Finite Group Databasebeta

← C2×#10591233 #11800709

Subgroups — C2×#10591233 #11800709

Order 1152.

3057 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic
2C22×#3752C211yesmaximal, characteristic
3C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
4C22×#3722C211yesmaximal, characteristic
5C22×Dic32C211yesmaximal, characteristic, complemented
6C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#10591233C218yesmaximal, direct product factor
9C2×C4×(C2×D3)⋊C4—31nomaximal
10C2×#4666—31nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#624—24no—
19C22×#624—24no—
20C22×#624C418yescomplemented
21C22×#624C2214yes—
22C2×#3752C418yescomplemented
23C2×#3752C2214yes—
24C2×C3×C4×Dic3—24no—
25C2×C3×C4×Dic3C2214yescomplemented
26C2×#3722C418yescomplemented
27C2×#3722C2214yes—
28C2×Dic32—24no—
29C2×Dic32C2214yescomplemented
30C3×C3⋊#95C2214yescomplemented
31#63579C2214yescomplemented
32C23×C4×D3—31no—
33C23×C4×D3—31no—
34C22×C3×C42—31no—
35C22×(C2×D3)⋊C4—31no—
36C22×(C2×D3)⋊C4—31no—
37C22×(C2×D3)⋊C4—31no—
38C22×(C2×D3)⋊C4—31no—
39C22×(C2×D3)⋊C4—61no—
40C22×C4×Dic3—31no—
41C22×C4×Dic3—31no—
42C22×C4×Dic3D311yescharacteristic, complemented
43C2×C3×#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95D311yescharacteristic, complemented
47C4×(C2×D3)⋊C4—38no—
48#4666—38no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3—22no—
51C23×C3⋊D3—22no—
52C23×C3⋊D3—22no—
53C23×C3⋊D3—22no—
54C23×C3⋊D3C2×C414yes—
55C23×C3⋊D3C2×C414yes—
56C23×C3⋊D3C2×C414yes—
57C23×C3⋊D3C2312yes—
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4C2×C414yescomplemented
61C22×C32×C4C2312yes—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3C2×C414yescomplemented
65C22×C3⋊Dic3C2312yes—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3C2×C414yes—
73C22×C3×Dic3C2×C414yes—
74C22×C3×Dic3C2×C414yescomplemented
75C22×C3×Dic3C2×C414yescomplemented
76C22×C3×Dic3D414yes—
77C22×C3×Dic3D414yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×#624—232no—
83C2×#624—28no—
84C2×#624—28no—
85C2×#624C2×C4116yescomplemented
86#3752C2×C4116yescomplemented
87C3×C4×Dic3—28no—
88#3722C2×C4116yescomplemented
89Dic32—28no—
90C2×C4×C22⋊C4—91noSylow
91C24×D3—31no—
92C24×D3—31no—
93C24×D3—61no—
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4—31no—
97C23×C3×C4—31no—
98C23×C3×C4—31no—
99C23×C3×C4C2×D311yescharacteristic
100C23×C3×C4C2×D311yescharacteristic
101C23×Dic3—31no—
102C23×Dic3—31no—
103C23×Dic3—61no—
104C23×Dic3C2×D311yescharacteristic
105C23×Dic3C2×D311yescharacteristic
106C23×Dic3C2×D311yescharacteristic
107C23×Dic3C2×D311yescharacteristic
108C22×C4×D3—38no—
109C22×C4×D3—38no—
110C22×C4×D3—34no—
111C22×C4×D3—34no—
112C22×C4×D3—64no—
113C22×C4×D3—64no—
114C22×C4×D3—64no—
115C22×C4×D3—64no—
116C2×C3×C42—34no—
117C2×C3×C42—64no—
118C2×(C2×D3)⋊C4—38no—
119C2×(C2×D3)⋊C4—38no—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—38no—
123C2×(C2×D3)⋊C4—38no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×(C2×D3)⋊C4—68no—
127C2×(C2×D3)⋊C4—64no—
128C2×C4×Dic3—24no—
129C2×C4×Dic3—34no—
130C2×C4×Dic3—34no—
131C2×C4×Dic3—64no—
132C2×C4×Dic3—64no—
133C2×C4×Dic3C2×D314yescomplemented
134C3×#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95C2×D314yescomplemented
