Finite Group Databasebeta

← C2×#10595500 #11902429

Subgroups — C2×#10595500 #11902429

Order 1152.

4481 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#638C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×C3×#953C211yesmaximal, characteristic, complemented
4C22×C3×#217C211yesmaximal, characteristic, complemented
5C2×#63982C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63978C211yesmaximal, characteristic, complemented
8C2×#63975C211yesmaximal, characteristic, complemented
9C2×#63974C211yesmaximal, characteristic, complemented
10#10595500C2116yesmaximal, direct product factor
11C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
12C2×#63971C211yesmaximal, characteristic, complemented
13C2×#63966C211yesmaximal, characteristic, complemented
14C2×#63958C211yesmaximal, characteristic, complemented
15C2×#63953C211yesmaximal, characteristic, complemented
16C2×#63952C211yesmaximal, characteristic, complemented
17C2×#5591—31nomaximal
18C2×#5490—31nomaximal
19C25×C32C2211yescharacteristic
20C24×C3⋊D3C2211yescharacteristic
21C22×#638—28no—
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic
24C22×#638C2211yescharacteristic
25C22×#638C2211yescharacteristic
26C22×#638C2218yescomplemented
27C23×C3⋊Dic3C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C22×C3×#67C2211yescharacteristic, complemented
30C22×C3×#67C2211yescharacteristic, complemented
31C23×C3×Dic3C2211yescharacteristic, complemented
32C23×C3×Dic3C2211yescharacteristic, complemented
33C22×#627C2211yescharacteristic, complemented
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic, complemented
38C2×#3804—28no—
39C2×#3804C2218yescomplemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C3×#953C2218yescomplemented
42C2×C3×#217C2211yescharacteristic
43C2×C3×#217C2211yescharacteristic
44C2×C3×#217C2211yescharacteristic
45C2×C3×#217C2218yescomplemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×#217C2211yescharacteristic, complemented
48C2×C3×#217C2211yescharacteristic, complemented
49C2×C3×#217C2211yescharacteristic, complemented
50#63982C2218yescomplemented
51#63981C2218yescomplemented
52#63978C2218yescomplemented
53#63975C2218yescomplemented
54#63974C2218yescomplemented
55#67⋊Dic3C2218yescomplemented
56#63971C2218yescomplemented
57C2×#3724C2211yescharacteristic, complemented
58#63966C2218yescomplemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×Dic3⋊Dic3C2211yescharacteristic, complemented
61C2×Dic3⋊Dic3C2211yescharacteristic, complemented
62C2×#3722C2211yescharacteristic, complemented
63C2×#3722C2211yescharacteristic, complemented
64C2×#3722C2211yescharacteristic, complemented
65C2×#3722C2211yescharacteristic, complemented
66C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
67#63958C2218yescomplemented
68C2×Dic32C2211yescharacteristic, complemented
69#63953C2218yescomplemented
70#63952C2218yescomplemented
71C23×#67—31no—
72C23×#67—31no—
73C23×#67—61no—
74C22×#237—31no—
75C22×#235—31no—
76C2×C3×#120—31no—
77C22×C3×C22⋊C4—31no—
78C2×#953D311yescharacteristic, complemented
79C22×#217D311yescharacteristic, complemented
80C2×#939—31no—
81C2×#939—31no—
82C2×#938—31no—
83C2×#937—31no—
