Finite Group Databasebeta

← C2×#10595294 #11902448

Subgroups — C2×#10595294 #11902448

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64147C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×C3×#937C211yesmaximal, characteristic, complemented
6C2×#63983C211yesmaximal, characteristic, complemented
7C2×#63975C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×D3×#217C211yesmaximal, characteristic, complemented
11C2×#63959C211yesmaximal, characteristic, complemented
12#10595294C2116yesmaximal, direct product factor
13C2×#63921C211yesmaximal, characteristic, complemented
14C2×#63893C211yesmaximal, characteristic, complemented
15C2×#63891C211yesmaximal, characteristic, complemented
16C2×#63881C211yesmaximal, characteristic, complemented
17C2×#5612—31nomaximal
18C2×#5591—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×#67C2211yescharacteristic, complemented
29C23×C3×Dic3C2211yescharacteristic, complemented
30C2×D3×#67—28no—
31C2×D3×#67C2218yescomplemented
32C22×#627C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic
34C22×#625C2211yescharacteristic
35C22×#624C2211yescharacteristic, complemented
36C2×#3804—28no—
37C2×#3804C2218yescomplemented
38C22×D3×Dic3C2211yescharacteristic
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43#64147C2218yescomplemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#939C2218yescomplemented
48C3×#937C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53#63983C2218yescomplemented
54#63975C2218yescomplemented
55Dic3×#67C2218yescomplemented
56#63970C2218yescomplemented
57D3×#217C2218yescomplemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65#63959C2218yescomplemented
66C2×Dic32C2211yescharacteristic, complemented
67#63921C2218yescomplemented
68#63893C2218yescomplemented
69#63891C2218yescomplemented
70#63881C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C2×C3×#120—31no—
77C22×#217—31no—
78C2×#939—31no—
79C2×#939D311yescharacteristic, complemented
80C2×#938—31no—
81C2×#938—31no—
82C2×#938—31no—
83C2×#938—61no—
84C2×#937—31no—
85C2×#937—31no—
86C2×#937D311yescharacteristic, complemented
87C2×#936—31no—
88C2×D4×Dic3—31no—
89C2×C4×#67—31no—
90#5612—316no—
91#5591—316no—
92C2×#897—31no—
93C2×#893—31no—
94C2×#886—31no—
95C2×#885—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#883—31no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—42no—
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C2×C32×D4—42no—
119C2×C32×D4C2314yescomplemented
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638—24no—
123C2×#638C2314yes—
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128C2×C4×C3⋊D3—42no—
129C2×C4×C3⋊D3C2314yescomplemented
130C2×C3×#67—24no—
131C2×C3×#67—24no—
132C2×C3×#67—24no—
133C2×C3×#67—42no—
134C2×C3×#67C2314yes—
135C2×C3×#67C2314yes—
136C2×C3×#67C2314yescomplemented
137C2×C3×#67C2314yescomplemented
138C22×C3×Dic3—24no—
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2314yescomplemented
145D3×#67—232no—
146C2×#627—24no—
147C2×#627C2314yescomplemented
148C2×#626D418yescomplemented
149C2×#626C2314yes—
150C2×#625—24no—
151C2×#625C2314yes—
152C2×#624—24no—
153C2×#624C2314yescomplemented
154#3804—232no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3—24no—
157C2×D3×Dic3—42no—
158C2×D3×Dic3C2314yes—
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3757C2314yescomplemented
163C4⋊(C3⋊Dic3)C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—21no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4C2×D311yescharacteristic, complemented
189C22×C3×D4C2×D311yescharacteristic, complemented
190C23×C3×C4—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—38no—
198C22×#67—31no—
199C22×#67—61no—
200C22×#67—61no—
201C22×#67—68no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic, complemented
205C22×#67C2×D311yescharacteristic, complemented
206C23×Dic3—31no—
207C23×Dic3—31no—
208C23×Dic3—31no—
209C23×Dic3C2×D311yescharacteristic, complemented
210C2×#237—38no—
211C2×#237—68no—
212C2×D3×D4—38no—
213C2×D3×D4—68no—
214C2×#235—38no—
215C2×#235—68no—
