Finite Group Databasebeta

← C3×#82780 #11824474

Subgroups — C3×#82780 #11824474

Order 1152.

1513 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic
5C2×C3×#924C211yesmaximal, characteristic, complemented
6C2×C3×#897C211yesmaximal, characteristic, complemented
7C3×#4993C212yesmaximal, complemented
8C3×#4975C212yesmaximal, complemented
9C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
10C3×#4957C212yesmaximal
11C3×#4949C212yesmaximal, complemented
12C3×#2542—31nomaximal
13#82780C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C32×C22⋊Q8—24no—
20C2×C32×C4⋊C4C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2211yescharacteristic
25C3×#946—24no—
26C3×#944—24no—
27C3×C4×#67—24no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C3×#924—24no—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2212yes—
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#897—24no—
42C3×C3⋊#95C2212yes—
43C2×C3×C4⋊Q8—31no—
44C2×C3×C22⋊Q8—21no—
45C2×C3×C22⋊Q8—31no—
46C2×C3×C22⋊Q8—31no—
47C2×C3×C22⋊Q8—31no—
48C2×C3×C22⋊Q8D311yescharacteristic, complemented
49C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
50C2×C3×C4×D4—31no—
51C2×#946C2×C311yescharacteristic, complemented
52C2×#944C2×C311yescharacteristic, complemented
53C2×C4×#67C2×C311yescharacteristic
54C2×#924C2×C311yescharacteristic, complemented
55C2×#897C2×C311yescharacteristic, complemented
56C3×#399—32no—
57C3×#399—32no—
58C3×#390—32no—
59C3×#384—32no—
60C3×C4×C4⋊C4—31no—
61#4993C2×C312yescomplemented
62#4975C2×C312yescomplemented
63Dic3×C4⋊C4C2×C311yescharacteristic, complemented
64#4957C2×C312yes—
65#4949C2×C312yescomplemented
66C24×C32C2311yescharacteristic
67C23×C3×D3C2311yescharacteristic
68C2×C32×Q8—22no—
69C2×C32×Q8—22no—
70C2×C32×Q8—22no—
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C2×C3×#67Q814yescomplemented
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3—22no—
89C2×C3×Dic6—22no—
90C2×C3×Dic6—22no—
91C2×C3×Dic6—22no—
92C32×C4⋊C4—24no—
93C32×C4⋊C4D414yescomplemented
94C32×C22⋊C4—24no—
95C3×#217—24no—
96C3×#217—22no—
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—22no—
99C3×(C2×D3)⋊C4—24no—
100C3×C4⋊Dic3—24no—
101C3×C4⋊Dic3D414yescomplemented
102C3×Dic3⋊C4—24no—
103C3×Dic3⋊C4—22no—
104C3×Dic3⋊C4—24no—
105C3×Dic3⋊C4—24no—
106C3×Dic3⋊C4—24no—
107C3×C4×Dic3—24no—
108C3×C4×Dic3D414yes—
109#2542—31noSylow
110C22×C3×Q8—21no—
111C22×C3×Q8—31no—
112C22×C3×Q8C2×D311yescharacteristic
113C22×C3×Q8C22×C311yescharacteristic
114C22×C3×D4—31no—
115C23×C3×C4—21no—
116C23×C3×C4—31no—
117C23×C3×C4C2×D311yescharacteristic
118C23×C3×C4C22×C311yescharacteristic
119C22×#67C22×C311yescharacteristic
120C22×C4×D3C22×C311yescharacteristic
121C22×Dic6C22×C311yescharacteristic
122C3×C4⋊Q8—64no—
123C3×C22⋊Q8—28no—
124C3×C22⋊Q8—24no—
125C3×C22⋊Q8—24no—
126C3×C22⋊Q8—64no—
127C3×C22⋊Q8—64no—
128C3×C22⋊Q8—64no—
129C3×C4×D4—64no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—32no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C4⋊C4—32no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C4⋊C4C2×D312yes—
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C4⋊C4C22×C312yes—
142C2×C3×C4⋊C4C22×C311yescharacteristic
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4C2×D312yes—
150C2×C3×C22⋊C4C22×C312yes—
151C2×C3×C42—31no—
152C2×C3×C42—32no—
153C2×#217C22×C311yescharacteristic
154C2×#217C22×C312yes—
155#946—24no—
156#944—24no—
157C4×#67—24no—
158C2×(C2×D3)⋊C4C22×C312yes—
159C2×(C2×D3)⋊C4C22×C312yes—
160C2×(C2×D3)⋊C4C22×C311yescharacteristic
