Finite Group Databasebeta

← C2×#10594184 #11902427

Subgroups — C2×#10594184 #11902427

Order 1152.

3961 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#625C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64087C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×D3×#217C211yesmaximal, characteristic, complemented
9C2×#63913C211yesmaximal, characteristic, complemented
10C2×#63908C211yesmaximal, characteristic, complemented
11C2×#63905C211yesmaximal, characteristic, complemented
12C2×#63891C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×#63879C211yesmaximal, characteristic, complemented
16#10594184C2116yesmaximal, direct product factor
17C2×#5591—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×#634C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic, complemented
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×#625—28no—
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2218yescomplemented
34C22×#625C2211yescharacteristic, complemented
35C22×#625C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C22×D3×Dic3C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3795—28no—
40C2×#3795C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×#3757C2211yescharacteristic
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46#64087C2218yescomplemented
47C2×C3×#217C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C3×#882C2218yescomplemented
53C3×D3×C22⋊C4C2218yescomplemented
54#63976C2218yescomplemented
55#67⋊Dic3C2218yescomplemented
56D3×#217C2218yescomplemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×Dic32C2211yescharacteristic, complemented
64#63913C2218yescomplemented
65#63908C2218yescomplemented
66#63905C2218yescomplemented
67#63891C2218yescomplemented
68#63885C2218yescomplemented
69#63885C2218yescomplemented
70#63879C2218yescomplemented
71C23×#67—31no—
72C23×#67—31no—
73C22×#237—31no—
74C22×#235—31no—
75C2×C3×#120—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C22×#217—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#938—31no—
82C2×#937—31no—
83C2×D4×Dic3—31no—
84C2×#930—31no—
85C2×#929—31no—
86C2×C4×#67—31no—
87#5591—316no—
88C2×#886—31no—
89C2×#885—31no—
90C2×#885—31no—
91#5490—316no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#882D311yescharacteristic, complemented
97C2×#67⋊C4—31no—
98C2×#67⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4D311yescharacteristic, complemented
101C2×#878—31no—
102C2×#878—31no—
103C2×#878—61no—
104C24×C32C2311yescharacteristic
105C23×C3×D3—24no—
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—42no—
110C23×C3×D3—42no—
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2314yes—
115C23×C3×D3C2314yes—
116C23×C3×D3C2311yescharacteristic
117C23×C3×D3C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C22×C3⋊Dic3—24no—
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2314yes—
125C22×C3⋊Dic3C2311yescharacteristic
126C2×#634—24no—
127C2×#634C2314yescomplemented
128C2×C3×#67—24no—
129C2×C3×#67C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×D12—24no—
134C2×C3×D12—42no—
135C2×C3×D12C2314yescomplemented
136C2×C3×D12C2314yescomplemented
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—42no—
139C2×C3×C4×D3C2314yescomplemented
140C2×C3×C4×D3C2314yescomplemented
141C2×#625—24no—
142C2×#625—24no—
143C2×#625—24no—
144C2×#625—24no—
145C2×#625—232no—
146C2×#625—42no—
147C2×#625D418yescomplemented
148C2×#625C2314yes—
149C2×#625C2314yes—
150C2×#625C2314yes—
151C2×#625C2314yes—
152C2×#625C2314yescomplemented
153C2×#625C2314yescomplemented
