Finite Group Databasebeta

← C2×#76468 #11429971

Subgroups — C2×#76468 #11429971

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×#937C211yesmaximal, characteristic
2C22×#898C211yesmaximal, characteristic, complemented
3C2×C3×#390C211yesmaximal, characteristic, complemented
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#4993C211yesmaximal, characteristic, complemented
6C2×#4959C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4955C211yesmaximal, characteristic, complemented
9C2×#4955C211yesmaximal, characteristic, complemented
10C2×#4948C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4945C211yesmaximal, characteristic, complemented
14C2×#4940C211yesmaximal, characteristic, complemented
15C2×#4940C211yesmaximal, characteristic, complemented
16#76468C2116yesmaximal, direct product factor
17C2×#2685—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic, complemented
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic, complemented
26C22×C3×C22⋊C4C2211yescharacteristic, complemented
27C22×C3×C42C2211yescharacteristic, complemented
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic, complemented
32C22×#217C2211yescharacteristic, complemented
33C2×#937—28no—
34C2×#937C2218yes—
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×C4⋊Dic3C2211yescharacteristic, complemented
46C22×Dic3⋊C4C2211yescharacteristic, complemented
47C22×Dic3⋊C4C2211yescharacteristic, complemented
48C22×Dic3⋊C4C2211yescharacteristic, complemented
49C22×Dic3⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic3C2211yescharacteristic, complemented
51C2×#898—28no—
52C2×#898C2218yescomplemented
53C3×#390C2218yescomplemented
54#5222C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58C2×C3⋊#95C2211yescharacteristic, complemented
59#4993C2218yescomplemented
60#4961C2218yescomplemented
61#4959C2218yescomplemented
62#4959C2218yescomplemented
63#4957C2218yescomplemented
64#4955C2218yescomplemented
65#4955C2218yescomplemented
66#4948C2218yescomplemented
67#4945C2218yescomplemented
68#4940C2218yescomplemented
69#4940C2218yescomplemented
70C22×#126—31no—
71C22×#120—31no—
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×#390D311yescharacteristic, complemented
81C2×#388—31no—
82C2×#388—31no—
83C2×#388—31no—
84C2×#379—31no—
85C2×#379—31no—
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C24×D3—24no—
89C24×D3—24no—
90C24×D3—24no—
91C24×D3—42no—
92C24×D3—42no—
93C24×D3—42no—
94C24×D3—42no—
95C24×D3C2311yescharacteristic
96C24×D3C2311yescharacteristic
97C24×D3C2314yes—
98C22×C3×D4—24no—
99C22×C3×D4—24no—
100C22×C3×D4—42no—
101C22×C3×D4C2314yes—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C22×#67—24no—
108C22×#67—24no—
109C22×#67—24no—
110C22×#67—42no—
111C22×#67—42no—
112C22×#67—42no—
113C22×#67C2314yes—
114C22×#67C2314yes—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4C2314yescomplemented
123C2×C3×C22⋊C4—42no—
124C2×C3×C22⋊C4—42no—
125C2×C3×C22⋊C4—42no—
126C2×C3×C22⋊C4—42no—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2314yescomplemented
130C2×C3×C22⋊C4C2314yescomplemented
131C2×C3×C42—42no—
132C2×C3×C42C2314yescomplemented
133C2×#217—24no—
134C2×#217—24no—
135C2×#217—42no—
136C2×#217—42no—
137C2×#217—42no—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yescomplemented
142C2×#217C2314yescomplemented
143#937—232no—
144C2×(C2×D3)⋊C4—24no—
145C2×(C2×D3)⋊C4—24no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4—42no—
150C2×(C2×D3)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4D418yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×C4⋊Dic3—24no—
165C2×C4⋊Dic3C2314yescomplemented
166C2×Dic3⋊C4—24no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4—42no—
169C2×Dic3⋊C4—42no—
170C2×Dic3⋊C4C2314yescomplemented
171C2×Dic3⋊C4C2314yescomplemented
172C2×Dic3⋊C4C2314yescomplemented
173C2×Dic3⋊C4C2314yescomplemented
174C2×C4×Dic3—24no—
175C2×C4×Dic3C2314yescomplemented
176#898—232no—
