Finite Group Databasebeta

← #11804922

Subgroups — #11804922

Order 1152.

1873 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
1C22×#3796C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×#63843C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic, complemented
6#10591384C212yesmaximal, complemented
7#10591383C212yesmaximal, complemented
8#10591366C212yesmaximal, complemented
9Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
10#10591325C211yesmaximal, characteristic, complemented
11#10591323C211yesmaximal, characteristic, complemented
12#82457—31nomaximal
13#76301—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×#626C2212yes—
18C22×D3×Dic3C2212yes—
19C2×#3796—24no—
20C2×#3796—24no—
21C2×#3796C418yescomplemented
22C2×C32×C42C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2212yes—
32C3×C4×Dic6—24no—
33C2×Dic3⋊Dic3C2212yes—
34C2×#3722C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×Dic32C2212yes—
38#63843—24no—
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41#63579C2212yes—
42C22×#239—31no—
43C22×#237—31no—
44C2×C3×C4×Q8—31no—
45C2×Q8×Dic3—31no—
46C2×#887—31no—
47C2×C4×Dic6D311yescharacteristic, complemented
48C3×#390—31no—
49#5221—31no—
50#4988—31no—
51#4988—32no—
52#4987—32no—
53#4987—31no—
54#4987—31no—
55#4957—32no—
56#4957—32no—
57#4942—32no—
58Dic3×C22⋊C4—32no—
59#4939—32no—
60#4939D311yescharacteristic, complemented
61C4×(C2×D3)⋊C4—31no—
62C4×(C2×D3)⋊C4—31no—
63C4×(C2×D3)⋊C4—32no—
64C4×(C2×D3)⋊C4—61no—
65C23×C3⋊D3C2311yescharacteristic
66C23×C3×D3C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3C2×C414yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×C3×D12—22no—
80C2×C3×D12—22no—
81C2×C3×D12C2×C414yes—
82C2×C3×Dic6C2×C414yes—
83C2×C3×Dic6D414yes—
84C2×C3×Dic6D414yes—
85C2×#626—24no—
86C2×#626—24no—
87C2×#626C2×C418yes—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—24no—
90C2×D3×Dic3C2×C418yes—
91#3796—232no—
92C32×C42—22no—
93#3752—22no—
94#3752—22no—
95C4×C3⋊Dic3—22no—
96C3×(C2×D3)⋊C4—24no—
97C3×(C2×D3)⋊C4—42no—
98C3×C4⋊Dic3—22no—
99C3×C4⋊Dic3—22no—
100C3×Dic3⋊C4—24no—
101C3×C4×Dic3—24no—
102Dic3⋊Dic3—24no—
103#3722—42no—
104(C2×D3)⋊Dic3—24no—
105(C2×D3)⋊Dic3—42no—
106Dic32—24no—
107#2341—91noSylow
108C22×C3×Q8—31no—
109C22×C3×D4—31no—
110C22×#67—32no—
111C23×Dic3—32no—
112C2×#239—38no—
113C2×#239—64no—
114C2×#239—64no—
115C2×#237—38no—
116C2×#237—64no—
117C2×#237—64no—
118C22×D12—32no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—61no—
124C22×Dic6C2×D311yescharacteristic
125C3×C4×Q8—64no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C42—21no—
132C2×C3×C42—32no—
133C2×C3×C42C2×D311yescharacteristic
134C2×C3×C42C2×D311yescharacteristic
135C2×#217—32no—
136C2×#217—32no—
137Q8×Dic3—64no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—61no—
147C2×(C2×D3)⋊C4—61no—
148C2×(C2×D3)⋊C4C2×D312yes—
149C2×(C2×D3)⋊C4C2×D312yes—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3C2×D311yescharacteristic
152C2×C4⋊Dic3C2×D311yescharacteristic
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4C2×D312yes—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—32no—
159C2×C4×Dic3—61no—
160C2×C4×Dic3C2×D312yes—
161#887—64no—
162C4×Dic6—24no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—31no—
167C3⋊#95—32no—
168C3⋊#95—32no—
169C3⋊#95—61no—
170C3⋊#95—61no—
171C23×C32C2411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3C22×C412yes—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3C22×C414yes—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4#4112yescomplemented
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3C22×C412yes—
203C2×C3⋊Dic3#4112yescomplemented
204C4×C3⋊D3—28no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3C22×C414yes—
212C2×C3×Dic3C2×D414yes—
213C2×C3×Dic3C2×D414yes—
214C3×D12—28no—
215C3×Dic6C22⋊C4116yescomplemented
216#626—216no—
217D3×Dic3—216no—
218C22×#41—91no—
219C2×C4×Q8—31no—
220C2×C4×Q8—91no—
221#390—31no—
222#390—92no—
223#390—92no—
224#390—91no—
225#380—92no—
226#380—91no—
227C4×C22⋊C4—92no—
228C4×C22⋊C4—91no—
229C24×C3—32no—
230C23×D3—31no—
231C23×D3—31no—
232C23×D3—61no—
233C23×D3C22×D312yes—
234C2×C3×Q8—34no—
235C2×C3×Q8—34no—
236C2×C3×Q8—34no—
237C2×C3×D4—34no—
238C2×C3×D4—62no—
239C2×C3×D4—62no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—38no—
253C2×#67—64no—
