Finite Group Databasebeta

← #11806907

Subgroups — #11806907

Order 1152.

1877 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic
4C2×C4×#626C212yesmaximal, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6#10591387C212yesmaximal, complemented
7#10591383C212yesmaximal, complemented
8#10591382C212yesmaximal, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#10591323C211yesmaximal, characteristic, complemented
11#10591320C211yesmaximal, characteristic, complemented
12#82343—31nomaximal
13#73653—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×#626C2212yes—
19C22×#626C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64102—24no—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#893—24no—
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36#63911C418yescomplemented
37C4×#626—28no—
38C3×C3⋊#95C2212yes—
39#63579C2211yescharacteristic
40#63579C2211yescharacteristic
41C2×C3×C4×D4—31no—
42C2×#940—31no—
43C2×C4×#67—32no—
44C2×#893—31no—
45C2×#893—31no—
46C2×#893—61no—
47C2×#893D311yescharacteristic, complemented
48C2×#874—31no—
49C2×C4×D12—32no—
50C3×C4×C4⋊C4—31no—
51#5221—31no—
52#5213—32no—
53#4988—31no—
54#4988—31no—
55Dic3×C4⋊C4D311yescharacteristic, complemented
56#4957—32no—
57#4956—32no—
58#4939—32no—
59#4939—31no—
60C4×C4⋊Dic3—31no—
61C4×Dic3⋊C4—31no—
62#4665—32no—
63#4665—32no—
64C23×C3⋊D3C2312yes—
65C23×C3×D3C2312yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)C2×C414yescomplemented
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3—42no—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C2×C3×D12—22no—
82C2×C3×D12—22no—
83C2×C3×D12C2×C414yescomplemented
84C2×C3×C4×D3—24no—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3—42no—
87C2×#626—24no—
88C2×#626—24no—
89C2×#626—42no—
90C2×#626—42no—
91C2×#626C2×C418yescomplemented
92C2×#626C2×C418yescomplemented
93C32×C4⋊C4D414yescomplemented
94#3752—24no—
95C4×C3⋊Dic3—22no—
96C3×(C2×D3)⋊C4—24no—
97C3×C4⋊Dic3—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3—24no—
100C3×C4×Dic3C2×C414yescomplemented
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3D414yescomplemented
103#3722—24no—
104#3722—42no—
105(C2×D3)⋊Dic3—24no—
106(C2×D3)⋊Dic3—42no—
107#2366—91noSylow
108C22×C3×D4—31no—
109C23×C3×C4—32no—
110C22×#67—32no—
111C22×#67—32no—
112C22×D12—32no—
113C22×D12—31no—
114C22×D12—31no—
115C22×D12—32no—
116C22×D12—61no—
117C22×D12C2×D311yescharacteristic
118C22×C4×D3—32no—
119C22×C4×D3—32no—
120C22×C4×D3—62no—
121C22×C4×D3C2×D312yes—
122C3×C4×D4—64no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4C2×D311yescharacteristic
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C22⋊C4—32no—
128C2×C3×C42—31no—
129C2×C3×C42—31no—
130C2×C3×C42—32no—
131C2×#217—32no—
132C2×#217—32no—
133#940—38no—
134C4×#67—68no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—62no—
144C2×(C2×D3)⋊C4C2×D312yes—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—61no—
153C2×C4×Dic3C2×D311yescharacteristic
154C2×C4×Dic3C2×D312yes—
155C2×C4×Dic3C2×D311yescharacteristic
156#893—24no—
157#893—68no—
158#893—64no—
159#893—64no—
160#874—38no—
161C4×D12—68no—
162C3×#95—32no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—31no—
167C3⋊#95C2×D312yes—
168C23×C32C2411yescharacteristic
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3C22×C414yes—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3C22×C414yes—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D414yes—