84C2×D4×Dic3—31no—
85C2×#930—31no—
86C2×#929—31no—
87C2×C4×#67—31no—
88#5591—316no—
89C2×#886—31no—
90C2×#885—31no—
91C2×#885—31no—
92#5490—316no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#882—31no—
98C2×#67⋊C4—31no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×#878—31no—
103C2×#878—31no—
104C24×C32—24no—
105C24×C32—24no—
106C24×C32—42no—
107C24×C32C2311yescharacteristic
108C24×C32C2314yes—
109C24×C32C2311yescharacteristic
110C24×C32C2311yescharacteristic
111C23×C3⋊D3—24no—
112C23×C3⋊D3—24no—
113C23×C3⋊D3—42no—
114C23×C3⋊D3C2311yescharacteristic
115C23×C3⋊D3C2314yes—
116C23×C3⋊D3C2311yescharacteristic
117C23×C3×D3C2311yescharacteristic
118C2×#638—24no—
119C2×#638—24no—
120C2×#638—232no—
121C2×#638—24no—
122C2×#638D418yescomplemented
123C2×#638C2314yes—
124C2×#638C2314yes—
125C2×#638C2314yes—
126C2×#638C2314yes—
127C22×C3⋊Dic3—24no—
128C22×C3⋊Dic3C2311yescharacteristic
129C22×C3⋊Dic3C2314yes—
130C22×C3⋊Dic3C2311yescharacteristic
131C2×C3×#67—24no—
132C2×C3×#67—24no—
133C2×C3×#67—42no—
134C2×C3×#67C2314yes—
135C2×C3×#67C2314yescomplemented
136C2×C3×#67C2314yescomplemented
137C22×C3×Dic3—24no—
138C22×C3×Dic3—42no—
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
145C22×C3×Dic3C2311yescharacteristic
146C22×C3×Dic3C2314yescomplemented
147C22×C3×Dic3C2314yescomplemented
148C2×#627—24no—
149C2×#627C2314yescomplemented
150C2×#626—24no—
151C2×#626—42no—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#624—24no—
155C2×#624—42no—
156C2×#624C2314yescomplemented
157C2×#624C2314yescomplemented
158#3804—232no—
159C2×D3×Dic3—24no—
160C2×D3×Dic3C2314yescomplemented
161C3×#217C2314yes—
162C3×#217C2314yes—
163C3×#217C2314yes—
164C3×#217C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×#217C2314yescomplemented
168#3724C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
173#3722C2314yescomplemented
174#3722C2314yescomplemented
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—21no—
180C25×C3C2×D311yescharacteristic
181C25×C3C2×D311yescharacteristic
182C24×D3—31no—
183C24×D3—31no—
184C24×D3—61no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C23×C3×C4—31no—
189C23×C3×C4—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—61no—
203C22×#67—61no—
204C22×#67—61no—
205C22×#67—61no—
206C22×#67—68no—
207C22×#67—68no—
208C22×#67—68no—
209C22×#67—616no—
210C22×#67C2×D311yescharacteristic
211C22×#67C2×D311yescharacteristic, complemented
212C22×#67C2×D311yescharacteristic, complemented
213C23×Dic3—31no—
214C23×Dic3—31no—
215C23×Dic3—31no—
216C23×Dic3—61no—
217C23×Dic3C2×D311yescharacteristic, complemented
218C23×Dic3C2×D311yescharacteristic, complemented
219C2×#237—38no—
220C2×#237—68no—
221C2×#235—38no—
222C2×#235—68no—
223C22×D12—31no—
224C22×D12—31no—
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—31no—
228C22×C4×D3—31no—
229C22×C4×D3—31no—
230C22×Dic6—31no—
231C22×Dic6—31no—
232C3×#120—38no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C22⋊C4—38no—
241#953C2×D318yescomplemented
242C2×#217—31no—
243C2×#217C2×D311yescharacteristic
244C2×#217C2×D311yescharacteristic
245C2×#217C2×D311yescharacteristic
246C2×#217C2×D318yescomplemented
