Finite Group Databasebeta

← #11805682

Subgroups — #11805682

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591713C212yesmaximal
6#10591705C212yesmaximal, complemented
7#10591316C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic, complemented
9#10591272C212yesmaximal, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591224C211yesmaximal, characteristic, complemented
12#82335—31nomaximal
13#73883—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)—24no—
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2211yescharacteristic
24C3×C4×#67C418yescomplemented
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63841—24no—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×C4×#67D311yescharacteristic
42C2×#926—31no—
43C22×C4⋊Dic3—31no—
44C22×C4⋊Dic3—31no—
45C22×C4⋊Dic3—61no—
46C2×#892—31no—
47C3×#380—31no—
48#5220—32no—
49#5212—31no—
50#5212D311yescharacteristic, complemented
51#4987—31no—
52#4980—32no—
53#4977—31no—
54Dic3×C4⋊C4—31no—
55#4958—32no—
56#4951—32no—
57Dic3×C22⋊C4—32no—
58Dic3×C22⋊C4—32no—
59#4936—31no—
60C4×C4⋊Dic3—31no—
61#4670—32no—
62#4655—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—42no—
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2312yes—
75C2×C3×#67—22no—
76C2×C3×#67—22no—
77C2×C3×#67C2×C414yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3C2×C414yescomplemented
86C4⋊(C3⋊Dic3)—22no—
87C4⋊(C3⋊Dic3)—24no—
88C4⋊(C3⋊Dic3)D414yescomplemented
89C3×#217—24no—
90C3×#217C2×C414yes—
91C3×(C2×D3)⋊C4C2×C414yescomplemented
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—22no—
94C3×Dic3⋊C4C2×C414yescomplemented
95C3×C4×Dic3C2×C414yescomplemented
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—42no—
98Dic32—24no—
99Dic32—42no—
100#2352—91noSylow
101C22×C3×D4—31no—
102C23×C3×C4—21no—
103C23×C3×C4—31no—
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C22×#67C2×D311yescharacteristic
107C23×Dic3—32no—
108C23×Dic3—32no—
109C23×Dic3—62no—
110C22×C4×D3C2×D311yescharacteristic
111C3×C4×D4—38no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—31no—
119C2×#217—32no—
120C2×#217—32no—
121C2×#217C2×D312yes—
122C2×#217C2×D311yescharacteristic
123C4×#67Dic318yescomplemented
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4C2×D311yescharacteristic
127#926—64no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3—62no—
137C2×C4⋊Dic3—64no—
138C2×C4⋊Dic3—64no—
139C2×C4⋊Dic3—68no—
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×Dic3⋊C4C2×D311yescharacteristic
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3C2×D311yescharacteristic
148#892—64no—
149C3×#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95C2×D312yes—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32C22×C412yes—
164C23×C32#4112yes—
165C23×C32#4112yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3C22×C412yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—28no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4#4112yes—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—48no—
187C2×C3⋊Dic3C2×D414yes—
188C3×#67—28no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3C22×C412yes—
202C2×C3×Dic3C22×C412yes—
203C2×C3×Dic3C22×C412yes—
204C3×C4×D3—28no—
205C2×C4×D4—31no—
206C2×#117—91no—
207C22×C4⋊C4—91no—
208#388—92no—
209#387—92no—
210#386—92no—
211#382—91no—
212#380—31no—
213#380—91no—
214C4×C4⋊C4—91no—
215C4×C22⋊C4—92no—
216C24×C3—21no—
217C24×C3—31no—
218C24×C3C22×D311yescharacteristic
219C24×C3C22×D311yescharacteristic
220C23×D3C22×D311yescharacteristic
221C2×C3×D4—34no—
222C2×C3×D4—62no—
223C2×C3×D4—62no—
224C22×C3×C4—24no—
225C22×C3×C4—24no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—24no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—34no—
237C22×C3×C4—32no—
238C22×C3×C4—32no—
239C22×C3×C4—62no—
240C22×C3×C4—62no—
241C22×C3×C4C4×D314yes—
242C22×C3×C4C2×Dic314yes—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—22no—
248C2×#67—22no—
249C2×#67C2×Dic314yes—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—62no—
255C22×Dic3—62no—
256C22×Dic3—64no—
257C22×Dic3—64no—
258C22×Dic3—68no—
259C22×Dic3—64no—
260C22×Dic3—64no—
261C22×Dic3—124no—
