Finite Group Databasebeta

← C3×#86574 #11906169

Subgroups — C3×#86574 #11906169

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#543C211yesmaximal, characteristic, complemented
2C3×#5636C214yesmaximal, complemented
3C3×#5636C214yesmaximal, complemented
4C3×#5635C214yesmaximal, complemented
5C3×#5634C212yesmaximal, complemented
6C3×#5632C214yesmaximal, complemented
7C3×D3×C22⋊Q8C212yesmaximal, complemented
8C3×#5623C212yesmaximal, complemented
9C3×#5622C212yesmaximal, complemented
10C3×#5486C212yesmaximal
11C2×C3×#67⋊C4C211yesmaximal, characteristic
12C3×#5483C211yesmaximal, characteristic, complemented
13C2×C3×#878C212yesmaximal, complemented
14C3×#3501—31nomaximal
15#86574C311yesmaximal, characteristic, direct product factor
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×C3×D3×Q8C2212yescomplemented
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2212yescomplemented
21C32×C22⋊Q8C2212yes—
22C32×C22⋊Q8C2212yes—
23C32×C22⋊Q8C2214yescomplemented
24C32×C22⋊Q8C2214yescomplemented
25C2×C32×C22⋊C4C2212yes—
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C3×#217C2212yes—
28C3×#946C2212yescomplemented
29C3×#946C2214yescomplemented
30C3×Q8×Dic3C2212yescomplemented
31C3×#944C2212yescomplemented
32C3×#944C2214yescomplemented
33C3×C4×#67C2214yes—
34C3×C4×#67C2214yes—
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2212yescomplemented
37C3×#924C2212yes—
38C3×#924C2212yes—
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2212yescomplemented
41C2×C3×Dic3⋊C4C2212yescomplemented
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#897C2212yescomplemented
44C3×#897C2214yescomplemented
45C3×#896C2214yescomplemented
46C3×#896C2214yescomplemented
47C3×#896C2214yescomplemented
48C3×D3×C4⋊C4C2214yescomplemented
49C3×D3×C4⋊C4C2212yescomplemented
50C3×#889C2214yescomplemented
51C3×#889C2214yescomplemented
52C3×#889C2214yescomplemented
53C3×#888C2212yescomplemented
54C3×#888C2214yescomplemented
55C3×#887C2214yescomplemented
56C3×#887C2212yescomplemented
57C3×#67⋊C4C2214yes—
58C3×#67⋊C4C2214yes—
59C3×#67⋊C4C2214yes—
60C3×#67⋊C4C2214yes—
61C3×D3×C22⋊C4C2214yes—
62C3×#878C2214yes—
63C3×#878C2214yes—
64C3×#878C2214yescomplemented
65C3×#878C2214yescomplemented
66C3×#878C2214yescomplemented
67C3×#878C2214yescomplemented
68C3×#877C2214yes—
69C3×#554—34no—
70C3×#554—34no—
71C3×#554—34no—
72C3×D4×Q8—34no—
73C3×#544—32no—
74C3×#543—21no—
75C3×#543—32no—
76C3×#543—31no—
77C3×#543D311yescharacteristic, complemented
78C3×#543C2×C311yescharacteristic, complemented
79C3×#533—32no—
80C2×C3×C22⋊Q8—32no—
81C2×C3×C22⋊Q8—32no—
82C3×#518—32no—
83C2×C3×C4×D4—31no—
84#5636C2×C314yescomplemented
85#5636C2×C314yescomplemented
86#5635C2×C314yescomplemented
87#5634C2×C312yescomplemented
88#5632C2×C314yescomplemented
89D3×C22⋊Q8C2×C312yescomplemented
90#5623C2×C312yescomplemented
91#5622C2×C312yescomplemented
92#5486C2×C312yes—
93C2×#67⋊C4C2×C311yescharacteristic
94#5483C2×C311yescharacteristic, complemented
95C2×#878C2×C312yescomplemented