247C2×#217C2×D311yescharacteristic, complemented
248C2×#217C2×D311yescharacteristic, complemented
249C2×#217C2×D311yescharacteristic, complemented
250C2×#217C2×D311yescharacteristic, complemented
251#939—38no—
252#939—38no—
253#938—38no—
254#937—38no—
255D4×Dic3—38no—
256#930—38no—
257#929—38no—
258C4×#67—38no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×C4⋊Dic3—31no—
269C2×C4⋊Dic3—31no—
270C2×C4⋊Dic3—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×C4×Dic3—31no—
277C2×C4×Dic3—31no—
278#886—38no—
279#885—38no—
280#885—38no—
281#884—38no—
282#884—38no—
283#883—38no—
284#883—38no—
285#882—38no—
286#67⋊C4—38no—
287#67⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4—38no—
290#878—38no—
291#878—38no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—28no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32—22no—
298C23×C32—22no—
299C23×C32—28no—
300C23×C32—22no—
301C23×C32—44no—
302C23×C32—416no—
303C23×C32C2×D414yes—
304C23×C32#4114yescomplemented
305C23×C32C2412yes—
306C23×C32C2412yes—
307C23×C32C2412yes—
308C23×C32C2411yescharacteristic
309C22×C3⋊D3—22no—
310C22×C3⋊D3—28no—
311C22×C3⋊D3—22no—
312C22×C3⋊D3—22no—
313C22×C3⋊D3—22no—
314C22×C3⋊D3—28no—
315C22×C3⋊D3—22no—
316C22×C3⋊D3—44no—
317C22×C3⋊D3—416no—
318C22×C3⋊D3C2×D414yes—
319C22×C3⋊D3C2412yes—
320C22×C3⋊D3C2412yes—
321C22×C3×D3—22no—
322C22×C3×D3—22no—
323C22×C3×D3—22no—
324C22×C3×D3C2412yes—
325#638—28no—
326#638—28no—
327#638—28no—
328#638C2×D4116yescomplemented
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—28no—
331C2×C3⋊Dic3C2×D414yes—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—44no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—28no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—22no—
345C2×C3×Dic3—44no—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353#627—28no—
354#626—28no—
355#626—44no—
356#624—28no—
357#624—44no—
358D3×Dic3—28no—
359C22×#41—91no—
360C23×D4—91no—
361#546—916no—
362C2×#124—91no—
363C2×#123—91no—
364C2×#123—91no—
365C2×C22⋊Q8—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#121—91no—
369C2×#120—31no—
370C2×#120—91no—
371C2×C4×D4—91no—
372C2×C4×D4—91no—
373C22×C22⋊C4—31no—
374C22×C22⋊C4—91no—
375C24×C3—28no—
376C24×C3—24no—
377C24×C3—24no—
378C24×C3—24no—
379C24×C3—24no—
380C24×C3—21no—
381C24×C3—21no—
382C24×C3—24no—
383C24×C3—21no—
384C24×C3—31no—
385C24×C3—44no—
386C24×C3—42no—
387C24×C3—42no—
388C24×C3—44no—
389C24×C3C22×D311yescharacteristic
390C24×C3C22×D311yescharacteristic
391C24×C3C22×D314yes—
392C24×C3C22×D314yes—
393C24×C3C22×D311yescharacteristic
394C24×C3C22×D311yescharacteristic
395C24×C3C22×D311yescharacteristic
396C24×C3C22×D311yescharacteristic
397C23×D3—31no—
398C23×D3—31no—
399C23×D3—31no—
400C23×D3—31no—
401C23×D3—34no—
402C23×D3—34no—
403C23×D3—61no—
404C23×D3—61no—
405C23×D3—64no—
406C23×D3—64no—
407C23×D3—64no—
408C23×D3—68no—
409C23×D3—64no—
410C23×D3—64no—
411C23×D3—124no—
412C23×D3—122no—
413C23×D3—122no—
414C23×D3—124no—
415C23×D3C22×D311yescharacteristic
416C2×C3×D4—34no—
417C2×C3×D4—34no—
418C2×C3×D4—34no—
419C2×C3×D4—64no—
420C2×C3×D4—64no—
421C2×C3×D4—122no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—34no—