177C3⋊#95C2314yescomplemented
178C3⋊#95C2314yescomplemented
179C3⋊#95C2314yescomplemented
180C3⋊#95C2314yescomplemented
181C26—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4C2×D311yescharacteristic
185C2×#126—38no—
186C2×#126—68no—
187C2×#120—38no—
188C2×#120—68no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4C2×D311yescharacteristic, complemented
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⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic, complemented
213C22×C22⋊C4C2×D311yescharacteristic, complemented
214C22×C42—31no—
215C22×C42C2×D311yescharacteristic, complemented
216#399—38no—
217#396—38no—
218#394—38no—
219#394—38no—
220#394—38no—
221#394—38no—
222#390—38no—
223#390C2×D318yescomplemented
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#4114yes—
247C24×C3C2412yes—
248C24×C3C2412yes—
249C24×C3C2411yescharacteristic
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—28no—
263C23×D3—28no—
264C23×D3—28no—
265C23×D3—44no—
266C23×D3—44no—
267C23×D3—44no—
268C23×D3—44no—
269C23×D3—416no—
270C23×D3—416no—
271C23×D3—416no—
272C23×D3—416no—
273C23×D3—416no—
274C23×D3—416no—
275C23×D3—416no—
276C23×D3C2×D414yes—
277C23×D3#4114yes—
278C23×D3C2412yes—
279C23×D3C2412yes—
280C2×C3×D4—28no—
281C2×C3×D4—28no—
282C2×C3×D4—44no—
283C2×C3×D4—416no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
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×C4C2×D414yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C2×#67—28no—
305C2×#67—28no—
306C2×#67—28no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—44no—
310C2×#67—416no—
311C2×#67—416no—
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×Dic3—22no—
329C22×Dic3C2×D414yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C3×C4⋊C4—28no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341C3×C42—44no—
342#217—28no—
343#217—28no—
344#217—44no—
345#217—44no—
346#217—44no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—28no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4C2×D4116yes—
357C4⋊Dic3—28no—
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361Dic3⋊C4—44no—
362C4×Dic3—28no—
363C25—31no—
364C25—31no—
365C25—34no—
366C25—64no—
367C25—64no—
368C25—64no—
369C25—122no—
370C25—122no—
371C25—122no—
372C25—122no—
373C25C22×D311yescharacteristic
374C25C22×D311yescharacteristic
375C22×D4—24no—
376C22×D4—24no—
377C22×D4—34no—
378C22×D4—34no—
379C22×D4—42no—
380C22×D4—64no—
381C22×D4—64no—
382C22×D4—64no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4C22×D314yes—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398#126—632no—
399#120—632no—
400C2×C4⋊C4—24no—
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—122no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4—122no—
411C2×C4⋊C4C22×D314yescomplemented
412C2×C22⋊C4—38no—
413C2×C22⋊C4—34no—
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—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
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⋊C4C22×D314yes—
447C2×C22⋊C4C22×D314yes—
448C2×C22⋊C4C22×D314yescomplemented
449C2×C22⋊C4C22×D314yescomplemented
450C2×C42—34no—
451C2×C42—42no—
452C2×C42—64no—
453C2×C42C22×D314yescomplemented
454#95—34no—
455#95—34no—
456#95—34no—
457#95—34no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
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—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3C22×D412yes—
486C23×C3C2×#4114yes—
487C23×C3C2×#4112yes—
488C23×C3C2×#4112yes—
489C23×C3H(5,𝔽2)12yes—
490C23×C3H(5,𝔽2)12yes—
491C23×C3H(5,𝔽2)12yes—
492C23×C3H(5,𝔽2)12yes—
493C23×C3C2511yescharacteristic
494C22×D3—28no—
495C22×D3—28no—
496C22×D3—28no—
497C22×D3—28no—
498C22×D3—28no—
499C22×D3—28no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—416no—
513C22×D3—416no—
514C22×D3—416no—
515C22×D3—416no—
516C22×D3—416no—
517C22×D3—416no—
518C22×D3—4128no—
519C22×D3—416no—
520C22×D3—44no—
521C22×D3—44no—
