Finite Group Databasebeta

← C2×#74919 #11429961

Subgroups — C2×#74919 #11429961

Order 768.

4270 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#937C211yesmaximal, characteristic
2C22×#885C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic, complemented
4C2×#5222C211yesmaximal, characteristic, complemented
5C2×#5213C211yesmaximal, characteristic, complemented
6C2×#5213C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4955C211yesmaximal, characteristic, complemented
9C2×#4955C211yesmaximal, characteristic, complemented
10C2×#4947C211yesmaximal, characteristic, complemented
11C2×#4945C211yesmaximal, characteristic, complemented
12#74919C2116yesmaximal, direct product factor
13C2×#4675C211yesmaximal, characteristic, complemented
14C2×#4675C211yesmaximal, characteristic, complemented
15C2×#4673C211yesmaximal, characteristic, complemented
16C2×#4669C211yesmaximal, characteristic, complemented
17C2×#2684—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic, complemented
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×Dic6C2211yescharacteristic, complemented
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic, complemented
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic, complemented
31C22×#217C2211yescharacteristic, complemented
32C2×#937—28no—
33C2×#937C2218yes—
34C22×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic, complemented
45C22×Dic3⋊C4C2211yescharacteristic, complemented
46C22×C4×Dic3C2211yescharacteristic, complemented
47C2×#885—28no—
48C2×#885C2218yescomplemented
49C3×#386C2218yescomplemented
50C2×C3×#95C2211yescharacteristic, complemented
51C2×C3×#95C2211yescharacteristic, complemented
52#5222C2218yescomplemented
53#5213C2218yescomplemented
54#5213C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58C2×C3⋊#95C2211yescharacteristic, complemented
59C2×C3⋊#95C2211yescharacteristic, complemented
60C2×C3⋊#95C2211yescharacteristic, complemented
61#4959C2218yescomplemented
62#4955C2218yescomplemented
63#4955C2218yescomplemented
64#4947C2218yescomplemented
65#4945C2218yescomplemented
66#4675C2218yescomplemented
67#4675C2218yescomplemented
68#4673C2218yescomplemented
69#4669C2218yescomplemented
70C22×#124—31no—
71C22×#120—31no—
72#2684—316no—
73C2×#397—31no—
74C2×#397—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#393—31no—
78C2×#393—31no—
79C2×#388—31no—
80C2×#388—31no—
81C2×#386—31no—
82C2×#386—31no—
83C2×#386D311yescharacteristic, complemented
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×C4—42no—
103C23×C3×C4—42no—
104C23×C3×C4—42no—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2314yescomplemented
111C22×#67—24no—
112C22×#67—24no—
113C22×#67—42no—
114C22×#67—42no—
115C22×#67—42no—
116C22×#67D418yes—
117C22×#67C2314yes—
118C22×#67C2314yes—
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C22×Dic6—24no—
126C22×Dic6—42no—
127C22×Dic6—42no—
128C22×Dic6C2314yescomplemented
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—42no—
131C2×C3×C22⋊C4—42no—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yescomplemented
135C2×#217—24no—
136C2×#217—24no—
137C2×#217—24no—
138C2×#217—42no—
139C2×#217—42no—
140C2×#217C2314yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143C2×#217C2314yescomplemented
144C2×#217C2314yescomplemented
145#937—232no—
146C2×(C2×D3)⋊C4—24no—
147C2×(C2×D3)⋊C4—24no—
148C2×(C2×D3)⋊C4—24no—
149C2×(C2×D3)⋊C4—24no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
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×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×Dic3⋊C4—42no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4C2314yescomplemented
169C2×Dic3⋊C4C2314yescomplemented
170C2×C4×Dic3—24no—
171C2×C4×Dic3C2314yescomplemented
172#885—232no—
173C3×#95C2314yescomplemented
174C3×#95C2314yescomplemented
175C3⋊#95C2314yescomplemented
176C3⋊#95C2314yescomplemented
177C3⋊#95C2314yescomplemented
178C3⋊#95C2314yescomplemented
