Finite Group Databasebeta

← C2×#82595 #11429760

Subgroups — C2×#82595 #11429760

Order 768.

5006 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#120C211yesmaximal, characteristic, complemented
2C22×#953C211yesmaximal, characteristic, complemented
3C22×#936C211yesmaximal, characteristic, complemented
4C22×#885C211yesmaximal, characteristic, complemented
5C2×#5247C211yesmaximal, characteristic, complemented
6C2×#5223C211yesmaximal, characteristic, complemented
7C2×#5223C211yesmaximal, characteristic, complemented
8C2×#5223C211yesmaximal, characteristic, complemented
9C2×#5222C211yesmaximal, characteristic, complemented
10C2×#5221C211yesmaximal, characteristic, complemented
11#82595C2116yesmaximal, direct product factor
12C2×#4961C211yesmaximal, characteristic, complemented
13C2×#4947C211yesmaximal, characteristic, complemented
14C2×#4957C211yesmaximal, characteristic, complemented
15C2×#4944C211yesmaximal, characteristic, complemented
16C2×#4951C211yesmaximal, characteristic, complemented
17C2×#2670—31nomaximal, Sylow
18C26×C3C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C23×#67C2211yescharacteristic
25C23×#67C2211yescharacteristic, complemented
26C23×Dic6C2211yescharacteristic, complemented
27C2×C3×#120—28no—
28C2×C3×#120C2218yescomplemented
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C2×#953—28no—
33C2×#953C2218yescomplemented
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C22×#217C2211yescharacteristic
40C22×#217C2211yescharacteristic
41C22×#217C2211yescharacteristic
42C22×#217C2211yescharacteristic
43C22×#217C2211yescharacteristic, complemented
44C22×#217C2211yescharacteristic, complemented
45C22×#217C2211yescharacteristic, complemented
46C2×#936—28no—
47C2×#936C2218yescomplemented
48C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C22×C4⋊Dic3C2211yescharacteristic, complemented
52C22×Dic3⋊C4C2211yescharacteristic, complemented
53C22×C4×Dic3C2211yescharacteristic, complemented
54C22×C4×Dic3C2211yescharacteristic, complemented
55C2×#885—28no—
56C2×#885C2218yescomplemented
57#5247C2218yescomplemented
58#5223C2218yescomplemented
59#5223C2218yescomplemented
60#5223C2218yescomplemented
61#5222C2218yescomplemented
62#5221C2218yescomplemented
63C2×C3⋊#95C2211yescharacteristic, complemented
64C2×C3⋊#95C2211yescharacteristic, complemented
65C2×C3⋊#95C2211yescharacteristic, complemented
66C2×C3⋊#95C2211yescharacteristic, complemented
67#4961C2218yescomplemented
68#4957C2218yescomplemented
69#4951C2218yescomplemented
70#4947C2218yescomplemented
71#4944C2218yescomplemented
72C22×#124—31no—
73C22×#124—31no—
74C22×#120—31no—
75C22×#120D311yescharacteristic, complemented
76#2670—316no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#393—31no—
80C2×#392—31no—
81C2×#392—31no—
82C2×#392—31no—
83C2×#390—31no—
84C2×#390—31no—
85C2×#388—31no—
86C2×#388—31no—
87C2×#379—31no—
88C25×C3—24no—
