Finite Group Databasebeta

← C3×#86215 #11906327

Subgroups — C3×#86215 #11906327

Order 1152.

2265 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×Q8×#67C214yesmaximal, complemented
3C3×#5730C212yesmaximal, complemented
4C3×#5729C214yesmaximal, complemented
5C3×#5728C212yesmaximal, complemented
6C3×#5727C212yesmaximal, complemented
7C3×D3×C4⋊Q8C212yesmaximal, complemented
8C3×#5722C212yesmaximal, complemented
9C3×#5721C212yesmaximal, complemented
10C3×#5511C214yesmaximal, complemented
11C3×#5504C212yesmaximal
12C3×#5500C212yesmaximal, complemented
13C3×C4×#235C211yesmaximal, characteristic
14C3×#5470C211yesmaximal, characteristic, complemented
15C3×#3503—31nomaximal
16#86215C311yesmaximal, characteristic, direct product factor
17C22×C32×Q8C2212yes—
18C2×C3×D3×Q8C2214yes—
19C2×C3×#235C2211yescharacteristic
20C32×C4⋊Q8C2212yes—
21C32×C4⋊Q8C2212yes—
22C32×C4⋊Q8C2212yes—
23C32×C4⋊Q8C2212yes—
24C2×C32×C4⋊C4C2212yes—
25C2×C32×C4⋊C4C2212yes—
26C2×C32×C42C2211yescharacteristic
27C3×#946C2214yes—
28C3×#946C2218yes—
29C3×Q8×Dic3C2214yes—
30C3×#944C2214yes—
31C3×#944C2218yes—
32C3×C4×#67C2218yes—
33C3×C4×#67C2212yes—
34C3×C4×#67C2212yes—
35C3×#926C2211yescharacteristic
36C3×#926C2212yes—
37C3×#924C2218yes—
38C3×#924C2212yes—
39C3×#924C2212yes—
40C3×#897C2214yes—
41C3×#896C2218yes—
42C3×#893C2214yes—
43C3×#892C2214yes—
44C3×D3×C4⋊C4C2214yes—
45C3×D3×C4⋊C4C2214yes—
46C3×#890C2214yes—
47C3×#890C2214yes—
48C3×#889C2218yes—
49C3×#888C2214yes—
50C3×#888C2214yes—
51C3×#888C2214yes—
52C3×#887C2214yes—
53C3×#887C2214yes—
54C3×C4×D12C2211yescharacteristic
55C3×C4×D12C2211yescharacteristic
56C3×#872C2212yes—
57C3×C42×D3C2212yes—
58C3×#870C2212yes—
59C3×#869C2211yescharacteristic
60C3×#869C2211yescharacteristic
61C3×C4×Dic6C2211yescharacteristic
62C3×C4×Dic6C2212yes—
63C3×C4×Dic6C2211yescharacteristic
64C3×C4×Dic6C2212yes—
65C3×Q82—32no—
66C3×#557—32no—
67C3×#554—32no—
68C3×#554—34no—
69C3×D4×Q8—34no—
70C3×D4×Q8—32no—
71C3×#544—34no—
72C3×#544—32no—
73C3×#533—32no—
74C3×#533—31no—
75C2×C3×C4⋊Q8—21no—
76C2×C3×C4⋊Q8—32no—
77C2×C3×C4⋊Q8D311yescharacteristic, complemented
78C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
79C3×#520—32no—
80C3×C4×#41—31no—
81Q8×#67C2×C314yescomplemented
82#5730C2×C312yescomplemented
83#5729C2×C314yescomplemented
84#5728C2×C312yescomplemented
85#5727C2×C312yescomplemented
86D3×C4⋊Q8C2×C312yescomplemented
87#5722C2×C312yescomplemented
88#5721C2×C312yescomplemented
89#5511C2×C314yescomplemented
90#5504C2×C312yes—
91#5500C2×C312yescomplemented
92C4×#235C2×C311yescharacteristic
93#5470C2×C311yescharacteristic, complemented
94C2×C32×Q8—44no—
95C2×C32×Q8C2314yes—
96C2×C32×Q8C2314yes—
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2314yes—
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67C2312yes—
102C3×D3×Q8—48no—
103C3×#235Q818yescomplemented
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2312yes—