262C22×Dic3—122no—
263C22×Dic3—122no—
264C22×Dic3—124no—
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3C2×Dic314yescomplemented
273C3×C4⋊C4—34no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—62no—
276C3×C22⋊C4—34no—
277C3×C22⋊C4—34no—
278C3×C22⋊C4—64no—
279C3×C42—34no—
280#217—24no—
281#217—64no—
282#217—122no—
283#217C2×Dic314yes—
284(C2×D3)⋊C4—64no—
285(C2×D3)⋊C4—122no—
286(C2×D3)⋊C4C2×Dic314yescomplemented
287C4⋊Dic3—22no—
288C4⋊Dic3—22no—
289C4⋊Dic3—34no—
290C4⋊Dic3—34no—
291C4⋊Dic3—64no—
292C4⋊Dic3—64no—
293C4⋊Dic3—64no—
294C4⋊Dic3—68no—
295C4⋊Dic3—64no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298Dic3⋊C4C2×Dic314yescomplemented
299C4×Dic3—64no—
300C4×Dic3—64no—
301C4×Dic3—122no—
302C4×Dic3—122no—
303C4×Dic3C2×Dic314yescomplemented
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32#11714yescomplemented
311C22×C32C23×C411yescharacteristic
312C22×C32C22×D411yescharacteristic
313C22×C32C2×#4111yescharacteristic
314C22×C32C2×#4111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C32H(5,𝔽2)11yescharacteristic
317C22×C322−1+411yescharacteristic
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C32×C4—22no—
326C32×C4C4×D414yes—
327C3⋊Dic3—24no—
328C3⋊Dic3—42no—
329C3×Dic3—22no—
330C3×Dic3—22no—
331C3×Dic3—22no—
332C3×Dic3—42no—
333C3×Dic3—42no—
334C22×D4—31no—
335C23×C4—31no—
336C23×C4—92no—
337C23×C4D3211yescharacteristic
338C4×D4—38no—
339#117—184no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—91no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—92no—
346C2×C4⋊C4—184no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—92no—
351C2×C22⋊C4—92no—
352C2×C42—31no—
353C2×C42—92no—
354C2×C42—92no—
355#95—32no—
356#95—92no—
357#95—92no—
358#95—92no—
359#95—92no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—32no—
377C23×C3—61no—
378C23×C3—61no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3C2×C4×D312yes—
384C23×C3#23512yes—
385C23×C3#23512yes—
386C23×C3#23712yes—
387C23×C3#23912yes—
388C23×C3C22×Dic312yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3C22×Dic312yes—
398C3×D4—68no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—216no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—28no—
407C2×C3×C4—28no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—68no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4C2×C4×D312yes—
429C2×C3×C4C2×C4×D312yes—
430C2×C3×C4D3×D412yes—
431C2×C3×C4D3×D412yes—
432C2×C3×C4#23712yes—
433C2×C3×C4#23712yes—
434C2×C3×C4C22×Dic312yes—
435C2×C3×C4C22×Dic312yes—
436#67—28no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—34no—
450C2×Dic3—34no—
451C2×Dic3—64no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—64no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—62no—
462C2×Dic3—62no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3—122no—
466C2×Dic3—122no—
467C2×Dic3—128no—
468C2×Dic3—128no—
469C2×Dic3—1216no—
470C2×Dic3C22×Dic312yes—
471C2×Dic3C22×Dic312yes—
472C2×Dic3C22×Dic312yes—
473C4×D3—28no—
474C2×C32—24no—
475C2×C32C2×#11711yescharacteristic
476C2×C32C2×C4×D411yescharacteristic
477C2×C32#52011yescharacteristic
478C2×C32#54611yescharacteristic
479C2×C32#54811yescharacteristic
480C2×C32#55211yescharacteristic
481C2×C32#55311yescharacteristic
482C3×D3—42no—
483C24—31no—
484C24C2×D3211yescharacteristic
485C2×D4—34no—
486C2×D4—62no—
487C2×D4—62no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—31no—
493C22×C4—34no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—92no—
499C22×C4—92no—
500C22×C4—184no—
501C22×C4—184no—
502C22×C4—362no—
503C22×C4D3×Dic314yes—
504C22×C4C2×D3211yescharacteristic
505C22×C4C2×D3211yescharacteristic
506C4⋊C4—34no—
507C4⋊C4—62no—
508C4⋊C4—62no—
509C4⋊C4—94no—
510C4⋊C4—184no—
511C4⋊C4—182no—
512C22⋊C4—34no—
513C22⋊C4—34no—
514C22⋊C4—64no—
515C22⋊C4—184no—
516C22⋊C4—362no—
517C42—34no—
518C42—184no—
519C42—362no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—24no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—24no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—121no—
550C22×C3—121no—
551C22×C3—121no—
552C22×C3—121no—
553C22×C3#89214yescomplemented
