Finite Group Databasebeta

← C2×#10594305 #11902906

Subgroups — C2×#10594305 #11902906

Order 1152.

2869 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#883C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic
5C2×#63975C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63962C211yesmaximal, characteristic, complemented
8C2×#63921C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63887C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63862C211yesmaximal, characteristic, complemented
13C2×#63858C211yesmaximal, characteristic, complemented
14C2×#63855C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594305C2116yesmaximal, direct product factor
17C2×#5679—31nomaximal
18C2×#5658—31nomaximal
19C23×D32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#624C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic, complemented
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic, complemented
32C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
33#64090C2218yescomplemented
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C3×#885C2218yescomplemented
43C3×#883C2218yescomplemented
44#63983C2218yes—
45#63975C2218yescomplemented
46#67⋊Dic3C2218yescomplemented
47C2×Dic3⋊Dic3C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54#63962C2218yescomplemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×Dic32C2211yescharacteristic, complemented
61#63921C2218yescomplemented
62D3×(C2×D3)⋊C4C2218yescomplemented
63#63887C2218yescomplemented
64#63871C2218yescomplemented
65#63862C2218yescomplemented
66#63858C2218yescomplemented
67#63855C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#123—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#937—31no—
74C2×#937—31no—
75C2×#935—31no—
76C2×D4×Dic3—31no—
77C22×(C2×D3)⋊C4—31no—
78C2×#926—31no—
79#5679—316no—
80#5658—316no—
81C2×#898—31no—
82C2×#898—31no—
83C2×#897—31no—
84C2×#892—31no—
85C2×#886—31no—
86C2×#885D311yescharacteristic, complemented
87C2×#883—31no—
88C2×#883—31no—
89C2×#883D311yescharacteristic, complemented
90C2×#67⋊C4—31no—
91C2×#67⋊C4—31no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—61no—
94C2×D3×C22⋊C4—31no—
95C2×D3×C22⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×#879—31no—
98C2×#879—31no—
99C2×#878—31no—
100C2×#872—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×D32—24no—
107C22×D32—24no—
108C22×D32—42no—
109C22×D32C2314yes—
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C2×#638—24no—
113C2×#638C2314yes—
114C22×C3⋊Dic3—42no—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2314yescomplemented
119C2×C4×C3⋊D3—42no—
120C2×C4×C3⋊D3C2314yes—
121C2×C3×#67—24no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—42no—
134C2×C3×Dic6C2314yescomplemented
135C2×#624—24no—
136C2×#624C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yes—
139C32×C22⋊C4C2314yescomplemented
140#3752C2314yes—
141#3750C2314yescomplemented
142C4×C3⋊Dic3C2314yescomplemented
143C3×#217C2314yescomplemented
144C3×#217C2314yescomplemented
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×C4⋊Dic3C2314yescomplemented
149C3×Dic3⋊C4C2314yescomplemented
150C3×C4×Dic3C2314yescomplemented
151Dic3⋊Dic3C2314yescomplemented
152Dic3⋊Dic3C2314yescomplemented
153Dic3⋊Dic3C2314yescomplemented
154Dic3⋊Dic3C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156#3722C2314yes—
157#3722C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C24×D3—31no—
166C24×D3—31no—
167C22×C3×Q8—31no—
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C23×C3×C4—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—61no—
174C22×#67C2×D311yescharacteristic
175C22×#67C2×D311yescharacteristic
176C23×Dic3—31no—
177C23×Dic3—31no—
178C23×Dic3—31no—
179C23×Dic3—61no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—61no—
186C22×C4×D3C2×D311yescharacteristic
187C22×Dic6C2×D311yescharacteristic, complemented
188C3×#124—38no—
189C3×#123—38no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C22⋊C4—21no—
193C2×C3×C22⋊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⋊C4C2×D311yescharacteristic, complemented
199C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
200C2×C3×C42—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217C2×D311yescharacteristic, complemented
207C2×#217C2×D311yescharacteristic, complemented
208#946—38no—
209#946—38no—