106C2×C3×C4×D3C2312yes—
107C2×C3×C4×D3C2318yes—
108C2×C3×C4×D3C2312yes—
109C2×C3×Dic6C2312yes—
110C2×C3×Dic6C2312yes—
111C2×C3×Dic6C2318yes—
112C2×C3×Dic6C2311yescharacteristic
113C32×C4⋊C4C2314yes—
114C32×C4⋊C4C2314yes—
115C32×C4⋊C4C2314yes—
116C32×C4⋊C4C2314yes—
117C32×C42C2311yescharacteristic
118C32×C42C2311yescharacteristic
119C32×C42C2311yescharacteristic
120C32×C42C2311yescharacteristic
121C3×#217C2314yes—
122C3×#217C2312yes—
123C3×(C2×D3)⋊C4C2318yes—
124C3×(C2×D3)⋊C4C2312yes—
125C3×(C2×D3)⋊C4C2312yes—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2312yes—
128C3×C4⋊Dic3C2312yes—
129C3×C4⋊Dic3C2318yes—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2312yes—
132C3×C4⋊Dic3C2312yes—
133C3×Dic3⋊C4C2318yes—
134C3×Dic3⋊C4C2318yes—
135C3×Dic3⋊C4C2318yes—
136C3×Dic3⋊C4C2312yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2312yes—
140C3×C4×Dic3C2312yes—
141C3×C4×Dic3C2318yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2312yes—
144C3×C4×Dic3C2312yes—
145#3503—31noSylow
146C2×C3×#41—31no—
147C22×C3×Q8—22no—
148C22×C3×Q8—34no—
149C22×C3×Q8C2×D312yes—
150C22×C3×Q8C22×C312yes—
151C2×D3×Q8C22×C314yes—
152C2×#235C22×C311yescharacteristic
153C3×C4⋊Q8—22no—
154C3×C4⋊Q8—22no—
155C3×C4⋊Q8—22no—
156C3×C4⋊Q8—22no—
157C3×C4⋊Q8—38no—
158C3×C4⋊Q8—34no—
159C3×C4⋊Q8—34no—
160C3×C4⋊Q8—34no—
161C3×C4⋊Q8—34no—
162C3×C4⋊Q8—31no—
163C3×C4⋊Q8—31no—
164C3×C4⋊Q8C2×D312yes—
165C3×C4⋊Q8C2×D312yes—
166C3×C4⋊Q8C2×D312yes—
167C3×C4⋊Q8C2×D312yes—
168C3×C4⋊Q8C22×C312yes—
169C3×C4⋊Q8C22×C312yes—
170C3×C4⋊Q8C22×C312yes—
171C3×C4⋊Q8C22×C312yes—
172C3×#125—38no—
173C3×#125—34no—
174C3×#125—34no—
175C3×#125—32no—
176C3×C22⋊Q8—34no—
177C3×C22⋊Q8—38no—
178C3×C22⋊Q8—32no—
179C3×C22⋊Q8—32no—
180C3×C22⋊Q8—38no—
181C3×C22⋊Q8—38no—
182C3×C22⋊Q8—34no—
183C3×C4×Q8—34no—
184C3×C4×Q8—34no—
185C3×C4×Q8—34no—
186C3×C4×Q8—31no—
187C3×C4×Q8—32no—
188C3×C4×Q8—31no—
189C3×C4×Q8—32no—
190C3×C4×D4—32no—
191C3×C4×D4—32no—
192C3×C4×D4—38no—
193C3×C4×D4—34no—
194C3×C4×D4—31no—
195C3×C4×D4—31no—
196C3×#117—31no—
197C3×#117—32no—
198C3×#117—34no—
199C3×#117—32no—
200C2×C3×C4⋊C4—22no—
201C2×C3×C4⋊C4—22no—
202C2×C3×C4⋊C4—34no—
203C2×C3×C4⋊C4—34no—
204C2×C3×C4⋊C4C2×D312yes—
205C2×C3×C4⋊C4C2×D312yes—
206C2×C3×C4⋊C4C22×C312yes—
207C2×C3×C4⋊C4C22×C312yes—
208C2×C3×C42—21no—
209C2×C3×C42—32no—
210C2×C3×C42C2×D311yescharacteristic
211C2×C3×C42C22×C311yescharacteristic
212#946C22×C314yes—
213#946C22×C318yes—
214Q8×Dic3C22×C314yes—
215#944C22×C314yes—
216#944C22×C318yes—
217C4×#67C22×C312yes—
218C4×#67C22×C312yes—
219C4×#67C22×C318yes—
220#926C22×C312yes—
221#926C22×C311yescharacteristic
222#924C22×C312yes—
223#924C22×C312yes—
224#924C22×C318yes—
225#897C22×C314yes—
226#896C22×C318yes—
227#893C22×C314yes—
228#892C22×C314yes—
229D3×C4⋊C4C22×C314yes—
230D3×C4⋊C4C22×C314yes—
231#890C22×C314yes—
232#890C22×C314yes—
233#889C22×C318yes—
