Finite Group Databasebeta

← #11773297

Subgroups — #11773297

Order 1152.

2340 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×#3752C211yesmaximal, characteristic
3C22×#3752C211yesmaximal, characteristic
4C22×#3750C211yesmaximal, characteristic, complemented
5C2×C32×#95C211yesmaximal, characteristic, complemented
6C2×#63658C211yesmaximal, characteristic, complemented
7C2×#63658C211yesmaximal, characteristic, complemented
8#69428—34nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C2×#3752—22no—
17C2×#3752—22no—
18C2×#3752—22no—
19C2×#3752—22no—
20C2×#3752—22no—
21C2×#3752—22no—
22C2×#3752—22no—
23C2×#3752—22no—
24C2×#3752C414yescomplemented
25C2×#3750—22no—
26C2×#3750—22no—
27C2×#3750—22no—
28C32×#95—22no—
29#63658—22no—
30#63658—22no—
31C22×(C2×D3)⋊C4—34no—
32C22×(C2×D3)⋊C4—34no—
33C22×(C2×D3)⋊C4—34no—
34C22×Dic3⋊C4—34no—
35C2×C3×#95D314yescomplemented
36C2×C3⋊#95—34no—
37C2×C3⋊#95—34no—
38C24×C32C2311yescharacteristic
39C23×C3⋊D3—21no—
40C23×C3⋊D3—21no—
41C23×C3⋊D3—21no—
42C23×C3⋊D3—21no—
43C23×C3⋊D3—21no—
44C23×C3⋊D3—21no—
45C23×C3⋊D3—21no—
46C23×C3⋊D3—21no—
47C23×C3⋊D3—21no—
48C23×C3⋊D3—21no—
49C23×C3⋊D3—21no—
50C23×C3⋊D3—21no—
51C23×C3⋊D3C2×C412yes—
52C23×C3⋊D3D412yes—
53C23×C3⋊D3Q812yes—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4C2×C412yes—
73C22×C32×C4D412yes—
74C22×C32×C4D412yes—
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3—21no—
77C22×C3⋊Dic3—21no—
78C22×C3⋊Dic3—21no—
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3—21no—
82C22×C3⋊Dic3—21no—
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—21no—
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3—21no—
87C22×C3⋊Dic3—21no—
88C22×C3⋊Dic3—21no—
89C22×C3⋊Dic3—21no—
90C22×C3⋊Dic3—21no—
91C22×C3⋊Dic3C2×C412yes—
92C22×C3⋊Dic3D412yes—
93C22×C3⋊Dic3D412yes—
94C22×C3⋊Dic3D412yes—
95C22×C3⋊Dic3D412yes—
96#3752—28no—
97#3752—28no—
98#3752—28no—
99#3750—28no—
100#1439—91noSylow
101C24×D3—34no—
102C23×C3×C4C2×D314yes—
103C23×C3×C4C2×D314yes—
104C23×C3×C4C2×D314yes—
105C23×Dic3—34no—
106C23×Dic3—34no—
107C23×Dic3—34no—
108C2×(C2×D3)⋊C4—316no—
109C2×(C2×D3)⋊C4—68no—
110C2×(C2×D3)⋊C4—68no—
111C2×(C2×D3)⋊C4—68no—
112C2×(C2×D3)⋊C4—68no—
113C2×(C2×D3)⋊C4—68no—
114C2×(C2×D3)⋊C4—68no—
115C2×(C2×D3)⋊C4—68no—
116C2×(C2×D3)⋊C4—68no—
117C2×Dic3⋊C4—68no—
118C2×Dic3⋊C4—68no—
119C2×Dic3⋊C4—68no—
120C3×#95—28no—
121C3⋊#95—68no—
122C3⋊#95—68no—
123C23×C32C22×C411yescharacteristic
124C23×C32C2×D411yescharacteristic
125C23×C32C2×D411yescharacteristic
126C23×C32C2×D411yescharacteristic
127C23×C32C2×D411yescharacteristic
128C23×C32C2×D411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32C2×Q811yescharacteristic
132C23×C32#4111yescharacteristic
133C23×C32#4111yescharacteristic
134C23×C32#4111yescharacteristic
135C23×C32#4111yescharacteristic
136C23×C32#4111yescharacteristic
137C23×C32#4111yescharacteristic
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—41no—
157C22×C3⋊D3—41no—
158C22×C3⋊D3—41no—
159C22×C3⋊D3—41no—