210#937—38no—
211#937—38no—
212#935—38no—
213D4×Dic3—38no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
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—38no—
226C2×(C2×D3)⋊C4—61no—
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230#926—38no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3C2×D311yescharacteristic, complemented
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—61no—
245C2×Dic3⋊C4C2×D311yescharacteristic, complemented
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—61no—
251C2×C4×Dic3C2×D311yescharacteristic, complemented
252#898—38no—
253#898—38no—
254#897—38no—
255#892—38no—
256#886—38no—
257#885C2×D318yescomplemented
258#883—38no—
259#883—38no—
260#883C2×D318yescomplemented
261#67⋊C4—38no—
262#67⋊C4—38no—
263#67⋊C4—38no—
264#67⋊C4—68no—
265D3×C22⋊C4—38no—
266D3×C22⋊C4—38no—
267D3×C22⋊C4—38no—
268#879—38no—
269#879—38no—
270#878—38no—
271#872—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3#4114yes—
281C22×C3⋊D3C2412yes—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3#4114yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×D32—28no—
291C2×D32—28no—
292C2×D32—44no—
293C2×D32—416no—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4C2412yes—
297C2×C32×C4C2412yes—
298#638—28no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3—44no—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C4×C3⋊D3—44no—
307C3×#67—28no—
308C3×#67—44no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×C4×D3—28no—
322C3×Dic6—44no—
323#624—28no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—31no—
329C2×#123—31no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×#117—91no—
338C2×#117—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3C22×D311yescharacteristic
345C24×C3C22×D311yescharacteristic
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—34no—
349C23×D3—34no—
350C23×D3—61no—
351C23×D3—64no—
352C23×D3—64no—
353C23×D3—64no—
354C23×D3—64no—
355C23×D3—122no—
356C23×D3—122no—
357C23×D3C22×D311yescharacteristic
358C23×D3C22×D311yescharacteristic
359C2×C3×Q8—34no—
360C2×C3×Q8—122no—
361C2×C3×D4—34no—
362C2×C3×D4—34no—
363C2×C3×D4—64no—
364C2×C3×D4—122no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—34no—
374C22×C3×C4—64no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C2×#67—24no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—42no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67—68no—
387C2×#67C22×D314yes—
388C2×#67C22×D314yes—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—34no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—64no—
401C22×Dic3—61no—
402C22×Dic3—122no—
403C22×Dic3—122no—
404C22×Dic3—122no—
405C22×Dic3—124no—
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C2×C4×D3—24no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—64no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—122no—
422C2×C4×D3—122no—
423C2×C4×D3—124no—
424C2×C4×D3—122no—
425C2×C4×D3C22×D314yes—
426C2×Dic6—42no—
427C2×Dic6C22×D314yescomplemented
428C3×C4⋊C4—34no—
429C3×C4⋊C4—34no—
430C3×C22⋊C4—24no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4C22×D314yescomplemented
437C3×C22⋊C4C22×D314yescomplemented
438C3×C42—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217C22×D314yescomplemented
445#217C22×D314yescomplemented
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
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—64no—
458(C2×D3)⋊C4C22×D314yes—
459(C2×D3)⋊C4C22×D314yes—
460(C2×D3)⋊C4C22×D314yes—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466C4⋊Dic3C22×D314yescomplemented
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—64no—
475Dic3⋊C4C22×D314yescomplemented
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—64no—
481C4×Dic3C22×D314yescomplemented
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—44no—
486C22×C32C2×#4112yes—
487C22×C32C2×#4112yes—
488C22×C32H(5,𝔽2)12yes—
489C22×C32C2511yescharacteristic
490C2×C3⋊D3—28no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3C2×#4114yes—
494C2×C3×D3—28no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—44no—
501C2×C3×D3C2×#4114yes—
502D32—416no—
503C32×C4—22no—
504C32×C4—22no—
505C3⋊Dic3—22no—
506C3⋊Dic3—22no—
507C3⋊Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C25—91no—
515C22×Q8—31no—
516C22×D4—31no—