254C2×#67—64no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—38no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—61no—
265C22×Dic3—64no—
266C22×Dic3—64no—
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270#239—632no—
271#237—632no—
272C2×D12—22no—
273C2×D12—22no—
274C2×D12—38no—
275C2×D12—64no—
276C2×D12—64no—
277C2×D12C4×D314yes—
278C2×C4×D3—38no—
279C2×C4×D3—34no—
280C2×C4×D3—34no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—64no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3—122no—
289C2×C4×D3—122no—
290C2×Dic6C4×D314yes—
291C2×Dic6D1214yes—
292C2×Dic6#6714yes—
293C3×C4⋊C4—64no—
294C3×C4⋊C4—62no—
295C3×C4⋊C4—62no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—122no—
298C3×C42—22no—
299C3×C42—22no—
300C3×C42—42no—
301C3×C42—64no—
302#217—64no—
303#217—122no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—64no—
310(C2×D3)⋊C4—64no—
311(C2×D3)⋊C4—62no—
312(C2×D3)⋊C4—62no—
313(C2×D3)⋊C4—122no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316C4⋊Dic3—22no—
317C4⋊Dic3—22no—
318C4⋊Dic3—64no—
319Dic3⋊C4—24no—
320Dic3⋊C4—64no—
321C4×Dic3—24no—
322C4×Dic3—64no—
323C4×Dic3—62no—
324C4×Dic3—62no—
325C4×Dic3—64no—
326C4×Dic3—122no—
327C22×C32C23×C411yescharacteristic
328C22×C32C22×D411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32C2×#4111yescharacteristic
332C22×C32H(5,𝔽2)11yescharacteristic
333C22×C322−1+411yescharacteristic
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C2×C3⋊D3—41no—
340C2×C3⋊D3—41no—
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C32×C4—22no—
349C32×C4—41no—
350C32×C4C2×C22⋊C414yes—
351C3⋊Dic3—22no—
352C3⋊Dic3—22no—
353C3⋊Dic3—41no—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C3×Dic3C2×C22⋊C418yes—
357C2×#41—98no—
358C2×#41—184no—
359C2×#41—184no—
360C22×Q8—31no—
361C22×D4—31no—
362C22×D4—92no—
363C23×C4—92no—
364C23×C4—91no—
365C4×Q8—64no—
366C4×Q8—184no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—92no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C42—32no—
379C2×C42—92no—
380C2×C42—91no—
381C2×C42D3211yescharacteristic
382#95—92no—
383#95—91no—
384#95—91no—
385C23×C3—21no—
386C23×C3—34no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3C23×D311yescharacteristic
394C23×C3C23×D311yescharacteristic
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3—61no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—121no—
419C22×D3—121no—
420C22×D3—121no—
421C22×D3—121no—
422C22×D3C2×C4×D314yes—
423C3×Q8—316no—
424C3×D4—68no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—34no—
441C2×C3×C4—34no—
442C2×C3×C4—34no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4C2×C4×D312yes—
454C2×C3×C4C2×C4×D312yes—
455C2×C3×C4C2×D1212yes—
456C2×C3×C4D3×D412yes—
457C2×C3×C4D3×D412yes—
458C2×C3×C4#23712yescomplemented
459C2×C3×C4#23912yescomplemented
460C2×C3×C4C2×#6712yes—
461#67—616no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—32no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—32no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—616no—
483C2×Dic3—62no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3—121no—
496C2×Dic3C2×C4×D314yes—
497C2×Dic3C2×D1214yes—
498C2×Dic3C2×#6714yes—
499D12—28no—
500D12—616no—
501C4×D3—616no—
502C4×D3—68no—
503C4×D3—68no—
504C4×D3—128no—
505Dic6(C2×D3)⋊C4116yescomplemented
506C2×C32C22×C22⋊C411yescharacteristic
507C2×C32C4×#4111yescharacteristic
508C2×C32#52011yescharacteristic
509C2×C32#54811yescharacteristic
510C2×C32#54811yescharacteristic
511C2×C32#55011yescharacteristic
512C2×C32#55011yescharacteristic
513C3⋊D3—42no—
514C3×D3—44no—
515C24—32no—
516C24—91no—
517#41—1832no—
518C2×Q8—34no—
519C2×Q8—34no—
520C2×Q8—34no—
521C2×D4—34no—
522C2×D4—62no—
523C2×D4—62no—
524C2×D4—98no—
525C2×D4—184no—
526C2×D4—184no—
527C22×C4—32no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—98no—
531C22×C4—91no—
532C22×C4—91no—
533C22×C4—94no—
534C22×C4—91no—
535C22×C4—184no—
536C22×C4—184no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4C2×D3211yescharacteristic
540C22×C4C2×D3211yescharacteristic
541C22×C4C2×D3211yescharacteristic
542C4⋊C4—64no—
543C4⋊C4—62no—
544C4⋊C4—62no—
545C4⋊C4—184no—
546C22⋊C4—64no—
547C22⋊C4—122no—
548C22⋊C4—182no—
549C22⋊C4—184no—
550C22⋊C4—182no—
551C22⋊C4—362no—
552C22⋊C4—362no—
553C42—22no—
554C42—64no—
555C42—184no—