96C24×C32C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C2×C32×Q8C2312yes—
99C2×C32×Q8C2312yes—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2312yes—
103C22×C32×C4C2312yes—
104C2×C3×#67Q818yescomplemented
105C2×C3×#67C2314yes—
106C22×C3×Dic3—42no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2312yes—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2312yes—
112C22×C3×Dic3C2312yes—
113C22×C3×Dic3C2311yescharacteristic
114C3×D3×Q8—44no—
115C2×C3×C4×D3—42no—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×C4×D3C2314yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6—44no—
121C2×C3×Dic6C2314yes—
122C2×C3×Dic6C2314yes—
123C2×C3×Dic6C2312yes—
124C2×C3×Dic6C2312yes—
125C32×C4⋊C4C2312yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2314yes—
128C32×C4⋊C4C2312yes—
129C32×C22⋊C4C2314yes—
130C32×C22⋊C4C2314yes—
131C32×C22⋊C4C2314yes—
132C3×#217C2314yes—
133C3×#217C2314yes—
134C3×(C2×D3)⋊C4C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×C4⋊Dic3C2312yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2312yes—
153C3×C4×Dic3C2312yes—
154#3501—31noSylow
155C22×C3×Q8—32no—
156C22×C3×Q8—32no—
157C22×C3×D4—31no—
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C22×#67C22×C311yescharacteristic
161C23×Dic3C22×C311yescharacteristic
162C2×D3×Q8C22×C312yescomplemented
163C22×C4×D3C22×C311yescharacteristic
164C22×Dic6C22×C312yescomplemented
165C3×C4⋊Q8—32no—
166C3×C4⋊Q8—34no—
167C3×C4⋊Q8—32no—
168C3×C4⋊Q8—34no—
169C3×#125—34no—
170C3×#125—34no—
171C3×#125—34no—
172C3×C22⋊Q8—22no—
173C3×C22⋊Q8—22no—
174C3×C22⋊Q8—24no—
175C3×C22⋊Q8—24no—
176C3×C22⋊Q8—32no—
177C3×C22⋊Q8—34no—
178C3×C22⋊Q8—32no—
179C3×C22⋊Q8—32no—
180C3×C22⋊Q8—34no—
181C3×C22⋊Q8—34no—
182C3×C22⋊Q8—34no—
183C3×C22⋊Q8—32no—
184C3×C22⋊Q8—34no—
185C3×C22⋊Q8—34no—
186C3×C22⋊Q8—34no—
187C3×C22⋊Q8—34no—
188C3×C22⋊Q8—34no—
189C3×C22⋊Q8—34no—
190C3×C22⋊Q8—34no—
191C3×C22⋊Q8C2×D312yes—
192C3×C22⋊Q8C2×D312yes—
193C3×C22⋊Q8C2×D314yescomplemented
194C3×C22⋊Q8C2×D314yescomplemented
195C3×C22⋊Q8C22×C312yes—
196C3×C22⋊Q8C22×C312yes—
197C3×C22⋊Q8C22×C314yescomplemented
198C3×C22⋊Q8C22×C314yescomplemented
199C3×C4×Q8—32no—
200C3×C4×Q8—34no—
201C3×C4×Q8—32no—
202C3×C4×D4—34no—
203C3×C4×D4—34no—
204C3×C4×D4—34no—
205C3×C4×D4—34no—
206C3×C4×D4—34no—
207C3×C4×D4—34no—
208C3×#117—34no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—32no—
211C2×C3×C4⋊C4—32no—
212C2×C3×C4⋊C4—32no—
213C2×C3×C4⋊C4—34no—
214C2×C3×C4⋊C4—32no—
215C2×C3×C22⋊C4—21no—
216C2×C3×C22⋊C4—22no—
217C2×C3×C22⋊C4—32no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—34no—
220C2×C3×C22⋊C4C2×D311yescharacteristic
221C2×C3×C22⋊C4C2×D312yes—
222C2×C3×C22⋊C4C22×C312yes—
223C2×C3×C22⋊C4C22×C311yescharacteristic
224C2×C3×C42—31no—
225C2×#217C22×C312yes—
226#946C22×C314yescomplemented
227#946C22×C312yescomplemented
228Q8×Dic3C22×C312yescomplemented
229#944C22×C314yescomplemented
230#944C22×C312yescomplemented
231C4×#67C22×C314yes—
232C4×#67C22×C314yes—
233C2×(C2×D3)⋊C4C22×C311yescharacteristic
234C2×C4⋊Dic3C22×C312yescomplemented
235#924C22×C312yes—
236#924C22×C312yes—