160C22×C3⋊D3—41no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—41no—
164C22×C3⋊D3—41no—
165C22×C3⋊D3—41no—
166C22×C3⋊D3—41no—
167C22×C3⋊D3—41no—
168C22×C3⋊D3—41no—
169C22×C3⋊D3—41no—
170C22×C3⋊D3—41no—
171C22×C3⋊D3—41no—
172C22×C3⋊D3C4⋊C414yescomplemented
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—41no—
183C2×C32×C4—41no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—41no—
190C2×C32×C4—41no—
191C2×C32×C4—41no—
192C2×C32×C4—41no—
193C2×C32×C4—41no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3—41no—
207C2×C3⋊Dic3—41no—
208C2×C3⋊Dic3—41no—
209C2×C3⋊Dic3—41no—
210C2×C3⋊Dic3—41no—
211C2×C3⋊Dic3—41no—
212C2×C3⋊Dic3—41no—
213C2×C3⋊Dic3—41no—
214C2×C3⋊Dic3C22⋊C414yescomplemented
215C22×C4⋊C4—91no—
216C22×C22⋊C4—91no—
217C22×C22⋊C4—91no—
218C22×C22⋊C4—91no—
219C2×#95—91no—
220C2×#95—91no—
221C2×#95C3⋊D311yescharacteristic, complemented
222C24×C3C22×D314yes—
223C23×D3—38no—
224C23×D3—38no—
225C23×D3—38no—
226C23×D3—64no—
227C23×D3—64no—
228C23×D3—64no—
229C23×D3—64no—
230C23×D3—64no—
231C23×D3—64no—
232C23×D3—64no—
233C23×D3—64no—
234C23×D3—64no—
235C23×D3—64no—
236C23×D3—64no—
237C23×D3—64no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—24no—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4—24no—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—24no—
256C22×C3×C4C4×D318yes—
257C22×C3×C4D1218yes—
258C22×C3×C4#6718yes—
259C22×Dic3—38no—
260C22×Dic3—38no—
261C22×Dic3—38no—
262C22×Dic3—38no—
263C22×Dic3—38no—
264C22×Dic3—64no—
265C22×Dic3—64no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3—64no—
269C22×Dic3—64no—
270C22×Dic3—64no—
271C22×Dic3—64no—
272C22×Dic3—64no—
273C22×Dic3—64no—
274C22×Dic3—64no—
275C22×Dic3—64no—
276C22×Dic3—64no—
277C22×Dic3—64no—
278C22×Dic3—64no—
279C22×Dic3—64no—
280(C2×D3)⋊C4—632no—
281(C2×D3)⋊C4—632no—
282(C2×D3)⋊C4—632no—
283Dic3⋊C4—632no—
284C22×C32C2×C22⋊C411yescharacteristic
285C22×C32C2×C4⋊C411yescharacteristic
286C22×C32#11711yescharacteristic
287C22×C32C4×D411yescharacteristic
288C22×C32C4×D411yescharacteristic
289C22×C32C4×D411yescharacteristic
290C22×C32C4×D411yescharacteristic
291C22×C32#12011yescharacteristic
292C22×C32#12011yescharacteristic
293C22×C32#12011yescharacteristic
294C22×C32#12111yescharacteristic
295C22×C32#12111yescharacteristic
296C22×C32#12111yescharacteristic
297C22×C32#12111yescharacteristic
298C22×C32#12111yescharacteristic
299C22×C32#12111yescharacteristic
300C22×C32#12111yescharacteristic
301C22×C32#12111yescharacteristic
302C22×C32C22⋊Q811yescharacteristic
303C22×C32C22⋊Q811yescharacteristic
304C22×C32C22⋊Q811yescharacteristic
305C22×C32C22⋊Q811yescharacteristic
306C22×C32C22⋊Q811yescharacteristic
307C22×C32C22⋊Q811yescharacteristic
308C22×C32#12311yescharacteristic
309C22×C32#12311yescharacteristic
310C22×C32#12311yescharacteristic
311C22×C32#12311yescharacteristic
312C22×C32#12311yescharacteristic
313C22×C32#12411yescharacteristic
314C22×C32#12411yescharacteristic
315C22×C32#12411yescharacteristic
316C22×C32#12611yescharacteristic
317C22×C32#12611yescharacteristic