216C22×D12—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—61no—
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#121—38no—
228C3×#120—38no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×#217—31no—
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×#217—61no—
246C2×#217C2×D311yescharacteristic, complemented
247C2×#217C2×D311yescharacteristic, complemented
248#939—38no—
249#939C2×D318yescomplemented
250#938—38no—
251#938—38no—
252#938—38no—
253#938—68no—
254#937—38no—
255#937—38no—
256#937C2×D318yescomplemented
257#936—38no—
258D4×Dic3—38no—
259C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
267C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
268C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
269C2×C4⋊Dic3—31no—
270C2×C4⋊Dic3—31no—
271C2×C4⋊Dic3—31no—
272C2×C4⋊Dic3—31no—
273C2×C4⋊Dic3—61no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4C2×D311yescharacteristic, complemented
277C2×C4×Dic3—31no—
278C2×C4×Dic3—31no—
279#897—38no—
280#893—38no—
281#886—38no—
282#885—38no—
283#883—38no—
284#883—38no—
285#883—38no—
286#67⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4—38no—
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3C2×D414yes—
303C22×C3⋊D3C2412yes—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
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—416no—
315C22×C3×D3C2×D414yes—
316C22×C3×D3#4114yescomplemented
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C32×D4—44no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327#638—28no—
328#638—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C4×C3⋊D3—44no—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—28no—
339C3×#67—44no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—28no—
345C2×C3×Dic3C2×D414yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351#627—28no—
352#626C2×D4116yescomplemented
353#625—28no—
354#624—28no—
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—31no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—34no—
380C24×C3—64no—
381C24×C3—64no—
382C24×C3—122no—
383C24×C3C22×D311yescharacteristic
384C24×C3C22×D311yescharacteristic
385C24×C3C22×D311yescharacteristic
386C24×C3C22×D311yescharacteristic
387C23×D3—24no—
388C23×D3—24no—
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—34no—
392C23×D3—34no—
393C23×D3—42no—
394C23×D3—61no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—122no—
400C23×D3—122no—
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D314yes—
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×D4—24no—
406C2×C3×D4—34no—
407C2×C3×D4—34no—
408C2×C3×D4—34no—
409C2×C3×D4—34no—
410C2×C3×D4—42no—
411C2×C3×D4—42no—
412C2×C3×D4—44no—
413C2×C3×D4—64no—
414C2×C3×D4—64no—
415C2×C3×D4—64no—
416C2×C3×D4—122no—
417C2×C3×D4C22×D314yescomplemented
418C2×C3×D4C22×D314yescomplemented
419C22×C3×C4—21no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—34no—
426C22×C3×C4—64no—
427C22×C3×C4C22×D311yescharacteristic
428C22×C3×C4C22×D311yescharacteristic
429C2×#67—24no—
430C2×#67—24no—
431C2×#67—24no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—38no—
439C2×#67—34no—
440C2×#67—42no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—632no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—124no—
451C2×#67—124no—
452C2×#67C22×D314yes—
453C2×#67C22×D314yes—
454C2×#67C22×D314yescomplemented
455C2×#67C22×D314yescomplemented
456C22×Dic3—24no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—34no—
464C22×Dic3—34no—
465C22×Dic3—34no—
466C22×Dic3—61no—
467C22×Dic3—61no—
468C22×Dic3—61no—
469C22×Dic3—64no—
470C22×Dic3—64no—
471C22×Dic3—122no—
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D314yescomplemented
478#237—632no—
479D3×D4—632no—
480#235—632no—
481C2×D12—38no—
482C2×D12—34no—
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—64no—
495C2×C4×D3—122no—
496C2×C4×D3—122no—
497C2×C4×D3—122no—
498C2×C4×D3—124no—
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—34no—
517#217—64no—
518#217—64no—
519#217C22×D314yescomplemented
520#217C22×D314yescomplemented