154C2×D3×Dic3—24no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3—42no—
157C2×D3×Dic3C2314yescomplemented
158C2×D3×Dic3C2314yescomplemented
159C2×D3×Dic3C2314yescomplemented
160#3795—232no—
161C32×C22⋊C4C2314yes—
162#3757C2314yes—
163C4⋊(C3⋊Dic3)C2314yescomplemented
164#3750C2314yescomplemented
165#3750C2314yescomplemented
166C3×#217C2314yes—
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172(C2×D3)⋊Dic3C2314yescomplemented
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C25×C3—31no—
181C24×D3C2×D311yescharacteristic
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—38no—
199C22×#67—38no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—68no—
203C22×#67—68no—
204C22×#67C2×D311yescharacteristic
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—31no—
208C23×Dic3—31no—
209C23×Dic3—31no—
210C23×Dic3—61no—
211C2×#237—38no—
212C2×#237—68no—
213C2×#235—38no—
214C2×#235—68no—
215C22×D12C2×D311yescharacteristic, complemented
216C22×D12C2×D311yescharacteristic, complemented
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3C2×D311yescharacteristic, complemented
221C22×C4×D3C2×D311yescharacteristic, complemented
222C22×Dic6—31no—
223C22×Dic6—31no—
224C22×Dic6—61no—
225C3×#120—38no—
226C2×C3×C22⋊C4—21no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—38no—
233C2×C3×C22⋊C4C2×D311yescharacteristic
234C2×C3×C22⋊C4C2×D311yescharacteristic
235#953—38no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—38no—
244C2×#217—61no—
245C2×#217C2×D311yescharacteristic
246#939—38no—
247#939—38no—
248#938—38no—
249#937—38no—
250D4×Dic3—38no—
251#930—38no—
252#929—38no—
253C4×#67—38no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
260C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
261C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×C4⋊Dic3—31no—
264C2×C4⋊Dic3—31no—
265C2×C4⋊Dic3—31no—
266C2×C4⋊Dic3—61no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—61no—
273C2×Dic3⋊C4—61no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3—31no—
276#886—38no—
277#885—38no—
278#885—38no—
279#884—38no—
280#884—38no—
281#883—38no—
282#883—38no—
283#882C2×D318yescomplemented
284#67⋊C4—38no—
285#67⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4C2×D318yescomplemented
288#878—38no—
289#878—38no—
290#878—68no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—28no—
307C22×C3×D3—28no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—28no—
312C22×C3×D3—28no—
313C22×C3×D3—44no—
314C22×C3×D3—44no—
315C22×C3×D3—416no—
316C22×C3×D3—416no—
317C22×C3×D3C2×D414yes—
318C22×C3×D3C2×D414yes—
319C22×C3×D3C2412yes—
320C22×C3×D3C2412yes—
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C32×C4C2412yes—
328C2×C3⋊Dic3—22no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—28no—
332C2×C3⋊Dic3C2×D414yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337#634—28no—
338C3×#67—28no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C3×D12—28no—
346C3×D12—44no—
347C3×C4×D3—28no—
348C3×C4×D3—44no—
349#625—28no—
350#625—28no—
351#625—28no—
352#625—28no—
353#625—44no—
354#625C2×D4116yescomplemented
355D3×Dic3—28no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—31no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—31no—
380C24×C3—34no—
381C24×C3—34no—
382C24×C3—64no—
383C24×C3—64no—
384C24×C3—64no—
385C24×C3—64no—
386C24×C3—122no—
387C24×C3—122no—
388C24×C3C22×D311yescharacteristic
389C24×C3C22×D311yescharacteristic
390C23×D3—24no—
391C23×D3—24no—
392C23×D3—24no—
393C23×D3—24no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3C22×D311yescharacteristic