89C25×C3—24no—
90C25×C3—24no—
91C25×C3—42no—
92C25×C3—42no—
93C25×C3—42no—
94C25×C3—42no—
95C25×C3C2311yescharacteristic
96C25×C3C2311yescharacteristic
97C25×C3C2311yescharacteristic
98C25×C3C2311yescharacteristic
99C25×C3C2314yes—
100C24×D3C2311yescharacteristic
101C22×C3×D4—24no—
102C22×C3×D4—24no—
103C22×C3×D4—24no—
104C22×C3×D4—24no—
105C22×C3×D4—24no—
106C22×C3×D4—42no—
107C22×C3×D4—42no—
108C22×C3×D4—42no—
109C22×C3×D4—42no—
110C22×C3×D4C2314yes—
111C22×C3×D4C2314yes—
112C22×C3×D4C2314yes—
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C22×#67—24no—
117C22×#67—24no—
118C22×#67—24no—
119C22×#67—24no—
120C22×#67—24no—
121C22×#67—42no—
122C22×#67—42no—
123C22×#67—42no—
124C22×#67—42no—
125C22×#67—42no—
126C22×#67—42no—
127C22×#67—42no—
128C22×#67C2314yes—
129C22×#67C2314yes—
130C22×#67C2314yes—
131C22×#67C2314yescomplemented
132C23×Dic3C2311yescharacteristic
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2311yescharacteristic
135C23×Dic3C2311yescharacteristic
136C23×Dic3C2311yescharacteristic
137C23×Dic3C2311yescharacteristic
138C23×Dic3C2311yescharacteristic
139C22×Dic6—24no—
140C22×Dic6—24no—
141C22×Dic6—42no—
142C22×Dic6C2314yescomplemented
143C3×#120—232no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4D418yescomplemented
147C2×C3×C22⋊C4C2314yes—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150#953—232no—
151C2×#217—24no—
152C2×#217—24no—
153C2×#217—24no—
154C2×#217—24no—
155C2×#217—24no—
156C2×#217—24no—
157C2×#217—42no—
158C2×#217—42no—
159C2×#217—42no—
160C2×#217—42no—
161C2×#217—42no—
162C2×#217D418yescomplemented
163C2×#217C2314yes—
164C2×#217C2314yes—
165C2×#217C2314yes—
166C2×#217C2314yes—
167C2×#217C2314yes—
168C2×#217C2314yes—
169C2×#217C2314yes—
170C2×#217C2314yes—
171C2×#217C2314yes—
172C2×#217C2314yescomplemented
173C2×#217C2314yescomplemented
174C2×#217C2314yescomplemented
175#936—232no—
176C2×(C2×D3)⋊C4—24no—
177C2×(C2×D3)⋊C4—24no—
178C2×(C2×D3)⋊C4—42no—
179C2×(C2×D3)⋊C4C2314yescomplemented
180C2×(C2×D3)⋊C4C2314yescomplemented
181C2×(C2×D3)⋊C4C2314yescomplemented
182C2×C4⋊Dic3—42no—
183C2×C4⋊Dic3C2314yescomplemented
184C2×Dic3⋊C4—42no—
185C2×Dic3⋊C4C2314yescomplemented
186C2×C4×Dic3—24no—
187C2×C4×Dic3—24no—
188C2×C4×Dic3C2314yescomplemented
189C2×C4×Dic3C2314yescomplemented
190#885—232no—
191C3⋊#95C2314yescomplemented
192C3⋊#95C2314yescomplemented
193C3⋊#95C2314yescomplemented
194C3⋊#95C2314yescomplemented
195C26C2×D311yescharacteristic
196C23×Q8—31no—
197C23×D4—31no—
198C23×D4—31no—
199C23×D4—31no—
200C23×D4—31no—
201C23×D4C2×D311yescharacteristic
202C23×D4C2×D311yescharacteristic
203C23×D4C2×D311yescharacteristic
204C2×#124—38no—
205C2×#124—38no—
206C2×#124—68no—
207C2×#124—68no—
208C2×#120—28no—
209C2×#120—38no—
210C2×#120—68no—
211C2×#120C2×D318yescomplemented
212C22×C4⋊C4—31no—
213C22×C4⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4—31no—