318C22×C32#12711yescharacteristic
319C2×C3⋊D3—24no—
320C2×C3⋊D3—24no—
321C2×C3⋊D3—24no—
322C2×C3⋊D3—42no—
323C2×C3⋊D3—42no—
324C2×C3⋊D3—42no—
325C2×C3⋊D3—42no—
326C2×C3⋊D3—42no—
327C2×C3⋊D3—42no—
328C2×C3⋊D3—42no—
329C2×C3⋊D3—42no—
330C2×C3⋊D3—42no—
331C2×C3⋊D3—42no—
332C2×C3⋊D3—42no—
333C2×C3⋊D3—42no—
334C32×C4—42no—
335C32×C4—42no—
336C32×C4—42no—
337C3⋊Dic3—24no—
338C3⋊Dic3—42no—
339C3⋊Dic3—42no—
340C25—91no—
341C23×C4—91no—
342C23×C4—91no—
343C23×C4—91no—
344C23×C4C2×C3⋊D311yescharacteristic
345C23×C4C2×C3⋊D311yescharacteristic
346C23×C4C2×C3⋊D311yescharacteristic
347C2×C4⋊C4—182no—
348C2×C4⋊C4—182no—
349C2×C4⋊C4—182no—
350C2×C22⋊C4—94no—
351C2×C22⋊C4—182no—
352C2×C22⋊C4—182no—
353C2×C22⋊C4—182no—
354C2×C22⋊C4—182no—
355C2×C22⋊C4—182no—
356C2×C22⋊C4—182no—
357C2×C22⋊C4—182no—
358C2×C22⋊C4—182no—
359#95—22no—
360#95—182no—
361#95—182no—
362C23×C3C2×C4×D314yes—
363C23×C3C2×D1214yes—
364C23×C3#23514yes—
365C23×C3#23514yes—
366C23×C3#23514yes—
367C23×C3#23514yes—
368C23×C3D3×D414yes—
369C23×C3D3×D414yes—
370C23×C3D3×D414yes—
371C23×C3D3×D414yes—
372C23×C3D3×D414yes—
373C23×C3#23714yes—
374C23×C3D3×Q814yes—
375C23×C3#23914yes—
376C23×C3C2×#6714yes—
377C22×D3—316no—
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—68no—
391C22×D3—68no—
392C22×D3—68no—
393C22×D3—68no—
394C22×D3—68no—
395C22×D3—68no—
396C22×D3—124no—
397C22×D3—124no—
398C22×D3—124no—
399C22×D3—124no—
400C22×D3—124no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3—124no—
404C22×D3—124no—
405C22×D3—124no—
406C22×D3—124no—
407C22×D3—124no—
408C22×D3—124no—
409C22×D3—124no—
410C22×D3—124no—
411C22×D3—124no—
412C2×C3×C4—28no—
413C2×C3×C4—28no—
414C2×C3×C4—28no—
415C2×C3×C4—28no—
416C2×C3×C4—28no—
417C2×C3×C4—28no—
418C2×C3×C4—28no—
419C2×C3×C4—28no—
420C2×C3×C4—28no—
421C2×C3×C4—44no—
422C2×C3×C4—44no—
423C2×C3×C4—44no—
424C2×C3×C4—44no—
425C2×C3×C4—44no—
426C2×C3×C4—44no—
427C2×C3×C4—44no—
428C2×C3×C4—44no—
429C2×C3×C4—44no—
430C2×C3×C4—44no—
431C2×C3×C4—44no—
432C2×C3×C4—44no—
433C2×Dic3—316no—
434C2×Dic3—68no—
435C2×Dic3—68no—
436C2×Dic3—68no—
437C2×Dic3—68no—
438C2×Dic3—68no—
439C2×Dic3—68no—
440C2×Dic3—68no—
441C2×Dic3—68no—
442C2×Dic3—68no—
443C2×Dic3—68no—
444C2×Dic3—68no—
445C2×Dic3—68no—
446C2×Dic3—124no—
447C2×Dic3—124no—
448C2×Dic3—124no—
449C2×Dic3—124no—
450C2×Dic3—124no—
451C2×Dic3—124no—
452C2×Dic3—124no—
453C2×Dic3—124no—
454C2×C32#38011yescharacteristic
455C2×C32#38511yescharacteristic
456C2×C32#38511yescharacteristic
457C2×C32#38611yescharacteristic
458C2×C32#38811yescharacteristic
459C2×C32#38811yescharacteristic
460C2×C32#39011yescharacteristic
461C2×C32#39211yescharacteristic
462C2×C32#39311yescharacteristic
463C2×C32#39411yescharacteristic
464C2×C32#39411yescharacteristic
465C2×C32#39611yescharacteristic
466C2×C32#39611yescharacteristic
467C2×C32#39711yescharacteristic
468C2×C32#39911yescharacteristic
469C3⋊D3—44no—
470C24—92no—
471C24—92no—
472C24—92no—
473C24—181no—
474C24—181no—
475C24—181no—
476C24—181no—
477C24—181no—
478C24—181no—
479C24—181no—