237C2×Dic3⋊C4C22×C311yescharacteristic
238C2×Dic3⋊C4C22×C312yescomplemented
239C2×Dic3⋊C4C22×C312yescomplemented
240C2×C4×Dic3C22×C311yescharacteristic
241#897C22×C314yescomplemented
242#897C22×C312yescomplemented
243#896C22×C314yescomplemented
244#896C22×C314yescomplemented
245#896C22×C314yescomplemented
246D3×C4⋊C4C22×C314yescomplemented
247D3×C4⋊C4C22×C312yescomplemented
248#889C22×C314yescomplemented
249#889C22×C314yescomplemented
250#889C22×C314yescomplemented
251#888C22×C312yescomplemented
252#888C22×C314yescomplemented
253#887C22×C314yescomplemented
254#887C22×C312yescomplemented
255#67⋊C4C22×C314yes—
256#67⋊C4C22×C314yes—
257#67⋊C4C22×C314yes—
258#67⋊C4C22×C314yes—
259D3×C22⋊C4C22×C314yes—
260#878C22×C314yes—
261#878C22×C314yes—
262#878C22×C314yescomplemented
263#878C22×C314yescomplemented
264#878C22×C314yescomplemented
265#878C22×C314yescomplemented
266#877C22×C314yes—
267C23×C32—41no—
268C23×C32—41no—
269C23×C32C2×Q814yescomplemented
270C23×C32C2411yescharacteristic
271C23×C32C2412yes—
272C22×C3×D3—41no—
273C22×C3×D3—41no—
274C22×C3×D3C2×Q814yescomplemented
275C22×C3×D3C2412yes—
276C32×Q8—42no—
277C32×Q8—42no—
278C2×C32×C4—42no—
279C2×C32×C4—41no—
280C2×C32×C4—41no—
281C2×C32×C4—42no—
282C2×C32×C4C2412yes—
283C2×C32×C4C2414yes—
284C2×C32×C4C2414yes—
285C2×C32×C4C2412yes—
286C3×#67C2×Q8116yescomplemented
287C2×C3×Dic3—24no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—42no—
290C2×C3×Dic3—41no—
291C2×C3×Dic3—42no—
292C2×C3×Dic3—42no—
293C2×C3×Dic3C2×Q814yescomplemented
294C2×C3×Dic3C2411yescharacteristic
295C2×C3×Dic3C2414yes—
296C2×C3×Dic3C2414yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2411yescharacteristic
300C3×C4×D3—24no—
301C3×C4×D3—42no—
302C3×C4×D3—44no—
303C3×C4×D3—44no—
304C3×Dic6—28no—
305C3×Dic6—44no—
306C3×Dic6—42no—
307C3×Dic6—42no—
308#554—34no—
309#554—34no—
310#554—34no—
311D4×Q8—34no—
312#544—32no—
313#543—32no—
314#543—31no—
315#543C3×D311yescharacteristic, complemented
316#533—32no—
317C2×C22⋊Q8—32no—
318C2×C22⋊Q8—32no—
319#518—32no—
320C2×C4×D4—31no—
321C24×C3—21no—
322C24×C3—31no—
323C24×C3C22×D311yescharacteristic
324C24×C3C23×C311yescharacteristic
325C23×D3C23×C311yescharacteristic
326C2×C3×Q8—22no—
327C2×C3×Q8—22no—
328C2×C3×Q8—34no—
329C2×C3×Q8—32no—
330C2×C3×Q8—32no—
331C2×C3×Q8—34no—
332C2×C3×Q8—124no—
333C2×C3×Q8—124no—
334C2×C3×Q8C22×D312yes—
335C2×C3×Q8C22×D312yes—
336C2×C3×Q8C23×C312yes—
337C2×C3×Q8C23×C312yes—
338C2×C3×D4—38no—
339C2×C3×D4—34no—
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—22no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C22×C3×C4—32no—
349C22×C3×C4—31no—
350C22×C3×C4—32no—
351C22×C3×C4—32no—
352C22×C3×C4—34no—
353C22×C3×C4—34no—
354C22×C3×C4—32no—
355C22×C3×C4—122no—
356C22×C3×C4—122no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D312yes—
359C22×C3×C4C22×D312yes—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C23×C311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C22×C3×C4C23×C312yes—
364C22×C3×C4C23×C312yes—
365C2×#67C3×Q818yescomplemented