187C2×C32×C4C2×D412yes—
188C2×C32×C4#4112yes—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3C2×D412yes—
195C4⋊(C3⋊D3)—28no—
196C4×C3⋊D3—48no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3C22×C412yes—
208C2×C3×Dic3C22×C412yes—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3C2×D412yes—
211C2×C3×Dic3#4112yes—
212C3×D12—28no—
213C3×C4×D3—48no—
214#626—216no—
215#626—48no—
216C2×#127—91no—
217C2×C4×D4—31no—
218C2×C4×D4—92no—
219C2×C4×D4—91no—
220#390—92no—
221#390—91no—
222#390—91no—
223#386—92no—
224#386—92no—
225C4×C4⋊C4—31no—
226C4×C4⋊C4—91no—
227C24×C3—32no—
228C23×D3—32no—
229C23×D3—32no—
230C23×D3—62no—
231C23×D3C22×D312yes—
232C2×C3×D4—34no—
233C2×C3×D4—62no—
234C2×C3×D4—62no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—64no—
243C22×C3×C4—64no—
244C22×C3×C4—122no—
245C22×C3×C4C22×D312yes—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—38no—
250C2×#67—38no—
251C2×#67—64no—
252C2×#67—64no—
253C2×#67—122no—
254C2×#67—122no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D311yescharacteristic
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—38no—
269C2×D12—34no—
270C2×D12—34no—
271C2×D12—38no—
272C2×D12—64no—
273C2×D12—64no—
274C2×D12—64no—
275C2×D12—64no—
276C2×D12—64no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12—62no—
280C2×D12—62no—
281C2×D12—122no—
282C2×D12—122no—
283C2×D12C4×D314yescomplemented
284C2×C4×D3—24no—
285C2×C4×D3—24no—
286C2×C4×D3—42no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—68no—
290C2×C4×D3—64no—
291C2×C4×D3—64no—
292C2×C4×D3—124no—
293C2×C4×D3—122no—
294C2×C4×D3—122no—
295C2×C4×D3—124no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—62no—
298C3×C4⋊C4D1214yescomplemented
299C3×C4⋊C4#6714yescomplemented
300C3×C22⋊C4—64no—
301C3×C42—34no—
302C3×C42—64no—
303C3×C42—62no—
304#217—64no—
305#217—122no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—68no—
310(C2×D3)⋊C4—64no—
311(C2×D3)⋊C4—64no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—122no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316C4⋊Dic3—22no—
317C4⋊Dic3—34no—
318C4⋊Dic3—62no—
319Dic3⋊C4—34no—
320Dic3⋊C4—62no—
321C4×Dic3—22no—
322C4×Dic3—24no—
323C4×Dic3—64no—
324C4×Dic3—62no—
325C4×Dic3—62no—
326C4×Dic3C4×D314yescomplemented
327C22×C32C23×C411yescharacteristic
328C22×C32C22×D411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32C2×#4111yescharacteristic
332C22×C32H(5,𝔽2)11yescharacteristic
333C22×C32H(5,𝔽2)11yescharacteristic
334C2×C3⋊D3—24no—
335C2×C3⋊D3—24no—
336C2×C3⋊D3—24no—
337C2×C3⋊D3—42no—
338C2×C3⋊D3—42no—
339C2×C3⋊D3—42no—
340C2×C3⋊D3—42no—
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—24no—
349C32×C4C4×D414yescomplemented
350C3⋊Dic3—22no—
351C3⋊Dic3—41no—
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3—42no—
355C3×Dic3—41no—
356C3×Dic3C4×D414yescomplemented
357C22×D4—31no—
358C22×D4—92no—
359C22×D4—92no—
360C22×D4—91no—
361C23×C4—32no—
362C23×C4—92no—
363#127—98no—
364C4×D4—64no—
365C4×D4—188no—
366C4×D4—184no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4D3211yescharacteristic
371C2×C22⋊C4—32no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—32no—
380C2×C42—91no—
381#95—32no—
382#95—91no—
383#95—91no—
384C23×C3—21no—
385C23×C3—34no—
386C23×C3—62no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3C23×D311yescharacteristic