397C23×D3C22×D311yescharacteristic
398C23×D3C22×D311yescharacteristic
399C23×D3C22×D314yes—
400C23×D3C22×D314yes—
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D311yescharacteristic
403C2×C3×D4—34no—
404C2×C3×D4—34no—
405C2×C3×D4—34no—
406C2×C3×D4—64no—
407C2×C3×D4—64no—
408C2×C3×D4—122no—
409C22×C3×C4—21no—
410C22×C3×C4—21no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—34no—
415C22×C3×C4—34no—
416C22×C3×C4—64no—
417C22×C3×C4—122no—
418C22×C3×C4C22×D311yescharacteristic
419C22×C3×C4C22×D311yescharacteristic
420C22×C3×C4C22×D311yescharacteristic
421C22×C3×C4C22×D311yescharacteristic
422C2×#67—24no—
423C2×#67—38no—
424C2×#67—38no—
425C2×#67—34no—
426C2×#67—34no—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67—632no—
440C2×#67—632no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—122no—
448C2×#67—122no—
449C2×#67C22×D314yes—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—34no—
453C22×Dic3—34no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—34no—
461C22×Dic3—34no—
462C22×Dic3—34no—
463C22×Dic3—61no—
464C22×Dic3—64no—
465C22×Dic3—61no—
466C22×Dic3—61no—
467C22×Dic3—61no—
468C22×Dic3—64no—
469C22×Dic3—64no—
470C22×Dic3—64no—
471C22×Dic3—64no—
472C22×Dic3—124no—
473C22×Dic3—122no—
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477#237—632no—
478#235—632no—
479C2×D12—24no—
480C2×D12—42no—
481C2×D12C22×D314yescomplemented
482C2×D12C22×D314yescomplemented
483C2×C4×D3—24no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—42no—
488C2×C4×D3—64no—
489C2×C4×D3—64no—
490C2×C4×D3—122no—
491C2×C4×D3C22×D314yescomplemented
492C2×C4×D3C22×D314yescomplemented
493C2×Dic6—34no—
494C2×Dic6—34no—
495C2×Dic6—64no—
496C2×Dic6—64no—
497C2×Dic6—64no—
498C2×Dic6—124no—
499C3×C22⋊C4—24no—
500C3×C22⋊C4—34no—
501C3×C22⋊C4—34no—
502C3×C22⋊C4—34no—
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4C22×D314yes—
506C3×C22⋊C4C22×D314yes—
507#217—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—64no—
515#217C22×D314yes—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4C22×D314yescomplemented
522(C2×D3)⋊C4C22×D314yescomplemented
523(C2×D3)⋊C4C22×D314yescomplemented
524(C2×D3)⋊C4C22×D314yescomplemented
525C4⋊Dic3—34no—
526C4⋊Dic3—34no—
527C4⋊Dic3—34no—
528C4⋊Dic3—64no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—64no—
535Dic3⋊C4—64no—
536C4×Dic3—34no—
537C4×Dic3—34no—
538C22×C32—28no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32C22×D412yes—
542C22×C32C2×#4112yes—
543C22×C32C2×#4114yescomplemented
544C22×C32H(5,𝔽2)12yes—
545C22×C32C2511yescharacteristic
546C2×C3×D3—28no—
547C2×C3×D3—28no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—416no—
562C2×C3×D3—416no—
563C2×C3×D3—44no—
564C2×C3×D3—44no—
565C2×C3×D3—44no—
566C2×C3×D3C22×D414yes—
567C2×C3×D3C22×D414yes—
568C32×C4—22no—
569C32×C4—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3C22×D414yes—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C25—31no—
578C25—31no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—91no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—98no—
591C22×D4—91no—
592C22×D4—188no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—91no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—98no—
600#123—98no—
601#123—98no—
602C22⋊Q8—98no—
603#121—98no—
604#121—98no—
605#121—98no—
606#120—38no—
607#120—98no—
608C4×D4—98no—
609C4×D4—98no—
610C2×C4⋊C4—91no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—91no—
613C2×C4⋊C4—91no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—38no—