223C22×C22⋊C4—31no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4—31no—
226C22×C22⋊C4—31no—
227C22×C22⋊C4—31no—
228C22×C22⋊C4—31no—
229C22×C22⋊C4C2×D311yescharacteristic
230C22×C22⋊C4C2×D311yescharacteristic
231C22×C22⋊C4C2×D311yescharacteristic
232C22×C42—31no—
233C22×C42—31no—
234#394—38no—
235#394—38no—
236#393—38no—
237#392—38no—
238#392—38no—
239#392—38no—
240#390—38no—
241#390—38no—
242#388—38no—
243#388—38no—
244#379—38no—
245C2×#95—31no—
246C2×#95—31no—
247C2×#95—31no—
248C2×#95—31no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3—22no—
260C24×C3—22no—
261C24×C3—22no—
262C24×C3—22no—
263C24×C3—22no—
264C24×C3—22no—
265C24×C3—22no—
266C24×C3—22no—
267C24×C3—28no—
268C24×C3—28no—
269C24×C3—22no—
270C24×C3—22no—
271C24×C3—28no—
272C24×C3—22no—
273C24×C3—22no—
274C24×C3—22no—
275C24×C3—22no—
276C24×C3—22no—
277C24×C3—44no—
278C24×C3—44no—
279C24×C3—44no—
280C24×C3—44no—
281C24×C3—416no—
282C24×C3—416no—
283C24×C3—416no—
284C24×C3—416no—
285C24×C3—416no—
286C24×C3—416no—
287C24×C3—416no—
288C24×C3C2×D414yes—
289C24×C3C2×D414yes—
290C24×C3#4114yes—
291C24×C3C2412yes—
292C24×C3C2412yes—
293C24×C3C2412yes—
294C24×C3C2412yes—
295C24×C3C2411yescharacteristic
296C23×D3—22no—
297C23×D3—22no—
298C23×D3—22no—
299C23×D3—22no—
300C23×D3—22no—
301C23×D3—22no—
302C23×D3—22no—
303C23×D3C2412yes—
304C2×C3×D4—28no—
305C2×C3×D4—28no—
306C2×C3×D4—28no—
307C2×C3×D4—28no—
308C2×C3×D4—28no—
309C2×C3×D4—44no—
310C2×C3×D4—44no—
311C2×C3×D4—44no—
312C2×C3×D4—44no—
313C2×C3×D4—416no—
314C2×C3×D4—416no—
315C2×C3×D4—416no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4C2×D414yes—
324C22×C3×C4C2×D414yes—
325C22×C3×C4C2412yes—
326C22×C3×C4C2412yes—
327C22×C3×C4C2412yes—
328C2×#67—28no—
329C2×#67—28no—
330C2×#67—28no—
331C2×#67—28no—
332C2×#67—28no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—416no—
341C2×#67—416no—
342C2×#67—416no—
343C2×#67—416no—
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—22no—
348C22×Dic3—22no—
349C22×Dic3—22no—
350C22×Dic3—22no—
351C22×Dic3—22no—
352C22×Dic3—22no—
353C22×Dic3—22no—
354C22×Dic3—22no—
355C22×Dic3—22no—
356C22×Dic3—22no—
357C22×Dic3—22no—
358C22×Dic3—22no—
359C22×Dic3—22no—
360C22×Dic3—22no—
361C22×Dic3—22no—
362C22×Dic3—22no—
363C22×Dic3C2×D414yes—
364C22×Dic3C2×D414yes—
365C22×Dic3C2412yes—
366C22×Dic3C2412yes—
367C22×Dic3C2412yes—
368C22×Dic3C2412yes—
369C22×Dic3C2412yes—
370C22×Dic3C2412yes—
371C22×Dic3C2412yes—
372C2×Dic6—28no—
373C2×Dic6—28no—
374C2×Dic6—44no—
375C2×Dic6—416no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—28no—
378C3×C22⋊C4C2×D4116yescomplemented
379#217—28no—
380#217—28no—
381#217—28no—
382#217—28no—
383#217—28no—
384#217—28no—
385#217—44no—
386#217—44no—
387#217—44no—
388#217—44no—
389#217—44no—
390#217C2×D4116yescomplemented
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—28no—
393(C2×D3)⋊C4—44no—
394C4⋊Dic3—44no—
395Dic3⋊C4—44no—