138C23×C32C22×C412yes—
139C23×C32C22×C412yes—
140C23×C32C22×C412yes—
141C23×C32C2×D412yes—
142C23×C32C2×D412yes—
143C23×C32#4112yes—
144C23×C32#4112yes—
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—28no—
147C22×C3⋊D3—28no—
148C22×C3⋊D3—28no—
149C22×C3⋊D3—28no—
150C22×C3⋊D3—28no—
151C22×C3⋊D3—28no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3C42116yescomplemented
157C22×C3⋊D3C22×C414yes—
158C22×C3⋊D3C22×C414yes—
159C22×C3⋊D3C22×C414yes—
160C2×C32×C4—28no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C22×C414yescomplemented
164C2×C3⋊Dic3—28no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C22×C414yescomplemented
168C2×C3×Dic3—28no—
169C2×C3×Dic3—28no—
170C2×C3×Dic3—28no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22⋊C4116yescomplemented
178C2×C3×Dic3C22×C414yes—
179C2×C3×Dic3C22×C414yes—
180C2×C3×Dic3C22×C414yescomplemented
181C2×C3×Dic3C22×C414yescomplemented
182C2×C3×Dic3C2×D414yes—
183C2×C3×Dic3C2×D414yes—
184#624—232no—
185C24×C4—91no—
186C22×C22⋊C4—91no—
187C22×C22⋊C4—91no—
188C22×C42—31no—
189C22×C42—91no—
190C4×C22⋊C4—98no—
191C2×#95—31no—
192C2×#95—91no—
193C24×C3—21no—
194C24×C3C22×D311yescharacteristic
195C24×C3C22×D311yescharacteristic
196C23×D3—34no—
197C23×D3—34no—
198C23×D3—34no—
199C23×D3—34no—
200C23×D3—34no—
201C23×D3—34no—
202C23×D3—32no—
203C23×D3—32no—
204C23×D3—64no—
205C23×D3—64no—
206C23×D3—64no—
207C23×D3—62no—
208C23×D3—62no—
209C23×D3—62no—
210C23×D3—62no—
211C23×D3—62no—
212C23×D3—62no—
213C23×D3—62no—
214C23×D3—62no—
215C23×D3—62no—
216C23×D3—122no—
217C23×D3—122no—
218C23×D3—122no—
219C23×D3—122no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—24no—
225C22×C3×C4—22no—
226C22×C3×C4—34no—
227C22×C3×C4—34no—
228C22×C3×C4—34no—
229C22×C3×C4—32no—
230C22×C3×C4—34no—
231C22×C3×C4—34no—
232C22×C3×C4—34no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—32no—
236C22×C3×C4—42no—
237C22×C3×C4—42no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4—62no—
241C22×C3×C4—62no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4C4×D314yescomplemented
245C22×C3×C4C4×D314yescomplemented
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D312yes—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—34no—
255C22×Dic3—34no—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—64no—
259C22×Dic3—62no—
260C22×Dic3—62no—
261C22×Dic3—62no—
262C22×Dic3—62no—
263C22×Dic3—62no—
264C22×Dic3—122no—
265C22×Dic3—122no—
266C22×Dic3C4×D314yes—
267C22×Dic3C4×D314yes—
268C22×Dic3C4×D314yescomplemented
269C22×Dic3C4×D314yescomplemented
270C22×Dic3D1214yes—
271C22×Dic3#6714yes—
272C22×Dic3C22×D312yes—
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D312yes—
275C22×Dic3C22×D312yes—
276C2×C4×D3—316no—
277C2×C4×D3—316no—
278C2×C4×D3—632no—
279C2×C4×D3—68no—
280C2×C4×D3—68no—
281C2×C4×D3—632no—
282C2×C4×D3—68no—
283C2×C4×D3—68no—
284C3×C42—68no—
285(C2×D3)⋊C4—316no—
286(C2×D3)⋊C4—316no—
287(C2×D3)⋊C4—316no—
288(C2×D3)⋊C4—316no—
289(C2×D3)⋊C4—616no—
290C4×Dic3—28no—
291C4×Dic3—68no—
292C4×Dic3—68no—
293C22×C32C2×C4214yes—
294C22×C32C2×C22⋊C414yes—
295C22×C32#11714yes—
296C22×C32C4×D414yes—
297C22×C32C4×D414yes—