620C2×C22⋊C4—98no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4D3211yescharacteristic
628C2×C42—91no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—21no—
635C23×C3—24no—
636C23×C3—34no—
637C23×C3—34no—
638C23×C3—32no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—68no—
646C23×C3—68no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—68no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—68no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—124no—
663C23×C3—124no—
664C23×C3—1216no—
665C23×C3—1216no—
666C23×C3#23514yescomplemented
667C23×C3#23714yescomplemented
668C23×C3C23×D312yes—
669C23×C3C23×D312yes—
670C23×C3C23×D311yescharacteristic
671C23×C3C23×D311yescharacteristic
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—22no—
676C22×D3—22no—
677C22×D3—28no—
678C22×D3—22no—
679C22×D3—22no—
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—22no—
683C22×D3—28no—
684C22×D3—22no—
685C22×D3—22no—
686C22×D3—22no—
687C22×D3—28no—
688C22×D3—28no—
689C22×D3—44no—
690C22×D3—44no—
691C22×D3—416no—
692C22×D3—416no—
693C22×D3D3×D414yes—
694C22×D3D3×D414yes—
695C22×D3C23×D312yes—
696C22×D3C23×D312yes—
697C22×D3C23×D312yes—
698C22×D3C23×D312yes—
699C22×D3C23×D312yes—
700C3×D4—68no—
701C3×D4—68no—
702C3×D4—124no—
703C2×C3×C4—22no—
704C2×C3×C4—22no—
705C2×C3×C4—22no—
706C2×C3×C4—22no—
707C2×C3×C4—22no—
708C2×C3×C4—22no—
709C2×C3×C4—32no—
710C2×C3×C4—32no—
711C2×C3×C4—32no—
712C2×C3×C4—42no—
713C2×C3×C4—42no—
714C2×C3×C4—68no—
715C2×C3×C4—62no—
716C2×C3×C4—62no—
717C2×C3×C4—62no—
718C2×C3×C4—124no—
719C2×C3×C4C23×D312yes—
720C2×C3×C4C23×D312yes—
721C2×C3×C4C23×D312yes—
722C2×C3×C4C23×D312yes—
723#67—28no—
724#67—316no—
725#67—316no—
726#67—68no—
727#67—68no—
728#67—68no—
729#67—68no—
730#67—68no—
731#67—68no—
732#67—68no—
733#67—68no—
734#67—124no—
735#67—124no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—22no—
739C2×Dic3—34no—
740C2×Dic3—34no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—64no—
750C2×Dic3—62no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—68no—
755C2×Dic3—68no—
756C2×Dic3—68no—
757C2×Dic3—68no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—128no—
765C2×Dic3—122no—
766C2×Dic3—122no—
767C2×Dic3—122no—
768C2×Dic3—124no—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772D12—28no—
773D12—44no—
774C4×D3—28no—
775C4×D3—44no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—124no—
779Dic6—68no—
780Dic6—68no—
781Dic6—128no—
782C2×C32—24no—
783C2×C32#54614yescomplemented
784C2×C32C23×D411yescharacteristic
785C2×C32C22×#4111yescharacteristic
786C2×C32C2×H(5,𝔽2)11yescharacteristic
787C3×D3—24no—
788C3×D3—24no—
789C3×D3—42no—
790C3×D3—42no—
791C3×D3—42no—
792C24—31no—
793C24—31no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—34no—
798C24—34no—
799C24—64no—
800C24—64no—
801C24—64no—
802C24—64no—
803C24—122no—
804C24—122no—
805C24C2×D3211yescharacteristic
806#41—1832no—
807C2×Q8—94no—
808C2×Q8—184no—
809C2×D4—34no—
810C2×D4—34no—
811C2×D4—34no—
812C2×D4—64no—
813C2×D4—64no—
814C2×D4—94no—
815C2×D4—98no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—94no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—122no—
822C2×D4—184no—
823C2×D4—1832no—
824C2×D4—184no—
825C2×D4—184no—
826C2×D4—184no—
827C2×D4—362no—
828C22×C4—31no—
829C22×C4—31no—
830C22×C4—31no—
831C22×C4—34no—
832C22×C4—34no—
833C22×C4—64no—
834C22×C4—94no—
835C22×C4—94no—
836C22×C4—94no—
837C22×C4—91no—
838C22×C4—94no—
839C22×C4—91no—
840C22×C4—91no—
841C22×C4—91no—
842C22×C4—122no—
843C22×C4—184no—
844C22×C4—184no—
