Finite Group Databasebeta

← #11805438

Subgroups — #11805438

Order 1152.

1645 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#625C211yesmaximal, characteristic
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63879C212yesmaximal
5#10592674C211yesmaximal, characteristic, complemented
6C3×#4987C211yesmaximal, characteristic, complemented
7#10591372C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic, complemented
9#10591278C212yesmaximal, complemented
10#10591274C211yesmaximal, characteristic, complemented
11#10591256C212yesmaximal, complemented
12C4⋊C4×#67—31nomaximal
13#74010—31nomaximal
14C22×C3×C4×D3C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750C2212yes—
22C2×#3750C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C3×D3×C4⋊C4—24no—
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×Dic32C2212yes—
35C4×#625C418yescomplemented
36D3×C4⋊Dic3—24no—
37#63879—28no—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C22×C3×C4⋊C4—31no—
42C2×C4×#67—31no—
43C2×C4×#67—31no—
44C2×C4×#67—32no—
45C22×C4⋊Dic3—31no—
46C2×D3×C4⋊C4—31no—
47C2×D3×C4⋊C4D311yescharacteristic, complemented
48C2×#67⋊C4—32no—
49C3×#380—31no—
50#5212—31no—
51#5210—32no—
52#4989—32no—
53#4987—31no—
54#4987D311yescharacteristic, complemented
55#4976—32no—
56#4975—31no—
57#4975—31no—
58#4975—61no—
59Dic3×C4⋊C4—31no—
60Dic3×C4⋊C4—31no—
61#4946—32no—
62#4668—32no—
63#4647—32no—
64C23×C3×D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—42no—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×C3×C4×D3C2×C414yescomplemented
84C2×#625C2×C414yes—
85C2×#625D414yes—
86C2×#625Q814yes—
87C2×D3×Dic3—24no—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—42no—
90C32×C4⋊C4—22no—
91C4⋊(C3⋊Dic3)—22no—
92#3750—24no—
93#3750—42no—
94C4×C3⋊Dic3C2×C414yescomplemented
95C3×(C2×D3)⋊C4—24no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3D414yescomplemented
98C3×Dic3⋊C4—24no—
99#3724C2×C414yescomplemented
100Dic3⋊Dic3—24no—
101(C2×D3)⋊Dic3—24no—
102(C2×D3)⋊Dic3C2×C414yescomplemented
103(C2×D3)⋊Dic3C2×C414yescomplemented
104Dic32—24no—
105D4×C4⋊C4—91noSylow
106C23×C3×C4—31no—
107C23×C3×C4—31no—
108C23×C3×C4—32no—
109C22×#67—31no—
110C22×#67—31no—
111C23×Dic3—32no—
112C22×C4×D3—32no—
113C22×C4×D3C2×D312yes—
114C22×C4×D3C2×D311yescharacteristic
115C22×C4×D3C2×D311yescharacteristic
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—64no—
121C2×C3×C4⋊C4C2×D311yescharacteristic
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C22⋊C4—32no—
124C2×#217—31no—
125C2×#217—31no—
126C2×#217—32no—
127C4×#67—38no—
128C4×#67—38no—
129C4×#67—68no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—61no—
138C2×C4⋊Dic3—64no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4—62no—
149C2×Dic3⋊C4—62no—
150C2×Dic3⋊C4C2×D312yes—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—61no—
156D3×C4⋊C4—24no—
157D3×C4⋊C4—64no—
158#67⋊C4—68no—
159C3×#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95C2×D312yes—
165C23×C32C2411yescharacteristic
166C22×C3×D3—21no—
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×D3—21no—
174C22×C3×D3C22×C412yes—
175C22×C3×D3C22×C412yes—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×D412yes—
178C22×C3×D3C2×Q812yes—
179C22×C3×D3C2×Q812yes—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4#4112yes—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C22×C412yes—