161C2×C4⋊Dic3C22×C312yes—
162C2×C4⋊Dic3C22×C311yescharacteristic
163#924—24no—
164C2×Dic3⋊C4C22×C312yes—
165C2×Dic3⋊C4C22×C312yes—
166C2×Dic3⋊C4C22×C312yes—
167C2×Dic3⋊C4C22×C311yescharacteristic
168C2×Dic3⋊C4C22×C312yes—
169C2×C4×Dic3C22×C312yes—
170C2×C4×Dic3C22×C311yescharacteristic
171#897—24no—
172C3×#95—32no—
173C3⋊#95C22×C312yes—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32C2×Q812yes—
181C23×C32C2411yescharacteristic
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3C2×Q812yes—
189C32×Q8—44no—
190C2×C32×C4—22no—
191C2×C32×C4—21no—
192C2×C32×C4—22no—
193C2×C32×C4—22no—
194C2×C32×C4—21no—
195C2×C32×C4—22no—
196C2×C32×C4—21no—
197C2×C32×C4—22no—
198C2×C32×C4—44no—
199C2×C32×C4C2×D412yes—
200C2×C32×C4C2×D412yes—
201C2×C32×C4C2×D414yes—
202C2×C32×C4C2×D412yes—
203C3×#67—28no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3C2×D412yes—
215C2×C3×Dic3C2×D414yes—
216C2×C3×Dic3C2×D412yes—
217C2×C3×Dic3C2×Q812yes—
218C2×C3×Dic3#4112yes—
219C3×C4×D3—44no—
220C3×Dic6—44no—
221C2×C4⋊Q8—31no—
222C2×C22⋊Q8—31no—
223C2×C22⋊Q8—31no—
224C2×C22⋊Q8—31no—
225C2×C22⋊Q8C3×D311yescharacteristic, complemented
226C2×C4×D4—31no—
227#399—32no—
228#399—32no—
229#390—32no—
230#384—32no—
231C4×C4⋊C4—31no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C23×C311yescharacteristic
236C23×D3C23×C311yescharacteristic
237C2×C3×Q8—24no—
238C2×C3×Q8—22no—
239C2×C3×Q8—22no—
240C2×C3×Q8—22no—
241C2×C3×Q8—22no—
242C2×C3×Q8—22no—
243C2×C3×Q8—22no—
244C2×C3×Q8—42no—
245C2×C3×Q8—42no—
246C2×C3×Q8—62no—
247C2×C3×Q8—62no—
248C2×C3×Q8—62no—
249C2×C3×D4—34no—
250C2×C3×D4—62no—
251C2×C3×D4—62no—
252C22×C3×C4—24no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—32no—
266C22×C3×C4—32no—
267C22×C3×C4—31no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4—62no—
271C22×C3×C4—62no—
272C22×C3×C4—62no—
273C22×C3×C4C22×D312yes—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D312yes—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C23×C312yes—
278C22×C3×C4C23×C311yescharacteristic
279C22×C3×C4C23×C312yes—
280C22×C3×C4C23×C311yescharacteristic
281C2×#67—22no—
282C2×#67—22no—
283C2×#67C3×Q814yescomplemented
284C22×Dic3C23×C311yescharacteristic
285C22×Dic3C23×C312yes—
286C22×Dic3C23×C311yescharacteristic
287C22×Dic3C23×C312yes—
288C22×Dic3C23×C311yescharacteristic
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—22no—
292C2×Dic6—22no—
293C2×Dic6—22no—
294C2×Dic6—22no—
295C3×C4⋊C4—28no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—24no—
299C3×C4⋊C4—34no—
300C3×C4⋊C4—62no—
301C3×C4⋊C4—64no—
302C3×C4⋊C4—64no—
303C3×C4⋊C4—64no—
304C3×C4⋊C4—64no—
305C3×C4⋊C4—64no—
306C3×C4⋊C4#6714yescomplemented
307C3×C4⋊C4C3×D414yescomplemented
308C3×C22⋊C4—28no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—64no—
313C3×C22⋊C4—62no—
314C3×C22⋊C4—64no—
315C3×C22⋊C4—64no—
316C3×C42—34no—
317C3×C42—64no—
318#217—24no—
319#217—22no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—22no—
322(C2×D3)⋊C4—24no—
323C4⋊Dic3—24no—
324C4⋊Dic3C3×D414yescomplemented
325Dic3⋊C4—24no—
326Dic3⋊C4—22no—
327Dic3⋊C4—24no—
328Dic3⋊C4—24no—
329Dic3⋊C4—24no—
330C4×Dic3—24no—
331C4×Dic3C3×D414yes—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32C22×D411yescharacteristic
340C22×C32C22×D411yescharacteristic
341C22×C32C22×D411yescharacteristic
342C22×C32C22×Q811yescharacteristic
343C22×C32C2×#4111yescharacteristic
344C22×C322−1+411yescharacteristic
345C22×C322−1+411yescharacteristic
346C2×C3×D3—22no—
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3—41no—