845C22×C4—184no—
846C22×C4—362no—
847C22×C4C2×D3211yescharacteristic
848C22×C4C2×D3211yescharacteristic
849C4⋊C4—94no—
850C4⋊C4—94no—
851C4⋊C4—94no—
852C4⋊C4—94no—
853C22⋊C4—34no—
854C22⋊C4—34no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—94no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4C2×D3214yes—
865C42—94no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—28no—
871C22×C3—28no—
872C22×C3—22no—
873C22×C3—24no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—21no—
877C22×C3—34no—
878C22×C3—34no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—48no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—68no—
887C22×C3—68no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—1216no—
898C22×C3—1216no—
899C22×C3—124no—
900C22×C3—124no—
901C22×C3—124no—
902C22×C3C2×#23512yes—
903C22×C3C2×#23514yescomplemented
904C22×C3C2×D3×D412yes—
905C22×C3C2×D3×D412yes—
906C22×C3C2×#23712yes—
907C22×C3C2×#23714yescomplemented
908C22×C3#100412yes—
909C22×C3#100412yes—
910C22×C3C24×D311yescharacteristic
911C22×C3C24×D311yescharacteristic
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—28no—
917C2×D3—28no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—416no—
928C2×D3—416no—
929C2×D3—44no—
930C2×D3—44no—
931C2×D3—44no—
932C2×D3C2×D3×D414yes—
933C2×D3C2×D3×D414yes—
934C3×C4—22no—
935C3×C4—22no—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—42no—
939C3×C4—42no—
940C3×C4—62no—
941C3×C4—62no—
942C3×C4—62no—
943Dic3—22no—
944Dic3—22no—
945Dic3—22no—
946Dic3—34no—
947Dic3—34no—
948Dic3—64no—
949Dic3—62no—
950Dic3—62no—
951Dic3—62no—
952Dic3—62no—
953Dic3—62no—
954Dic3—62no—
955Dic3—122no—
956Dic3—122no—
957Dic3—122no—
958C32C2×#54611yescharacteristic, complemented, Sylow
959C23—22no—
960C23—22no—
961C23—34no—
962C23—34no—
963C23—32no—
964C23—32no—
965C23—32no—
966C23—32no—
967C23—32no—
968C23—68no—
969C23—68no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—68no—
978C23—68no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—124no—
986C23—124no—
987C23—1216no—
988C23—1216no—
989C23#379514yescomplemented
990C23C22×D3212yes—
991C23C22×D3211yescharacteristic
992Q8—188no—
993D4—68no—
994D4—68no—
995D4—916no—
996D4—124no—
997D4—188no—
998D4—188no—
999D4—188no—
1000D4—188no—
1001D4—364no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—32no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—68no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—94no—
1012C2×C4—92no—
1013C2×C4—92no—
1014C2×C4—92no—
1015C2×C4—92no—
1016C2×C4—124no—
1017C2×C4—188no—
1018C2×C4—188no—
1019C2×C4—188no—
1020C2×C4—182no—
1021C2×C4—182no—
1022C2×C4—182no—
1023C2×C4—364no—
1024C2×C4C22×D3212yes—
1025C2×C4C22×D3212yes—
1026C2×C3—24no—
1027C2×C3—24no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—24no—
1032C2×C3—44no—
1033C2×C3—64no—
1034C2×C3—64no—
1035C2×C3—122no—
1036C2×C3—122no—
1037C2×C3—122no—
1038C2×C3#549014yescomplemented
1039C2×C3#559114yescomplemented
1040C2×C3C22×#23511yescharacteristic
1041C2×C3C22×D3×D411yescharacteristic
1042C2×C3C22×D3×D411yescharacteristic
1043C2×C3C22×#23711yescharacteristic
1044C2×C3C2×#100411yescharacteristic
1045C2×C3C2×#100411yescharacteristic
1046D3—24no—
1047D3—24no—
1048D3—42no—
1049D3—42no—
1050D3—42no—
1051C22—22no—
1052C22—22no—
1053C22—28no—
1054C22—34no—
1055C22—34no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—68no—
1061C22—68no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—1216no—
1072C22—1216no—
1073C22—124no—
1074C22—124no—
1075C22—124no—
1076C22C2×#379512yes—