430C22×C3×C4—34no—
431C22×C3×C4—64no—
432C22×C3×C4—122no—
433C2×#67—24no—
434C2×#67—24no—
435C2×#67—38no—
436C2×#67—38no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—34no—
444C2×#67—34no—
445C2×#67—34no—
446C2×#67—34no—
447C2×#67—42no—
448C2×#67—68no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—64no—
453C2×#67—64no—
454C2×#67—64no—
455C2×#67—64no—
456C2×#67—632no—
457C2×#67—632no—
458C2×#67—64no—
459C2×#67—64no—
460C2×#67—68no—
461C2×#67—664no—
462C2×#67—68no—
463C2×#67—68no—
464C2×#67—64no—
465C2×#67—64no—
466C2×#67—122no—
467C2×#67C22×D314yes—
468C2×#67C22×D314yescomplemented
469C2×#67C22×D314yescomplemented
470C22×Dic3—24no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—34no—
474C22×Dic3—34no—
475C22×Dic3—31no—
476C22×Dic3—31no—
477C22×Dic3—34no—
478C22×Dic3—42no—
479C22×Dic3—61no—
480C22×Dic3—64no—
481C22×Dic3—61no—
482C22×Dic3—64no—
483C22×Dic3—64no—
484C22×Dic3—64no—
485C22×Dic3—68no—
486C22×Dic3C22×D311yescharacteristic
487C22×Dic3C22×D311yescharacteristic
488C22×Dic3C22×D311yescharacteristic
489C22×Dic3C22×D311yescharacteristic
490C22×Dic3C22×D311yescharacteristic
491C22×Dic3C22×D311yescharacteristic
492C22×Dic3C22×D311yescharacteristic
493C22×Dic3C22×D314yescomplemented
494C22×Dic3C22×D314yescomplemented
495#237—632no—
496#235—632no—
497C2×D12—34no—
498C2×D12—34no—
499C2×D12—64no—
500C2×D12—122no—
501C2×C4×D3—34no—
502C2×C4×D3—34no—
503C2×C4×D3—34no—
504C2×C4×D3—34no—
505C2×C4×D3—34no—
506C2×C4×D3—64no—
507C2×C4×D3—64no—
508C2×C4×D3—64no—
509C2×C4×D3—122no—
510C2×C4×D3—122no—
511C2×Dic6—34no—
512C2×Dic6—34no—
513C2×Dic6—64no—
514C2×Dic6—64no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—34no—
517C3×C22⋊C4—34no—
518C3×C22⋊C4—34no—
519C3×C22⋊C4—34no—
520C3×C22⋊C4—34no—
521C3×C22⋊C4—34no—
522#217—34no—
523#217C22×D314yes—
524#217C22×D314yes—
525#217C22×D314yes—
526#217C22×D314yescomplemented
527#217C22×D314yescomplemented
528#217C22×D314yescomplemented
529#217C22×D314yescomplemented
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539C4⋊Dic3—34no—
540C4⋊Dic3—34no—
541C4⋊Dic3—34no—
542Dic3⋊C4—34no—
543Dic3⋊C4—34no—
544Dic3⋊C4—34no—
545Dic3⋊C4—34no—
546Dic3⋊C4—34no—
547C4×Dic3—34no—
548C4×Dic3—34no—
549C22×C32—28no—
550C22×C32—22no—
551C22×C32—22no—
552C22×C32—22no—
553C22×C32—28no—
554C22×C32—22no—
555C22×C32—22no—
556C22×C32—22no—
557C22×C32—22no—
558C22×C32—416no—
559C22×C32—44no—
560C22×C32C22×D414yes—
561C22×C32C22×D412yes—
562C22×C32C2×#4112yes—
563C22×C32C2×#4114yescomplemented
564C22×C32H(5,𝔽2)12yes—
565C22×C32C2511yescharacteristic
566C2×C3⋊D3—22no—
567C2×C3⋊D3—28no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—22no—
570C2×C3⋊D3—22no—
571C2×C3⋊D3—22no—
572C2×C3⋊D3—416no—
573C2×C3⋊D3—44no—
574C2×C3⋊D3C22×D414yes—
575C2×C3×D3—22no—
576C2×C3×D3—22no—
577C2×C3×D3—22no—
578C2×C3×D3—44no—
579C3⋊Dic3—22no—
580C3⋊Dic3C22×D414yes—
581C3×Dic3—22no—
582C3×Dic3—22no—
583C3×Dic3—22no—
584C3×Dic3—22no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587C3×Dic3—22no—
588C25—91no—
589C25D3211yescharacteristic
590C2×#41—98no—
591C2×#41—188no—
592C22×Q8—91no—
593C22×D4—31no—
594C22×D4—31no—
595C22×D4—31no—
596C22×D4—91no—