298C22×C32C4×D414yes—
299C22×C32C4×D414yes—
300C22×C32C23×C411yescharacteristic
301C22×C32C23×C411yescharacteristic
302C22×C32C23×C411yescharacteristic
303C22×C32C22×D411yescharacteristic
304C22×C32C22×D411yescharacteristic
305C22×C32C2×#4111yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C2×C3⋊D3—24no—
308C2×C3⋊D3—24no—
309C2×C3⋊D3—24no—
310C2×C3⋊D3—24no—
311C2×C3⋊D3—24no—
312C2×C3⋊D3—24no—
313C2×C3⋊D3—232no—
314C2×C3⋊D3C2×C4218yescomplemented
315C32×C4—24no—
316C3⋊Dic3—24no—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C3×Dic3—24no—
320C3×Dic3C2×C22⋊C418yescomplemented
321C25—91no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C23×C4—94no—
327C23×C4—98no—
328C23×C4—91no—
329C23×C4—184no—
330C23×C4—184no—
331C23×C4D3211yescharacteristic
332C2×C22⋊C4—94no—
333C2×C22⋊C4—98no—
334C2×C22⋊C4—98no—
335C2×C22⋊C4—94no—
336C2×C42—34no—
337C2×C42—64no—
338C2×C42—94no—
339C2×C42—184no—
340#95—34no—
341#95—94no—
342C23×C3—21no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3C2×C4×D312yes—
351C23×C3C2×C4×D312yes—
352C23×C3C2×C4×D312yes—
353C23×C3C2×C4×D312yes—
354C23×C3C2×C4×D312yes—
355C23×C3C2×C4×D312yes—
356C23×C3C2×D1212yes—
357C23×C3#23512yes—
358C23×C3#23512yes—
359C23×C3D3×D412yes—
360C23×C3D3×D412yes—
361C23×C3#23712yes—
362C23×C3#23912yes—
363C23×C3C2×#6712yes—
364C23×C3C23×D311yescharacteristic
365C23×C3C23×D311yescharacteristic
366C22×D3—316no—
367C22×D3—316no—
368C22×D3—34no—
369C22×D3—34no—
370C22×D3—34no—
371C22×D3—34no—
372C22×D3—34no—
373C22×D3—34no—
374C22×D3—616no—
375C22×D3—64no—
376C22×D3—64no—
377C22×D3—64no—
378C22×D3—68no—
379C22×D3—68no—
380C22×D3—68no—
381C22×D3—68no—
382C22×D3—68no—
383C22×D3—68no—
384C22×D3—68no—
385C22×D3—68no—
386C22×D3—68no—
387C22×D3—68no—
388C22×D3—68no—
389C22×D3—68no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—122no—
399C22×D3—122no—
400C22×D3—122no—
401C22×D3—122no—
402C22×D3—128no—
403C22×D3—128no—
404C22×D3—128no—
405C22×D3—128no—
406C22×D3—128no—
407C22×D3—128no—
408C2×C3×C4—28no—
409C2×C3×C4—28no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—316no—
416C2×C3×C4—34no—
417C2×C3×C4—34no—
418C2×C3×C4—34no—
419C2×C3×C4—34no—
420C2×C3×C4—34no—
421C2×C3×C4—34no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—48no—
425C2×C3×C4—68no—
426C2×C3×C4—68no—
427C2×C3×C4—68no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4C2×C4×D314yescomplemented
435C2×C3×C4C2×C4×D314yescomplemented
436C2×Dic3—28no—
437C2×Dic3—28no—
438C2×Dic3—28no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—34no—
446C2×Dic3—34no—
447C2×Dic3—64no—
448C2×Dic3—68no—
449C2×Dic3—68no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—122no—
455C2×Dic3—122no—
456C2×Dic3—128no—
457C2×Dic3(C2×D3)⋊C4116yescomplemented
458C2×Dic3C2×C4×D314yes—
459C2×Dic3C2×C4×D314yes—
460C2×Dic3C2×C4×D314yescomplemented
461C2×Dic3C2×C4×D314yescomplemented
462C2×Dic3C2×D1214yes—
463C2×Dic3C2×#6714yes—
464C4×D3—632no—
465C4×D3—632no—
466C2×C32C4×C22⋊C418yescomplemented
467C2×C32C22×C4211yescharacteristic
468C2×C32C22×C22⋊C411yescharacteristic
469C2×C32C2×#11711yescharacteristic
470C2×C32C2×C4×D411yescharacteristic
471C2×C32C2×C4×D411yescharacteristic
472C2×C32C2×C4×D411yescharacteristic