350C2×C3×D3—41no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C32×C4—24no—
354C32×C4—41no—
355C32×C4—42no—
356C32×C4#12714yes—
357C3×Dic3—22no—
358C3×Dic3—24no—
359C3×Dic3—42no—
360C3×Dic3—41no—
361C3×Dic3C22⋊Q814yescomplemented
362C22×Q8—31no—
363C22×Q8C2×C3×D311yescharacteristic
364C22×D4—31no—
365C23×C4—31no—
366C23×C4C2×C3×D311yescharacteristic
367C4⋊Q8—64no—
368C22⋊Q8—24no—
369C22⋊Q8—64no—
370C22⋊Q8—64no—
371C22⋊Q8—64no—
372C4×D4—64no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4C2×C3×D312yes—
381C2×C4⋊C4C2×C3×D311yescharacteristic
382C2×C22⋊C4—31no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4C2×C3×D312yes—
388C2×C42—31no—
389C2×C42—32no—
390#95—32no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—32no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3D3×Q812yes—
419C23×C3C2×C3×Q812yes—
420C23×C3C23×D311yescharacteristic
421C23×C3C24×C311yescharacteristic
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3C2×C3×Q812yes—
429C3×Q8—48no—
430C3×Q8—44no—
431C3×Q8—44no—
432C3×Q8—124no—
433C3×D4—68no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—24no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—34no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—48no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4—61no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—62no—
476C2×C3×C4—61no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—61no—
480C2×C3×C4—124no—
481C2×C3×C4D3×D412yes—
482C2×C3×C4D3×D412yes—
483C2×C3×C4C2×#6714yes—
484C2×C3×C4C2×#6712yes—
485C2×C3×C4C2×C3×D412yes—
486C2×C3×C4C2×C3×D412yes—
487C2×C3×C4C2×C3×D414yes—
488C2×C3×C4C2×C3×D412yes—
489#67—28no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—22no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3C2×C3×D412yes—
501C2×Dic3C2×C3×D414yes—
502C2×Dic3C2×C3×D412yes—
503C2×Dic3C2×C3×Q812yes—
504C2×Dic3C3×#4112yes—
505C4×D3—44no—
506Dic6—44no—
507C2×C32—42no—
508C2×C32C2×C22⋊Q811yescharacteristic
509C2×C32C2×#12711yescharacteristic
510C2×C32#53611yescharacteristic
511C2×C32#54711yescharacteristic
512C2×C32#54711yescharacteristic
513C2×C32D4×Q811yescharacteristic
514C2×C32D4×Q811yescharacteristic
515C3×D3—42no—
516C24—31no—
517C24C22×C3×D311yescharacteristic
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—62no—
522C2×Q8—62no—
523C2×Q8—62no—
524C2×D4—34no—
525C2×D4—62no—
526C2×D4—62no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—31no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4C22×C3×D312yes—
539C22×C4C22×C3×D311yescharacteristic
540C22×C4C22×C3×D312yes—
541C22×C4C22×C3×D311yescharacteristic
542C4⋊C4—24no—
543C4⋊C4—34no—
544C4⋊C4—62no—
545C4⋊C4—64no—
546C4⋊C4—64no—
547C4⋊C4—64no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4C3×#6714yescomplemented
551C22⋊C4—24no—
552C22⋊C4—62no—
553C22⋊C4—64no—
554C22⋊C4—62no—
555C22⋊C4—64no—
556C22⋊C4—64no—
557C42—34no—
558C42—64no—
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3C2×D3×D411yescharacteristic
595C22×C3C2×D3×D411yescharacteristic
596C22×C3C2×D3×Q811yescharacteristic
597C22×C3#100711yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3#101011yescharacteristic
600C22×C3C22×#6711yescharacteristic
601C22×C3C22×C3×D411yescharacteristic
602C22×C3C22×C3×D411yescharacteristic
603C22×C3C22×C3×D411yescharacteristic
604C22×C3C22×C3×Q811yescharacteristic
605C22×C3C2×C3×#4111yescharacteristic
606C22×C3C3×2−1+411yescharacteristic
607C22×C3C3×2−1+411yescharacteristic