597C22×D4—91no—
598C22×D4—91no—
599C22×D4—91no—
600C22×D4—91no—
601C22×D4—91no—
602C22×D4—98no—
603C22×D4—188no—
604C23×C4—31no—
605C23×C4—31no—
606C23×C4—91no—
607C23×C4—91no—
608C23×C4—91no—
609C23×C4—91no—
610#124—98no—
611#123—98no—
612#123—98no—
613C22⋊Q8—98no—
614#121—98no—
615#121—98no—
616#121—98no—
617#120—38no—
618#120—98no—
619C4×D4—98no—
620C4×D4—98no—
621C2×C4⋊C4—91no—
622C2×C4⋊C4—91no—
623C2×C4⋊C4—91no—
624C2×C4⋊C4—91no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—31no—
627C2×C22⋊C4—31no—
628C2×C22⋊C4—31no—
629C2×C22⋊C4—38no—
630C2×C22⋊C4—31no—
631C2×C22⋊C4—31no—
632C2×C22⋊C4—31no—
633C2×C22⋊C4—98no—
634C2×C22⋊C4—91no—
635C2×C22⋊C4—91no—
636C2×C22⋊C4—91no—
637C2×C22⋊C4—91no—
638C2×C22⋊C4—91no—
639C2×C42—91no—
640C23×C3—24no—
641C23×C3—24no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—216no—
651C23×C3—24no—
652C23×C3—22no—
653C23×C3—28no—
654C23×C3—28no—
655C23×C3—28no—
656C23×C3—22no—
657C23×C3—22no—
658C23×C3—22no—
659C23×C3—28no—
660C23×C3—22no—
661C23×C3—22no—
662C23×C3—22no—
663C23×C3—22no—
664C23×C3—22no—
665C23×C3—21no—
666C23×C3—24no—
667C23×C3—24no—
668C23×C3—32no—
669C23×C3—42no—
670C23×C3—42no—
671C23×C3—42no—
672C23×C3—48no—
673C23×C3—42no—
674C23×C3—44no—
675C23×C3—44no—
676C23×C3—416no—
677C23×C3—416no—
678C23×C3—48no—
679C23×C3—432no—
680C23×C3—62no—
681C23×C3—62no—
682C23×C3—62no—
683C23×C3#23514yescomplemented
684C23×C3D3×D414yes—
685C23×C3D3×D414yes—
686C23×C3#23714yescomplemented
687C23×C3C23×D312yes—
688C23×C3C23×D312yes—
689C23×C3C23×D312yes—
690C23×C3C23×D312yes—
691C23×C3C23×D312yes—
692C23×C3C23×D312yes—
693C23×C3C23×D311yescharacteristic
694C23×C3C23×D311yescharacteristic
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—34no—
699C22×D3—34no—
700C22×D3—32no—
701C22×D3—32no—
702C22×D3—32no—
703C22×D3—32no—
704C22×D3—64no—
705C22×D3—62no—
706C22×D3—62no—
707C22×D3—68no—
708C22×D3—68no—
709C22×D3—62no—
710C22×D3—62no—
711C22×D3—62no—
712C22×D3—62no—
713C22×D3—616no—
714C22×D3—64no—
715C22×D3—62no—
716C22×D3—68no—
717C22×D3—62no—
718C22×D3—62no—
719C22×D3—62no—
720C22×D3—68no—
721C22×D3—62no—
722C22×D3—62no—
723C22×D3—122no—
724C22×D3—122no—
725C22×D3—122no—
726C22×D3—128no—
727C22×D3—122no—
728C22×D3—124no—
729C22×D3—124no—
730C22×D3—1216no—
731C22×D3—1216no—
732C22×D3—128no—
733C22×D3—1232no—
734C22×D3C23×D312yes—
735C3×D4—68no—
736C3×D4—68no—
737C3×D4—124no—
738C2×C3×C4—32no—
739C2×C3×C4—32no—
740C2×C3×C4—32no—
741C2×C3×C4—32no—
742C2×C3×C4—32no—
743C2×C3×C4—32no—
744C2×C3×C4—32no—
745C2×C3×C4—62no—
746C2×C3×C4—62no—
747C2×C3×C4—62no—
748C2×C3×C4—62no—
749C2×C3×C4—68no—
750C2×C3×C4—62no—
751C2×C3×C4—62no—
752C2×C3×C4—62no—
753C2×C3×C4—124no—
754#67—28no—
755#67—28no—
756#67—316no—
757#67—316no—
758#67—44no—
759#67—616no—
760#67—68no—
761#67—68no—
762#67—68no—
763#67—68no—
764#67—68no—
765#67—616no—
766#67—616no—
767#67—616no—
768#67—68no—
769#67—68no—
770#67—124no—
771C2×Dic3—22no—
772C2×Dic3—22no—
773C2×Dic3—22no—
774C2×Dic3—28no—
775C2×Dic3—22no—
776C2×Dic3—22no—
777C2×Dic3—22no—
778C2×Dic3—22no—
779C2×Dic3—34no—
780C2×Dic3—34no—
781C2×Dic3—32no—
782C2×Dic3—32no—
783C2×Dic3—32no—
784C2×Dic3—32no—
785C2×Dic3—44no—