234#888C22×C314yes—
235#888C22×C314yes—
236#888C22×C314yes—
237#887C22×C314yes—
238#887C22×C314yes—
239C4×D12C22×C311yescharacteristic
240C4×D12C22×C311yescharacteristic
241#872C22×C312yes—
242C42×D3C22×C312yes—
243#870C22×C312yes—
244#869C22×C311yescharacteristic
245#869C22×C311yescharacteristic
246C4×Dic6C22×C311yescharacteristic
247C4×Dic6C22×C312yes—
248C4×Dic6C22×C311yescharacteristic
249C4×Dic6C22×C312yes—
250C23×C32C2411yescharacteristic
251C22×C3×D3C2412yes—
252C32×Q8—28no—
253C32×Q8—44no—
254C2×C32×C4—22no—
255C2×C32×C4—22no—
256C2×C32×C4—44no—
257C2×C32×C4C2×Q814yescomplemented
258C2×C32×C4C2418yes—
259C2×C32×C4C2411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C3×#67C2×Q818yescomplemented
266C2×C3×Dic3C2414yes—
267C2×C3×Dic3C2412yes—
268C2×C3×Dic3C2412yes—
269C2×C3×Dic3C2414yes—
270C2×C3×Dic3C2412yes—
271C3×D12C2×Q814yescomplemented
272C3×C4×D3—24no—
273C3×C4×D3—24no—
274C3×C4×D3—48no—
275C3×C4×D3C2×Q818yescomplemented
276C3×Dic6—24no—
277C3×Dic6—24no—
278C3×Dic6—48no—
279C3×Dic6C2×Q814yescomplemented
280Q82—32no—
281#557—32no—
282#554—32no—
283#554—34no—
284D4×Q8—34no—
285D4×Q8—32no—
286#544—34no—
287#544—32no—
288#533—32no—
289#533—31no—
290C2×C4⋊Q8—32no—
291C2×C4⋊Q8C3×D311yescharacteristic, complemented
292#520—32no—
293C4×#41—31no—
294C3×#41—38no—
295C2×C3×Q8—24no—
296C2×C3×Q8—24no—
297C2×C3×Q8—31no—
298C2×C3×Q8—32no—
299C2×C3×Q8—32no—
300C2×C3×Q8—38no—
301C2×C3×Q8—44no—
302C2×C3×Q8—44no—
303C2×C3×Q8—48no—
304C2×C3×Q8—128no—
305C2×C3×Q8C22×D314yes—
306C2×C3×Q8C22×D314yes—
307C2×C3×Q8C23×C314yes—
308C2×C3×Q8C23×C314yes—
309C2×C3×D4—32no—
310C2×C3×D4—31no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—24no—
315C22×C3×C4—32no—
316C22×C3×C4—32no—
317C22×C3×C4—32no—
318C22×C3×C4—38no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D314yes—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C22×C3×C4C23×C311yescharacteristic
325C22×C3×C4C23×C314yes—
326C22×C3×C4C23×C311yescharacteristic
327C2×#67C23×C312yes—
328D3×Q8—48no—
329#235C3×Q818yescomplemented
330C2×D12C23×C311yescharacteristic
331C2×C4×D3C23×C312yes—
332C2×C4×D3C23×C312yes—
333C2×C4×D3C23×C318yes—
334C2×C4×D3C23×C312yes—
335C2×Dic6C23×C312yes—
336C2×Dic6C23×C312yes—
337C2×Dic6C23×C318yes—
338C2×Dic6C23×C311yescharacteristic
339C3×C4⋊C4—24no—
340C3×C4⋊C4—24no—
341C3×C4⋊C4—24no—
342C3×C4⋊C4—24no—
343C3×C4⋊C4—38no—
344C3×C4⋊C4—38no—
345C3×C4⋊C4—32no—
346C3×C4⋊C4—32no—
347C3×C4⋊C4—34no—
348C3×C4⋊C4—38no—
349C3×C4⋊C4—34no—
350C3×C4⋊C4—32no—
351C3×C4⋊C4—32no—
352C3×C4⋊C4—32no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—32no—
356C3×C4⋊C4—38no—
357C3×C4⋊C4C22×D314yes—
358C3×C4⋊C4C22×D314yes—
359C3×C4⋊C4C22×D314yes—
360C3×C4⋊C4C22×D314yes—
361C3×C4⋊C4C23×C314yes—
362C3×C4⋊C4C23×C314yes—
363C3×C4⋊C4C23×C314yes—
364C3×C4⋊C4C23×C314yes—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—32no—
367C3×C22⋊C4—38no—