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—24no—
618C3×C4—34no—
619C3×C4—44no—
620C3×C4—42no—
621C3×C4—44no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—42no—
626C3×C4—62no—
627C3×C4—64no—
628C3×C4—121no—
629C3×C4—122no—
630C3×C4#94014yes—
631C3×C4C3×#12714yes—
632Dic3—22no—
633Dic3—24no—
634Dic3—42no—
635Dic3—41no—
636Dic3C3×C22⋊Q814yescomplemented
637C32#254211yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—32no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23C3×D3×Q812yes—
652C23C23×C3×D311yescharacteristic
653Q8—44no—
654Q8—124no—
655D4—68no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—34no—
669C2×C4—44no—
670C2×C4—61no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—62no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—124no—
681C2×C4C3×D3×D412yes—
682C2×C4C3×D3×D412yes—
683C2×C4C2×C3×#6714yes—
684C2×C4C2×C3×#6712yes—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—44no—
693C2×C3—42no—
694C2×C3—42no—
695C2×C3—122no—
696C2×C3D3×C22⋊Q811yescharacteristic
697C2×C3#562811yescharacteristic
698C2×C3#563111yescharacteristic
699C2×C3#563211yescharacteristic
700C2×C3C2×#94011yescharacteristic
701C2×C3Q8×#6711yescharacteristic
702C2×C3#582411yescharacteristic
703C2×C3C2×C3×C22⋊Q811yescharacteristic
704C2×C3C2×C3×#12711yescharacteristic
705C2×C3C3×#53611yescharacteristic
706C2×C3C3×#54711yescharacteristic
707C2×C3C3×#54711yescharacteristic
708C2×C3C3×D4×Q811yescharacteristic
709C2×C3C3×D4×Q811yescharacteristic
710D3—42no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—62no—
719C22—62no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22C2×C3×D3×D411yescharacteristic
726C22C2×C3×D3×D411yescharacteristic
727C22C2×C3×D3×Q811yescharacteristic
728C22C3×#100711yescharacteristic
729C22C3×D3×#4111yescharacteristic
730C22C3×#101011yescharacteristic
731C22C22×C3×#6711yescharacteristic
732C4—24no—
733C4—34no—
734C4—41no—
735C4—42no—
736C4—62no—
737C4—64no—
738C4—121no—
739C4—122no—
740C4C3×#94014yes—
741C3—21no—
742C3#8278011yescharacteristic, direct product factor
743C3C3×#254211yescharacteristic, complemented
744C2—42no—
745C2—122no—
746C2C3×D3×C22⋊Q811yescharacteristic
747C2C3×#562811yescharacteristic
748C2C3×#563111yescharacteristic
749C2C3×#563211yescharacteristic
750C2C2×C3×#94011yescharacteristic
751C2C3×Q8×#6711yescharacteristic
752C2C3×#582411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C3×#2542
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×#944C2semidirect
5. C2×C3×#924C2semidirect
6. C2×C3×#897C2semidirect
7. C3×#4993C2semidirect
8. C3×#4975C2semidirect
9. C3×Dic3×C4⋊C4C2semidirect
11. C3×#4949C2semidirect
13. #82780C3direct (N × H)
48. C2×C3×C22⋊Q8D3semidirect
49. C2×C3×C22⋊Q8C2×C3semidirect
51. C2×#946C2×C3semidirect
52. C2×#944C2×C3semidirect
54. C2×#924C2×C3semidirect
55. C2×#897C2×C3semidirect
61. #4993C2×C3semidirect
62. #4975C2×C3semidirect
63. Dic3×C4⋊C4C2×C3semidirect
65. #4949C2×C3semidirect
80. C2×C3×#67Q8semidirect
93. C32×C4⋊C4D4semidirect
101. C3×C4⋊Dic3D4semidirect
225. C2×C22⋊Q8C3×D3semidirect
283. C2×#67C3×Q8semidirect
306. C3×C4⋊C4#67semidirect
307. C3×C4⋊C4C3×D4semidirect
324. C4⋊Dic3C3×D4semidirect
361. C3×Dic3C22⋊Q8semidirect
550. C4⋊C4C3×#67semidirect
636. Dic3C3×C22⋊Q8semidirect
637. C32#2542semidirect
742. C3#82780direct (N × H)
743. C3C3×#2542semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×C3×#9462
C2×C3×#9442
C2×C3×C4×#672
C2×C3×#9242
C2×C3×#8972
C3×#49932
C3×#49752
C3×Dic3×C4⋊C42
C3×#49572
C3×#49492
C3×#25423
#827803