786C2×Dic3—64no—
787C2×Dic3—62no—
788C2×Dic3—62no—
789C2×Dic3—68no—
790C2×Dic3—68no—
791C2×Dic3—68no—
792C2×Dic3—616no—
793C2×Dic3—64no—
794C2×Dic3—62no—
795C2×Dic3—62no—
796C2×Dic3C23×D312yes—
797C2×Dic3C23×D312yes—
798C2×Dic3C23×D312yes—
799C2×Dic3C23×D312yes—
800C2×Dic3C23×D312yes—
801C2×Dic3C23×D312yes—
802C2×Dic3C23×D312yes—
803D12—68no—
804D12—124no—
805C4×D3—68no—
806C4×D3—68no—
807C4×D3—68no—
808C4×D3—124no—
809C4×D3—124no—
810Dic6—68no—
811Dic6—68no—
812C2×C32—24no—
813C2×C32—24no—
814C2×C32—42no—
815C2×C32#54614yescomplemented
816C2×C32C23×D411yescharacteristic
817C2×C32C22×#4111yescharacteristic
818C2×C32C2×H(5,𝔽2)11yescharacteristic
819C3⋊D3—24no—
820C3⋊D3—42no—
821C3×D3—42no—
822C24—24no—
823C24—24no—
824C24—31no—
825C24—42no—
826C24—91no—
827C24—91no—
828C24—94no—
829C24—184no—
830C24—184no—
831C24—362no—
832C24C2×D3211yescharacteristic
833C24C2×D3214yes—
834C24C2×D3211yescharacteristic
835C24C2×D3211yescharacteristic
836#41—1832no—
837C2×Q8—94no—
838C2×Q8—184no—
839C2×D4—34no—
840C2×D4—34no—
841C2×D4—34no—
842C2×D4—64no—
843C2×D4—64no—
844C2×D4—94no—
845C2×D4—94no—
846C2×D4—94no—
847C2×D4—98no—
848C2×D4—94no—
849C2×D4—94no—
850C2×D4—94no—
851C2×D4—122no—
852C2×D4—184no—
853C2×D4—184no—
854C2×D4—1832no—
855C2×D4—184no—
856C2×D4—184no—
857C2×D4—362no—
858C22×C4—34no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—31no—
862C22×C4—31no—
863C22×C4—31no—
864C22×C4—31no—
865C22×C4—31no—
866C22×C4—34no—
867C22×C4—64no—
868C22×C4—94no—
869C22×C4—94no—
870C22×C4—94no—
871C22×C4—91no—
872C22×C4—94no—
873C22×C4—91no—
874C22×C4—122no—
875C22×C4—184no—
876C22×C4—184no—
877C22×C4—184no—
878C22×C4—362no—
879C4⋊C4—94no—
880C4⋊C4—94no—
881C4⋊C4—94no—
882C4⋊C4—94no—
883C22⋊C4—34no—
884C22⋊C4—34no—
885C22⋊C4—34no—
886C22⋊C4—34no—
887C22⋊C4—34no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—94no—
891C22⋊C4—94no—
892C22⋊C4—94no—
893C22⋊C4—94no—
894C22⋊C4—94no—
895C42—94no—
896C22×C3—24no—
897C22×C3—24no—
898C22×C3—216no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—28no—
908C22×C3—28no—
909C22×C3—28no—
910C22×C3—28no—
911C22×C3—24no—
912C22×C3—22no—
913C22×C3—22no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—22no—
917C22×C3—22no—
918C22×C3—22no—
919C22×C3—24no—
920C22×C3—22no—
921C22×C3—24no—
922C22×C3—22no—
923C22×C3—21no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—48no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—416no—
930C22×C3—416no—
931C22×C3—432no—
932C22×C3—48no—
933C22×C3—44no—
934C22×C3—44no—
935C22×C3—62no—
936C22×C3—62no—
937C22×C3—62no—
938C22×C3—124no—
939C22×C3C2×#23512yes—
940C22×C3C2×#23514yescomplemented
941C22×C3C2×D3×D414yes—
942C22×C3C2×D3×D414yes—
943C22×C3C2×D3×D412yes—
944C22×C3C2×D3×D412yes—
945C22×C3C2×#23712yes—
946C22×C3C2×#23714yescomplemented
947C22×C3#100412yes—
948C22×C3#100412yes—
949C22×C3C24×D311yescharacteristic
950C22×C3C24×D311yescharacteristic
951C2×D3—22no—
952C2×D3—22no—
953C2×D3—22no—
954C2×D3—34no—
955C2×D3—34no—
956C2×D3—44no—
957C2×D3—64no—
958C2×D3—62no—
959C2×D3—62no—
960C2×D3—62no—
961C2×D3—62no—
962C2×D3—68no—
963C2×D3—68no—
964C2×D3—64no—
965C2×D3—62no—
966C2×D3—62no—
967C2×D3—62no—
