Finite Group Databasebeta

← C2×#19132847 #25018269

Subgroups — C2×#19132847 #25018269

Order 11008.

3246 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic43C211yesmaximal, characteristic
2C23×Dic43⋊C4C211yesmaximal, characteristic
3C22×C43⋊#95C211yesmaximal, characteristic
4C22×C43⋊#95C211yesmaximal, characteristic
5C22×C43⋊#95C211yesmaximal, characteristic
6C22×C43⋊#95C211yesmaximal, characteristic
7#19132847C218yesmaximal, direct product factor
8C22×#95×C43C211yesmaximal, characteristic
9C24×Dic43C2211yescharacteristic
10C24×Dic43C2211yescharacteristic
11C24×Dic43C2211yescharacteristic
12C24×Dic43C2211yescharacteristic
13C22×C4⋊Dic43—24no—
14C22×C4⋊Dic43—24no—
15C22×C4⋊Dic43C418yescomplemented
16C22×C4⋊Dic43C2214yes—
17C22×Dic43⋊C4—24no—
18C22×Dic43⋊C4—24no—
19C22×Dic43⋊C4—24no—
20C22×Dic43⋊C4C2214yes—
21C2×C43⋊#95—24no—
22C2×C43⋊#95—24no—
23C2×C43⋊#95—24no—
24C2×C43⋊#95—24no—
25C2×C43⋊#95C2214yes—
26C2×C43⋊#95C2214yes—
27C2×C43⋊#95C2214yes—
28C2×C43⋊#95C2214yes—
29C24×C4×C43C2211yescharacteristic
30C24×C4×C43C2211yescharacteristic
31C24×C4×C43C2211yescharacteristic
32C2×#95×C43—24no—
33C2×#95×C43C2214yes—
34C23×Dic43—22no—
35C23×Dic43—22no—
36C23×Dic43—22no—
37C23×Dic43—22no—
38C23×Dic43—22no—
39C23×Dic43—22no—
40C23×Dic43—22no—
41C23×Dic43—22no—
42C23×Dic43—22no—
43C23×Dic43—22no—
44C23×Dic43—22no—
45C23×Dic43—22no—
46C23×Dic43—22no—
47C23×Dic43—22no—
48C23×Dic43—22no—
49C23×Dic43—22no—
50C23×Dic43—22no—
51C23×Dic43—22no—
52C23×Dic43—22no—
53C23×Dic43—22no—
54C23×Dic43—22no—
55C23×Dic43—22no—
56C23×Dic43C2×C414yes—
57C23×Dic43C2×C414yes—
58C23×Dic43D414yes—
59C23×Dic43D414yes—
60C23×Dic43D414yes—
61C23×Dic43Q814yes—
62C23×Dic43C2312yes—
63C23×Dic43C2312yes—
64C23×Dic43C2312yes—
65C23×Dic43C2312yes—
66C2×C4⋊Dic43—232no—
67C2×C4⋊Dic43—28no—
68C2×C4⋊Dic43—28no—
69C2×C4⋊Dic43C2×C4116yescomplemented
70C2×Dic43⋊C4—232no—
71C2×Dic43⋊C4—28no—
72C2×Dic43⋊C4—28no—
73C2×Dic43⋊C4—28no—
74C43⋊#95—28no—
75C43⋊#95—28no—
76C43⋊#95—28no—
77C43⋊#95—28no—
78C25×C43C2311yescharacteristic
79C23×C4×C43—22no—
80C23×C4×C43—22no—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43—22no—
93C23×C4×C43—22no—
94C23×C4×C43—22no—
95C23×C4×C43C2×C414yes—
96C23×C4×C43D414yes—
97C23×C4×C43D414yes—
98C23×C4×C43Q814yes—
99C23×C4×C43Q814yes—
100C23×C4×C43C2312yes—
101C23×C4×C43C2312yes—
102C23×C4×C43C2312yes—
103#95×C43—28no—
104C24×C43C22×C412yes—
105C24×C43C2×D412yes—
106C24×C43C2×D412yes—
107C24×C43C2×D412yes—
108C24×C43C2×D412yes—
109C24×C43C2×D412yes—
110C24×C43C2×Q812yes—
111C24×C43C2×Q812yes—
112C24×C43C2×Q812yes—
113C24×C43#4112yes—
114C24×C43#4112yes—
115C24×C43#4112yes—
116C24×C43#4112yes—
117C24×C43#4112yes—
118C24×C43#4112yes—
119C24×C43C2411yescharacteristic
120C22×C4×C43—28no—
121C22×C4×C43—28no—
122C22×C4×C43—28no—
123C22×C4×C43—28no—
124C22×C4×C43—28no—
125C22×C4×C43—28no—
126C22×C4×C43—28no—
127C22×C4×C43—28no—
128C22×C4×C43—28no—
129C22×C4×C43—28no—