473C2×C32C2×C4×D411yescharacteristic
474C3⋊D3—28no—
475C24—92no—
476C24—94no—
477C24—94no—
478C24—94no—
479C24—182no—
480C24—182no—
481C24—182no—
482C24—182no—
483C24C2×D3211yescharacteristic
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—32no—
487C22×C4—34no—
488C22×C4—34no—
489C22×C4—34no—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—34no—
494C22×C4—34no—
495C22×C4—34no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—916no—
503C22×C4—92no—
504C22×C4—94no—
505C22×C4—188no—
506C22×C4—188no—
507C22×C4—1832no—
508C22×C4—182no—
509C22×C4—182no—
510C22×C4#62414yescomplemented
511C22×C4C2×D3212yes—
512C22⋊C4—916no—
513C22⋊C4—916no—
514C42—68no—
515C42—188no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3C42×D314yes—
531C22×C3C42×D314yes—
532C22×C3#87214yes—
533C22×C3C4×D1214yes—
534C22×C3C4×D1214yes—
535C22×C3D3×C22⋊C414yes—
536C22×C3#67⋊C414yes—
537C22×C3#67⋊C414yes—
538C22×C3#89214yes—
539C22×C3#89314yes—
540C22×C3#89314yes—
541C22×C3C2×(C2×D3)⋊C414yes—
542C22×C3C4×#6714yes—
543C22×C3C4×#6714yes—
544C22×C3C22×C4×D311yescharacteristic
545C22×C3C22×C4×D311yescharacteristic
546C22×C3C22×C4×D311yescharacteristic
547C22×C3C22×C4×D311yescharacteristic
548C22×C3C22×C4×D311yescharacteristic
549C22×C3C22×C4×D311yescharacteristic
550C22×C3C22×D1211yescharacteristic
551C22×C3C2×#23511yescharacteristic
552C22×C3C2×#23511yescharacteristic
553C22×C3C2×D3×D411yescharacteristic
554C22×C3C2×D3×D411yescharacteristic
555C22×C3C2×#23711yescharacteristic
556C22×C3C2×#23911yescharacteristic
557C22×C3C22×#6711yescharacteristic
558C2×D3—38no—
559C2×D3—38no—
560C2×D3—68no—
561C2×D3—632no—
562C2×D3—632no—
563C2×D3—64no—
564C2×D3—64no—
565C2×D3—64no—
566C2×D3—64no—
567C2×D3—64no—
568C2×D3—64no—
569C2×D3—64no—
570C2×D3—64no—
571C2×D3—64no—
572C2×D3—64no—
573C2×D3—64no—
574C2×D3—64no—
575C2×D3—1232no—
576C2×D3—124no—
577C2×D3—124no—
578C2×D3—124no—
579C2×D3—124no—
580C2×D3—124no—
581C2×D3—124no—
582C3×C4—24no—
583C3×C4—24no—
584C3×C4—38no—
585C3×C4—44no—
586C3×C4—64no—
587C3×C4—64no—
588C3×C4—64no—
589Dic3—24no—
590Dic3—24no—
591Dic3—24no—
592Dic3—64no—
593Dic3—64no—
594Dic3—124no—
595Dic3C2×(C2×D3)⋊C418yescomplemented
596C32C2×C4×C22⋊C411yescharacteristic, complemented, Sylow
597C23—94no—
598C23—94no—
599C23—94no—
600C23—916no—
601C23—182no—
602C23—182no—
603C23—182no—
604C23—182no—
605C23—188no—
606C23—188no—
607C23—188no—
608C23—188no—
609C23—188no—
610C23—188no—
611C23#379912yes—
612C23C4×D3212yes—
613C23C4×D3212yes—
614C23D3×D1212yes—
615C23#380412yes—
616C23C2×#62412yes—
617C23D3×#6712yes—
618C23C22×D3211yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—34no—
623C2×C4—34no—
624C2×C4—34no—
625C2×C4—316no—
626C2×C4—34no—
627C2×C4—34no—
628C2×C4—34no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—68no—
636C2×C4—68no—
637C2×C4—68no—
638C2×C4—94no—
639C2×C4—1832no—
640C2×C4—182no—
641C2×C4—182no—
642C2×C4—188no—
643C2×C4C2×#62414yescomplemented
644C2×C3—28no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3#466618yescomplemented
653C2×C3C4×(C2×D3)⋊C418yescomplemented
654C2×C3C2×C42×D311yescharacteristic
655C2×C3C2×C42×D311yescharacteristic
656C2×C3C2×#87211yescharacteristic
