—416no—
268C24×C3—416no—
269C24×C3—416no—
270C24×C3—416no—
271C24×C3—416no—
272C24×C3C2×D414yes—
273C24×C3#4114yes—
274C24×C3#4114yes—
275C24×C3C2412yes—
276C24×C3C2412yes—
277C24×C3C2412yes—
278C24×C3C2412yes—
279C24×C3C2411yescharacteristic
280C2×C3×D4—28no—
281C2×C3×D4—28no—
282C2×C3×D4—28no—
283C2×C3×D4—28no—
284C2×C3×D4—28no—
285C2×C3×D4—44no—
286C2×C3×D4—44no—
287C2×C3×D4—44no—
288C2×C3×D4—44no—
289C2×C3×D4—416no—
290C2×C3×D4—416no—
291C2×C3×D4—416no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4C2×D414yes—
300C22×C3×C4C2×D414yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—22no—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C3×C22⋊C4—28no—
337C3×C22⋊C4—28no—
338C3×C22⋊C4C2×D4116yes—
339#217—28no—
340#217—28no—
341#217—28no—
342#217—28no—
343#217—44no—
344#217—44no—
345#217—44no—
346#217—44no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217—44no—
351#217—44no—
352#217—44no—
353#217—44no—
354#217—44no—
355C4⋊Dic3—28no—
356C4⋊Dic3—44no—
357Dic3⋊C4—28no—
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361C4×Dic3—28no—
362C4×Dic3—44no—
363C25—24no—
364C25—24no—
365C25—24no—
366C25—42no—
367C25—42no—
368C25—42no—
369C25—42no—
370C25C22×D311yescharacteristic
371C25C22×D311yescharacteristic
372C25C22×D311yescharacteristic
373C25C22×D311yescharacteristic
374C25C22×D314yes—
375C22×D4—24no—
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4C22×D314yes—
385C22×D4C22×D314yes—
386C22×D4C22×D314yes—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398#126—632no—
399#120—232no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—64no—
407C2×C4⋊C4—64no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4—122no—
411C2×C4⋊C4—122no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—122no—
435C2×C22⋊C4—122no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C22⋊C4—122no—
445C2×C22⋊C4—122no—
446C2×C22⋊C4#6718yes—
447C2×C22⋊C4C22×D314yes—
448C2×C22⋊C4C22×D314yes—
449C2×C22⋊C4C22×D314yes—
450C2×C42—34no—
451C2×C42—34no—
452C2×C42—64no—
453C2×C42—122no—
454#95—34no—
455#95—34no—
456#95—34no—
457#95—34no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—28no—
462C23×C3—28no—
463C23×C3—28no—
464C23×C3—28no—
465C23×C3—28no—
466C23×C3—28no—
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—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—416no—
493C23×C3—416no—
494C23×C3—416no—
495C23×C3—416no—
496C23×C3—416no—
497C23×C3—416no—
498C23×C3—4128no—
499C23×C3—416no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3—44no—
504C23×C3—44no—
505C23×C3—44no—
506C23×C3—44no—
507C23×C3—44no—
508C23×C3—44no—
509C23×C3—44no—
510C23×C3—44no—
511C23×C3—44no—
512C23×C3—44no—
513C23×C3—44no—
514C23×C3—44no—
515C23×C3—44no—
516C23×C3—44no—
517C23×C3—44no—
518C23×C3—44no—
519C23×C3C22×D414yes—
520C23×C3C22×D412yes—
521C23×C3C2×#4114yes—
522C23×C3C2×#4114yes—
523C23×C3C2×#4112yes—
524C23×C3C2×#4112yes—
525C23×C3H(5,𝔽2)12yes—
526C23×C3H(5,𝔽2)12yes—
527C23×C3H(5,𝔽2)12yes—
528C23×C3H(5,𝔽2)12yes—
529C23×C3C2511yescharacteristic
530C3×D4—416no—
531C3×D4—416no—
532C3×D4—416no—
533C2×C3×C4—28no—
534C2×C3×C4—28no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—44no—
543C2×C3×C4C22×D414yes—