393C23×C3C23×D311yescharacteristic
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—34no—
401C22×D3—34no—
402C22×D3—64no—
403C22×D3—64no—
404C22×D3—64no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—62no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—122no—
418C22×D3—122no—
419C22×D3—122no—
420C22×D3—122no—
421C22×D3C2×C4×D314yes—
422C3×D4—68no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—61no—
446C2×C3×C4—62no—
447C2×C3×C4—61no—
448C2×C3×C4—128no—
449C2×C3×C4C2×C4×D312yes—
450C2×C3×C4C2×C4×D312yes—
451C2×C3×C4C2×D1214yes—
452C2×C3×C4C2×D1212yes—
453C2×C3×C4#23512yes—
454C2×C3×C4#23512yes—
455C2×C3×C4C2×#6714yes—
456C2×C3×C4C2×#6712yes—
457#67—616no—
458#67—128no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—62no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×Dic3C2×C4×D312yes—
488C2×Dic3C2×C4×D312yes—
489C2×Dic3D3×D412yes—
490C2×Dic3D3×D412yes—
491C2×Dic3#23912yes—
492D12—28no—
493D12—616no—
494D12—616no—
495D12—68no—
496D12—68no—
497D12—128no—
498C4×D3—48no—
499C4×D3—128no—
500C4×D3—128no—
501C4×D3—1216no—
502C2×C32C2×C4×D411yescharacteristic
503C2×C32C2×C4×D411yescharacteristic
504C2×C32#51811yescharacteristic
505C2×C32D4211yescharacteristic
506C2×C32#55011yescharacteristic
507C2×C32#55011yescharacteristic
508C2×C32#55911yescharacteristic
509C3⋊D3—44no—
510C3×D3—44no—
511C24—32no—
512C24—92no—
513C2×D4—34no—
514C2×D4—62no—
515C2×D4—62no—
516C2×D4—98no—
517C2×D4—98no—
518C2×D4—94no—
519C2×D4—184no—
520C2×D4—184no—
521C2×D4—182no—
522C2×D4—182no—
523C2×D4—362no—
524C2×D4—362no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—32no—
529C22×C4—31no—
530C22×C4—64no—
531C22×C4—64no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4—122no—
535C22×C4—184no—
536C22×C4—184no—
537C22×C4—362no—
538C22×C4C2×D3212yes—
539C22×C4C2×D3211yescharacteristic
540C4⋊C4—62no—
541C4⋊C4—94no—
542C4⋊C4—182no—
543C4⋊C4#62614yescomplemented
544C22⋊C4—64no—
545C22⋊C4—184no—
546C22⋊C4—184no—
547C22⋊C4—184no—
548C22⋊C4—362no—
549C22⋊C4—362no—
550C42—34no—
551C42—64no—
552C42—62no—
553C42—182no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—64no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—122no—
567C22×C3—122no—
568C22×C3C22×C4×D311yescharacteristic
569C22×C3C22×C4×D311yescharacteristic
570C22×C3C22×D1211yescharacteristic
571C22×C3C2×#23511yescharacteristic
572C22×C3C2×#23511yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C22×C3#100411yescharacteristic
576C22×C3C2×#23911yescharacteristic
577C22×C3D3×#4111yescharacteristic
578C22×C3#100911yescharacteristic
579C22×C3#100911yescharacteristic
580C22×C3#100911yescharacteristic
581C22×C3C22×#6711yescharacteristic
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—68no—
590C2×D3—64no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—124no—
597C2×D3—124no—
598C2×D3—124no—
599C2×D3—124no—
600C2×D3—124no—
601C2×D3—124no—
602C2×D3—122no—
603C2×D3—122no—
604C2×D3—122no—
605C2×D3—122no—
606C2×D3—122no—
607C2×D3—122no—
608C2×D3—122no—
609C2×D3—122no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—24no—
613C3×C4—34no—
614C3×C4—44no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—122no—
618C3×C4—121no—
619C3×C4C4×D1214yescomplemented
620C3×C4C4×#6714yescomplemented
621Dic3—22no—
622Dic3—22no—
623Dic3—42no—
624Dic3—41no—
625Dic3—64no—
626Dic3—62no—
627Dic3—62no—
628Dic3—122no—
