Finite Group Databasebeta

← C2×#10595118 #11902920

Subgroups — C2×#10595118 #11902920

Order 1152.

2987 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63975C211yesmaximal, characteristic, complemented
5C2×#63974C211yesmaximal, characteristic, complemented
6C2×#63966C211yesmaximal, characteristic, complemented
7C2×#63964C211yesmaximal, characteristic, complemented
8C22×#3722C211yesmaximal, characteristic, complemented
9C2×#63955C211yesmaximal, characteristic, complemented
10C2×#63953C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595118C2116yesmaximal, direct product factor
13C2×#63895C211yesmaximal, characteristic, complemented
14C2×#63868C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16C2×#63836C211yesmaximal, characteristic, complemented
17C2×#5658—31nomaximal
18C2×#5556—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×#624C2211yescharacteristic
28C22×#624C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30#64146C2218yes—
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic, complemented
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic, complemented
38C3×#935C2218yescomplemented
39C3×D4×Dic3C2218yescomplemented
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×C4×Dic3C2211yescharacteristic, complemented
44#63975C2218yescomplemented
45#63974C2218yescomplemented
46C2×#3724C2211yescharacteristic, complemented
47#63966C2218yescomplemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52#63964C2218yescomplemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×#3722C2218yescomplemented
60#63955C2218yescomplemented
61C2×Dic32C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63953C2218yescomplemented
64#63952C2218yescomplemented
65#63895C2218yescomplemented
66#63868C2218yescomplemented
67#63848C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#937—31no—
72C2×#937—31no—
73C2×#937—61no—
74C2×#935D311yescharacteristic, complemented
75C2×D4×Dic3D311yescharacteristic, complemented
76C2×#929—31no—
77C2×C4×#67—31no—
78C22×(C2×D3)⋊C4—31no—
79C22×(C2×D3)⋊C4—31no—
80C2×#926—31no—
81C2×#924—31no—
82#5658—316no—
83#5556—316no—
84C2×#898—31no—
85C2×#898—31no—
86C2×#898—31no—
87C2×#897—31no—
88C2×#896—31no—
89C2×#892—31no—
90C2×#886—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#67⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#876—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3—24no—
105C23×C3⋊D3—24no—
106C23×C3⋊D3—42no—
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2314yes—
109C23×C3⋊D3C2311yescharacteristic
110C2×C32×D4—24no—
111C2×C32×D4C2314yes—
112C22×C32×C4C2311yescharacteristic
113C2×#638—24no—
114C2×#638—42no—
115C2×#638C2314yes—
116C2×#638C2314yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3×Dic3—24no—
120C22×C3×Dic3—42no—
121C22×C3×Dic3—42no—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2314yes—
131C22×C3×Dic3C2314yes—
132C22×C3×Dic3C2314yescomplemented
133C2×#627—42no—
134C2×#627C2314yescomplemented
135C2×#624—24no—
136C2×#624—42no—
137C2×#624C2314yes—
138C2×#624C2314yes—
139#3757C2314yes—
140#3752C2314yes—
141#3752C2314yes—
142C3×#217C2314yes—
143C3×#217C2314yes—
144C3×#217C2314yescomplemented
145C3×#217C2314yescomplemented
146C3×#217C2314yescomplemented
147C3×C4⋊Dic3C2314yescomplemented
148C3×Dic3⋊C4C2314yescomplemented
149C3×Dic3⋊C4C2314yescomplemented
150C3×C4×Dic3C2314yescomplemented
151#3724C2314yescomplemented
152Dic3⋊Dic3C2314yescomplemented
153Dic3⋊Dic3C2314yescomplemented
154Dic3⋊Dic3C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162Dic32C2314yescomplemented