179C3⋊#95C2314yescomplemented
180C3⋊#95C2314yescomplemented
181C26—31no—
182C23×Q8—31no—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4C2×D311yescharacteristic
186C24×C4C2×D311yescharacteristic, complemented
187C2×#124—38no—
188C2×#124—68no—
189C2×#120—38no—
190C2×#120—68no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊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⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic, complemented
211C22×C42—31no—
212#397—38no—
213#397—38no—
214#394—38no—
215#394—38no—
216#393—38no—
217#393—38no—
218#388—38no—
219#388—38no—
220#386—38no—
221#386—38no—
222#386C2×D318yescomplemented
223#379—38no—
224#379—38no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95C2×D311yescharacteristic, complemented
232C2×#95C2×D311yescharacteristic, complemented
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×C3C2×D414yes—
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×C4—22no—
299C22×C3×C4—44no—
300C22×C3×C4—44no—
301C22×C3×C4—44no—
302C22×C3×C4—416no—
303C22×C3×C4C2412yes—
304C22×C3×C4C2412yes—
305C22×C3×C4C2412yes—
306C22×C3×C4C2412yes—
307C22×C3×C4C2412yes—
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—416no—
311C2×#67—44no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—416no—
315C2×#67C2×D4116yes—
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×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—22no—
332C22×Dic3—22no—
333C22×Dic3C2×D414yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2412yes—
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C2×Dic6—28no—
341C2×Dic6—44no—
342C2×Dic6—44no—
343C2×Dic6—416no—
344C3×C22⋊C4—28no—
345C3×C22⋊C4—44no—
346C3×C22⋊C4—44no—
347#217—28no—
348#217—28no—
349#217—28no—
350#217—44no—
351#217—44no—
352(C2×D3)⋊C4—28no—
353(C2×D3)⋊C4—28no—
354(C2×D3)⋊C4—28no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360(C2×D3)⋊C4—44no—
361(C2×D3)⋊C4—44no—
362Dic3⋊C4—44no—
363Dic3⋊C4—44no—
364C4×Dic3—28no—
365C25—31no—
366C25—31no—
367C25—34no—
368C25—64no—
369C25—64no—
370C25—64no—
371C25—122no—
372C25—122no—
373C25—122no—
374C25—122no—
375C25C22×D311yescharacteristic
376C25C22×D311yescharacteristic
377C22×Q8—34no—
378C22×Q8—64no—
379C22×Q8—122no—
380C22×Q8—122no—
381C22×D4—24no—
382C22×D4—24no—
383C22×D4—38no—
384C22×D4—34no—
385C22×D4—34no—
386C22×D4—42no—
387C22×D4—64no—
388C22×D4—64no—
389C22×D4—122no—
390C22×D4—122no—
391C22×D4—122no—
392C22×D4C22×D314yes—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D314yescomplemented
408#124—632no—
409#120—632no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—122no—
413C2×C4⋊C4—122no—
414C2×C22⋊C4—24no—
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—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—64no—
439C2×C22⋊C4—64no—
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—122no—
447C2×C22⋊C4C22×D314yes—
448C2×C22⋊C4C22×D314yes—
449C2×C22⋊C4C22×D314yescomplemented
450C2×C42—34no—
451C2×C42—64no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95—34no—
456#95—34no—
457#95—34no—
458#95C22×D314yescomplemented
459#95C22×D314yescomplemented
460C23×C3—28no—
461C23×C3—28no—
462C23×C3—28no—
463C23×C3—28no—
464C23×C3—28no—
465C23×C3—28no—
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—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—44no—
479C23×C3—44no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3C22×D414yes—
487C23×C3C22×D412yes—
488C23×C3C2×#4114yes—
489C23×C3C2×#4112yes—
490C23×C3C2×#4112yes—
491C23×C3H(5,𝔽2)12yes—
492C23×C3H(5,𝔽2)12yes—
493C23×C3H(5,𝔽2)12yes—
494C23×C3H(5,𝔽2)12yes—
495C23×C3C2511yescharacteristic
496C22×D3—28no—
497C22×D3—28no—
498C22×D3—28no—
499C22×D3—28no—
500C22×D3—28no—
501C22×D3—28no—
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—22no—
513C22×D3—22no—
514C22×D3—416no—
515C22×D3—416no—
516C22×D3—416no—
517C22×D3—416no—
518C22×D3—416no—
519C22×D3—416no—
520C22×D3—4128no—
521C22×D3—416no—