193C2×C3⋊Dic3C2×D412yes—
194C2×C3⋊Dic3C2×Q812yes—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3C22×C412yes—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C2×D414yes—
207C3×C4×D3—28no—
208C3×C4×D3—28no—
209C3×C4×D3—48no—
210#625C4⋊C4116yescomplemented
211D3×Dic3—48no—
212C2×C4×D4—92no—
213C2×C4×D4—91no—
214C22×C4⋊C4—31no—
215C22×C4⋊C4—91no—
216#389—92no—
217#385—92no—
218#385—92no—
219#384—91no—
220#380—31no—
221#380—91no—
222C4×C4⋊C4—91no—
223C24×C3—31no—
224C24×C3—31no—
225C23×D3C22×D311yescharacteristic
226C23×D3C22×D311yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—22no—
229C22×C3×C4—31no—
230C22×C3×C4—32no—
231C22×C3×C4—31no—
232C22×C3×C4—34no—
233C22×C3×C4—34no—
234C22×C3×C4—32no—
235C22×C3×C4—64no—
236C22×C3×C4—64no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4—62no—
241C22×C3×C4—122no—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D312yes—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—34no—
247C2×#67—34no—
248C2×#67—34no—
249C2×#67—34no—
250C2×#67—34no—
251C2×#67—34no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—62no—
261C22×Dic3—64no—
262C22×Dic3—64no—
263C22×Dic3—122no—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D312yes—
268C2×C4×D3—22no—
269C2×C4×D3—22no—
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3—24no—
273C2×C4×D3—24no—
274C2×C4×D3—42no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3—122no—
278C2×C4×D3C4×D314yescomplemented
279C2×C4×D3C4×D314yescomplemented
280C3×C4⋊C4—22no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—34no—
283C3×C4⋊C4—42no—
284C3×C4⋊C4—64no—
285C3×C4⋊C4—62no—
286C3×C22⋊C4—64no—
287#217—34no—
288#217—34no—
289#217—64no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—34no—
293(C2×D3)⋊C4—64no—
294C4⋊Dic3—22no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—64no—
298C4⋊Dic3—122no—
299C4⋊Dic3#6714yescomplemented
300Dic3⋊C4—24no—
301Dic3⋊C4—34no—
302Dic3⋊C4—34no—
303Dic3⋊C4—64no—
304Dic3⋊C4—64no—
305Dic3⋊C4—64no—
306Dic3⋊C4—124no—
307Dic3⋊C4—122no—
308Dic3⋊C4—122no—
309Dic3⋊C4—124no—
310C4×Dic3—34no—
311C4×Dic3—34no—
312C4×Dic3—64no—
313C4×Dic3—64no—
314C4×Dic3—64no—
315C22×C32C23×C411yescharacteristic
316C22×C32C22×D411yescharacteristic
317C22×C32C22×D411yescharacteristic
318C22×C32C22×Q811yescharacteristic
319C22×C32C2×#4111yescharacteristic
320C22×C32H(5,𝔽2)11yescharacteristic
321C22×C322−1+411yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3C2×C4⋊C414yescomplemented
335C2×C3×D3C2×C4⋊C414yescomplemented
336C32×C4—42no—
337C32×C4C4×D414yescomplemented
338C3⋊Dic3—22no—
339C3⋊Dic3—42no—
340C3⋊Dic3C2×C4⋊C414yescomplemented
341C3×Dic3—22no—
342C3×Dic3—22no—
343C3×Dic3—24no—
344C3×Dic3—42no—
345C22×D4—91no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—32no—
349C23×C4—92no—
350C4×D4—98no—
351C4×D4—188no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—64no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—92no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—184no—
362C2×C4⋊C4D3211yescharacteristic
363C2×C22⋊C4—32no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—92no—
367C2×C42—91no—
368C2×C42—92no—
369#95—32no—
370#95—92no—
371#95—92no—
372C23×C3—21no—
373C23×C3—32no—
374C23×C3—32no—
375C23×C3—32no—
376C23×C3—32no—
377C23×C3—32no—