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C24×D3—31no—
166C24×D3—31no—
167C24×D3—61no—
168C22×C3×D4—21no—
169C22×C3×D4C2×D311yescharacteristic
170C22×C3×D4C2×D311yescharacteristic
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—61no—
179C22×#67—61no—
180C23×Dic3C2×D311yescharacteristic
181C23×Dic3C2×D311yescharacteristic
182C23×Dic3C2×D311yescharacteristic, complemented
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×Dic6—31no—
188C22×Dic6—31no—
189C3×#123—38no—
190C3×C4×D4—38no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C42—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—61no—
203C2×#217C2×D311yescharacteristic
204C2×#217C2×D311yescharacteristic
205C2×#217C2×D311yescharacteristic, complemented
206C2×#217C2×D311yescharacteristic, complemented
207C2×#217C2×D311yescharacteristic, complemented
208#937—38no—
209#937—38no—
210#937—68no—
211#935C2×D318yescomplemented
212D4×Dic3C2×D318yescomplemented
213#929—38no—
214C4×#67—38no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—38no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—38no—
233C2×(C2×D3)⋊C4—61no—
234C2×(C2×D3)⋊C4—61no—
235#926—38no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3C2×D311yescharacteristic, complemented
241#924—38no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249C2×Dic3⋊C4C2×D311yescharacteristic, complemented
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3C2×D311yescharacteristic, complemented
255#898—38no—
256#898—38no—
257#898—38no—
258#897—38no—
259#896—38no—
260#892—38no—
261#886—38no—
262#885—38no—
263#885—38no—
264#883—38no—
265#883—38no—
266#67⋊C4—38no—
267D3×C22⋊C4—38no—
268D3×C22⋊C4—38no—
269#878—38no—
270#877—38no—
271#876—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32#4114yes—
279C23×C32C2412yes—
280C23×C32C2412yes—
281C23×C32C2411yescharacteristic
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—28no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—28no—
289C22×C3⋊D3—44no—
290C22×C3⋊D3—416no—
291C22×C3⋊D3#4114yes—
292C22×C3⋊D3C2412yes—
293C22×C3⋊D3C2412yes—
294C32×D4—28no—
295C2×C32×C4—22no—
296C2×C32×C4C2412yes—
297#638—28no—
298#638—44no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—28no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—44no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322#627—44no—
323#624—28no—
324#624—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—31no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—91no—
335C2×C4×D4—31no—
336C2×C4×D4—91no—
337C2×#117—91no—
338C2×#117—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—21no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C24×C3C22×D311yescharacteristic
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—31no—
350C23×D3—31no—
351C23×D3—34no—
352C23×D3—34no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—64no—
356C23×D3—64no—
357C23×D3—64no—
358C23×D3—64no—
359C23×D3—64no—
360C23×D3—124no—
361C23×D3—124no—
362C23×D3—122no—
363C23×D3—122no—
364C23×D3—124no—
365C2×C3×D4—24no—
366C2×C3×D4—24no—
367C2×C3×D4—24no—
368C2×C3×D4—44no—
369C2×C3×D4C22×D314yes—
370C2×C3×D4C22×D314yes—
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—34no—
381C22×C3×C4—34no—
382C22×C3×C4—34no—
383C22×C3×C4—64no—
384C22×C3×C4—122no—
385C22×C3×C4—122no—
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—64no—
393C2×#67—64no—
394C2×#67—64no—
395C2×#67—64no—
396C2×#67—124no—
397C2×#67—122no—
398C2×#67—122no—
399C2×#67—124no—