544C2×C3×C4C22×D414yes—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—44no—
570C2×Dic3—44no—
571C2×Dic3—44no—
572C2×Dic3—44no—
573C2×Dic3—44no—
574C2×Dic3—44no—
575C2×Dic3—44no—
576C2×Dic3—44no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—28no—
598C24—28no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—28no—
604C24—22no—
605C24—44no—
606C24—44no—
607C24—44no—
608C24—44no—
609C24—416no—
610C24—416no—
611C24—416no—
612C24—416no—
613C24—416no—
614C24—416no—
615C24—416no—
616C24#23714yes—
617C24#23714yes—
618C24C2×#6714yes—
619C24C23×D312yes—
620C24C23×D312yes—
621C24C23×D312yes—
622C24C23×D312yes—
623C24C23×D311yescharacteristic
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—416no—
634C2×D4—416no—
635C2×D4—416no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4C2×#6714yes—
676C22×C4C2×#6714yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C4⋊C4—68no—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C4⋊C4—124no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—68no—
692C22⋊C4—124no—
693C22⋊C4—124no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C22⋊C4—124no—
700C22⋊C4—124no—
701C22⋊C4—124no—
702C22⋊C4—124no—
703C22⋊C4—124no—
704C22⋊C4C2×#67116yes—
705C42—68no—
706C42—124no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—24no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—464no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—416no—
724C22×C3—416no—
725C22×C3—416no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—88no—
740C22×C3#53514yes—
741C22×C3#53814yes—
742C22×C3#53814yes—
743C22×C3#54614yes—
744C22×C3#54614yes—
745C22×C3#55114yes—
746C22×C3#56014yes—
747C22×C3C23×D411yescharacteristic
748C22×C3C22×#4111yescharacteristic
749C22×C3C22×#4111yescharacteristic
750C22×C3C2×H(5,𝔽2)11yescharacteristic
751C22×C3C2×H(5,𝔽2)11yescharacteristic
752C22×C3C2×H(5,𝔽2)11yescharacteristic
753C22×C3C2×H(5,𝔽2)11yescharacteristic
754C3×C4—24no—
755C3×C4—24no—
756C3×C4—42no—
757Dic3—42no—
758Dic3—42no—
759Dic3—42no—
760Dic3—42no—
761Dic3—42no—
762Dic3—42no—
763Dic3—42no—
764Dic3—42no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—28no—
784C23—28no—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—28no—
789C23—28no—
790C23—28no—
791C23—28no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—416no—
800C23—416no—
801C23—416no—
802C23—416no—
803C23—416no—
804C23—416no—
805C23—416no—
806C23—4128no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23C2×#23714yes—
827C23C2×#23714yes—
828C23C2×#23712yes—
829C23C2×#23712yes—
830C23#100412yes—
831C23#100412yes—
832C23#100412yes—
833C23#100412yes—
834C23C22×#6714yes—
835C23C22×#6712yes—
836C23C24×D311yescharacteristic
837D4—416no—
838D4—416no—
839D4—416no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—44no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C4—124no—
878C2×C4—124no—
879C2×C4—124no—
880C2×C4—124no—
881C2×C4—124no—
882C2×C4C22×#6714yes—
883C2×C4C22×#6714yes—
884C2×C3—44no—
885C2×C3—44no—
886C2×C3—44no—
887C2×C3—82no—
888C2×C3#268518yescomplemented
889C2×C3C2×#53511yescharacteristic
890C2×C3C2×#53811yescharacteristic
891C2×C3C2×#53811yescharacteristic
892C2×C3C2×#54611yescharacteristic