378C23×C3—32no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3C23×D311yescharacteristic
388C23×C3C23×D311yescharacteristic
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3C2×C4×D312yes—
398C22×D3C2×C4×D312yes—
399C22×D3D3×D412yes—
400C22×D3D3×D412yes—
401C22×D3D3×Q812yes—
402C22×D3D3×Q812yes—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
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—34no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—62no—
423C2×C3×C4—61no—
424C2×C3×C4—68no—
425C2×C3×C4—68no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—128no—
430C2×C3×C4C2×C4×D312yes—
431C2×C3×C4C2×C4×D312yes—
432C2×C3×C4#23512yes—
433C2×C3×C4D3×D412yes—
434C2×C3×C4#23712yes—
435C2×C3×C4C2×#6712yes—
436#67—316no—
437#67—316no—
438C2×Dic3—21no—
439C2×Dic3—22no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—22no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—32no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—61no—
465C2×Dic3—62no—
466C2×Dic3—62no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—122no—
472C2×Dic3—122no—
473C2×Dic3—122no—
474C2×Dic3—128no—
475C2×Dic3C2×C4×D312yes—
476C2×Dic3C2×C4×D312yes—
477C2×Dic3C2×#6714yes—
478C4×D3—28no—
479C4×D3—28no—
480C4×D3—48no—
481C4×D3—128no—
482C2×C32C22×C4⋊C411yescharacteristic
483C2×C32C2×C4×D411yescharacteristic
484C2×C32#52011yescharacteristic
485C2×C32D4211yescharacteristic
486C2×C32#54711yescharacteristic
487C2×C32D4×Q811yescharacteristic
488C2×C32#55411yescharacteristic
489C3×D3—24no—
490C3×D3—24no—
491C24—31no—
492C24—31no—
493C2×D4—94no—
494C2×D4—94no—
495C2×D4—94no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—32no—
499C22×C4—34no—
500C22×C4—34no—
501C22×C4—32no—
502C22×C4—64no—
503C22×C4—64no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—92no—
511C22×C4—122no—
512C22×C4—184no—
513C22×C4—184no—
514C22×C4—362no—
515C22×C4C2×D3212yes—
516C22×C4C2×D3211yescharacteristic
517C4⋊C4—22no—
518C4⋊C4—34no—
519C4⋊C4—64no—
520C4⋊C4—62no—
521C4⋊C4—94no—
522C4⋊C4—184no—
523C4⋊C4—184no—
524C4⋊C4—182no—
525C4⋊C4—362no—
526C22⋊C4—64no—
527C22⋊C4—94no—
528C22⋊C4—94no—
529C22⋊C4—184no—
530C42—94no—
531C42—184no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—34no—
540C22×C3—34no—
541C22×C3—62no—
542C22×C3—62no—
543C22×C3—62no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3C22×C4×D311yescharacteristic
554C22×C3C22×C4×D311yescharacteristic
555C22×C3C2×#23511yescharacteristic
556C22×C3C2×D3×D411yescharacteristic
557C22×C3C2×D3×D411yescharacteristic
558C22×C3C2×D3×D411yescharacteristic
559C22×C3C2×#23711yescharacteristic
560C22×C3#100411yescharacteristic
561C22×C3C2×D3×Q811yescharacteristic
562C22×C3C2×D3×Q811yescharacteristic
563C22×C3#100711yescharacteristic
564C22×C3#100911yescharacteristic
565C22×C3#101011yescharacteristic
566C22×C3C22×#6711yescharacteristic
567C2×D3—22no—
568C2×D3—22no—
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3D3×C4⋊C414yescomplemented
580C2×D3D3×C4⋊C414yescomplemented
581C3×C4—24no—
582C3×C4—42no—
583C3×C4—42no—
584C3×C4—62no—
585C3×C4—62no—
586C3×C4—64no—
587C3×C4—82no—
588C3×C4—122no—
589C3×C4#67⋊C414yescomplemented
590C3×C4C4×#6714yescomplemented
591Dic3—22no—
592Dic3—22no—
593Dic3—24no—
594Dic3—34no—
595Dic3—34no—
596Dic3—42no—
597Dic3—64no—
598Dic3—64no—
599Dic3—62no—
600Dic3—62no—
601Dic3—122no—
602Dic3—122no—
603Dic3—242no—