366C2×#67C23×C314yes—
367C22×Dic3—42no—
368C22×Dic3C23×C311yescharacteristic
369C22×Dic3C23×C312yes—
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C312yes—
372C22×Dic3C23×C312yes—
373C22×Dic3C23×C312yes—
374C22×Dic3C23×C311yescharacteristic
375D3×Q8—44no—
376C2×C4×D3—42no—
377C2×C4×D3C23×C312yes—
378C2×C4×D3C23×C314yes—
379C2×C4×D3C23×C314yes—
380C2×C4×D3C23×C312yes—
381C2×Dic6—44no—
382C2×Dic6C23×C314yes—
383C2×Dic6C23×C314yes—
384C2×Dic6C23×C312yes—
385C2×Dic6C23×C312yes—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—24no—
388C3×C4⋊C4—24no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—32no—
401C3×C4⋊C4—34no—
402C3×C4⋊C4—32no—
403C3×C4⋊C4C22×D312yes—
404C3×C4⋊C4C22×D314yes—
405C3×C4⋊C4C22×D314yes—
406C3×C4⋊C4C22×D312yes—
407C3×C4⋊C4C23×C312yes—
408C3×C4⋊C4C23×C314yes—
409C3×C4⋊C4C23×C314yes—
410C3×C4⋊C4C23×C312yes—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—24no—
413C3×C22⋊C4—24no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4C22×D314yes—
420C3×C22⋊C4C22×D314yes—
421C3×C22⋊C4C22×D314yes—
422C3×C22⋊C4C23×C314yes—
423C3×C22⋊C4C23×C314yes—
424C3×C22⋊C4C23×C314yes—
425C3×C42—32no—
426C3×C42—32no—
427C3×C42—34no—
428C3×C42—34no—
429#217C23×C314yes—
430#217C23×C314yes—
431(C2×D3)⋊C4C23×C314yes—
432(C2×D3)⋊C4C23×C314yes—
433(C2×D3)⋊C4C23×C314yes—
434C4⋊Dic3C23×C314yes—
435C4⋊Dic3C23×C314yes—
436C4⋊Dic3C23×C312yes—
437C4⋊Dic3C23×C312yes—
438Dic3⋊C4C23×C314yes—
439Dic3⋊C4C23×C314yes—
440Dic3⋊C4C23×C314yes—
441Dic3⋊C4C23×C314yes—
442Dic3⋊C4C23×C314yes—
443Dic3⋊C4C23×C314yes—
444Dic3⋊C4C23×C314yes—
445Dic3⋊C4C23×C314yes—
446Dic3⋊C4C23×C314yes—
447C4×Dic3C23×C314yes—
448C4×Dic3C23×C314yes—
449C4×Dic3C23×C312yes—
450C4×Dic3C23×C312yes—
451C22×C32—22no—
452C22×C32—21no—
453C22×C32—22no—
454C22×C32—21no—
455C22×C32—44no—
456C22×C32C22×Q812yes—
457C22×C32C22×Q814yes—
458C22×C32C2511yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—44no—
462C2×C3×D3C22×Q814yes—
463C32×C4—24no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—24no—
467C3×Dic3—24no—
468C3×Dic3—22no—
469C3×Dic3—21no—
470C3×Dic3—24no—
471C3×Dic3C22×Q814yes—
472C3×Dic3H(5,𝔽2)12yes—
473C22×Q8—32no—
474C22×Q8—32no—
475C22×D4—31no—
476C23×C4—31no—
477C23×C4—31no—
478C4⋊Q8—32no—
479C4⋊Q8—34no—
480C4⋊Q8—32no—
481C4⋊Q8—34no—
482#125—34no—
483#125—34no—
484#125—34no—
485C22⋊Q8—32no—
486C22⋊Q8—34no—
487C22⋊Q8—32no—
488C22⋊Q8—32no—
489C22⋊Q8—34no—
490C22⋊Q8—32no—
491C22⋊Q8—34no—
492C22⋊Q8—34no—
493C22⋊Q8—34no—
494C22⋊Q8—34no—
495C22⋊Q8—34no—
496C22⋊Q8—34no—
497C22⋊Q8—34no—
498C22⋊Q8—34no—
499C22⋊Q8—34no—
500C22⋊Q8C2×C3×D312yes—
501C22⋊Q8C2×C3×D312yes—
502C22⋊Q8C2×C3×D314yescomplemented
503C22⋊Q8C2×C3×D314yescomplemented
504C4×Q8—32no—
505C4×Q8—34no—
506C4×Q8—32no—
507C4×D4—34no—
508C4×D4—34no—
509C4×D4—34no—
510C4×D4—34no—
511C4×D4—34no—
512C4×D4—34no—
513#117—34no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—32no—
516C2×C4⋊C4—32no—
517C2×C4⋊C4—32no—
518C2×C4⋊C4—34no—
519C2×C4⋊C4—32no—
520C2×C22⋊C4—32no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—34no—