1077C22C2×#379514yescomplemented
1078C22D32×D412yes—
1079C22#6431312yes—
1080C22C23×D3211yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—62no—
1084C4—62no—
1085C4—62no—
1086C4—94no—
1087C4—182no—
1088C4—182no—
1089C4—182no—
1090C3—21no—
1091C3C2×#549011yescharacteristic, complemented
1092C3C2×#559111yescharacteristic, complemented
1093C2—24no—
1094C2—64no—
1095C2—64no—
1096C2—122no—
1097C2—122no—
1098C2—122no—
1099C2#1059418414yesdirect product factor
1100C2C22×#379511yescharacteristic
1101C2C2×D32×D411yescharacteristic
1102C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#625C2semidirect
2. C22×#3795C2semidirect
3. C2×#64087C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63976C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×D3×#217C2semidirect
9. C2×#63913C2semidirect
10. C2×#63908C2semidirect
11. C2×#63905C2semidirect
12. C2×#63891C2semidirect
13. C2×#63885C2semidirect
14. C2×#63885C2semidirect
15. C2×#63879C2semidirect
16. #10594184C2direct (N × H)
22. C22×#634C22semidirect
24. C22×C3×D12C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
33. C22×#625C22semidirect
34. C22×#625C22semidirect
35. C22×#625C22semidirect
36. C22×D3×Dic3C22semidirect
37. C22×D3×Dic3C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3795C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×#3750C22semidirect
45. C2×#3750C22semidirect
46. #64087C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C3×#882C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. #63976C22semidirect
55. #67⋊Dic3C22semidirect
56. D3×#217C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×Dic32C22semidirect
64. #63913C22semidirect
65. #63908C22semidirect
66. #63905C22semidirect
67. #63891C22semidirect
68. #63885C22semidirect
69. #63885C22semidirect
70. #63879C22semidirect
96. C2×#882D3semidirect
100. C2×D3×C22⋊C4D3semidirect
127. C2×#634C23semidirect
135. C2×C3×D12C23semidirect
136. C2×C3×D12C23semidirect
139. C2×C3×C4×D3C23semidirect
140. C2×C3×C4×D3C23semidirect
147. C2×#625D4semidirect
152. C2×#625C23semidirect
153. C2×#625C23semidirect
157. C2×D3×Dic3C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
163. C4⋊(C3⋊Dic3)C23semidirect
164. #3750C23semidirect
165. #3750C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. Dic3⋊Dic3C23semidirect
172. (C2×D3)⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
215. C22×D12C2×D3semidirect
216. C22×D12C2×D3semidirect
220. C22×C4×D3C2×D3semidirect
221. C22×C4×D3C2×D3semidirect
259. C2×(C2×D3)⋊C4C2×D3semidirect
260. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
283. #882C2×D3semidirect
287. D3×C22⋊C4C2×D3semidirect
293. C23×C32#41semidirect
354. #625C2×D4semidirect
481. C2×D12C22×D3semidirect
482. C2×D12C22×D3semidirect
491. C2×C4×D3C22×D3semidirect
492. C2×C4×D3C22×D3semidirect
521. (C2×D3)⋊C4C22×D3semidirect
522. (C2×D3)⋊C4C22×D3semidirect
523. (C2×D3)⋊C4C22×D3semidirect
524. (C2×D3)⋊C4C22×D3semidirect
543. C22×C32C2×#41semidirect
666. C23×C3#235semidirect
667. C23×C3#237semidirect
783. C2×C32#546semidirect
903. C22×C3C2×#235semidirect
907. C22×C3C2×#237semidirect
958. C32C2×#546semidirect
989. C23#3795semidirect
1038. C2×C3#5490semidirect
1039. C2×C3#5591semidirect
1077. C22C2×#3795semidirect
1091. C3C2×#5490semidirect
1092. C3C2×#5591semidirect
1099. C2#10594184direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6252
C22×#37952
C2×#640872
C2×C3×#8822
C2×C3×D3×C22⋊C42
C2×#639762
C2×#67⋊Dic32
C2×D3×#2172
C2×#639132
C2×#639082
C2×#639052
C2×#638912
C2×#638852
C2×#638792
#105941842
C2×#55913
C2×#54903