Finite Group Databasebeta

← #11806899

Subgroups — #11806899

Order 1152.

1793 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C2×#63898C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63880C212yesmaximal, complemented
5#10592687C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8#10591383C212yesmaximal, complemented
9#10591364C212yesmaximal, complemented
10C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
11#10591275C212yesmaximal, complemented
12#76306—31nomaximal
13#73653—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626C2212yes—
17C22×#626C2212yes—
18C22×#624C2212yes—
19C22×D3×Dic3C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34#63911C418yescomplemented
35#63898—24no—
36#63894—24no—
37#63880—28no—
38C3×C3⋊#95C2212yes—
39#63579C2211yescharacteristic
40#63579C2211yescharacteristic
41C2×#940—31no—
42C2×D4×Dic3—31no—
43C2×#893—31no—
44C2×#893—31no—
45C2×#67⋊C4—32no—
46C2×#874—31no—
47C2×C4×D12—32no—
48C2×C4×D12—31no—
49C3×#390—31no—
50C3×C4×C4⋊C4—31no—
51#4988—31no—
52#4988—31no—
53#4988—61no—
54#4988D311yescharacteristic, complemented
55Dic3×C4⋊C4D311yescharacteristic, complemented
56#4958—32no—
57#4957—32no—
58#4956—32no—
59#4939—32no—
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
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12C2×C414yescomplemented
81C2×#626—24no—
82C2×#626—24no—
83C2×#626—42no—
84C2×#626—42no—
85C2×#626C2×C418yescomplemented
86C2×#626C2×C418yescomplemented
87C2×#624—24no—
88C2×#624—24no—
89C2×#624—42no—
90C2×D3×Dic3—24no—
91C2×D3×Dic3—24no—
92C2×D3×Dic3—42no—
93C32×C4⋊C4—22no—
94#3752—24no—
95#3752—42no—
96C4×C3⋊Dic3—22no—
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—42no—
99C3×C4⋊Dic3D414yescomplemented
100C3×C4×Dic3—22no—
101C3×C4×Dic3—24no—
102C3×C4×Dic3C2×C414yescomplemented
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3D414yescomplemented
105#3722—24no—
106(C2×D3)⋊Dic3—24no—
107#2366—91noSylow
108C22×C3×D4—31no—
109C22×#67—32no—
110C22×#67—32no—
111C23×Dic3—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—32no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C42—31no—
128C2×C3×C42—31no—
129C2×C3×C42—32no—
130C2×#217—32no—
131#940—38no—
132D4×Dic3—64no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
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—62no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4C2×D312yes—
143C2×(C2×D3)⋊C4C2×D312yes—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3C2×D311yescharacteristic
153C2×C4×Dic3C2×D312yes—
154C2×C4×Dic3C2×D311yescharacteristic
155#893—64no—
156#893—64no—
157#67⋊C4—68no—
158#874—38no—
159C4×D12—68no—
160C4×D12—64no—
161C3×#95—32no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95C2×D312yes—
167C23×C32C2411yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3C22×C414yes—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3C22×C414yes—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4112yes—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×D412yes—
194C4⋊(C3⋊D3)—28no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3C22×C412yes—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C2×D414yes—
207C2×C3×Dic3C2×D412yes—
208C2×C3×Dic3C2×D412yes—
209C2×C3×Dic3#4112yes—
210C3×D12—28no—
211#626—216no—
212#626—48no—
213#624—48no—
214D3×Dic3—48no—
215C2×#127—91no—
216C2×C4×D4—92no—