657C2×C3C2×C4×D1211yescharacteristic
658C2×C3C2×C4×D1211yescharacteristic
659C2×C3C2×D3×C22⋊C411yescharacteristic
660C2×C3C2×#67⋊C411yescharacteristic
661C2×C3C2×#67⋊C411yescharacteristic
662C2×C3C2×#89211yescharacteristic
663C2×C3C2×#89311yescharacteristic
664C2×C3C2×#89311yescharacteristic
665C2×C3C22×(C2×D3)⋊C411yescharacteristic
666C2×C3C2×C4×#6711yescharacteristic
667C2×C3C2×C4×#6711yescharacteristic
668D3—68no—
669D3—68no—
670D3—128no—
671C22—98no—
672C22—1832no—
673C22—184no—
674C22—184no—
675C22—184no—
676C22—184no—
677C22—184no—
678C22—184no—
679C22#6383614yes—
680C22#6388014yes—
681C22C4×#62414yes—
682C22#6389414yes—
683C22#6390414yes—
684C22D3×(C2×D3)⋊C414yes—
685C22#6395214yes—
686C22C2×#379911yescharacteristic
687C22C2×C4×D3211yescharacteristic
688C22C2×C4×D3211yescharacteristic
689C22C2×D3×D1211yescharacteristic
690C22C2×#380411yescharacteristic
691C22C22×#62411yescharacteristic
692C22C2×D3×#6711yescharacteristic
693C4—24no—
694C4—38no—
695C4—64no—
696C4—64no—
697C4—64no—
698C4—184no—
699C3—21no—
700C3C2×#466611yescharacteristic, complemented
701C3C2×C4×(C2×D3)⋊C411yescharacteristic, complemented
702C2—188no—
703C2#1059123318yesdirect product factor
704C2C2×#6383611yescharacteristic
705C2C2×#6388011yescharacteristic
706C2C2×C4×#62411yescharacteristic
707C2C2×#6389411yescharacteristic
708C2C2×#6390411yescharacteristic
709C2C2×D3×(C2×D3)⋊C411yescharacteristic
710C2C2×#6395211yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3⋊D3C22
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C22×C3×C4×Dic3C2semidirect
5. C22×Dic32C2semidirect
6. C2×C3×C3⋊#95C2semidirect
7. C2×#63579C2semidirect
8. #10591233C2direct (N × H)
20. C22×#624C4semidirect
22. C2×#3752C4semidirect
25. C2×C3×C4×Dic3C22semidirect
26. C2×#3722C4semidirect
29. C2×Dic32C22semidirect
30. C3×C3⋊#95C22semidirect
31. #63579C22semidirect
42. C22×C4×Dic3D3semidirect
46. C2×C3⋊#95D3semidirect
60. C22×C32×C4C2×C4semidirect
64. C22×C3⋊Dic3C2×C4semidirect
74. C22×C3×Dic3C2×C4semidirect
75. C22×C3×Dic3C2×C4semidirect
85. C2×#624C2×C4semidirect
86. #3752C2×C4semidirect
88. #3722C2×C4semidirect
133. C2×C4×Dic3C2×D3semidirect
137. C3⋊#95C2×D3semidirect
156. C22×C3⋊D3C42semidirect
163. C2×C32×C4C22×C4semidirect
167. C2×C3⋊Dic3C22×C4semidirect
177. C2×C3×Dic3C22⋊C4semidirect
180. C2×C3×Dic3C22×C4semidirect
181. C2×C3×Dic3C22×C4semidirect
244. C22×C3×C4C4×D3semidirect
245. C22×C3×C4C4×D3semidirect
268. C22×Dic3C4×D3semidirect
269. C22×Dic3C4×D3semidirect
314. C2×C3⋊D3C2×C42semidirect
320. C3×Dic3C2×C22⋊C4semidirect
434. C2×C3×C4C2×C4×D3semidirect
435. C2×C3×C4C2×C4×D3semidirect
457. C2×Dic3(C2×D3)⋊C4semidirect
460. C2×Dic3C2×C4×D3semidirect
461. C2×Dic3C2×C4×D3semidirect
466. C2×C32C4×C22⋊C4semidirect
510. C22×C4#624semidirect
595. Dic3C2×(C2×D3)⋊C4semidirect
596. C32C2×C4×C22⋊C4semidirect
643. C2×C4C2×#624semidirect
652. C2×C3#4666semidirect
653. C2×C3C4×(C2×D3)⋊C4semidirect
700. C3C2×#4666semidirect
701. C3C2×C4×(C2×D3)⋊C4semidirect
703. C2#10591233direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6242
C22×#37522
C22×C3×C4×Dic32
C22×#37222
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105912332
C2×C4×(C2×D3)⋊C43
C2×#46663