604C32D4×C4⋊C411yescharacteristic, complemented, Sylow
605C23—32no—
606C23—32no—
607C23—32no—
608C23—32no—
609C23—32no—
610C23—32no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23C22×D3211yescharacteristic
620D4—916no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—32no—
625C2×C4—32no—
626C2×C4—34no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—68no—
634C2×C4—68no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—92no—
639C2×C4—92no—
640C2×C4—92no—
641C2×C4—92no—
642C2×C4—128no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—182no—
646C2×C4—182no—
647C2×C4—182no—
648C2×C4—368no—
649C2×C4#379512yes—
650C2×C4C4×D3212yes—
651C2×C4D3×#6712yes—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—64no—
660C2×C3—64no—
661C2×C3C2×#67⋊C411yescharacteristic
662C2×C3C2×D3×C4⋊C411yescharacteristic
663C2×C3C2×D3×C4⋊C411yescharacteristic
664C2×C3#550411yescharacteristic
665C2×C3#550711yescharacteristic
666C2×C3#551111yescharacteristic
667C2×C3#552311yescharacteristic
668C2×C3#560911yescharacteristic
669C2×C3#561111yescharacteristic
670C2×C3#563211yescharacteristic
671C2×C3#563511yescharacteristic
672C2×C3C2×C4×#6711yescharacteristic
673C2×C3D4×#6711yescharacteristic
674C2×C3Q8×#6711yescharacteristic
675D3—24no—
676D3—24no—
677C22—34no—
678C22—34no—
679C22—62no—
680C22—62no—
681C22—62no—
682C22—62no—
683C22—62no—
684C22—62no—
685C22—62no—
686C22—62no—
687C22—62no—
688C22—62no—
689C22—62no—
690C22—62no—
691C22C2×#379511yescharacteristic
692C22C2×C4×D3211yescharacteristic
693C22D32×D411yescharacteristic
694C22#6431411yescharacteristic
695C22#6431511yescharacteristic
696C22D32×Q811yescharacteristic
697C22C2×D3×#6711yescharacteristic
698C4—42no—
699C4—62no—
700C4—62no—
701C4—64no—
702C4—94no—
703C4—122no—
704C4—182no—
705C4—362no—
706C4#6387914yescomplemented
707C3—21no—
708C3#7401011yescharacteristic, complemented
709C3C4⋊C4×#6711yescharacteristic, complemented
710C2—64no—
711C2—64no—
712C2#1059437011yescharacteristic
713C2#1059451011yescharacteristic
714C2#1059453211yescharacteristic
715C2D32×C4⋊C411yescharacteristic
716C2C2×#6387911yescharacteristic
717C2#1059528811yescharacteristic
718C2#1059540011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
3. C2×D3×C4⋊Dic3C2semidirect
5. #10592674C2semidirect
6. C3×#4987C2semidirect
7. #10591372C2semidirect
8. #10591313C2semidirect
9. #10591278C2semidirect
10. #10591274C2semidirect
11. #10591256C2semidirect
35. C4×#625C4semidirect
47. C2×D3×C4⋊C4D3semidirect
54. #4987D3semidirect
82. C2×C3×C4×D3C2×C4semidirect
83. C2×C3×C4×D3C2×C4semidirect
94. C4×C3⋊Dic3C2×C4semidirect
97. C3×C4⋊Dic3D4semidirect
99. #3724C2×C4semidirect
102. (C2×D3)⋊Dic3C2×C4semidirect
103. (C2×D3)⋊Dic3C2×C4semidirect
210. #625C4⋊C4semidirect
278. C2×C4×D3C4×D3semidirect
279. C2×C4×D3C4×D3semidirect
299. C4⋊Dic3#67semidirect
334. C2×C3×D3C2×C4⋊C4semidirect
335. C2×C3×D3C2×C4⋊C4semidirect
337. C32×C4C4×D4semidirect
340. C3⋊Dic3C2×C4⋊C4semidirect
579. C2×D3D3×C4⋊C4semidirect
580. C2×D3D3×C4⋊C4semidirect
589. C3×C4#67⋊C4semidirect
590. C3×C4C4×#67semidirect
604. C32D4×C4⋊C4semidirect
706. C4#63879semidirect
708. C3#74010semidirect
709. C3C4⋊C4×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×C4×#6252
C2×D3×C4⋊Dic32
C2×#638792
#105926742
C3×#49872
#105913722
#105913132
#105912782
#105912742
#105912562
C4⋊C4×#673
#740103