396C4×Dic3—28no—
397C4×Dic3—28no—
398C25—24no—
399C25—24no—
400C25—24no—
401C25—31no—
402C25—42no—
403C25—42no—
404C25—42no—
405C25—42no—
406C25C22×D311yescharacteristic
407C25C22×D311yescharacteristic
408C25C22×D311yescharacteristic
409C25C22×D311yescharacteristic
410C25C22×D314yes—
411C22×Q8—34no—
412C22×Q8—64no—
413C22×Q8—64no—
414C22×Q8—122no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—24no—
420C22×D4—34no—
421C22×D4—34no—
422C22×D4—34no—
423C22×D4—34no—
424C22×D4—42no—
425C22×D4—42no—
426C22×D4—42no—
427C22×D4—42no—
428C22×D4—64no—
429C22×D4—64no—
430C22×D4—64no—
431C22×D4—64no—
432C22×D4—64no—
433C22×D4—122no—
434C22×D4—122no—
435C22×D4—122no—
436C22×D4—122no—
437C22×D4—122no—
438C22×D4—122no—
439C22×D4—122no—
440C22×D4C22×D314yes—
441C22×D4C22×D314yes—
442C22×D4C22×D314yes—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4—31no—
448C23×C4—31no—
449C23×C4—31no—
450C23×C4C22×D311yescharacteristic
451C23×C4C22×D311yescharacteristic
452C23×C4C22×D311yescharacteristic
453#124—632no—
454#124—632no—
455#120—232no—
456#120—632no—
457C2×C4⋊C4—34no—
458C2×C4⋊C4—34no—
459C2×C4⋊C4—122no—
460C2×C4⋊C4—122no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—38no—
464C2×C22⋊C4—34no—
465C2×C22⋊C4—34no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—34no—
469C2×C22⋊C4—34no—
470C2×C22⋊C4—34no—
471C2×C22⋊C4—34no—
472C2×C22⋊C4—34no—
473C2×C22⋊C4—34no—
474C2×C22⋊C4—34no—
475C2×C22⋊C4—34no—
476C2×C22⋊C4—34no—
477C2×C22⋊C4—34no—
478C2×C22⋊C4—34no—
479C2×C22⋊C4—64no—
480C2×C22⋊C4—64no—
481C2×C22⋊C4—64no—
482C2×C22⋊C4—64no—
483C2×C22⋊C4—64no—
484C2×C22⋊C4—64no—
485C2×C22⋊C4—64no—
486C2×C22⋊C4—64no—
487C2×C22⋊C4—122no—
488C2×C22⋊C4—122no—
489C2×C22⋊C4—122no—
490C2×C22⋊C4—122no—
491C2×C22⋊C4—122no—
492C2×C22⋊C4—122no—
493C2×C22⋊C4#6718yescomplemented
494C2×C22⋊C4C22×D314yes—
495C2×C22⋊C4C22×D314yes—
496C2×C22⋊C4C22×D314yes—
497C2×C42—34no—
498C2×C42—34no—
499C2×C42—64no—
500C2×C42—64no—
501#95—34no—
502#95—34no—
503#95—34no—
504#95—34no—
505C23×C3—28no—
506C23×C3—28no—
507C23×C3—28no—
508C23×C3—28no—
509C23×C3—28no—
510C23×C3—28no—
511C23×C3—28no—
512C23×C3—28no—
513C23×C3—28no—
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—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—416no—
540C23×C3—416no—
541C23×C3—416no—
542C23×C3—416no—
543C23×C3—416no—
544C23×C3—416no—
545C23×C3—4128no—
546C23×C3—416no—
547C23×C3—44no—
548C23×C3—44no—
549C23×C3—44no—
550C23×C3—44no—
551C23×C3—44no—
552C23×C3—44no—
553C23×C3—44no—
554C23×C3—44no—
555C23×C3—44no—
556C23×C3—44no—
557C23×C3—44no—
558C23×C3—44no—
559C23×C3—44no—
560C23×C3—44no—
561C23×C3—44no—
562C23×C3—44no—
563C23×C3—44no—
564C23×C3—44no—
565C23×C3—44no—
566C23×C3C22×D414yes—
567C23×C3C22×D412yes—
568C23×C3C22×D414yes—
569C23×C3C22×D412yes—
570C23×C3C2×#4114yes—
571C23×C3C2×#4112yes—
572C23×C3H(5,𝔽2)12yes—
573C23×C3H(5,𝔽2)12yes—
574C23×C3H(5,𝔽2)12yes—