480C24—181no—
481C24—181no—
482C24—181no—
483C24—181no—
484C24—181no—
485C24C22×C3⋊D311yescharacteristic
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—92no—
505C22×C4—92no—
506C22×C4—92no—
507C22×C4—92no—
508C22×C4—92no—
509C22×C4—181no—
510C22×C4—181no—
511C22×C4—181no—
512C22×C4—181no—
513C22×C4—181no—
514C22×C4—181no—
515C22×C4—181no—
516C22×C4—181no—
517C22×C4—181no—
518C22×C4—181no—
519C22×C4—181no—
520C22×C4—181no—
521C22×C4—181no—
522C22×C4—181no—
523C22×C4—181no—
524C22×C4—181no—
525C22×C4C4×C3⋊D312yes—
526C22×C4C4⋊(C3⋊D3)12yes—
527C22×C4#63812yes—
528C4⋊C4—188no—
529C22⋊C4—188no—
530C22⋊C4—188no—
531C22⋊C4—188no—
532C22×C3#87214yes—
533C22×C3C4×D1214yes—
534C22×C3#87514yes—
535C22×C3#87614yes—
536C22×C3D3×C22⋊C414yes—
537C22×C3#67⋊C414yes—
538C22×C3#88214yes—
539C22×C3#88214yes—
540C22×C3#88314yes—
541C22×C3#88414yes—
542C22×C3#88414yes—
543C22×C3#88414yes—
544C22×C3#88414yes—
545C22×C3#88414yes—
546C22×C3#88514yes—
547C22×C3#88514yes—
548C22×C3D3×C4⋊C414yes—
549C22×C3#89314yes—
550C22×C3#89414yes—
551C22×C3#89414yes—
552C22×C3#89414yes—
553C22×C3#89514yes—
554C22×C3#89614yes—
555C22×C3#89614yes—
556C22×C3#89614yes—
557C22×C3#89614yes—
558C22×C3#89714yes—
559C22×C3#89814yes—
560C22×C3C4×#6714yes—
561C22×C3#92914yes—
562C22×C3#93014yes—
563C22×C3#93714yes—
564C22×C3#93914yes—
565C22×C3#94014yes—
566C22×C3#94614yes—
567C2×D3—616no—
568C2×D3—616no—
569C2×D3—616no—
570C2×D3—128no—
571C2×D3—128no—
572C2×D3—128no—
573C2×D3—128no—
574C2×D3—128no—
575C2×D3—128no—
576C2×D3—128no—
577C2×D3—128no—
578C2×D3—128no—
579C2×D3—128no—
580C2×D3—128no—
581C2×D3—128no—
582C3×C4—48no—
583C3×C4—48no—
584C3×C4—48no—
585Dic3—616no—
586Dic3—128no—
587Dic3—128no—
588C32#143911yescharacteristic, complemented, Sylow
589C23—94no—
590C23—182no—
591C23—182no—
592C23—182no—
593C23—182no—
594C23—182no—
595C23—182no—
596C23—182no—
597C23—182no—
598C23—182no—
599C23—182no—
600C23—182no—
601C23—182no—
602C23—182no—
603C23—182no—
604C23—182no—
605C23—182no—
606C23—182no—
607C23—182no—
608C23—361no—
609C23—361no—
610C23—361no—
611C23—361no—
612C23—361no—
613C23—361no—
614C23—361no—
615C23—361no—
616C23—361no—
617C23—361no—
618C23—361no—
619C23—361no—
620C23—361no—
621C23—361no—
622C23—361no—
623C23—361no—
624C23C2×C4×C3⋊D311yescharacteristic
625C23C2×C4⋊(C3⋊D3)11yescharacteristic
626C23#382811yescharacteristic
627C23#382811yescharacteristic
628C23#382811yescharacteristic
629C23#382811yescharacteristic
630C23D4×C3⋊D311yescharacteristic
631C23D4×C3⋊D311yescharacteristic
632C23D4×C3⋊D311yescharacteristic
633C23D4×C3⋊D311yescharacteristic
634C23D4×C3⋊D311yescharacteristic
635C23#383011yescharacteristic
636C23Q8×C3⋊D311yescharacteristic
637C23#383211yescharacteristic
638C23C2×#63811yescharacteristic
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—94no—
661C2×C4—182no—
662C2×C4—182no—
663C2×C4—182no—
664C2×C4—182no—
665C2×C4—182no—
666C2×C4—182no—
667C2×C4—182no—
668C2×C4—182no—
669C2×C4—182no—
670C2×C4—182no—
671C2×C4—182no—
672C2×C4—182no—