217C2×C4×D4—91no—
218C2×C4×D4—91no—
219#390—31no—
220#390—92no—
221#390—91no—
222#386—92no—
223#386—92no—
224C4×C4⋊C4—31no—
225C4×C4⋊C4—91no—
226C24×C3—32no—
227C23×D3—32no—
228C23×D3—32no—
229C23×D3—62no—
230C23×D3C22×D312yes—
231C2×C3×D4—34no—
232C2×C3×D4—62no—
233C2×C3×D4—62no—
234C22×C3×C4—21no—
235C22×C3×C4—22no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—32no—
240C22×C3×C4—31no—
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—38no—
246C2×#67—38no—
247C2×#67—64no—
248C2×#67—64no—
249C2×#67—122no—
250C2×#67—122no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—64no—
258C22×Dic3—64no—
259C22×Dic3—122no—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C2×D12—22no—
266C2×D12—22no—
267C2×D12—38no—
268C2×D12—34no—
269C2×D12—34no—
270C2×D12—38no—
271C2×D12—64no—
272C2×D12—64no—
273C2×D12—64no—
274C2×D12—62no—
275C2×D12—62no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—122no—
279C2×D12—122no—
280C2×D12—122no—
281C2×D12—122no—
282C2×D12C4×D314yescomplemented
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C2×C4×D3—64no—
286C2×C4×D3—64no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—122no—
290C2×C4×D3—122no—
291C2×C4×D3—122no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—42no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—122no—
298C3×C42—34no—
299C3×C42—64no—
300C3×C42—62no—
301#217—64no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—64no—
305(C2×D3)⋊C4—64no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—124no—
310(C2×D3)⋊C4—122no—
311(C2×D3)⋊C4—122no—
312(C2×D3)⋊C4—124no—
313C4⋊Dic3—34no—
314C4⋊Dic3—62no—
315C4⋊Dic3D1214yescomplemented
316Dic3⋊C4—34no—
317Dic3⋊C4—62no—
318C4×Dic3—22no—
319C4×Dic3—24no—
320C4×Dic3—62no—
321C4×Dic3—62no—
322C4×Dic3—122no—
323C4×Dic3C4×D314yescomplemented
324C22×C32C23×C411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C22×D411yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C22×C32H(5,𝔽2)11yescharacteristic
330C22×C32H(5,𝔽2)11yescharacteristic
331C2×C3⋊D3—24no—
332C2×C3⋊D3—24no—
333C2×C3⋊D3—24no—
334C2×C3⋊D3—42no—
335C2×C3⋊D3—42no—
336C2×C3⋊D3—42no—
337C2×C3⋊D3—42no—
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—42no—
342C2×C3×D3—42no—
343C2×C3×D3—42no—
344C2×C3×D3—42no—
345C32×C4—42no—
346C32×C4C4×D414yescomplemented
347C3⋊Dic3—22no—
348C3⋊Dic3—41no—
349C3×Dic3—22no—
350C3×Dic3—24no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3C4×D414yescomplemented
354C22×D4—31no—
355C22×D4—92no—
356C22×D4—92no—
357C22×D4—91no—
358C23×C4—92no—
359C23×C4—92no—
360#127—98no—
361C4×D4—188no—
362C4×D4—184no—
363C4×D4—184no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4D3211yescharacteristic
368C2×C22⋊C4—32no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C42—31no—
375C2×C42—32no—
376C2×C42—31no—
377C2×C42—91no—
378#95—32no—
379#95—91no—
380#95—91no—
381C23×C3—21no—
382C23×C3—34no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3—62no—
386C23×C3—62no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—34no—
398C22×D3—34no—
399C22×D3—64no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—122no—
413C22×D3—122no—
414C22×D3—122no—
415C22×D3—122no—
416C22×D3—122no—
417C22×D3—122no—
418C22×D3C2×C4×D314yes—
419C3×D4—68no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