968C2×D3—62no—
969C2×D3—62no—
970C2×D3—62no—
971C2×D3—122no—
972C2×D3—122no—
973C2×D3—128no—
974C2×D3—122no—
975C2×D3—122no—
976C2×D3—1216no—
977C2×D3—1216no—
978C2×D3—1232no—
979C2×D3—128no—
980C2×D3—124no—
981C2×D3—124no—
982C3×C4—62no—
983C3×C4—62no—
984C3×C4—62no—
985C3×C4—62no—
986C3×C4—62no—
987C3×C4—62no—
988C3×C4—62no—
989Dic3—22no—
990Dic3—22no—
991Dic3—22no—
992Dic3—22no—
993Dic3—22no—
994Dic3—22no—
995Dic3—22no—
996Dic3—34no—
997Dic3—34no—
998Dic3—64no—
999Dic3—64no—
1000Dic3—62no—
1001Dic3—62no—
1002C32C2×#54611yescharacteristic, complemented, Sylow
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—28no—
1009C23—28no—
1010C23—22no—
1011C23—22no—
1012C23—32no—
1013C23—44no—
1014C23—416no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—94no—
1019C23—92no—
1020C23—92no—
1021C23—188no—
1022C23—182no—
1023C23—182no—
1024C23—182no—
1025C23—188no—
1026C23—182no—
1027C23—182no—
1028C23—364no—
1029C23—3616no—
1030C23#380414yescomplemented
1031C23#381114yes—
1032C23C22×D3212yes—
1033C23C22×D3212yes—
1034C23C22×D3212yes—
1035C23C22×D3211yescharacteristic
1036Q8—188no—
1037D4—68no—
1038D4—68no—
1039D4—916no—
1040D4—124no—
1041D4—188no—
1042D4—188no—
1043D4—188no—
1044D4—188no—
1045D4—364no—
1046C2×C4—32no—
1047C2×C4—32no—
1048C2×C4—32no—
1049C2×C4—32no—
1050C2×C4—32no—
1051C2×C4—32no—
1052C2×C4—32no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—68no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—94no—
1062C2×C4—92no—
1063C2×C4—92no—
1064C2×C4—124no—
1065C2×C4—188no—
1066C2×C4—188no—
1067C2×C4—188no—
1068C2×C4—182no—
1069C2×C4—364no—
1070C2×C3—28no—
1071C2×C3—24no—
1072C2×C3—24no—
1073C2×C3—24no—
1074C2×C3—24no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—24no—
1079C2×C3—44no—
1080C2×C3—44no—
1081C2×C3—42no—
1082C2×C3—42no—
1083C2×C3—122no—
1084C2×C3#549014yescomplemented
1085C2×C3#559114yescomplemented
1086C2×C3C22×#23511yescharacteristic
1087C2×C3C22×D3×D411yescharacteristic
1088C2×C3C22×D3×D411yescharacteristic
1089C2×C3C22×#23711yescharacteristic
1090C2×C3C2×#100411yescharacteristic
1091C2×C3C2×#100411yescharacteristic
1092D3—42no—
1093D3—64no—
1094D3—64no—
1095D3—124no—
1096D3—124no—
1097D3—122no—
1098D3—122no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—28no—
1104C22—28no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—416no—
1109C22—44no—
1110C22—62no—
1111C22—62no—
1112C22—62no—
1113C22—94no—
1114C22—124no—
1115C22—182no—
1116C22—182no—
1117C22—188no—
1118C22—182no—
1119C22—182no—
1120C22—182no—
1121C22—3616no—
1122C22—364no—
1123C22C2×#380412yes—
1124C22C2×#380414yescomplemented
1125C22C2×#381114yes—
1126C22C2×#381112yes—
1127C22#6433012yes—
1128C22C23×D3211yescharacteristic
1129C4—62no—
1130C4—62no—
1131C4—62no—
1132C4—62no—
1133C4—62no—
1134C4—62no—
1135C4—62no—
1136C4—94no—
1137C4—182no—
1138C3—21no—
1139C3C2×#549011yescharacteristic, complemented
1140C3C2×#559111yescharacteristic, complemented
1141C2—24no—
1142C2—24no—
1143C2—42no—
1144C2—122no—
1145C2—184no—
1146C2—362no—
1147C2#1059550014yesdirect product factor
1148C2C22×#380411yescharacteristic
1149C2C22×#381111yescharacteristic
1150C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×#638C2semidirect