368C3×C22⋊C4—32no—
369C3×C22⋊C4—32no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—32no—
375C3×C42—32no—
376C3×C42—32no—
377C3×C42—38no—
378C3×C42—34no—
379C3×C42C22×D311yescharacteristic
380C3×C42C22×D311yescharacteristic
381C3×C42C22×D311yescharacteristic
382C3×C42C22×D311yescharacteristic
383C3×C42C23×C311yescharacteristic
384C3×C42C23×C311yescharacteristic
385C3×C42C23×C311yescharacteristic
386C3×C42C23×C311yescharacteristic
387#217C23×C314yes—
388#217C23×C312yes—
389(C2×D3)⋊C4C23×C312yes—
390(C2×D3)⋊C4C23×C312yes—
391(C2×D3)⋊C4C23×C318yes—
392C4⋊Dic3C23×C312yes—
393C4⋊Dic3C23×C312yes—
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396C4⋊Dic3C23×C312yes—
397C4⋊Dic3C23×C312yes—
398C4⋊Dic3C23×C318yes—
399Dic3⋊C4C23×C314yes—
400Dic3⋊C4C23×C314yes—
401Dic3⋊C4C23×C312yes—
402Dic3⋊C4C23×C312yes—
403Dic3⋊C4C23×C318yes—
404Dic3⋊C4C23×C318yes—
405Dic3⋊C4C23×C318yes—
406C4×Dic3C23×C314yes—
407C4×Dic3C23×C312yes—
408C4×Dic3C23×C312yes—
409C4×Dic3C23×C312yes—
410C4×Dic3C23×C318yes—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C22×Q812yes—
414C22×C32C2511yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3C22×Q814yes—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—28no—
421C32×C4C22×Q812yes—
422C32×C4C22×Q812yes—
423C32×C4H(5,𝔽2)12yes—
424C32×C42−1+412yes—
425C3×Dic3—24no—
426C3×Dic3—22no—
427C3×Dic3—24no—
428C3×Dic3—22no—
429C3×Dic3C22×Q814yes—
430C2×#41—31no—
431C22×Q8—34no—
432C22×Q8C2×C3×D312yes—
433C4⋊Q8—34no—
434C4⋊Q8—38no—
435C4⋊Q8—34no—
436C4⋊Q8—34no—
437C4⋊Q8—34no—
438C4⋊Q8—31no—
439C4⋊Q8—31no—
440C4⋊Q8C2×C3×D312yes—
441C4⋊Q8C2×C3×D312yes—
442C4⋊Q8C2×C3×D312yes—
443C4⋊Q8C2×C3×D312yes—
444#125—34no—
445#125—38no—
446#125—34no—
447#125—32no—
448C22⋊Q8—34no—
449C22⋊Q8—38no—
450C22⋊Q8—32no—
451C22⋊Q8—32no—
452C22⋊Q8—38no—
453C22⋊Q8—34no—
454C22⋊Q8—38no—
455C4×Q8—34no—
456C4×Q8—34no—
457C4×Q8—34no—
458C4×Q8—31no—
459C4×Q8—31no—
460C4×Q8—32no—
461C4×Q8—32no—
462C4×D4—32no—
463C4×D4—32no—
464C4×D4—38no—
465C4×D4—34no—
466C4×D4—31no—
467C4×D4—31no—
468#117—31no—
469#117—32no—
470#117—34no—
471#117—32no—
472C2×C4⋊C4—34no—
473C2×C4⋊C4—34no—
474C2×C4⋊C4C2×C3×D312yes—
475C2×C4⋊C4C2×C3×D312yes—
476C2×C42—32no—
477C2×C42C2×C3×D311yescharacteristic
478C23×C3—21no—
479C23×C3—32no—
480C23×C3C23×D311yescharacteristic
481C23×C3C24×C311yescharacteristic
482C22×D3C24×C312yes—
483C3×Q8—28no—
484C3×Q8—28no—
485C3×Q8—34no—
486C3×Q8—48no—
487C3×Q8—44no—
488C3×Q8—44no—
489C3×Q8—48no—
490C3×Q8—64no—
491C3×Q8—64no—
492C3×Q8—128no—
493C3×D4—38no—
494C3×D4—34no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—28no—
508C2×C3×C4—24no—
509C2×C3×C4—32no—
510C2×C3×C4—38no—
511C2×C3×C4—34no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—34no—
515C2×C3×C4—44no—
516C2×C3×C4—44no—
517C2×C3×C4—48no—
518C2×C3×C4—64no—
519C2×C3×C4—64no—
520C2×C3×C4—128no—
521C2×C3×C4D3×Q814yescomplemented