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—32no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—34no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—61no—
439C2×C3×C4—62no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4C2×C4×D312yes—
449C2×C3×C4C2×D1212yes—
450C2×C3×C4#23512yes—
451C2×C3×C4D3×D412yes—
452C2×C3×C4#23712yes—
453#67—616no—
454#67—128no—
455C2×Dic3—21no—
456C2×Dic3—22no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—62no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—62no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—121no—
479C2×Dic3—121no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—128no—
483C2×Dic3C2×C4×D312yes—
484C2×Dic3C2×C4×D312yes—
485C2×Dic3C2×D1214yes—
486C2×Dic3D3×D412yes—
487C2×Dic3D3×D412yes—
488C2×Dic3#23912yes—
489D12—28no—
490D12—616no—
491D12—68no—
492D12—68no—
493D12—128no—
494D12—128no—
495C4×D3—128no—
496C4×D3—128no—
497C4×D3—128no—
498C2×C32C2×C4×D411yescharacteristic
499C2×C32C2×C4×D411yescharacteristic
500C2×C32#51811yescharacteristic
501C2×C32D4211yescharacteristic
502C2×C32#55011yescharacteristic
503C2×C32#55011yescharacteristic
504C2×C32#55911yescharacteristic
505C3⋊D3—44no—
506C3×D3—44no—
507C24—32no—
508C24—92no—
509C2×D4—34no—
510C2×D4—62no—
511C2×D4—62no—
512C2×D4—98no—
513C2×D4—98no—
514C2×D4—94no—
515C2×D4—184no—
516C2×D4—184no—
517C2×D4—182no—
518C2×D4—182no—
519C2×D4—362no—
520C2×D4—362no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—32no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—184no—
529C22×C4—184no—
530C22×C4—184no—
531C22×C4—184no—
532C22×C4—362no—
533C22×C4—362no—
534C22×C4C2×D3212yes—
535C22×C4C2×D3211yescharacteristic
536C4⋊C4—22no—
537C4⋊C4—34no—
538C4⋊C4—94no—
539C4⋊C4—182no—
540C22⋊C4—64no—
541C22⋊C4—122no—
542C22⋊C4—184no—
543C22⋊C4—184no—
544C22⋊C4—184no—
545C22⋊C4—362no—
546C42—34no—
547C42—64no—
548C42—62no—
549C42—182no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—64no—
558C22×C3—64no—
559C22×C3—64no—
560C22×C3—122no—
561C22×C3—122no—
562C22×C3—122no—
563C22×C3—122no—
564C22×C3C22×C4×D311yescharacteristic
565C22×C3C22×C4×D311yescharacteristic
566C22×C3C22×D1211yescharacteristic
567C22×C3C2×#23511yescharacteristic
568C22×C3C2×D3×D411yescharacteristic
569C22×C3C2×D3×D411yescharacteristic
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C2×#23711yescharacteristic
572C22×C3#100411yescharacteristic
573C22×C3C2×#23911yescharacteristic
574C22×C3D3×#4111yescharacteristic
575C22×C3#100911yescharacteristic
576C22×C3#100911yescharacteristic
577C22×C3#100911yescharacteristic
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—24no—
581C2×D3—42no—
582C2×D3—42no—
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—64no—
586C2×D3—64no—
587C2×D3—64no—
588C2×D3—64no—
589C2×D3—64no—
590C2×D3—64no—
591C2×D3—124no—
592C2×D3—124no—
593C2×D3—124no—
594C2×D3—122no—
595C2×D3—122no—
596C2×D3—122no—
597C2×D3—122no—
598C2×D3—122no—
599C2×D3—122no—
600C2×D3—122no—
601C2×D3—122no—
602C2×D3—242no—
603C2×D3—242no—
604C2×D3—242no—
605C2×D3—242no—
606C3×C4—24no—
607C3×C4—34no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4—62no—
611C3×C4—62no—
612C3×C4—64no—
613C3×C4—82no—
614C3×C4—121no—
615C3×C4C4×D1214yescomplemented
616C3×C4#67⋊C414yescomplemented
617Dic3—22no—
618Dic3—24no—
619Dic3—22no—
620Dic3—41no—
621Dic3—62no—
622Dic3—62no—
623Dic3—122no—
624Dic3—122no—
625Dic3—121no—