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4C22×D314yes—
528(C2×D3)⋊C4C22×D314yescomplemented
529(C2×D3)⋊C4C22×D314yescomplemented
530C4⋊Dic3—34no—
531C4⋊Dic3—34no—
532C4⋊Dic3—34no—
533C4⋊Dic3—34no—
534C4⋊Dic3—64no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4C22×D314yescomplemented
538C4×Dic3—34no—
539C4×Dic3—34no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—44no—
547C22×C32—44no—
548C22×C32C22×D412yes—
549C22×C32C2×#4112yes—
550C22×C32H(5,𝔽2)12yes—
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—28no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3C22×D414yes—
556C2×C3×D3—28no—
557C2×C3×D3—28no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—416no—
566C2×C3×D3—44no—
567C2×C3×D3C22×D414yes—
568C2×C3×D3C2×#4114yescomplemented
569D32—416no—
570C32×C4—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3C22×D414yes—
579C25—31no—
580C25—91no—
581C2×#41—98no—
582C2×#41—188no—
583C22×Q8—91no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—91no—
589C22×D4—98no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—188no—
594C22×D4D3211yescharacteristic, complemented
595C23×C4—31no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#124—98no—
602#123—98no—
603#123—98no—
604C22⋊Q8—98no—
605#121—38no—
606#121—98no—
607#121—98no—
608#120—38no—
609#120—98no—
610C4×D4—98no—
611C4×D4—98no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—91no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—98no—
622C2×C22⋊C4—98no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C42—91no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—21no—
646C23×C3—34no—
647C23×C3—34no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3—32no—
651C23×C3—42no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—42no—
655C23×C3—42no—
656C23×C3—42no—
657C23×C3—68no—
658C23×C3—68no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—62no—
663C23×C3—62no—
664C23×C3—62no—
665C23×C3—62no—
666C23×C3—124no—
667C23×C3—1216no—
668C23×C3C23×D312yes—
669C23×C3C23×D312yes—
670C23×C3C23×D312yes—
671C23×C3C23×D312yes—
672C23×C3C23×D311yescharacteristic
673C23×C3C23×D311yescharacteristic
674C22×D3—22no—
675C22×D3—22no—
676C22×D3—22no—
677C22×D3—22no—
678C22×D3—22no—
679C22×D3—22no—
680C22×D3—22no—
681C22×D3—28no—
682C22×D3—28no—
683C22×D3—34no—
684C22×D3—34no—
685C22×D3—32no—
686C22×D3—32no—
687C22×D3—44no—
688C22×D3—416no—
689C22×D3—64no—
690C22×D3—62no—
691C22×D3—68no—
692C22×D3—68no—
693C22×D3—68no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3—68no—
699C22×D3—122no—
700C22×D3—122no—
701C22×D3—124no—
702C22×D3—124no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3D3×D414yes—
706C22×D3#23714yescomplemented
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×D4—44no—
711C3×D4—44no—
712C3×D4—48no—
713C3×D4—68no—
714C3×D4—68no—
715C3×D4—68no—
716C3×D4—124no—
717C2×C3×C4—24no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—34no—
722C2×C3×C4—32no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—32no—
726C2×C3×C4—32no—
727C2×C3×C4—68no—
728C2×C3×C4—62no—
729C2×C3×C4—62no—
730C2×C3×C4—62no—
731C2×C3×C4—62no—
732C2×C3×C4C23×D312yes—
733C2×C3×C4C23×D312yes—
734#67—28no—
735#67—28no—
736#67—28no—
737#67—316no—
738#67—44no—
739#67—68no—
740#67—68no—
741#67—68no—
742#67—68no—
743#67—68no—
744#67—68no—
745#67—128no—
746#67—128no—
747C2×Dic3—22no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—28no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—32no—
755C2×Dic3—32no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—68no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—68no—
769C2×Dic3—122no—
770C2×Dic3—122no—
771C2×Dic3—122no—
772C2×Dic3—124no—
773C2×Dic3D3×D414yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776C2×Dic3C23×D312yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779D12—316no—
780C4×D3—68no—
781C4×D3—68no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—124no—
785C4×D3—124no—
786C4×D3—124no—
787C4×D3—128no—
788Dic6—68no—
789Dic6—68no—
790C2×C32—42no—
791C2×C32—42no—