556C42—182no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—64no—
565C22×C3—64no—
566C22×C3—64no—
567C22×C3—122no—
568C22×C3—122no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3C22×C4×D311yescharacteristic
572C22×C3C22×C4×D311yescharacteristic
573C22×C3C22×D1211yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C22×C3C2×#23711yescharacteristic
577C22×C3#100411yescharacteristic
578C22×C3C2×#23911yescharacteristic
579C22×C3#100711yescharacteristic
580C22×C3D3×#4111yescharacteristic
581C22×C3D3×#4111yescharacteristic
582C22×C3#100911yescharacteristic
583C22×C3#101011yescharacteristic
584C22×C3C22×#6711yescharacteristic
585C2×D3—24no—
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—64no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—122no—
600C2×D3—122no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—122no—
604C2×D3—122no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—24no—
616C3×C4—38no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—122no—
622C3×C4—122no—
623C3×C4D3×C22⋊C414yes—
624C3×C4C2×(C2×D3)⋊C414yes—
625Dic3—42no—
626Dic3—42no—
627Dic3—62no—
628Dic3—62no—
629Dic3—62no—
630Dic3—62no—
631Dic3—122no—
632Dic3—122no—
633Dic3—122no—
634Dic3—121no—
635Dic3—121no—
636Dic3C2×(C2×D3)⋊C418yes—
637C32#234111yescharacteristic, complemented, Sylow
638C23—34no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—92no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23C22×D3211yescharacteristic
653Q8—316no—
654D4—68no—
655D4—1816no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—34no—
662C2×C4—34no—
663C2×C4—34no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—92no—
671C2×C4—92no—
672C2×C4—1816no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—188no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4#379612yescomplemented
682C2×C4C4×D3212yes—
683C2×C4D3×D1212yes—
684C2×C4D3×#6712yes—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—124no—
693C2×C3C2×D3×C22⋊C411yescharacteristic
694C2×C3C4×#23711yescharacteristic
695C2×C3#554611yescharacteristic
696C2×C3C4×#23911yescharacteristic
697C2×C3#557411yescharacteristic
698C2×C3#557611yescharacteristic
699C2×C3#557711yescharacteristic
700C2×C3#559811yescharacteristic
701C2×C3#559911yescharacteristic
702C2×C3#567711yescharacteristic
703C2×C3#571811yescharacteristic
704C2×C3C22×(C2×D3)⋊C411yescharacteristic
705C2×C3#581711yescharacteristic
706C2×C3#583411yescharacteristic
707D3—44no—
708D3—124no—
709D3—122no—
710D3—122no—
711C22—64no—
712C22—64no—
713C22—64no—
714C22—122no—
715C22—122no—
716C22—122no—
717C22—122no—
718C22—182no—
719C22—182no—
720C22—182no—
721C22—361no—
722C22—361no—
723C22—361no—
724C22—361no—
725C22C2×#379611yescharacteristic
726C22#6429711yescharacteristic
727C22C2×C4×D3211yescharacteristic
728C22C2×D3×D1211yescharacteristic
729C22#6430611yescharacteristic
730C22#6430711yescharacteristic
731C22C2×D3×#6711yescharacteristic
732C4—22no—
733C4—38no—
734C4—41no—
735C4—122no—
736C4—122no—
737C4—182no—
738C4—182no—
739C4—361no—
740C4D3×(C2×D3)⋊C414yes—
741C3—21no—
742C3#7630111yescharacteristic, complemented
743C3#8245711yescharacteristic, complemented
744C2—124no—
745C2—362no—
746C2C4×#379611yescharacteristic
747C2#1059388911yescharacteristic
748C2#1059390011yescharacteristic
749C2#1059390111yescharacteristic
750C2#1059490011yescharacteristic
751C2#1059500611yescharacteristic
752C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3796C2
hypercenterC2×C42D32
hypocenterC32#2341
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C2×#63843C2semidirect
4. C4×#3752C2semidirect
5. C3×#4939C2semidirect
6. #10591384C2semidirect
7. #10591383C2semidirect
8. #10591366C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. #10591325C2semidirect
11. #10591323C2semidirect
21. C2×#3796C4semidirect
47. C2×C4×Dic6D3semidirect
60. #4939D3semidirect
194. C2×C32×C4#41semidirect
203. C2×C3⋊Dic3#41semidirect
215. C3×Dic6C22⋊C4semidirect
458. C2×C3×C4#237semidirect
459. C2×C3×C4#239semidirect
505. Dic6(C2×D3)⋊C4semidirect
637. C32#2341semidirect
681. C2×C4#3796semidirect
742. C3#76301semidirect
743. C3#82457semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C3×C4×Dic62
C2×#638432
C4×#37522
C3×#49392
#105913842
#105913832
#105913662
Dic3×(C2×D3)⋊C42
#105913252
#105913232
#824573
#763013