626Dic3—121no—
627Dic3#89314yescomplemented
628C32#236611yescharacteristic, complemented, Sylow
629C23—34no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—94no—
637C23—182no—
638C23—182no—
639C23—182no—
640C23—182no—
641C23—182no—
642C23—182no—
643C23C22×D3211yescharacteristic
644D4—68no—
645D4—1816no—
646D4—188no—
647D4—368no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—32no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—34no—
656C2×C4—32no—
657C2×C4—61no—
658C2×C4—62no—
659C2×C4—61no—
660C2×C4—62no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—92no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—368no—
673C2×C4—368no—
674C2×C4C4×D3212yes—
675C2×C4D3×D1212yes—
676C2×C4#380412yes—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—124no—
685C2×C3C2×C4×D1211yescharacteristic
686C2×C3C2×#67⋊C411yescharacteristic
687C2×C3C2×#89311yescharacteristic
688C2×C3#552111yescharacteristic
689C2×C3C4×D3×D411yescharacteristic
690C2×C3#554511yescharacteristic
691C2×C3D4×D1211yescharacteristic
692C2×C3#555311yescharacteristic
693C2×C3#557711yescharacteristic
694C2×C3#558511yescharacteristic
695C2×C3#559911yescharacteristic
696C2×C3#560911yescharacteristic
697C2×C3#568111yescharacteristic
698C2×C3#571811yescharacteristic
699D3—44no—
700D3—124no—
701D3—124no—
702D3—244no—
703C22—64no—
704C22—64no—
705C22—64no—
706C22—122no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—184no—
711C22—184no—
712C22—184no—
713C22—362no—
714C22—362no—
715C22—362no—
716C22—362no—
717C22C2×C4×D3211yescharacteristic
718C22C2×D3×D1211yescharacteristic
719C22D32×D411yescharacteristic
720C22#6431411yescharacteristic
721C22D3×#23911yescharacteristic
722C22#6432011yescharacteristic
723C22C2×#380411yescharacteristic
724C4—34no—
725C4—42no—
726C4—62no—
727C4—64no—
728C4—62no—
729C4—121no—
730C4—182no—
731C4—361no—
732C4#6388014yescomplemented
733C3—21no—
734C3#7365311yescharacteristic, complemented
735C3#7630611yescharacteristic, complemented
736C2—124no—
737C2—364no—
738C2#1059452411yescharacteristic
739C2D3×#89311yescharacteristic
740C2#1059460411yescharacteristic
741C2#1059462111yescharacteristic
742C2C2×#6388011yescharacteristic
743C2#1059514311yescharacteristic
744C2#1059538811yescharacteristic
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
2. C2×#63898C2semidirect
3. C2×#63894C2semidirect
4. C2×#63880C2semidirect
5. #10592687C2semidirect
6. C3×#4988C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
8. #10591383C2semidirect
9. #10591364C2semidirect
10. C4×Dic3⋊Dic3C2semidirect
11. #10591275C2semidirect
34. #63911C4semidirect
54. #4988D3semidirect
55. Dic3×C4⋊C4D3semidirect
72. C2×C4⋊(C3⋊D3)C2×C4semidirect
80. C2×C3×D12C2×C4semidirect
85. C2×#626C2×C4semidirect
86. C2×#626C2×C4semidirect
99. C3×C4⋊Dic3D4semidirect
102. C3×C4×Dic3C2×C4semidirect
104. Dic3⋊Dic3D4semidirect
282. C2×D12C4×D3semidirect
315. C4⋊Dic3D12semidirect
323. C4×Dic3C4×D3semidirect
346. C32×C4C4×D4semidirect
353. C3×Dic3C4×D4semidirect
615. C3×C4C4×D12semidirect
616. C3×C4#67⋊C4semidirect
627. Dic3#893semidirect
628. C32#2366semidirect
732. C4#63880semidirect
734. C3#73653semidirect
735. C3#76306semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C2×#638982
C2×#638942
C2×#638802
#105926872
C3×#49882
C3×Dic3×C4⋊C42
#105913832
#105913642
C4×Dic3⋊Dic32
#105912752
#763063
#736533