792C2×C32#54614yescomplemented
793C2×C32C23×D411yescharacteristic
794C2×C32C22×#4111yescharacteristic
795C2×C32C2×H(5,𝔽2)11yescharacteristic
796C3⋊D3—24no—
797C3×D3—24no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—31no—
803C24—34no—
804C24—64no—
805C24—64no—
806C24—94no—
807C24—91no—
808C24—122no—
809C24—184no—
810C24—184no—
811C24—362no—
812C24C2×D3211yescharacteristic
813C24C2×D3211yescharacteristic
814#41—1832no—
815C2×Q8—94no—
816C2×Q8—184no—
817C2×D4—34no—
818C2×D4—34no—
819C2×D4—34no—
820C2×D4—34no—
821C2×D4—42no—
822C2×D4—64no—
823C2×D4—64no—
824C2×D4—64no—
825C2×D4—94no—
826C2×D4—98no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—122no—
831C2×D4—1832no—
832C2×D4—184no—
833C2×D4—184no—
834C2×D4—184no—
835C2×D4C2×D3214yescomplemented
836C22×C4—31no—
837C22×C4—34no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—64no—
843C22×C4—94no—
844C22×C4—94no—
845C22×C4—94no—
846C22×C4—94no—
847C22×C4—91no—
848C22×C4—91no—
849C22×C4—91no—
850C22×C4—94no—
851C22×C4—184no—
852C22×C4—184no—
853C22×C4—184no—
854C22×C4—362no—
855C22×C4—362no—
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—34no—
858C4⋊C4—94no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C42—94no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—21no—
890C22×C3—34no—
891C22×C3—34no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—44no—
899C22×C3—44no—
900C22×C3—44no—
901C22×C3—44no—
902C22×C3—62no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—62no—
906C22×C3—68no—
907C22×C3—68no—
908C22×C3—62no—
909C22×C3—62no—
910C22×C3—62no—
911C22×C3—84no—
912C22×C3—84no—
913C22×C3—1216no—
914C22×C3—124no—
915C22×C3C2×D3×D412yes—
916C22×C3C2×D3×D412yes—
917C22×C3C2×#23712yes—
918C22×C3#100412yes—
919C22×C3#100412yes—
920C22×C3D3×#4112yes—
921C22×C3C24×D311yescharacteristic
922C22×C3C24×D311yescharacteristic
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—28no—
928C2×D3—28no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—34no—
933C2×D3—34no—
934C2×D3—416no—
935C2×D3—44no—
936C2×D3—64no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—68no—
942C2×D3—68no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—128no—
946C2×D3—1216no—
947C2×D3—1216no—
948C2×D3C2×D3×D414yes—
949C2×D3C2×#23714yescomplemented
950C3×C4—24no—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—34no—
954C3×C4—62no—
955C3×C4—62no—
956C3×C4—62no—
957C3×C4—62no—
958Dic3—22no—
959Dic3—22no—
960Dic3—22no—
961Dic3—22no—
962Dic3—62no—
963Dic3—62no—
964Dic3—62no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—122no—
969Dic3—122no—
970Dic3—122no—
971Dic3C2×D3×D414yes—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—34no—
980C23—34no—
981C23—32no—
982C23—32no—
983C23—32no—
984C23—68no—
985C23—68no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—94no—
994C23—92no—
995C23—124no—
996C23—1216no—
997C23—188no—
998C23—188no—
999C23—182no—
1000C23—182no—
1001C23—364no—
1002C23—3616no—
1003C23C22×D3212yes—
1004C23C22×D3212yes—
1005C23C22×D3211yescharacteristic
1006Q8—188no—
1007D4—44no—
1008D4—68no—
1009D4—68no—
1010D4—68no—
1011D4—916no—
1012D4—124no—
1013D4—188no—
1014D4—188no—
1015D4—188no—
1016C2×C4—22no—
1017C2×C4—34no—
1018C2×C4—32no—
1019C2×C4—32no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—68no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—92no—
1029C2×C4—92no—
1030C2×C4—92no—
1031C2×C4—188no—
1032C2×C4—188no—
1033C2×C4—188no—
1034C2×C4—182no—
1035C2×C4—182no—
1036C2×C4—182no—
1037C2×C4—364no—
1038C2×C4—364no—
1039C2×C4C22×D3212yes—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—24no—
1044C2×C3—42no—
1045C2×C3—42no—
1046C2×C3—42no—
1047C2×C3—42no—
1048C2×C3—64no—
1049C2×C3—64no—
1050C2×C3—82no—
1051C2×C3—82no—
1052C2×C3—122no—
1053C2×C3#559114yescomplemented
1054C2×C3#561214yescomplemented
1055C2×C3C22×D3×D411yescharacteristic
1056C2×C3C22×D3×D411yescharacteristic
1057C2×C3C22×#23711yescharacteristic
1058C2×C3C2×#100411yescharacteristic
1059C2×C3C2×#100411yescharacteristic
1060C2×C3C2×D3×#4111yescharacteristic
1061D3—24no—
1062D3—24no—
1063D3—42no—