517C22×D4—31no—
518C22×D4—91no—
519C23×C4—31no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523C23×C4—91no—
524#126—98no—
525#126—98no—
526#124—38no—
527#123—38no—
528#123—98no—
529#123—98no—
530C22⋊Q8—98no—
531C22⋊Q8—98no—
532#120—98no—
533C4×D4—98no—
534C4×D4—98no—
535#117—98no—
536#117—98no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—98no—
551C2×C22⋊C4—98no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic, complemented
561C2×C42—31no—
562C2×C42—91no—
563C2×C42—91no—
564C23×C3—24no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—21no—
573C23×C3—34no—
574C23×C3—32no—
575C23×C3—32no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3C23×D312yes—
584C23×C3C23×D312yes—
585C23×C3C23×D311yescharacteristic
586C23×C3C23×D311yescharacteristic
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—34no—
593C22×D3—34no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—64no—
597C22×D3—62no—
598C22×D3—68no—
599C22×D3—68no—
600C22×D3—68no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—68no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—1216no—
611C22×D3—1216no—
612C22×D3#23714yes—
613C22×D3C23×D312yes—
614C22×D3C23×D312yes—
615C3×Q8—124no—
616C3×D4—68no—
617C3×D4—124no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—42no—
631C2×C3×C4—42no—
632C2×C3×C4—68no—
633C2×C3×C4—62no—
634C2×C3×C4—62no—
635C2×C3×C4—62no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4C23×D312yes—
640C2×C3×C4C23×D312yes—
641C2×C3×C4C23×D312yes—
642C2×C3×C4C23×D312yes—
643#67—28no—
644#67—44no—
645#67—68no—
646#67—68no—
647#67—616no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—64no—
664C2×Dic3—64no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—122no—
672C2×Dic3—124no—
673C2×Dic3—124no—
674C2×Dic3—124no—
675C2×Dic3—128no—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C4×D3—28no—
683C4×D3—68no—
684C4×D3—68no—
685C4×D3—124no—
686C4×D3—124no—
687C4×D3—128no—
688C4×D3—124no—
689Dic6—44no—
690C2×C32—42no—
691C2×C32#55114yescomplemented
692C2×C32C22×#4111yescharacteristic
693C2×C32C22×#4111yescharacteristic
694C2×C32C2×H(5,𝔽2)11yescharacteristic
695C3⋊D3—24no—
696C3×D3—24no—
697C3×D3—42no—
698C24—31no—
699C24—31no—
700C24—94no—
701C24—91no—
702C24—184no—
703C24—184no—
704C24—362no—
705C24C2×D3211yescharacteristic
706C2×Q8—34no—
707C2×Q8—122no—
708C2×D4—34no—
709C2×D4—34no—
710C2×D4—64no—
711C2×D4—94no—
712C2×D4—122no—
713C2×D4—184no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—34no—
721C22×C4—64no—
722C22×C4—94no—
723C22×C4—94no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—94no—
728C22×C4—94no—
729C22×C4—184no—
730C22×C4—362no—
731C22×C4—362no—
732C22×C4—362no—
733C22×C4C2×D3211yescharacteristic
734C22×C4C2×D3211yescharacteristic
735C4⋊C4—34no—
736C4⋊C4—34no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—34no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—94no—
756C22⋊C4C2×D3214yescomplemented
757C42—34no—
758C42—94no—
759C42—94no—
760C22×C3—24no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—21no—
771C22×C3—34no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—48no—
775C22×C3—44no—
776C22×C3—44no—
777C22×C3—68no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—124no—
784C22×C3C2×#23712yes—
785C22×C3#100412yes—
786C22×C3D3×#4112yes—
787C22×C3D3×#4112yes—
788C22×C3D3×#4112yes—
789C22×C3#100912yes—
790C22×C3C24×D311yescharacteristic
791C22×C3C24×D311yescharacteristic
792C2×D3—28no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—34no—
799C2×D3—34no—
800C2×D3—44no—
801C2×D3—64no—
802C2×D3—68no—
803C2×D3—68no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—122no—
809C2×D3—128no—
810C2×D3—122no—
811C2×D3—1216no—
812C2×D3—1216no—
813C2×D3C2×#23714yes—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826Dic3—22no—
827Dic3—22no—
828Dic3—22no—
829Dic3—22no—
830Dic3—22no—
831Dic3—22no—
832Dic3—64no—
833Dic3—64no—
834Dic3—62no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—62no—
839Dic3—62no—
840Dic3—122no—
841C32C2×#55111yescharacteristic, complemented, Sylow
842C23—22no—
843C23—22no—
844C23—22no—
845C23—34no—
846C23—32no—
847C23—32no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—94no—
854C23—92no—
855C23—188no—
856C23—188no—
857C23—182no—
858C23—182no—
859C23—364no—
860C23—3616no—
861C23C22×D3212yes—