629Dic3—121no—
630Dic3—121no—
631Dic3#89314yescomplemented
632C32#236611yescharacteristic, complemented, Sylow
633C23—34no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—94no—
641C23—182no—
642C23—182no—
643C23—182no—
644C23—182no—
645C23—182no—
646C23—182no—
647C23C22×D3211yescharacteristic
648D4—68no—
649D4—1816no—
650D4—188no—
651D4—368no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—61no—
669C2×C4—92no—
670C2×C4—128no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—368no—
677C2×C4#379812yes—
678C2×C4C4×D3212yes—
679C2×C4C2×#62614yes—
680C2×C4C2×#62612yes—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—124no—
689C2×C3C2×C4×D1211yescharacteristic
690C2×C3C2×#89311yescharacteristic
691C2×C3#552111yescharacteristic
692C2×C3C4×D3×D411yescharacteristic
693C2×C3#554511yescharacteristic
694C2×C3D4×D1211yescharacteristic
695C2×C3#555311yescharacteristic
696C2×C3#555311yescharacteristic
697C2×C3#555911yescharacteristic
698C2×C3#557711yescharacteristic
699C2×C3#558511yescharacteristic
700C2×C3C2×C4×#6711yescharacteristic
701C2×C3D4×#6711yescharacteristic
702C2×C3#583411yescharacteristic
703D3—44no—
704D3—128no—
705D3—124no—
706D3—124no—
707C22—64no—
708C22—64no—
709C22—64no—
710C22—122no—
711C22—122no—
712C22—122no—
713C22—122no—
714C22—184no—
715C22—184no—
716C22—184no—
717C22—362no—
718C22—362no—
719C22—362no—
720C22—362no—
721C22C2×#379811yescharacteristic
722C22C2×C4×D3211yescharacteristic
723C22D32×D411yescharacteristic
724C22#6431411yescharacteristic
725C22D3×#23911yescharacteristic
726C22#6432011yescharacteristic
727C22C22×#62611yescharacteristic
728C4—24no—
729C4—34no—
730C4—62no—
731C4—62no—
732C4—121no—
733C4—122no—
734C4—182no—
735C4—361no—
736C4C4×#62614yescomplemented
737C3—21no—
738C3#7365311yescharacteristic, complemented
739C3#8234311yescharacteristic, complemented
740C2—124no—
741C2—364no—
742C2#1059452011yescharacteristic
743C2#1059456611yescharacteristic
744C2D3×#89311yescharacteristic
745C2#1059460411yescharacteristic
746C2C2×C4×#62611yescharacteristic
747C2D4×#62611yescharacteristic
748C2#1059541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63911C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2366
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×#64102C2semidirect
2. C2×C3×#893C2semidirect
4. C2×C4×#626C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
6. #10591387C2semidirect
7. #10591383C2semidirect
8. #10591382C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
10. #10591323C2semidirect
11. #10591320C2semidirect
36. #63911C4semidirect
47. C2×#893D3semidirect
55. Dic3×C4⋊C4D3semidirect
72. C2×C4⋊(C3⋊D3)C2×C4semidirect
83. C2×C3×D12C2×C4semidirect
91. C2×#626C2×C4semidirect
92. C2×#626C2×C4semidirect
93. C32×C4⋊C4D4semidirect
100. C3×C4×Dic3C2×C4semidirect
102. Dic3⋊Dic3D4semidirect
283. C2×D12C4×D3semidirect
298. C3×C4⋊C4D12semidirect
299. C3×C4⋊C4#67semidirect
326. C4×Dic3C4×D3semidirect
349. C32×C4C4×D4semidirect
356. C3×Dic3C4×D4semidirect
543. C4⋊C4#626semidirect
619. C3×C4C4×D12semidirect
620. C3×C4C4×#67semidirect
631. Dic3#893semidirect
632. C32#2366semidirect
736. C4C4×#626semidirect
738. C3#73653semidirect
739. C3#82343semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C3×#8932
C2×#639112
C2×C4×#6262
C3×Dic3×C4⋊C42
#105913872
#105913832
#105913822
C4×Dic3⋊Dic32
#105913232
#105913202
#823433
#736533