523C2×C22⋊C4C2×C3×D311yescharacteristic
524C2×C22⋊C4C2×C3×D312yes—
525C2×C42—31no—
526C23×C3—21no—
527C23×C3—22no—
528C23×C3—24no—
529C23×C3—32no—
530C23×C3—34no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—81no—
536C23×C3—81no—
537C23×C3—121no—
538C23×C3—121no—
539C23×C3D3×Q814yescomplemented
540C23×C3C2×C3×Q814yescomplemented
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D312yes—
543C23×C3C24×C311yescharacteristic
544C23×C3C24×C312yes—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3C2×C3×Q814yescomplemented
548C22×D3C24×C312yes—
549C3×Q8—42no—
550C3×Q8—42no—
551C3×Q8—42no—
552C3×Q8—42no—
553C3×Q8—68no—
554C3×Q8—82no—
555C3×Q8—82no—
556C3×Q8—122no—
557C3×Q8—122no—
558C3×Q8—124no—
559C3×D4—316no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—24no—
563C2×C3×C4—22no—
564C2×C3×C4—34no—
565C2×C3×C4—32no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—32no—
571C2×C3×C4—42no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—42no—
575C2×C3×C4—41no—
576C2×C3×C4—42no—
577C2×C3×C4—41no—
578C2×C3×C4—42no—
579C2×C3×C4—64no—
580C2×C3×C4—62no—
581C2×C3×C4—64no—
582C2×C3×C4—81no—
583C2×C3×C4—82no—
584C2×C3×C4—82no—
585C2×C3×C4—81no—
586C2×C3×C4—124no—
587C2×C3×C4—122no—
588C2×C3×C4—124no—
589C2×C3×C4—122no—
590C2×C3×C4—122no—
591C2×C3×C4—121no—
592C2×C3×C4—122no—
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D314yes—
595C2×C3×C4C23×D314yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C24×C312yes—
598C2×C3×C4C24×C314yes—
599C2×C3×C4C24×C314yes—
600C2×C3×C4C24×C312yes—
601#67C2×C3×Q8116yescomplemented
602C2×Dic3—24no—
603C2×Dic3—22no—
604C2×Dic3—42no—
605C2×Dic3—41no—
606C2×Dic3—42no—
607C2×Dic3—42no—
608C2×Dic3C2×C3×Q814yescomplemented
609C2×Dic3C24×C311yescharacteristic
610C2×Dic3C24×C314yes—
611C2×Dic3C24×C314yes—
612C2×Dic3C24×C312yes—
613C2×Dic3C24×C312yes—
614C2×Dic3C24×C311yescharacteristic
615C4×D3—24no—
616C4×D3—42no—
617C4×D3—44no—
618C4×D3—44no—
619Dic6—28no—
620Dic6—44no—
621Dic6—42no—
622Dic6—42no—
623C2×C32—22no—
624C2×C32—24no—
625C2×C32C23×Q811yescharacteristic
626C2×C32C2×H(5,𝔽2)11yescharacteristic
627C2×C32#58511yescharacteristic
628C3×D3—24no—
629C24—31no—
630C24C22×C3×D311yescharacteristic
631C2×Q8—34no—
632C2×Q8—32no—
633C2×Q8—32no—
634C2×Q8—34no—
635C2×Q8—124no—
636C2×Q8—124no—
637C2×Q8C22×C3×D312yes—
638C2×Q8C22×C3×D312yes—
639C2×D4—34no—
640C2×D4—38no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—31no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—34no—
650C22×C4—34no—
651C22×C4—32no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4C22×C3×D311yescharacteristic
655C22×C4C22×C3×D312yes—
656C22×C4C22×C3×D312yes—
657C22×C4C22×C3×D311yescharacteristic
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—32no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4—34no—
667C4⋊C4—34no—
668C4⋊C4—34no—
669C4⋊C4—34no—
670C4⋊C4—32no—
671C4⋊C4C22×C3×D312yes—
672C4⋊C4C22×C3×D314yes—
673C4⋊C4C22×C3×D314yes—
674C4⋊C4C22×C3×D312yes—
675C22⋊C4—34no—
676C22⋊C4—34no—
677C22⋊C4—34no—
678C22⋊C4—34no—