2. C22×#3804C2semidirect
3. C2×C3×#953C2semidirect
4. C22×C3×#217C2semidirect
5. C2×#63982C2semidirect
6. C2×#63981C2semidirect
7. C2×#63978C2semidirect
8. C2×#63975C2semidirect
9. C2×#63974C2semidirect
10. #10595500C2direct (N × H)
11. C2×#67⋊Dic3C2semidirect
12. C2×#63971C2semidirect
13. C2×#63966C2semidirect
14. C2×#63958C2semidirect
15. C2×#63953C2semidirect
16. C2×#63952C2semidirect
26. C22×#638C22semidirect
29. C22×C3×#67C22semidirect
30. C22×C3×#67C22semidirect
31. C23×C3×Dic3C22semidirect
32. C23×C3×Dic3C22semidirect
33. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#624C22semidirect
37. C22×#624C22semidirect
39. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. C3×#953C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×#217C22semidirect
48. C2×C3×#217C22semidirect
49. C2×C3×#217C22semidirect
50. #63982C22semidirect
51. #63981C22semidirect
52. #63978C22semidirect
53. #63975C22semidirect
54. #63974C22semidirect
55. #67⋊Dic3C22semidirect
56. #63971C22semidirect
57. C2×#3724C22semidirect
58. #63966C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
62. C2×#3722C22semidirect
63. C2×#3722C22semidirect
64. C2×#3722C22semidirect
65. C2×#3722C22semidirect
66. C2×(C2×D3)⋊Dic3C22semidirect
67. #63958C22semidirect
68. C2×Dic32C22semidirect
69. #63953C22semidirect
70. #63952C22semidirect
78. C2×#953D3semidirect
79. C22×#217D3semidirect
122. C2×#638D4semidirect
135. C2×C3×#67C23semidirect
136. C2×C3×#67C23semidirect
146. C22×C3×Dic3C23semidirect
147. C22×C3×Dic3C23semidirect
149. C2×#627C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
156. C2×#624C23semidirect
157. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
164. C3×#217C23semidirect
165. C3×#217C23semidirect
166. C3×#217C23semidirect
167. C3×#217C23semidirect
168. #3724C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
173. #3722C23semidirect
174. #3722C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
211. C22×#67C2×D3semidirect
212. C22×#67C2×D3semidirect
217. C23×Dic3C2×D3semidirect
218. C23×Dic3C2×D3semidirect
241. #953C2×D3semidirect
246. C2×#217C2×D3semidirect
247. C2×#217C2×D3semidirect
248. C2×#217C2×D3semidirect
249. C2×#217C2×D3semidirect
250. C2×#217C2×D3semidirect
304. C23×C32#41semidirect
328. #638C2×D4semidirect
468. C2×#67C22×D3semidirect
469. C2×#67C22×D3semidirect
493. C22×Dic3C22×D3semidirect
494. C22×Dic3C22×D3semidirect
526. #217C22×D3semidirect
527. #217C22×D3semidirect
528. #217C22×D3semidirect
529. #217C22×D3semidirect
563. C22×C32C2×#41semidirect
683. C23×C3#235semidirect
686. C23×C3#237semidirect
815. C2×C32#546semidirect
940. C22×C3C2×#235semidirect
946. C22×C3C2×#237semidirect
1002. C32C2×#546semidirect
1030. C23#3804semidirect
1084. C2×C3#5490semidirect
1085. C2×C3#5591semidirect
1124. C22C2×#3804semidirect
1139. C3C2×#5490semidirect
1140. C3C2×#5591semidirect
1147. C2#10595500direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6382
C22×#38042
C2×C3×#9532
C22×C3×#2172
C2×#639822
C2×#639812
C2×#639782
C2×#639752
C2×#639742
#105955002
C2×#67⋊Dic32
C2×#639712
C2×#639662
C2×#639582
C2×#639532
C2×#639522
C2×#55913
C2×#54903