522C2×C3×C4C2×C3×Q814yescomplemented
523C2×C3×C4C23×D318yes—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C318yes—
531C2×C3×C4C24×C311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533C2×C3×C4C24×C311yescharacteristic
534C2×C3×C4C24×C311yescharacteristic
535C2×C3×C4C24×C311yescharacteristic
536C2×C3×C4C24×C311yescharacteristic
537#67C2×C3×Q818yescomplemented
538C2×Dic3C24×C314yes—
539C2×Dic3C24×C312yes—
540C2×Dic3C24×C312yes—
541C2×Dic3C24×C314yes—
542C2×Dic3C24×C312yes—
543D12C2×C3×Q814yescomplemented
544C4×D3—24no—
545C4×D3—24no—
546C4×D3—48no—
547C4×D3C2×C3×Q818yescomplemented
548Dic6—24no—
549Dic6—24no—
550Dic6—48no—
551Dic6C2×C3×Q814yescomplemented
552C2×C32—22no—
553C2×C32C23×Q811yescharacteristic
554C2×C32C2×H(5,𝔽2)11yescharacteristic
555C2×C32C2×2−1+411yescharacteristic
556C3×D3—24no—
557#41—38no—
558C2×Q8—31no—
559C2×Q8—32no—
560C2×Q8—32no—
561C2×Q8—38no—
562C2×Q8—44no—
563C2×Q8—128no—
564C2×Q8C22×C3×D314yes—
565C2×Q8C22×C3×D314yes—
566C2×D4—32no—
567C2×D4—31no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—38no—
572C22×C4C22×C3×D311yescharacteristic
573C22×C4C22×C3×D311yescharacteristic
574C22×C4C22×C3×D314yes—
575C22×C4C22×C3×D311yescharacteristic
576C4⋊C4—32no—
577C4⋊C4—32no—
578C4⋊C4—38no—
579C4⋊C4—38no—
580C4⋊C4—32no—
581C4⋊C4—32no—
582C4⋊C4—31no—
583C4⋊C4—32no—
584C4⋊C4—31no—
585C4⋊C4—32no—
586C4⋊C4—34no—
587C4⋊C4—38no—
588C4⋊C4—38no—
589C4⋊C4—34no—
590C4⋊C4C22×C3×D314yes—
591C4⋊C4C22×C3×D314yes—
592C4⋊C4C22×C3×D314yes—
593C4⋊C4C22×C3×D314yes—
594C22⋊C4—34no—
595C22⋊C4—32no—
596C22⋊C4—38no—
597C22⋊C4—32no—
598C22⋊C4—32no—
599C42—32no—
600C42—32no—
601C42—32no—
602C42—38no—
603C42—34no—
604C42C22×C3×D311yescharacteristic
605C42C22×C3×D311yescharacteristic
606C42C22×C3×D311yescharacteristic
607C42C22×C3×D311yescharacteristic
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—22no—
615C22×C3—21no—
616C22×C3—34no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3C2×D3×Q812yes—
620C22×C3C22×C3×Q812yes—
621C22×C3C24×D311yescharacteristic
622C22×C3C25×C311yescharacteristic
623C2×D3—22no—
624C2×D3—22no—
625C2×D3C22×C3×Q814yes—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—21no—
629C3×C4—28no—
630C3×C4—21no—
631C3×C4—28no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—34no—
639C3×C4—48no—
640C3×C4—62no—
641C3×C4—64no—
642C3×C4—62no—
643C3×C4—64no—
644C3×C4#100412yes—
645C3×C4C2×D3×Q812yes—
646C3×C4C2×D3×Q812yes—
647C3×C4#100712yes—
648C3×C4C22×C3×Q812yes—
649C3×C4C22×C3×Q812yes—
650C3×C4C3×H(5,𝔽2)12yes—
651C3×C4C3×2−1+412yes—
652Dic3—24no—
653Dic3—22no—
654Dic3—24no—
655Dic3—22no—
656Dic3C22×C3×Q814yes—
657C32#350311yescharacteristic, complemented, Sylow
658C23—32no—
659C23C23×C3×D311yescharacteristic
660Q8—28no—
661Q8—34no—
662Q8—44no—
663Q8—64no—
664Q8—64no—
665Q8—128no—
666D4—38no—
667D4—34no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—32no—
671C2×C4—38no—