1064D3—64no—
1065D3—64no—
1066D3—124no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—34no—
1074C22—34no—
1075C22—44no—
1076C22—44no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—68no—
1082C22—68no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—94no—
1087C22—1216no—
1088C22—124no—
1089C22—182no—
1090C22—182no—
1091C22—188no—
1092C22—3616no—
1093C22D32×D412yes—
1094C22D3×#23712yes—
1095C22#6433012yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—34no—
1099C4—62no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—182no—
1104C4—182no—
1105C4—182no—
1106C3—21no—
1107C3C2×#559111yescharacteristic, complemented
1108C3C2×#561211yescharacteristic, complemented
1109C2—42no—
1110C2—42no—
1111C2—64no—
1112C2—64no—
1113C2—122no—
1114C2—184no—
1115C2#1059529414yesdirect product factor
1116C2C2×D32×D411yescharacteristic
1117C2C2×D3×#23711yescharacteristic
1118C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C22×#3804C2semidirect
3. C2×#64147C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#937C2semidirect
6. C2×#63983C2semidirect
7. C2×#63975C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63970C2semidirect
10. C2×D3×#217C2semidirect
11. C2×#63959C2semidirect
12. #10595294C2direct (N × H)
13. C2×#63921C2semidirect
14. C2×#63893C2semidirect
15. C2×#63891C2semidirect
16. C2×#63881C2semidirect
21. C22×C32×D4C22semidirect
23. C22×#638C22semidirect
24. C22×C4×C3⋊D3C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×#67C22semidirect
29. C23×C3×Dic3C22semidirect
31. C2×D3×#67C22semidirect
32. C22×#627C22semidirect
35. C22×#624C22semidirect
37. C2×#3804C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. C2×#3757C22semidirect
43. #64147C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#939C22semidirect
48. C3×#937C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. #63983C22semidirect
54. #63975C22semidirect
55. Dic3×#67C22semidirect
56. #63970C22semidirect
57. D3×#217C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×#3722C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. #63959C22semidirect
66. C2×Dic32C22semidirect
67. #63921C22semidirect
68. #63893C22semidirect
69. #63891C22semidirect
70. #63881C22semidirect
79. C2×#939D3semidirect
86. C2×#937D3semidirect
119. C2×C32×D4C23semidirect
124. C2×#638C23semidirect
129. C2×C4×C3⋊D3C23semidirect
136. C2×C3×#67C23semidirect
137. C2×C3×#67C23semidirect
144. C22×C3×Dic3C23semidirect
147. C2×#627C23semidirect
148. C2×#626D4semidirect
153. C2×#624C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
162. #3757C23semidirect
163. C4⋊(C3⋊Dic3)C23semidirect
164. C3×#217C23semidirect
165. C3×#217C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. Dic3⋊Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
188. C22×C3×D4C2×D3semidirect
189. C22×C3×D4C2×D3semidirect
204. C22×#67C2×D3semidirect
205. C22×#67C2×D3semidirect
209. C23×Dic3C2×D3semidirect
246. C2×#217C2×D3semidirect
247. C2×#217C2×D3semidirect
249. #939C2×D3semidirect
256. #937C2×D3semidirect
267. C2×(C2×D3)⋊C4C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
276. C2×Dic3⋊C4C2×D3semidirect
316. C22×C3×D3#41semidirect
352. #626C2×D4semidirect
417. C2×C3×D4C22×D3semidirect
418. C2×C3×D4C22×D3semidirect
454. C2×#67C22×D3semidirect
455. C2×#67C22×D3semidirect
477. C22×Dic3C22×D3semidirect
519. #217C22×D3semidirect
520. #217C22×D3semidirect
528. (C2×D3)⋊C4C22×D3semidirect
529. (C2×D3)⋊C4C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
568. C2×C3×D3C2×#41semidirect
594. C22×D4D32semidirect
706. C22×D3#237semidirect
792. C2×C32#546semidirect
835. C2×D4C2×D32semidirect
949. C2×D3C2×#237semidirect
972. C32C2×#546semidirect
1053. C2×C3#5591semidirect
1054. C2×C3#5612semidirect
1107. C3C2×#5591semidirect
1108. C3C2×#5612semidirect
1115. C2#10595294direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C22×#38042
C2×#641472
C2×C3×#9392
C2×C3×#9372
C2×#639832
C2×#639752
C2×Dic3×#672
C2×#639702
C2×D3×#2172
C2×#639592
#105952942
C2×#639212
C2×#638932
C2×#638912
C2×#638812
C2×#56123
C2×#55913