679C22⋊C4—34no—
680C22⋊C4C22×C3×D314yes—
681C22⋊C4C22×C3×D314yes—
682C22⋊C4C22×C3×D314yes—
683C42—32no—
684C42—32no—
685C42—34no—
686C42—34no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—22no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—21no—
693C22×C3—22no—
694C22×C3—21no—
695C22×C3—22no—
696C22×C3—24no—
697C22×C3—21no—
698C22×C3—34no—
699C22×C3—42no—
700C22×C3—41no—
701C22×C3—42no—
702C22×C3—41no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—84no—
708C22×C3—124no—
709C22×C3C2×D3×Q812yes—
710C22×C3C2×D3×Q814yes—
711C22×C3C22×C3×Q812yes—
712C22×C3C22×C3×Q814yes—
713C22×C3C24×D311yescharacteristic
714C22×C3C25×C311yescharacteristic
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—44no—
718C2×D3C22×C3×Q814yes—
719C3×C4—22no—
720C3×C4—24no—
721C3×C4—24no—
722C3×C4—22no—
723C3×C4—24no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—24no—
727C3×C4—34no—
728C3×C4—32no—
729C3×C4—42no—
730C3×C4—44no—
731C3×C4—44no—
732C3×C4—42no—
733C3×C4—61no—
734C3×C4—62no—
735C3×C4—64no—
736C3×C4—64no—
737Dic3—24no—
738Dic3—22no—
739Dic3—21no—
740Dic3—24no—
741Dic3C22×C3×Q814yes—
742Dic3C3×H(5,𝔽2)12yes—
743C32#350111yescharacteristic, complemented, Sylow
744C23—32no—
745C23—34no—
746C23—41no—
747C23—41no—
748C23—121no—
749C23—121no—
750C23C3×D3×Q814yescomplemented
751C23C23×C3×D311yescharacteristic
752C23C23×C3×D312yes—
753Q8—42no—
754Q8—42no—
755Q8—68no—
756Q8—122no—
757Q8—124no—
758Q8—122no—
759D4—316no—
760C2×C4—34no—
761C2×C4—32no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—34no—
765C2×C4—34no—
766C2×C4—32no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—64no—
772C2×C4—62no—
773C2×C4—64no—
774C2×C4—122no—
775C2×C4—124no—
776C2×C4—124no—
777C2×C4—122no—
778C2×C4—121no—
779C2×C4—122no—
780C2×C4—122no—
781C2×C4C23×C3×D312yes—
782C2×C4C23×C3×D314yes—
783C2×C4C23×C3×D314yes—
784C2×C4C23×C3×D312yes—
785C2×C3—22no—
786C2×C3—24no—
787C2×C3—22no—
788C2×C3—24no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—42no—
793C2×C3—44no—
794C2×C3—64no—
795C2×C3C22×D3×Q811yescharacteristic
796C2×C3D3×H(5,𝔽2)11yescharacteristic
797C2×C3#596611yescharacteristic
798C2×C3C23×C3×Q811yescharacteristic
799C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
800C2×C3C3×#58511yescharacteristic
801D3—24no—
802C22—22no—
803C22—21no—
804C22—22no—
805C22—21no—
806C22—34no—
807C22—44no—
808C22—62no—
809C22—62no—
810C22—124no—
811C22C2×C3×D3×Q812yes—
812C22C2×C3×D3×Q814yes—
813C22C24×C3×D311yescharacteristic
814C4—22no—
815C4—24no—
816C4—24no—
817C4—22no—
818C4—34no—
819C4—32no—
820C4—61no—
821C4—62no—
822C4—64no—
823C4—64no—
824C3—21no—
825C3#8657411yescharacteristic, direct product factor
826C3C3×#350111yescharacteristic, complemented
827C2—22no—
828C2—24no—
829C2—64no—
830C2C22×C3×D3×Q811yescharacteristic
831C2C3×D3×H(5,𝔽2)11yescharacteristic
832C2C3×#596611yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#543C2
socleC22×C32C25
prime radicalC22×C3×#67C22
hypercenterC3×#543D3
hypocenterC3C3×#3501
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#543