575C23×C3H(5,𝔽2)12yes—
576C23×C3C2511yescharacteristic
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—44no—
585C22×D3—44no—
586C22×D3—44no—
587C22×D3—44no—
588C22×D3—44no—
589C22×D3—44no—
590C22×D3—44no—
591C3×D4—416no—
592C3×D4—416no—
593C3×D4—416no—
594C2×C3×C4—28no—
595C2×C3×C4—28no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—44no—
604C2×C3×C4C22×D414yes—
605C2×C3×C4C22×D414yes—
606#67—416no—
607#67—416no—
608#67—416no—
609#67—416no—
610C2×Dic3—28no—
611C2×Dic3—28no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—44no—
632C2×Dic3—44no—
633C2×Dic3—44no—
634C2×Dic3—44no—
635C2×Dic3—44no—
636C2×Dic3C22×D414yes—
637C2×Dic3C22×D414yes—
638Dic6—416no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—28no—
659C24—22no—
660C24—28no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—28no—
666C24—22no—
667C24—32no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—416no—
673C24—416no—
674C24—416no—
675C24—416no—
676C24—416no—
677C24—416no—
678C24—416no—
679C24—62no—
680C24—62no—
681C24—62no—
682C24—62no—
683C24—62no—
684C24—62no—
685C24—62no—
686C24D3×D414yes—
687C24#23714yes—
688C24C2×#6714yes—
689C24C23×D312yes—
690C24C23×D312yes—
691C24C23×D312yes—
692C24C23×D312yes—
693C24C23×D311yescharacteristic
694C2×Q8—68no—
695C2×Q8—68no—
696C2×Q8—124no—
697C2×Q8—1216no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—416no—
708C2×D4—416no—
709C2×D4—416no—
710C2×D4—68no—
711C2×D4—68no—
712C2×D4—68no—
713C2×D4—68no—
714C2×D4—68no—
715C2×D4—124no—
716C2×D4—124no—
717C2×D4—124no—
718C2×D4—124no—
719C2×D4—124no—
720C2×D4—124no—
721C2×D4—124no—
722C2×D4—1216no—
723C2×D4—1216no—
724C2×D4—1216no—
725C2×D4—1216no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—34no—
734C22×C4—34no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—62no—
743C22×C4—62no—
744C22×C4—62no—
745C22×C4—62no—
746C22×C4—62no—
747C22×C4—62no—
748C22×C4—62no—
749C22×C4—62no—
750C22×C4—62no—
751C22×C4—62no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—62no—
755C22×C4—62no—
756C22×C4—62no—
757C22×C4—62no—
758C22×C4—62no—
759C22×C4—62no—
760C22×C4—62no—
761C22×C4C2×#6714yes—
762C22×C4C2×#6714yes—
763C22×C4C23×D312yes—
764C22×C4C23×D312yes—
765C22×C4C23×D312yes—
766C4⋊C4—124no—
767C4⋊C4—124no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—316no—
771C22⋊C4—68no—
772C22⋊C4—68no—
773C22⋊C4—68no—
774C22⋊C4—68no—
775C22⋊C4—68no—
776C22⋊C4—68no—
777C22⋊C4—68no—
778C22⋊C4—68no—
779C22⋊C4—124no—
780C22⋊C4—124no—
781C22⋊C4—124no—
782C22⋊C4—124no—
783C22⋊C4—124no—
784C22⋊C4—124no—
785C22⋊C4C2×#67116yescomplemented
786C42—68no—
787C42—68no—
788C22×C3—24no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—24no—
794C22×C3—24no—
795C22×C3—24no—
796C22×C3—24no—
797C22×C3—464no—
798C22×C3—416no—
799C22×C3—416no—
800C22×C3—416no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—88no—
821C22×C3#53514yes—
822C22×C3#53514yes—