400C22×Dic3—24no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—42no—
406C22×Dic3—42no—
407C22×Dic3—61no—
408C22×Dic3—61no—
409C22×Dic3C22×D314yes—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D314yes—
419C22×Dic3C22×D314yescomplemented
420C2×C4×D3—34no—
421C2×C4×D3—34no—
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—64no—
425C2×C4×D3—64no—
426C2×C4×D3—122no—
427C2×C4×D3—122no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—122no—
431C2×Dic6—122no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440C3×C42—34no—
441#217—34no—
442#217—34no—
443#217—64no—
444#217C22×D314yes—
445#217C22×D314yes—
446#217C22×D314yescomplemented
447#217C22×D314yescomplemented
448#217C22×D314yescomplemented
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—64no—
466(C2×D3)⋊C4—64no—
467C4⋊Dic3—34no—
468C4⋊Dic3—34no—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3C22×D314yescomplemented
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4C22×D314yescomplemented
479Dic3⋊C4C22×D314yescomplemented
480C4×Dic3—34no—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3—34no—
484C4×Dic3C22×D314yescomplemented
485C22×C32—28no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—44no—
492C22×C32C2×#4114yes—
493C22×C32C2×#4112yes—
494C22×C32C2×#4112yes—
495C22×C32H(5,𝔽2)12yes—
496C22×C32C2511yescharacteristic
497C2×C3⋊D3—22no—
498C2×C3⋊D3—28no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—416no—
504C2×C3⋊D3—44no—
505C2×C3⋊D3C2×#4114yes—
506C32×C4—22no—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—22no—
517C25—91no—
518C22×Q8—91no—
519C22×D4—91no—
520C22×D4—91no—
521C22×D4D3211yescharacteristic
522C23×C4—31no—
523C23×C4—31no—
524C23×C4—31no—
525C23×C4—91no—
526C23×C4—91no—
527#126—98no—
528#126—98no—
529#124—98no—
530#123—38no—
531#123—98no—
532#123—98no—
533C22⋊Q8—98no—
534C22⋊Q8—98no—
535#120—98no—
536C4×D4—38no—
537C4×D4—98no—
538#117—98no—
539#117—98no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—98no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—98no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C42—31no—
565C2×C42—91no—
566C2×C42—91no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—21no—
580C23×C3—24no—
581C23×C3—42no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3#23514yes—
587C23×C3#23714yes—
588C23×C3C23×D312yes—
589C23×C3C23×D312yes—
590C23×C3C23×D312yes—
591C23×C3C23×D312yes—
592C23×C3C23×D311yescharacteristic
593C23×C3C23×D311yescharacteristic
594C22×D3—34no—
595C22×D3—34no—
596C22×D3—32no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—32no—
600C22×D3—64no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—68no—
604C22×D3—68no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—64no—
610C22×D3—68no—
611C22×D3—62no—
612C22×D3—68no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—128no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—122no—
623C22×D3—128no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—1216no—
627C22×D3—1216no—
628C22×D3—128no—
629C22×D3—1232no—
630C3×D4—28no—
631C3×D4—28no—
632C3×D4—48no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—42no—
645C2×C3×C4—68no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—124no—
655C2×C3×C4—124no—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D312yes—
658#67—68no—
659#67—68no—
660#67—128no—
661#67—124no—
662#67—124no—
663#67—128no—
664C2×Dic3—28no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—44no—
678C2×Dic3—44no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—122no—