130C22×C4×C43—28no—
131C22×C4×C43—28no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—44no—
149C22×C4×C43—44no—
150C22×C4×C43—44no—
151C22×C4×C43—44no—
152C22×C4×C43—44no—
153C22×C4×C43—44no—
154C22×C4×C43—44no—
155C22×C4×C43—44no—
156C22×C4×C43C4⋊C4116yescomplemented
157C22×C4×C43C22×C414yes—
158C22×C4×C43C2×D414yes—
159C22×C4×C43C2×D414yes—
160C22×C4×C43C2×Q814yes—
161C22×C4×C43C2×Q814yes—
162C22×Dic43—28no—
163C22×Dic43—28no—
164C22×Dic43—28no—
165C22×Dic43—28no—
166C22×Dic43—28no—
167C22×Dic43—28no—
168C22×Dic43—28no—
169C22×Dic43—28no—
170C22×Dic43—28no—
171C22×Dic43—28no—
172C22×Dic43—28no—
173C22×Dic43—28no—
174C22×Dic43—28no—
175C22×Dic43—28no—
176C22×Dic43—28no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—44no—
200C22×Dic43—44no—
201C22×Dic43—44no—
202C22×Dic43—44no—
203C22×Dic43—44no—
204C22×Dic43—44no—
205C22×Dic43—44no—
206C22×Dic43—44no—
207C22×Dic43—44no—
208C22×Dic43—44no—
209C22×Dic43—44no—
210C22×Dic43—44no—
211C22×Dic43C22⋊C4116yes—
212C22×Dic43C22×C414yes—
213C22×Dic43C22×C414yes—
214C22×Dic43C2×D414yes—
215C22×Dic43C2×D414yes—
216C22×Dic43C2×D414yes—
217C22×Dic43C2×Q814yes—
218C4⋊Dic43—232no—
219Dic43⋊C4—232no—
220C23×C43C2×C22⋊C414yes—
221C23×C43C2×C4⋊C414yes—
222C23×C43#11714yes—
223C23×C43C4×D414yes—
224C23×C43C4×D414yes—
225C23×C43C4×Q814yes—
226C23×C43C4×Q814yes—
227C23×C43#12014yes—
228C23×C43#12114yes—
229C23×C43#12114yes—
230C23×C43#12114yes—
231C23×C43#12114yes—
232C23×C43#12114yes—
233C23×C43#12114yes—
234C23×C43C22⋊Q814yes—
235C23×C43C22⋊Q814yes—
236C23×C43C22⋊Q814yes—
237C23×C43C22⋊Q814yes—
238C23×C43C22⋊Q814yes—
239C23×C43C22⋊Q814yes—
240C23×C43C22⋊Q814yes—
241C23×C43C22⋊Q814yes—
242C23×C43#12314yes—
243C23×C43#12314yes—
244C23×C43#12314yes—
245C23×C43#12414yes—
246C23×C43#12514yes—
247C23×C43#12514yes—
248C23×C43#12514yes—
249C23×C43#12514yes—
250C23×C43#12614yes—
251C23×C43#12614yes—
252C23×C43C4⋊Q814yes—
253C23×C43C4⋊Q814yes—
254C23×C43C4⋊Q814yes—
255C23×C43C23×C411yescharacteristic
256C23×C43C22×D411yescharacteristic
257C23×C43C22×D411yescharacteristic
258C23×C43C22×D411yescharacteristic
259C23×C43C22×D411yescharacteristic
260C23×C43C22×D411yescharacteristic
261C23×C43C22×Q811yescharacteristic
262C23×C43C22×Q811yescharacteristic
263C23×C43C22×Q811yescharacteristic
264C23×C43C2×#4111yescharacteristic
265C23×C43C2×#4111yescharacteristic
266C23×C43C2×#4111yescharacteristic
267C23×C43C2×#4111yescharacteristic
268C23×C43C2×#4111yescharacteristic
269C23×C43C2×#4111yescharacteristic
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—232no—
277C2×C4×C43—24no—
278C2×C4×C43—24no—
279C2×C4×C43—24no—
280C2×C4×C43—24no—
281C2×C4×C43—24no—
282C2×C4×C43—24no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—416no—
292C2×C4×C43—416no—
293C2×C4×C43C2×C4⋊C418yescomplemented
294C2×Dic43—24no—
295C2×Dic43—24no—
296C2×Dic43—24no—
297C2×Dic43—24no—
298C2×Dic43—24no—
299C2×Dic43—24no—
300C2×Dic43—232no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—24no—