823C22×C3#53814yes—
824C22×C3D4214yes—
825C22×C3#54614yes—
826C22×C3#54614yes—
827C22×C3H(3,𝔽4)14yes—
828C22×C3C23×D411yescharacteristic
829C22×C3C23×D411yescharacteristic
830C22×C3C22×#4111yescharacteristic
831C22×C3C2×H(5,𝔽2)11yescharacteristic
832C22×C3C2×H(5,𝔽2)11yescharacteristic
833C22×C3C2×H(5,𝔽2)11yescharacteristic
834C22×C3C2×H(5,𝔽2)11yescharacteristic
835C2×D3—42no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3—42no—
842C2×D3—88no—
843C3×C4—24no—
844C3×C4—24no—
845C3×C4—42no—
846Dic3—24no—
847Dic3—24no—
848Dic3—42no—
849Dic3—42no—
850Dic3—42no—
851Dic3—42no—
852Dic3—42no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—28no—
872C23—28no—
873C23—28no—
874C23—28no—
875C23—28no—
876C23—28no—
877C23—28no—
878C23—28no—
879C23—28no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—416no—
888C23—416no—
889C23—416no—
890C23—416no—
891C23—416no—
892C23—416no—
893C23—416no—
894C23—4128no—
895C23—44no—
896C23—44no—
897C23—44no—
898C23—44no—
899C23—44no—
900C23—44no—
901C23—44no—
902C23—44no—
903C23—44no—
904C23—44no—
905C23—44no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—124no—
922C23—124no—
923C23—124no—
924C23—124no—
925C23—124no—
926C23—124no—
927C23—124no—
928C23C2×D3×D414yes—
929C23C2×D3×D412yes—
930C23C2×#23714yes—
931C23C2×#23712yes—
932C23#100412yes—
933C23#100412yes—
934C23#100412yes—
935C23#100412yes—
936C23C22×#6714yes—
937C23C22×#6712yes—
938C23C24×D311yescharacteristic
939Q8—1216no—
940D4—416no—
941D4—416no—
942D4—416no—
943D4—1216no—
944D4—1216no—
945D4—1216no—
946D4—1216no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—34no—
957C2×C4—34no—
958C2×C4—44no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—68no—
964C2×C4—68no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—124no—
981C2×C4—124no—
982C2×C4—124no—
983C2×C4—124no—
984C2×C4—124no—
985C2×C4C22×#6714yes—
986C2×C4C22×#6714yes—
987C2×C3—44no—
988C2×C3—44no—
989C2×C3—44no—
990C2×C3—82no—
991C2×C3#267018yescomplemented
992C2×C3C2×#53511yescharacteristic
993C2×C3C2×#53511yescharacteristic
994C2×C3C2×#53811yescharacteristic
995C2×C3C2×D4211yescharacteristic
996C2×C3C2×#54611yescharacteristic
997C2×C3C2×#54611yescharacteristic
998C2×C3C2×H(3,𝔽4)11yescharacteristic
999D3—82no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—464no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—416no—
1019C22—416no—
1020C22—416no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—88no—
1033C22—122no—
1034C22—122no—
1035C22—122no—
1036C22—122no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—248no—
1041C22#559114yes—
1042C22#559214yes—
1043C22#559314yes—
1044C22#559414yes—
1045C22D4×#6714yes—
1046C22#580514yes—
1047C22#580614yes—
1048C22C22×D3×D411yescharacteristic
1049C22C22×#23711yescharacteristic
1050C22C2×#100411yescharacteristic
1051C22C2×#100411yescharacteristic
1052C22C2×#100411yescharacteristic