862C23C22×D3211yescharacteristic
863Q8—124no—
864D4—68no—
865D4—124no—
866D4—188no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—68no—
876C2×C4—62no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—92no—
883C2×C4—92no—
884C2×C4—92no—
885C2×C4—188no—
886C2×C4—182no—
887C2×C4—182no—
888C2×C4—182no—
889C2×C4—364no—
890C2×C4—364no—
891C2×C4—364no—
892C2×C4C22×D3212yes—
893C2×C4C22×D3212yes—
894C2×C3—24no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—44no—
899C2×C3—42no—
900C2×C3—42no—
901C2×C3—64no—
902C2×C3—122no—
903C2×C3#565814yescomplemented
904C2×C3#567914yescomplemented
905C2×C3C22×#23711yescharacteristic
906C2×C3C2×#100411yescharacteristic
907C2×C3C2×D3×#4111yescharacteristic
908C2×C3C2×D3×#4111yescharacteristic
909C2×C3C2×D3×#4111yescharacteristic
910C2×C3C2×#100911yescharacteristic
911D3—24no—
912D3—42no—
913D3—64no—
914D3—64no—
915D3—124no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—34no—
920C22—44no—
921C22—68no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—94no—
928C22—124no—
929C22—188no—
930C22—182no—
931C22—182no—
932C22—3616no—
933C22#6430612yes—
934C22D3×#23712yes—
935C22#6431412yes—
936C22C23×D3211yescharacteristic
937C4—22no—
938C4—22no—
939C4—62no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—62no—
944C4—62no—
945C4—182no—
946C4—182no—
947C4—182no—
948C3—21no—
949C3C2×#565811yescharacteristic, complemented
950C3C2×#567911yescharacteristic, complemented
951C2—42no—
952C2—64no—
953C2—122no—
954C2—184no—
955C2#1059430514yesdirect product factor
956C2C2×#6430611yescharacteristic
957C2C2×D3×#23711yescharacteristic
958C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63983C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64090C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#883C2semidirect
5. C2×#63975C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63962C2semidirect
8. C2×#63921C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63887C2semidirect
11. C2×#63871C2semidirect
12. C2×#63862C2semidirect
13. C2×#63858C2semidirect
14. C2×#63855C2semidirect
15. C2×#63836C2semidirect
16. #10594305C2direct (N × H)
21. C23×C3⋊Dic3C22semidirect
26. C22×C3×Dic6C22semidirect
29. C2×C32×C22⋊C4C22semidirect
31. C2×#3750C22semidirect
32. C2×C4×C3⋊Dic3C22semidirect
33. #64090C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×C4×Dic3C22semidirect
42. C3×#885C22semidirect
43. C3×#883C22semidirect
45. #63975C22semidirect
46. #67⋊Dic3C22semidirect
47. C2×Dic3⋊Dic3C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
54. #63962C22semidirect
60. C2×Dic32C22semidirect
61. #63921C22semidirect
62. D3×(C2×D3)⋊C4C22semidirect
63. #63887C22semidirect
64. #63871C22semidirect
65. #63862C22semidirect
66. #63858C22semidirect
67. #63855C22semidirect
68. #63836C22semidirect
86. C2×#885D3semidirect
89. C2×#883D3semidirect
118. C22×C3⋊Dic3C23semidirect
134. C2×C3×Dic6C23semidirect
139. C32×C22⋊C4C23semidirect
141. #3750C23semidirect
142. C4×C3⋊Dic3C23semidirect
143. C3×#217C23semidirect
144. C3×#217C23semidirect
148. C3×C4⋊Dic3C23semidirect
149. C3×Dic3⋊C4C23semidirect
150. C3×C4×Dic3C23semidirect
151. Dic3⋊Dic3C23semidirect
152. Dic3⋊Dic3C23semidirect
153. Dic3⋊Dic3C23semidirect
154. Dic3⋊Dic3C23semidirect
155. Dic3⋊Dic3C23semidirect
163. Dic32C23semidirect
187. C22×Dic6C2×D3semidirect
198. C2×C3×C22⋊C4C2×D3semidirect
199. C2×C3×C22⋊C4C2×D3semidirect
206. C2×#217C2×D3semidirect
207. C2×#217C2×D3semidirect
236. C2×C4⋊Dic3C2×D3semidirect
245. C2×Dic3⋊C4C2×D3semidirect
251. C2×C4×Dic3C2×D3semidirect
257. #885C2×D3semidirect
260. #883C2×D3semidirect
427. C2×Dic6C22×D3semidirect
436. C3×C22⋊C4C22×D3semidirect
437. C3×C22⋊C4C22×D3semidirect
444. #217C22×D3semidirect
445. #217C22×D3semidirect
466. C4⋊Dic3C22×D3semidirect
475. Dic3⋊C4C22×D3semidirect
481. C4×Dic3C22×D3semidirect
560. C2×C22⋊C4D32semidirect
691. C2×C32#551semidirect
756. C22⋊C4C2×D32semidirect
841. C32C2×#551semidirect
903. C2×C3#5658semidirect
904. C2×C3#5679semidirect
949. C3C2×#5658semidirect
950. C3C2×#5679semidirect
955. C2#10594305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640902
C2×C3×#8852
C2×C3×#8832
C2×#639832
C2×#639752
C2×#67⋊Dic32
C2×#639622
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#638872
C2×#638712
C2×#638622
C2×#638582
C2×#638552
C2×#638362
#105943052
C2×#56793
C2×#56583