673C2×C4—361no—
674C2×C4—361no—
675C2×C4—361no—
676C2×C4—361no—
677C2×C4—361no—
678C2×C4—361no—
679C2×C4—361no—
680C2×C4—361no—
681C2×C3#466514yes—
682C2×C3#466714yes—
683C2×C3#466814yes—
684C2×C3#466914yes—
685C2×C3#467214yes—
686C2×C3#467314yes—
687C2×C3#467514yes—
688C2×C3#467614yes—
689C2×C3#494014yes—
690C2×C3#495714yes—
691C2×C3#495914yes—
692C2×C3#496014yes—
693C2×C3#498914yes—
694C2×C3#499314yes—
695C2×C3#499414yes—
696D3—1216no—
697C22—184no—
698C22—184no—
699C22—184no—
700C22—362no—
701C22—362no—
702C22—362no—
703C22—362no—
704C22—362no—
705C22—362no—
706C22—362no—
707C22—362no—
708C22—362no—
709C22—362no—
710C22—362no—
711C22—362no—
712C22#6408111yescharacteristic
713C22C4×C4⋊(C3⋊D3)11yescharacteristic
714C22#6408411yescharacteristic
715C22#6408511yescharacteristic
716C22C22⋊C4×C3⋊D311yescharacteristic
717C22#6409011yescharacteristic
718C22#6409111yescharacteristic
719C22#6409111yescharacteristic
720C22#6409211yescharacteristic
721C22#6409311yescharacteristic
722C22#6409311yescharacteristic
723C22#6409311yescharacteristic
724C22#6409311yescharacteristic
725C22#6409311yescharacteristic
726C22#6409411yescharacteristic
727C22#6409411yescharacteristic
728C22C4⋊C4×C3⋊D311yescharacteristic
729C22#6410211yescharacteristic
730C22#6410311yescharacteristic
731C22#6410311yescharacteristic
732C22#6410311yescharacteristic
733C22#6410411yescharacteristic
734C22#6410511yescharacteristic
735C22#6410511yescharacteristic
736C22#6410511yescharacteristic
737C22#6410511yescharacteristic
738C22#6410611yescharacteristic
739C22#6410711yescharacteristic
740C22C4×#63811yescharacteristic
741C22#6413811yescharacteristic
742C22#6413911yescharacteristic
743C22#6414611yescharacteristic
744C22#6414811yescharacteristic
745C22#6414911yescharacteristic
746C22#6415511yescharacteristic
747C4—42no—
748C4—42no—
749C4—42no—
750C4—184no—
751C4—362no—
752C4—362no—
753C3#6942814yescomplemented
754C2—364no—
755C2#1059236411yescharacteristic
756C2#1059236611yescharacteristic
757C2#1059236711yescharacteristic
758C2#1059236811yescharacteristic
759C2#1059237111yescharacteristic
760C2#1059237211yescharacteristic
761C2#1059237411yescharacteristic
762C2#1059237511yescharacteristic
763C2#1059263911yescharacteristic
764C2#1059265611yescharacteristic
765C2#1059265811yescharacteristic
766C2#1059265911yescharacteristic
767C2#1059268811yescharacteristic
768C2#1059269211yescharacteristic
769C2#1059269311yescharacteristic
subgroupG/H
center, FrattiniC24C22×C3⋊D3
commutatorC23×C32C22×C4
FittingC2×C32×#95C2
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC2×#95C3⋊D3
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C22×#3750C2semidirect
5. C2×C32×#95C2semidirect
6. C2×#63658C2semidirect
7. C2×#63658C2semidirect
24. C2×#3752C4semidirect
35. C2×C3×#95D3semidirect
172. C22×C3⋊D3C4⋊C4semidirect
214. C2×C3⋊Dic3C22⋊C4semidirect
221. C2×#95C3⋊D3semidirect
588. C32#1439semidirect
753. C3#69428semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C22×#37502
C2×C32×#952
C2×#636582
#694283