1053C22C2×#100411yescharacteristic
1054C22C23×#6711yescharacteristic
1055C4—24no—
1056C4—24no—
1057C4—42no—
1058C4—64no—
1059C4—64no—
1060C4—122no—
1061C4—122no—
1062C4—122no—
1063C4—122no—
1064C4—122no—
1065C3C2×#267011yescharacteristic, complemented, Sylow
1066C2—44no—
1067C2—44no—
1068C2—44no—
1069C2—82no—
1070C2—242no—
1071C2#8259518yesdirect product factor
1072C2C2×#559211yescharacteristic
1073C2C2×#559311yescharacteristic
1074C2C2×#559411yescharacteristic
1075C2C2×#559111yescharacteristic
1076C2C2×#580611yescharacteristic
1077C2C2×#580511yescharacteristic
1078C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#120C2
socleC24×C3C24
hypercenterC22×#120D3
hypocenterC3C2×#2670
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C22×C3×#120C2semidirect
2. C22×#953C2semidirect
3. C22×#936C2semidirect
4. C22×#885C2semidirect
5. C2×#5247C2semidirect
6. C2×#5223C2semidirect
7. C2×#5223C2semidirect
8. C2×#5223C2semidirect
9. C2×#5222C2semidirect
10. C2×#5221C2semidirect
11. #82595C2direct (N × H)
12. C2×#4961C2semidirect
13. C2×#4947C2semidirect
14. C2×#4957C2semidirect
15. C2×#4944C2semidirect
16. C2×#4951C2semidirect
25. C23×#67C22semidirect
26. C23×Dic6C22semidirect
28. C2×C3×#120C22semidirect
33. C2×#953C22semidirect
43. C22×#217C22semidirect
44. C22×#217C22semidirect
45. C22×#217C22semidirect
47. C2×#936C22semidirect
48. C22×(C2×D3)⋊C4C22semidirect
49. C22×(C2×D3)⋊C4C22semidirect
50. C22×(C2×D3)⋊C4C22semidirect
51. C22×C4⋊Dic3C22semidirect
52. C22×Dic3⋊C4C22semidirect
53. C22×C4×Dic3C22semidirect
54. C22×C4×Dic3C22semidirect
56. C2×#885C22semidirect
57. #5247C22semidirect
58. #5223C22semidirect
59. #5223C22semidirect
60. #5223C22semidirect
61. #5222C22semidirect
62. #5221C22semidirect
63. C2×C3⋊#95C22semidirect
64. C2×C3⋊#95C22semidirect
65. C2×C3⋊#95C22semidirect
66. C2×C3⋊#95C22semidirect
67. #4961C22semidirect
68. #4957C22semidirect
69. #4951C22semidirect
70. #4947C22semidirect
71. #4944C22semidirect
75. C22×#120D3semidirect
131. C22×#67C23semidirect
142. C22×Dic6C23semidirect
146. C2×C3×C22⋊C4D4semidirect
162. C2×#217D4semidirect
172. C2×#217C23semidirect
173. C2×#217C23semidirect
174. C2×#217C23semidirect
179. C2×(C2×D3)⋊C4C23semidirect
180. C2×(C2×D3)⋊C4C23semidirect
181. C2×(C2×D3)⋊C4C23semidirect
183. C2×C4⋊Dic3C23semidirect
185. C2×Dic3⋊C4C23semidirect
188. C2×C4×Dic3C23semidirect
189. C2×C4×Dic3C23semidirect
191. C3⋊#95C23semidirect
192. C3⋊#95C23semidirect
193. C3⋊#95C23semidirect
194. C3⋊#95C23semidirect
211. C2×#120C2×D3semidirect
378. C3×C22⋊C4C2×D4semidirect
390. #217C2×D4semidirect
493. C2×C22⋊C4#67semidirect
785. C22⋊C4C2×#67semidirect
991. C2×C3#2670semidirect
1065. C3C2×#2670semidirect
1071. C2#82595direct (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×#9532
C22×#9362
C22×#8852
C2×#52472
C2×#52232
C2×#52222
C2×#52212
#825952
C2×#49612
C2×#49472
C2×#49572
C2×#49442
C2×#49512
C2×#26703