Complements

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

NH ≅ G/Ntype
1. C32×#543C2semidirect
2. C3×#5636C2semidirect
3. C3×#5636C2semidirect
4. C3×#5635C2semidirect
5. C3×#5634C2semidirect
6. C3×#5632C2semidirect
7. C3×D3×C22⋊Q8C2semidirect
8. C3×#5623C2semidirect
9. C3×#5622C2semidirect
12. C3×#5483C2semidirect
13. C2×C3×#878C2semidirect
15. #86574C3direct (N × H)
18. C2×C3×D3×Q8C22semidirect
20. C22×C3×Dic6C22semidirect
23. C32×C22⋊Q8C22semidirect
24. C32×C22⋊Q8C22semidirect
28. C3×#946C22semidirect
29. C3×#946C22semidirect
30. C3×Q8×Dic3C22semidirect
31. C3×#944C22semidirect
32. C3×#944C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
43. C3×#897C22semidirect
44. C3×#897C22semidirect
45. C3×#896C22semidirect
46. C3×#896C22semidirect
47. C3×#896C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×D3×C4⋊C4C22semidirect
50. C3×#889C22semidirect
51. C3×#889C22semidirect
52. C3×#889C22semidirect
53. C3×#888C22semidirect
54. C3×#888C22semidirect
55. C3×#887C22semidirect
56. C3×#887C22semidirect
64. C3×#878C22semidirect
65. C3×#878C22semidirect
66. C3×#878C22semidirect
67. C3×#878C22semidirect
77. C3×#543D3semidirect
78. C3×#543C2×C3semidirect
84. #5636C2×C3semidirect
85. #5636C2×C3semidirect
86. #5635C2×C3semidirect
87. #5634C2×C3semidirect
88. #5632C2×C3semidirect
89. D3×C22⋊Q8C2×C3semidirect
90. #5623C2×C3semidirect
91. #5622C2×C3semidirect
94. #5483C2×C3semidirect
95. C2×#878C2×C3semidirect
104. C2×C3×#67Q8semidirect
162. C2×D3×Q8C22×C3semidirect
164. C22×Dic6C22×C3semidirect
193. C3×C22⋊Q8C2×D3semidirect
194. C3×C22⋊Q8C2×D3semidirect
197. C3×C22⋊Q8C22×C3semidirect
198. C3×C22⋊Q8C22×C3semidirect
226. #946C22×C3semidirect
227. #946C22×C3semidirect
228. Q8×Dic3C22×C3semidirect
229. #944C22×C3semidirect
230. #944C22×C3semidirect
234. C2×C4⋊Dic3C22×C3semidirect
238. C2×Dic3⋊C4C22×C3semidirect
239. C2×Dic3⋊C4C22×C3semidirect
241. #897C22×C3semidirect
242. #897C22×C3semidirect
243. #896C22×C3semidirect
244. #896C22×C3semidirect
245. #896C22×C3semidirect
246. D3×C4⋊C4C22×C3semidirect
247. D3×C4⋊C4C22×C3semidirect
248. #889C22×C3semidirect
249. #889C22×C3semidirect
250. #889C22×C3semidirect
251. #888C22×C3semidirect
252. #888C22×C3semidirect
253. #887C22×C3semidirect
254. #887C22×C3semidirect
262. #878C22×C3semidirect
263. #878C22×C3semidirect
264. #878C22×C3semidirect
265. #878C22×C3semidirect
269. C23×C32C2×Q8semidirect
274. C22×C3×D3C2×Q8semidirect
286. C3×#67C2×Q8semidirect
293. C2×C3×Dic3C2×Q8semidirect
315. #543C3×D3semidirect
365. C2×#67C3×Q8semidirect
502. C22⋊Q8C2×C3×D3semidirect
503. C22⋊Q8C2×C3×D3semidirect
539. C23×C3D3×Q8semidirect
540. C23×C3C2×C3×Q8semidirect
547. C22×D3C2×C3×Q8semidirect
601. #67C2×C3×Q8semidirect
608. C2×Dic3C2×C3×Q8semidirect
743. C32#3501semidirect
750. C23C3×D3×Q8semidirect
825. C3#86574direct (N × H)
826. C3C3×#3501semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
C3×#56362
C3×#56352
C3×#56342
C3×#56322
C3×D3×C22⋊Q82
C3×#56232
C3×#56222
C3×#54862
C2×C3×#67⋊C42
C3×#54832
C2×C3×#8782
C3×#35013
#865743