893C2×C3C2×#54611yescharacteristic
894C2×C3C2×#55111yescharacteristic
895C2×C3C2×#56011yescharacteristic
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—464no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—416no—
915C22—416no—
916C22—416no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—88no—
929C22#558714yes—
930C22#559314yes—
931C22#559314yes—
932C22#559514yes—
933C22#580514yes—
934C22#580614yes—
935C22#580614yes—
936C22C22×#23711yescharacteristic
937C22C22×#23711yescharacteristic
938C22C2×#100411yescharacteristic
939C22C2×#100411yescharacteristic
940C22C2×#100411yescharacteristic
941C22C2×#100411yescharacteristic
942C22C23×#6711yescharacteristic
943C4—24no—
944C4—24no—
945C4—42no—
946C4—122no—
947C4—122no—
948C4—122no—
949C4—122no—
950C4—122no—
951C4—122no—
952C4—122no—
953C4—122no—
954C3C2×#268511yescharacteristic, complemented, Sylow
955C2—44no—
956C2—44no—
957C2—44no—
958C2—82no—
959C2#8259918yesdirect product factor
960C2C2×#559311yescharacteristic
961C2C2×#559311yescharacteristic
962C2C2×#558711yescharacteristic
963C2C2×#559511yescharacteristic
964C2C2×#580611yescharacteristic
965C2C2×#580611yescharacteristic
966C2C2×#580511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
Fitting, prime radicalC22×C3×#120C2
socleC24×C3C24
hypercenterC22×#120D3
hypocenterC3C2×#2685
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
2. C22×#879C2semidirect
3. C2×#5247C2semidirect
4. C2×#5247C2semidirect
5. C2×#5222C2semidirect
6. C2×#5222C2semidirect
7. C2×#5222C2semidirect
8. C2×#5222C2semidirect
9. C2×#5221C2semidirect
10. C2×#5221C2semidirect
11. #82599C2direct (N × H)
12. C2×#4949C2semidirect
13. C2×#4948C2semidirect
14. C2×#4945C2semidirect
15. C2×#4944C2semidirect
16. C2×#4951C2semidirect
39. C22×#217C22semidirect
40. C22×#217C22semidirect
41. C22×#217C22semidirect
42. C22×#217C22semidirect
43. C22×C4⋊Dic3C22semidirect
44. C22×C4⋊Dic3C22semidirect
45. C22×Dic3⋊C4C22semidirect
46. C22×Dic3⋊C4C22semidirect
47. C22×Dic3⋊C4C22semidirect
48. C22×Dic3⋊C4C22semidirect
49. C22×C4×Dic3C22semidirect
50. C22×C4×Dic3C22semidirect
52. C2×#879C22semidirect
53. #5247C22semidirect
54. #5247C22semidirect
55. #5222C22semidirect
56. #5222C22semidirect
57. #5222C22semidirect
58. #5222C22semidirect
59. #5221C22semidirect
60. #5221C22semidirect
61. C2×C3⋊#95C22semidirect
62. C2×C3⋊#95C22semidirect
63. C2×C3⋊#95C22semidirect
64. C2×C3⋊#95C22semidirect
65. #4951C22semidirect
66. #4949C22semidirect
67. #4948C22semidirect
68. #4945C22semidirect
69. #4944C22semidirect
156. C2×#217C23semidirect
157. C2×#217C23semidirect
158. C2×#217C23semidirect
159. C2×#217C23semidirect
162. C2×C4⋊Dic3C23semidirect
163. C2×C4⋊Dic3C23semidirect
168. C2×Dic3⋊C4C23semidirect
169. C2×Dic3⋊C4C23semidirect
170. C2×Dic3⋊C4C23semidirect
171. C2×Dic3⋊C4C23semidirect
174. C2×C4×Dic3C23semidirect
175. C2×C4×Dic3C23semidirect
177. C3⋊#95C23semidirect
178. C3⋊#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
888. C2×C3#2685semidirect
954. C3C2×#2685semidirect
959. C2#82599direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1202
C22×#8792
C2×#52472
C2×#52222
C2×#52212
#825992
C2×#49492
C2×#49482
C2×#49452
C2×#49442
C2×#49512
C2×#26853