522C22×D3—44no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3C22×D414yes—
529C22×D3C2×#4114yes—
530C3×D4—416no—
531C2×C3×C4—28no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
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—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—44no—
547C2×C3×C4—44no—
548C2×C3×C4—44no—
549C2×C3×C4—44no—
550C2×C3×C4C22×D414yes—
551#67—416no—
552#67—416no—
553C2×Dic3—28no—
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—22no—
570C2×Dic3—22no—
571C2×Dic3—44no—
572C2×Dic3—44no—
573C2×Dic3—44no—
574C2×Dic3—44no—
575C2×Dic3—44no—
576C2×Dic3C22×D414yes—
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—34no—
591C24—34no—
592C24—32no—
593C24—32no—
594C24—68no—
595C24—68no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24—62no—
602C24—62no—
603C24—62no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—68no—
609C24—124no—
610C24—124no—
611C24—124no—
612C24—124no—
613C24—1216no—
614C24—1216no—
615C24—1216no—
616C24—1216no—
617C24—1216no—
618C24—1216no—
619C24—1216no—
620C24#23514yes—
621C24C23×D312yes—
622C24C23×D312yes—
623C24C23×D311yescharacteristic
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—416no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—68no—
631C2×D4—124no—
632C2×D4—124no—
633C2×D4—124no—
634C2×D4—1216no—
635C2×D4—1216no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—34no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
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×C4D3×D414yes—
675C22×C4C23×D312yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C4⋊C4—28no—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C4⋊C4—124no—
686C22⋊C4—316no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—68no—
692C22⋊C4—68no—
693C22⋊C4—68no—
694C22⋊C4—68no—
695C22⋊C4—68no—
696C22⋊C4—68no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C22⋊C4—124no—
700C22⋊C4—124no—
701C22⋊C4—124no—
702C22⋊C4—124no—
703C22⋊C4—124no—
704C22⋊C4—124no—
705C42—44no—
706C42—68no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—416no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—88no—
723C22×C3#53514yes—
724C22×C3#53814yes—
725C22×C3#53814yes—
726C22×C3#54614yes—
727C22×C3#54614yes—
728C22×C3#55114yes—
729C22×C3#56014yes—
730C22×C3C23×D411yescharacteristic
731C22×C3C22×#4111yescharacteristic
732C22×C3C22×#4111yescharacteristic
733C22×C3C2×H(5,𝔽2)11yescharacteristic
734C22×C3C2×H(5,𝔽2)11yescharacteristic
735C22×C3C2×H(5,𝔽2)11yescharacteristic
736C22×C3C2×H(5,𝔽2)11yescharacteristic
737C2×D3—24no—
738C2×D3—24no—
739C2×D3—24no—
740C2×D3—24no—
741C2×D3—24no—
742C2×D3—24no—
743C2×D3—464no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—416no—
749C2×D3—416no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C3×C4—24no—
755C3×C4—42no—
756C3×C4—42no—
757C3×C4—42no—
758C3×C4—42no—
759Dic3—24no—
760Dic3—42no—
761Dic3—42no—
762Dic3—42no—
763Dic3—42no—
764Dic3—42no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—34no—
782C23—34no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—68no—
795C23—68no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—68no—
809C23—68no—
810C23—68no—
811C23—68no—
812C23—1216no—
813C23—1216no—
814C23—1216no—
815C23—1216no—
816C23—1216no—
817C23—1216no—
818C23—12128no—
819C23—1216no—
820C23—124no—
821C23—124no—
822C23—124no—
823C23—124no—
824C23—124no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23C2×#23514yes—
829C23C2×#23512yes—
830C23C2×D3×D412yes—
831C23#100412yes—
832C23#100412yes—
833C23#100412yes—
834C23D3×#4112yes—
835C23#100912yes—
836C23C24×D311yescharacteristic
837D4—416no—
838D4—1216no—
839D4—1216no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—28no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—34no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—68no—
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—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—124no—
879C2×C4—124no—
880C2×C4—124no—