686C2×Dic3—122no—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C4×D3—68no—
696C4×D3—68no—
697C4×D3—124no—
698C4×D3—124no—
699Dic6—124no—
700Dic6—124no—
701C2×C32—24no—
702C2×C32—42no—
703C2×C32#55114yescomplemented
704C2×C32C22×#4111yescharacteristic
705C2×C32C22×#4111yescharacteristic
706C2×C32C2×H(5,𝔽2)11yescharacteristic
707C3⋊D3—24no—
708C3⋊D3—42no—
709C24—91no—
710C24—91no—
711C24—94no—
712C24—184no—
713C24—184no—
714C24—362no—
715C24C2×D3211yescharacteristic
716C24C2×D3211yescharacteristic
717C2×Q8—94no—
718C2×Q8—362no—
719C2×D4—24no—
720C2×D4—94no—
721C2×D4—94no—
722C2×D4—184no—
723C2×D4—362no—
724C2×D4C2×D3214yes—
725C22×C4—34no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—31no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—34no—
735C22×C4—34no—
736C22×C4—64no—
737C22×C4—94no—
738C22×C4—94no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—122no—
742C22×C4—122no—
743C22×C4—184no—
744C22×C4—362no—
745C22×C4C2×D3211yescharacteristic
746C4⋊C4—34no—
747C4⋊C4—34no—
748C4⋊C4—34no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—94no—
754C22⋊C4—34no—
755C22⋊C4—34no—
756C22⋊C4—34no—
757C22⋊C4—34no—
758C22⋊C4—34no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C22⋊C4—94no—
764C22⋊C4—94no—
765C22⋊C4—94no—
766C22⋊C4—94no—
767C22⋊C4—94no—
768C42—34no—
769C42—94no—
770C42—94no—
771C22×C3—28no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—28no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—24no—
787C22×C3—21no—
788C22×C3—48no—
789C22×C3—42no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—44no—
795C22×C3—44no—
796C22×C3—84no—
797C22×C3C2×#23514yes—
798C22×C3C2×#23512yes—
799C22×C3C2×#23714yes—
800C22×C3C2×#23712yes—
801C22×C3#100412yes—
802C22×C3D3×#4112yes—
803C22×C3D3×#4112yes—
804C22×C3#100912yes—
805C22×C3C24×D311yescharacteristic
806C22×C3C24×D311yescharacteristic
807C2×D3—34no—
808C2×D3—34no—
809C2×D3—64no—
810C2×D3—68no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—68no—
816C2×D3—64no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—128no—
824C2×D3—122no—
825C2×D3—122no—
826C2×D3—122no—
827C2×D3—122no—
828C2×D3—1216no—
829C2×D3—1216no—
830C2×D3—128no—
831C2×D3—1232no—
832C2×D3—124no—
833C2×D3—124no—
834C3×C4—22no—
835C3×C4—22no—
836C3×C4—42no—
837C3×C4—62no—
838C3×C4—62no—
839C3×C4—62no—
840C3×C4—62no—
841C3×C4—62no—
842C3×C4—62no—
843C3×C4—62no—
844C3×C4—62no—
845Dic3—22no—
846Dic3—22no—
847Dic3—22no—
848Dic3—22no—
849Dic3—22no—
850Dic3—22no—
851Dic3—22no—
852Dic3—22no—
853Dic3—62no—
854Dic3—62no—
855Dic3—62no—
856Dic3—62no—
857Dic3—122no—
858Dic3—122no—
859C32C2×#55111yescharacteristic, complemented, Sylow
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—94no—
866C23—92no—
867C23—92no—
868C23—188no—
869C23—182no—
870C23—182no—
871C23—182no—
872C23—182no—
873C23—188no—
874C23—182no—
875C23—364no—
876C23—3616no—
877C23#380414yes—
878C23C22×D3212yes—
879C23C22×D3212yes—
880C23C22×D3211yescharacteristic
881Q8—364no—
882D4—28no—
883D4—188no—
884D4—364no—
885C2×C4—22no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—62no—
895C2×C4—62no—
896C2×C4—62no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—62no—
900C2×C4—68no—
901C2×C4—62no—
902C2×C4—62no—
903C2×C4—92no—
904C2×C4—92no—
905C2×C4—124no—
906C2×C4—124no—
907C2×C4—188no—
908C2×C4—182no—
909C2×C4—182no—
910C2×C4—364no—
911C2×C4C22×D3212yes—
912C2×C3—24no—
913C2×C3—24no—
914C2×C3—24no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—44no—
919C2×C3—42no—
920C2×C3—42no—
921C2×C3—82no—