522C22×D3—44no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C22×D3C22×D414yes—
531C22×D3C2×#4114yes—
532C3×D4—416no—
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—22no—
547C2×C3×C4—22no—
548C2×C3×C4—416no—
549C2×C3×C4—44no—
550C2×C3×C4—44no—
551C2×C3×C4—44no—
552C2×C3×C4—44no—
553C2×C3×C4—44no—
554#67—416no—
555#67—416no—
556C2×Dic3—28no—
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—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—44no—
575C2×Dic3—44no—
576C2×Dic3—44no—
577C2×Dic3—44no—
578C2×Dic3—44no—
579C2×Dic3C22×D414yes—
580Dic6—416no—
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—34no—
594C24—34no—
595C24—32no—
596C24—32no—
597C24—68no—
598C24—68no—
599C24—62no—
600C24—62no—
601C24—62no—
602C24—62no—
603C24—62no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—62no—
609C24—62no—
610C24—62no—
611C24—68no—
612C24—124no—
613C24—124no—
614C24—124no—
615C24—124no—
616C24—1216no—
617C24—1216no—
618C24—1216no—
619C24—1216no—
620C24—1216no—
621C24—1216no—
622C24—1216no—
623C24#23514yes—
624C24D3×D414yes—
625C24C23×D312yes—
626C24C23×D312yes—
627C24C23×D311yescharacteristic
628C2×Q8—68no—
629C2×Q8—124no—
630C2×Q8—124no—
631C2×Q8—1216no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—316no—
635C2×D4—44no—
636C2×D4—416no—
637C2×D4—68no—
638C2×D4—68no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—1216no—
642C2×D4—124no—
643C2×D4—1216no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—34no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—416no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4C23×D312yes—
688C22×C4C23×D312yes—
689C22×C4C23×D312yes—
690C22×C4C23×D312yes—
691C22×C4C23×D312yes—
692C4⋊C4—124no—
693C4⋊C4—124no—
694C22⋊C4—28no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—68no—
698C22⋊C4—68no—
699C22⋊C4—68no—
700C22⋊C4—68no—
701C22⋊C4—68no—
702C22⋊C4—68no—
703C22⋊C4—68no—
704C22⋊C4—68no—
705C22⋊C4—124no—
706C22⋊C4—124no—
707C22⋊C4—124no—
708C22⋊C4—124no—
709C22⋊C4—124no—
710C22⋊C4—124no—
711C22⋊C4—124no—
712C42—68no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—24no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—416no—
724C22×C3—416no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3#53414yes—
730C22×C3#53814yes—
731C22×C3#53814yes—
732C22×C3#54614yes—
733C22×C3#54614yes—
734C22×C3#55114yes—
735C22×C3H(3,𝔽4)14yes—
736C22×C3C23×D411yescharacteristic
737C22×C3C22×#4111yescharacteristic
738C22×C3C22×#4111yescharacteristic
739C22×C3C2×H(5,𝔽2)11yescharacteristic
740C22×C3C2×H(5,𝔽2)11yescharacteristic
741C22×C3C2×H(5,𝔽2)11yescharacteristic
742C22×C3C2×H(5,𝔽2)11yescharacteristic
743C2×D3—24no—
744C2×D3—24no—
745C2×D3—24no—
746C2×D3—24no—
747C2×D3—24no—
748C2×D3—24no—
749C2×D3—464no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—416no—
755C2×D3—416no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—42no—
759C2×D3—42no—
760C3×C4—42no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4—42no—
764C3×C4—42no—
765Dic3—24no—
766Dic3—42no—
767Dic3—42no—
768Dic3—42no—
769Dic3—42no—
770Dic3—42no—
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—34no—
790C23—34no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—68no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—62no—
812C23—68no—
813C23—68no—
814C23—68no—
815C23—68no—
816C23—68no—
817C23—1216no—
818C23—1216no—
819C23—1216no—
820C23—1216no—
821C23—1216no—
822C23—1216no—
823C23—1216no—
824C23—12128no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23—124no—
829C23—124no—
830C23—124no—
831C23—124no—
832C23—124no—
833C23C2×#23514yes—
834C23C2×#23512yes—
835C23C2×D3×D414yes—
836C23C2×D3×D412yes—
837C23#100412yes—
838C23#100412yes—
839C23#100412yes—
840C23D3×#4112yes—
841C23#100912yes—
842C23C24×D311yescharacteristic
843Q8—1216no—
844D4—416no—
845D4—1216no—
846D4—1216no—
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—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—34no—