881C2×C4—124no—
882C2×C4—124no—
883C2×C4C2×D3×D414yes—
884C2×C3—44no—
885C2×C3—82no—
886C2×C3#268518yescomplemented
887C2×C3C2×#53511yescharacteristic
888C2×C3C2×#53811yescharacteristic
889C2×C3C2×#53811yescharacteristic
890C2×C3C2×#54611yescharacteristic
891C2×C3C2×#54611yescharacteristic
892C2×C3C2×#55111yescharacteristic
893C2×C3C2×#56011yescharacteristic
894D3—44no—
895D3—44no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—42no—
900C22—42no—
901C22—416no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—64no—
912C22—64no—
913C22—64no—
914C22—64no—
915C22—64no—
916C22—64no—
917C22—88no—
918C22—1264no—
919C22—122no—
920C22—122no—
921C22—122no—
922C22—122no—
923C22—1216no—
924C22—1216no—
925C22—122no—
926C22—122no—
927C22—122no—
928C22—122no—
929C22#549014yes—
930C22#555614yes—
931C22#556014yes—
932C22#561314yes—
933C22#562014yes—
934C22#567614yes—
935C22#571514yes—
936C22C22×#23511yescharacteristic
937C22C22×D3×D411yescharacteristic
938C22C2×#100411yescharacteristic
939C22C2×#100411yescharacteristic
940C22C2×#100411yescharacteristic
941C22C2×D3×#4111yescharacteristic
942C22C2×#100911yescharacteristic
943C4—24no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—64no—
949C4—122no—
950C4—122no—
951C4—122no—
952C4—122no—
953C4—122no—
954C3C2×#268511yescharacteristic, complemented, Sylow
955C2—44no—
956C2—82no—
957C2—124no—
958C2—124no—
959C2#7646818yesdirect product factor
960C2C2×#549011yescharacteristic
961C2C2×#556011yescharacteristic
962C2C2×#555611yescharacteristic
963C2C2×#561311yescharacteristic
964C2C2×#562011yescharacteristic
965C2C2×#567611yescharacteristic
966C2C2×#571511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#390C2
socleC24×C3C24
prime radicalC22×#937C2
hypercenterC2×#390D3
hypocenterC3C2×#2685
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×#898C2semidirect
3. C2×C3×#390C2semidirect
4. C2×#5222C2semidirect
5. C2×#4993C2semidirect
6. C2×#4959C2semidirect
7. C2×#4959C2semidirect
8. C2×#4955C2semidirect
9. C2×#4955C2semidirect
10. C2×#4948C2semidirect
11. C2×#4961C2semidirect
12. C2×#4957C2semidirect
13. C2×#4945C2semidirect
14. C2×#4940C2semidirect
15. C2×#4940C2semidirect
16. #76468C2direct (N × H)
22. C22×C3×C4⋊C4C22semidirect
25. C22×C3×C22⋊C4C22semidirect
26. C22×C3×C22⋊C4C22semidirect
27. C22×C3×C42C22semidirect
31. C22×#217C22semidirect
32. C22×#217C22semidirect
45. C22×C4⋊Dic3C22semidirect
46. C22×Dic3⋊C4C22semidirect
47. C22×Dic3⋊C4C22semidirect
48. C22×Dic3⋊C4C22semidirect
49. C22×Dic3⋊C4C22semidirect
50. C22×C4×Dic3C22semidirect
52. C2×#898C22semidirect
53. C3×#390C22semidirect
54. #5222C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
58. C2×C3⋊#95C22semidirect
59. #4993C22semidirect
60. #4961C22semidirect
61. #4959C22semidirect
62. #4959C22semidirect
63. #4957C22semidirect
64. #4955C22semidirect
65. #4955C22semidirect
66. #4948C22semidirect
67. #4945C22semidirect
68. #4940C22semidirect
69. #4940C22semidirect
80. C2×#390D3semidirect
122. C2×C3×C4⋊C4C23semidirect
129. C2×C3×C22⋊C4C23semidirect
130. C2×C3×C22⋊C4C23semidirect
132. C2×C3×C42C23semidirect
141. C2×#217C23semidirect
142. C2×#217C23semidirect
165. C2×C4⋊Dic3C23semidirect
170. C2×Dic3⋊C4C23semidirect
171. C2×Dic3⋊C4C23semidirect
172. C2×Dic3⋊C4C23semidirect
173. C2×Dic3⋊C4C23semidirect
175. C2×C4×Dic3C23semidirect
177. C3⋊#95C23semidirect
178. C3⋊#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
194. C22×C4⋊C4C2×D3semidirect
212. C22×C22⋊C4C2×D3semidirect
213. C22×C22⋊C4C2×D3semidirect
215. C22×C42C2×D3semidirect
223. #390C2×D3semidirect
411. C2×C4⋊C4C22×D3semidirect
448. C2×C22⋊C4C22×D3semidirect
449. C2×C22⋊C4C22×D3semidirect
453. C2×C42C22×D3semidirect
886. C2×C3#2685semidirect
954. C3C2×#2685semidirect
959. C2#76468direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9372
C22×#8982
C2×C3×#3902
C2×#52222
C2×#49932
C2×#49592
C2×#49552
C2×#49482
C2×#49612
C2×#49572
C2×#49452
C2×#49402
#764682
C2×#26853