922C2×C3#555614yescomplemented
923C2×C3#565814yescomplemented
924C2×C3C22×#23511yescharacteristic
925C2×C3C22×#23711yescharacteristic
926C2×C3C2×#100411yescharacteristic
927C2×C3C2×D3×#4111yescharacteristic
928C2×C3C2×D3×#4111yescharacteristic
929C2×C3C2×#100911yescharacteristic
930D3—64no—
931D3—64no—
932D3—124no—
933D3—124no—
934D3—122no—
935D3—122no—
936C22—28no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—44no—
943C22—94no—
944C22—188no—
945C22—182no—
946C22—182no—
947C22—182no—
948C22—182no—
949C22—182no—
950C22—3616no—
951C22—364no—
952C22#6431212yes—
953C22#6431412yes—
954C22C2×#380414yes—
955C22C2×#380412yes—
956C22C23×D3211yescharacteristic
957C4—22no—
958C4—62no—
959C4—62no—
960C4—62no—
961C4—62no—
962C4—62no—
963C4—62no—
964C4—62no—
965C4—62no—
966C4—182no—
967C4—182no—
968C3—21no—
969C3C2×#555611yescharacteristic, complemented
970C3C2×#565811yescharacteristic, complemented
971C2—24no—
972C2—42no—
973C2—184no—
974C2—362no—
975C2#1059511814yesdirect product factor
976C2C2×#6431211yescharacteristic
977C2C2×#6431411yescharacteristic
978C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63975C2semidirect
5. C2×#63974C2semidirect
6. C2×#63966C2semidirect
7. C2×#63964C2semidirect
8. C22×#3722C2semidirect
9. C2×#63955C2semidirect
10. C2×#63953C2semidirect
11. C2×#63952C2semidirect
12. #10595118C2direct (N × H)
13. C2×#63895C2semidirect
14. C2×#63868C2semidirect
15. C2×#63848C2semidirect
16. C2×#63836C2semidirect
25. C23×C3×Dic3C22semidirect
26. C22×#627C22semidirect
35. C2×C3×#217C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
38. C3×#935C22semidirect
39. C3×D4×Dic3C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. #63975C22semidirect
45. #63974C22semidirect
46. C2×#3724C22semidirect
47. #63966C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. #63964C22semidirect
59. C2×#3722C22semidirect
60. #63955C22semidirect
61. C2×Dic32C22semidirect
62. C2×Dic32C22semidirect
63. #63953C22semidirect
64. #63952C22semidirect
65. #63895C22semidirect
66. #63868C22semidirect
67. #63848C22semidirect
68. #63836C22semidirect
74. C2×#935D3semidirect
75. C2×D4×Dic3D3semidirect
132. C22×C3×Dic3C23semidirect
134. C2×#627C23semidirect
144. C3×#217C23semidirect
145. C3×#217C23semidirect
146. C3×#217C23semidirect
147. C3×C4⋊Dic3C23semidirect
148. C3×Dic3⋊C4C23semidirect
149. C3×Dic3⋊C4C23semidirect
150. C3×C4×Dic3C23semidirect
151. #3724C23semidirect
152. Dic3⋊Dic3C23semidirect
153. Dic3⋊Dic3C23semidirect
154. Dic3⋊Dic3C23semidirect
155. Dic3⋊Dic3C23semidirect
162. Dic32C23semidirect
163. Dic32C23semidirect
182. C23×Dic3C2×D3semidirect
205. C2×#217C2×D3semidirect
206. C2×#217C2×D3semidirect
207. C2×#217C2×D3semidirect
211. #935C2×D3semidirect
212. D4×Dic3C2×D3semidirect
240. C2×C4⋊Dic3C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
249. C2×Dic3⋊C4C2×D3semidirect
254. C2×C4×Dic3C2×D3semidirect
419. C22×Dic3C22×D3semidirect
446. #217C22×D3semidirect
447. #217C22×D3semidirect
448. #217C22×D3semidirect
471. C4⋊Dic3C22×D3semidirect
478. Dic3⋊C4C22×D3semidirect
479. Dic3⋊C4C22×D3semidirect
484. C4×Dic3C22×D3semidirect
703. C2×C32#551semidirect
859. C32C2×#551semidirect
922. C2×C3#5556semidirect
923. C2×C3#5658semidirect
969. C3C2×#5556semidirect
970. C3C2×#5658semidirect
975. C2#10595118direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×#9352
C2×C3×D4×Dic32
C2×#639752
C2×#639742
C2×#639662
C2×#639642
C22×#37222
C2×#639552
C2×#639532
C2×#639522
#105951182
C2×#638952
C2×#638682
C2×#638482
C2×#638362
C2×#56583
C2×#55563