863C2×C4—416no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—68no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—124no—
888C2×C4—124no—
889C2×C4—124no—
890C2×C4—124no—
891C2×C4—124no—
892C2×C3—44no—
893C2×C3—44no—
894C2×C3#268418yescomplemented
895C2×C3C2×#53411yescharacteristic
896C2×C3C2×#53811yescharacteristic
897C2×C3C2×#53811yescharacteristic
898C2×C3C2×#54611yescharacteristic
899C2×C3C2×#54611yescharacteristic
900C2×C3C2×#55111yescharacteristic
901C2×C3C2×H(3,𝔽4)11yescharacteristic
902D3—44no—
903D3—44no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—416no—
915C22—416no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—64no—
921C22—64no—
922C22—64no—
923C22—64no—
924C22—64no—
925C22—64no—
926C22—1264no—
927C22—122no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—1216no—
933C22—1216no—
934C22—122no—
935C22—122no—
936C22—122no—
937C22#549014yes—
938C22#555614yes—
939C22#556014yes—
940C22#559414yes—
941C22#560514yes—
942C22#561014yes—
943C22#565714yes—
944C22C22×#23511yescharacteristic
945C22C22×D3×D411yescharacteristic
946C22C2×#100411yescharacteristic
947C22C2×#100411yescharacteristic
948C22C2×#100411yescharacteristic
949C22C2×D3×#4111yescharacteristic
950C22C2×#100911yescharacteristic
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—64no—
957C4—122no—
958C4—122no—
959C4—122no—
960C4—122no—
961C4—122no—
962C3C2×#268411yescharacteristic, complemented, Sylow
963C2—44no—
964C2—44no—
965C2—124no—
966C2—124no—
967C2#7491918yesdirect product factor
968C2C2×#549011yescharacteristic
969C2C2×#556011yescharacteristic
970C2C2×#555611yescharacteristic
971C2C2×#559411yescharacteristic
972C2C2×#560511yescharacteristic
973C2C2×#561011yescharacteristic
974C2C2×#565711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
prime radicalC22×#937C2
hypercenterC2×#386D3
hypocenterC3C2×#2684
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#885C2semidirect
3. C2×C3×#386C2semidirect
4. C2×#5222C2semidirect
5. C2×#5213C2semidirect
6. C2×#5213C2semidirect
7. C2×#4959C2semidirect
8. C2×#4955C2semidirect
9. C2×#4955C2semidirect
10. C2×#4947C2semidirect
11. C2×#4945C2semidirect
12. #74919C2direct (N × H)
13. C2×#4675C2semidirect
14. C2×#4675C2semidirect
15. C2×#4673C2semidirect
16. C2×#4669C2semidirect
20. C24×C3×C4C22semidirect
23. C23×Dic6C22semidirect
26. C22×C3×C22⋊C4C22semidirect
30. C22×#217C22semidirect
31. C22×#217C22semidirect
44. C22×Dic3⋊C4C22semidirect
45. C22×Dic3⋊C4C22semidirect
46. C22×C4×Dic3C22semidirect
48. C2×#885C22semidirect
49. C3×#386C22semidirect
50. C2×C3×#95C22semidirect
51. C2×C3×#95C22semidirect
52. #5222C22semidirect
53. #5213C22semidirect
54. #5213C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
58. C2×C3⋊#95C22semidirect
59. C2×C3⋊#95C22semidirect
60. C2×C3⋊#95C22semidirect
61. #4959C22semidirect
62. #4955C22semidirect
63. #4955C22semidirect
64. #4947C22semidirect
65. #4945C22semidirect
66. #4675C22semidirect
67. #4675C22semidirect
68. #4673C22semidirect
69. #4669C22semidirect
83. C2×#386D3semidirect
110. C23×C3×C4C23semidirect
128. C22×Dic6C23semidirect
134. C2×C3×C22⋊C4C23semidirect
143. C2×#217C23semidirect
144. C2×#217C23semidirect
168. C2×Dic3⋊C4C23semidirect
169. C2×Dic3⋊C4C23semidirect
171. C2×C4×Dic3C23semidirect
173. C3×#95C23semidirect
174. C3×#95C23semidirect
175. C3⋊#95C23semidirect
176. C3⋊#95C23semidirect
177. C3⋊#95C23semidirect
178. C3⋊#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
186. C24×C4C2×D3semidirect
210. C22×C22⋊C4C2×D3semidirect
222. #386C2×D3semidirect
231. C2×#95C2×D3semidirect
232. C2×#95C2×D3semidirect
407. C23×C4C22×D3semidirect
449. C2×C22⋊C4C22×D3semidirect
458. #95C22×D3semidirect
459. #95C22×D3semidirect
894. C2×C3#2684semidirect
962. C3C2×#2684semidirect
967. C2#74919direct (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×#8852
C2×C3×#3862
C2×#52222
C2×#52132
C2×#49592
C2×#49552
C2×#49472
C2×#49452
#749192
C2×#46752
C2×#46732
C2×#46692
C2×#26843