554C22×C3#92614yescomplemented
555C22×C3C22×C4×D311yescharacteristic
556C22×C3C2×#23511yescharacteristic
557C22×C3C2×#23511yescharacteristic
558C22×C3C2×D3×D411yescharacteristic
559C22×C3C2×D3×D411yescharacteristic
560C22×C3C2×#23711yescharacteristic
561C22×C3C2×#23711yescharacteristic
562C22×C3C2×#23711yescharacteristic
563C22×C3C2×#23911yescharacteristic
564C22×C3#100911yescharacteristic
565C22×C3#100911yescharacteristic
566C22×C3#101011yescharacteristic
567C22×C3#101011yescharacteristic
568C22×C3C23×Dic311yescharacteristic
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—41no—
573C2×D3—41no—
574C2×D3—41no—
575C2×D3—41no—
576C3×C4—24no—
577C3×C4—22no—
578C3×C4—22no—
579C3×C4—24no—
580C3×C4—62no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—122no—
584C3×C4—122no—
585C3×C4#67⋊C414yes—
586C3×C4D4×Dic314yes—
587Dic3—22no—
588Dic3—22no—
589Dic3—22no—
590Dic3—42no—
591Dic3—42no—
592Dic3—64no—
593Dic3—64no—
594Dic3—124no—
595Dic3—124no—
596Dic3—122no—
597Dic3—122no—
598C32#235211yescharacteristic, complemented, Sylow
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—32no—
604C23—61no—
605C23—61no—
606C23—61no—
607C23—61no—
608C23—61no—
609C23—61no—
610C23#379512yes—
611C23#379912yes—
612C23C2×D3×Dic312yes—
613C23C22×D3211yescharacteristic
614D4—68no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—28no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—68no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—94no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4—182no—
638C2×C4—182no—
639C2×C4—182no—
640C2×C4—368no—
641C2×C4C2×D3×Dic312yes—
642C2×C4C2×D3×Dic312yes—
643C2×C4#380512yes—
644C2×C4#381112yes—
645C2×C3—28no—
646C2×C3—24no—
647C2×C3—24no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—122no—
656C2×C3C2×#67⋊C411yescharacteristic
657C2×C3C2×#89211yescharacteristic
658C2×C3#552311yescharacteristic
659C2×C3#554111yescharacteristic
660C2×C3#555011yescharacteristic
661C2×C3#555211yescharacteristic
662C2×C3#556511yescharacteristic
663C2×C3#559811yescharacteristic
664C2×C3#561811yescharacteristic
665C2×C3#563011yescharacteristic
666C2×C3#564211yescharacteristic
667C2×C3C2×#92611yescharacteristic
668C2×C3C2×D4×Dic311yescharacteristic
669C2×C3#582711yescharacteristic
670D3—42no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—62no—
678C22—62no—
679C22—62no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22—121no—
684C22#6384114yescomplemented
685C22C2×#379511yescharacteristic
686C22#6429811yescharacteristic
687C22C2×#379911yescharacteristic
688C22#6430811yescharacteristic
689C22C22×D3×Dic311yescharacteristic
690C22C2×#380511yescharacteristic
691C22C2×#381111yescharacteristic
692C4—22no—
693C4—62no—
694C4—62no—
695C4—62no—
696C4—122no—
697C4—122no—
698C4—184no—
699C4—362no—
700C4#67⋊Dic314yes—
701C3—21no—
702C3#7388311yescharacteristic, complemented
703C3#8233511yescharacteristic, complemented
704C2—24no—
705C2—122no—
706C2C2×#6384111yescharacteristic
707C2#1059485311yescharacteristic
708C2#1059491811yescharacteristic
709C2#1059499211yescharacteristic
710C2#1059499511yescharacteristic
711C2#1059501811yescharacteristic
712C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C3⋊Dic3)C2semidirect
3. C2×#63841C2semidirect
4. C3×#5212C2semidirect
6. #10591705C2semidirect
7. #10591316C2semidirect
8. #10591313C2semidirect
9. #10591272C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591224C2semidirect
24. C3×C4×#67C4semidirect
50. #5212D3semidirect
85. C2×C3×C4×D3C2×C4semidirect
88. C4⋊(C3⋊Dic3)D4semidirect
91. C3×(C2×D3)⋊C4C2×C4semidirect
94. C3×Dic3⋊C4C2×C4semidirect
95. C3×C4×Dic3C2×C4semidirect
123. C4×#67Dic3semidirect
272. C2×C4×D3C2×Dic3semidirect
286. (C2×D3)⋊C4C2×Dic3semidirect
298. Dic3⋊C4C2×Dic3semidirect
303. C4×Dic3C2×Dic3semidirect
310. C22×C32#117semidirect
553. C22×C3#892semidirect
554. C22×C3#926semidirect
598. C32#2352semidirect
684. C22#63841semidirect
702. C3#73883semidirect
703. C3#82335semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C2×C3×C4×#672
C2×#638412
C3×#52122
#105917132
#105917052
#105913162
#105913132
#105912722
Dic3×C4⋊Dic32
#105912242
#823353
#738833