672C2×C4—34no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—34no—
676C2×C4—44no—
677C2×C4—64no—
678C2×C4—64no—
679C2×C4—128no—
680C2×C4C3×D3×Q814yescomplemented
681C2×C4C23×C3×D318yes—
682C2×C4C23×C3×D311yescharacteristic
683C2×C4C23×C3×D311yescharacteristic
684C2×C4C23×C3×D311yescharacteristic
685C2×C4C23×C3×D311yescharacteristic
686C2×C4C23×C3×D311yescharacteristic
687C2×C4C23×C3×D311yescharacteristic
688C2×C3—24no—
689C2×C3—22no—
690C2×C3—22no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—64no—
695C2×C3C2×#100411yescharacteristic
696C2×C3C22×D3×Q811yescharacteristic
697C2×C3C2×#100711yescharacteristic
698C2×C3C23×C3×Q811yescharacteristic
699C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
700C2×C3C2×C3×2−1+411yescharacteristic
701D3—24no—
702C22—21no—
703C22—21no—
704C22—34no—
705C22—62no—
706C22—62no—
707C22C2×C3×D3×Q812yes—
708C22C24×C3×D311yescharacteristic
709C4—21no—
710C4—28no—
711C4—21no—
712C4—34no—
713C4—62no—
714C4—64no—
715C4—62no—
716C4—64no—
717C4C3×#100412yes—
718C4C2×C3×D3×Q812yes—
719C4C2×C3×D3×Q812yes—
720C4C3×#100712yes—
721C3—21no—
722C3#8621511yescharacteristic, direct product factor
723C3C3×#350311yescharacteristic, complemented
724C2—22no—
725C2—64no—
726C2C2×C3×#100411yescharacteristic
727C2C22×C3×D3×Q811yescharacteristic
728C2C2×C3×#100711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32C25
prime radicalC2×C3×#235C22
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#3503
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4⋊Q8C2semidirect
2. C3×Q8×#67C2semidirect
3. C3×#5730C2semidirect
4. C3×#5729C2semidirect
5. C3×#5728C2semidirect
6. C3×#5727C2semidirect
7. C3×D3×C4⋊Q8C2semidirect
8. C3×#5722C2semidirect
9. C3×#5721C2semidirect
10. C3×#5511C2semidirect
12. C3×#5500C2semidirect
14. C3×#5470C2semidirect
16. #86215C3direct (N × H)
77. C2×C3×C4⋊Q8D3semidirect
78. C2×C3×C4⋊Q8C2×C3semidirect
81. Q8×#67C2×C3semidirect
82. #5730C2×C3semidirect
83. #5729C2×C3semidirect
84. #5728C2×C3semidirect
85. #5727C2×C3semidirect
86. D3×C4⋊Q8C2×C3semidirect
87. #5722C2×C3semidirect
88. #5721C2×C3semidirect
89. #5511C2×C3semidirect
91. #5500C2×C3semidirect
93. #5470C2×C3semidirect
103. C3×#235Q8semidirect
257. C2×C32×C4C2×Q8semidirect
265. C3×#67C2×Q8semidirect
271. C3×D12C2×Q8semidirect
275. C3×C4×D3C2×Q8semidirect
279. C3×Dic6C2×Q8semidirect
291. C2×C4⋊Q8C3×D3semidirect
329. #235C3×Q8semidirect
521. C2×C3×C4D3×Q8semidirect
522. C2×C3×C4C2×C3×Q8semidirect
537. #67C2×C3×Q8semidirect
543. D12C2×C3×Q8semidirect
547. C4×D3C2×C3×Q8semidirect
551. Dic6C2×C3×Q8semidirect
657. C32#3503semidirect
680. C2×C4C3×D3×Q8semidirect
722. C3#86215direct (N × H)
723. C3C3×#3503semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C3×Q8×#672
C3×#57302
C3×#57292
C3×#57282
C3×#57272
C3×D3×C4⋊Q82
C3×#57222
C3×#57212
C3×#55112
C3×#55042
C3×#55002
C3×C4×#2352
C3×#54702
C3×#35033
#862153