305C2×Dic43—24no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—416no—
323C2×Dic43—416no—
324C2×Dic43—416no—
325C2×Dic43C2×C22⋊C418yes—
326C2×#1441—431nomaximal, Sylow
327C22×C43#38018yes—
328C22×C43#38618yes—
329C22×C43#38718yes—
330C22×C43#38718yes—
331C22×C43#38918yes—
332C22×C43#38918yes—
333C22×C43#39118yes—
334C22×C43#39418yes—
335C22×C43#39518yes—
336C22×C43#39618yes—
337C22×C43#39618yes—
338C22×C43#39818yes—
339C22×C43#39818yes—
340C22×C43#39818yes—
341C22×C43#40018yes—
342C22×C43C22×C22⋊C411yescharacteristic
343C22×C43C22×C4⋊C411yescharacteristic
344C22×C43C2×#11711yescharacteristic
345C22×C43C2×C4×D411yescharacteristic
346C22×C43C2×C4×D411yescharacteristic
347C22×C43C2×C4×Q811yescharacteristic
348C22×C43C2×C4×Q811yescharacteristic
349C22×C43C2×#12011yescharacteristic
350C22×C43C2×#12111yescharacteristic
351C22×C43C2×#12111yescharacteristic
352C22×C43C2×#12111yescharacteristic
353C22×C43C2×#12111yescharacteristic
354C22×C43C2×#12111yescharacteristic
355C22×C43C2×#12111yescharacteristic
356C22×C43C2×C22⋊Q811yescharacteristic
357C22×C43C2×C22⋊Q811yescharacteristic
358C22×C43C2×C22⋊Q811yescharacteristic
359C22×C43C2×C22⋊Q811yescharacteristic
360C22×C43C2×C22⋊Q811yescharacteristic
361C22×C43C2×C22⋊Q811yescharacteristic
362C22×C43C2×C22⋊Q811yescharacteristic
363C22×C43C2×C22⋊Q811yescharacteristic
364C22×C43C2×#12311yescharacteristic
365C22×C43C2×#12311yescharacteristic
366C22×C43C2×#12311yescharacteristic
367C22×C43C2×#12411yescharacteristic
368C22×C43C2×#12511yescharacteristic
369C22×C43C2×#12511yescharacteristic
370C22×C43C2×#12511yescharacteristic
371C22×C43C2×#12511yescharacteristic
372C22×C43C2×#12611yescharacteristic
373C22×C43C2×#12611yescharacteristic
374C22×C43C2×C4⋊Q811yescharacteristic
375C22×C43C2×C4⋊Q811yescharacteristic
376C22×C43C2×C4⋊Q811yescharacteristic
377C4×C43—28no—
378C4×C43—44no—
379C4×C43—44no—
380Dic43—28no—
381Dic43—44no—
382Dic43—44no—
383Dic43—44no—
384C23×C4⋊C4—431no—
385C23×C4⋊C4—431no—
386C22×#95—431no—
387C22×#95—431no—
388C22×#95—431no—
389C22×#95—431no—
390C22×#95D4311yescharacteristic
391#1441—438no—
392C2×C43#1441116yescomplemented
393C2×C43C2×#38011yescharacteristic
394C2×C43C2×#38611yescharacteristic
395C2×C43C2×#38711yescharacteristic
396C2×C43C2×#38711yescharacteristic
397C2×C43C2×#38911yescharacteristic
398C2×C43C2×#38911yescharacteristic
399C2×C43C2×#39111yescharacteristic
400C2×C43C2×#39411yescharacteristic
401C2×C43C2×#39511yescharacteristic
402C2×C43C2×#39611yescharacteristic
403C2×C43C2×#39611yescharacteristic
404C2×C43C2×#39811yescharacteristic
405C2×C43C2×#39811yescharacteristic
406C2×C43C2×#39811yescharacteristic
407C2×C43C2×#40011yescharacteristic
408C24×C4—431no—
409C24×C4—431no—
410C24×C4—431no—
411C24×C4—431no—
412C24×C4C2×D4311yescharacteristic
413C24×C4C2×D4311yescharacteristic
414C24×C4C2×D4311yescharacteristic
415C22×C4⋊C4—434no—
416C22×C4⋊C4—438no—
417C22×C4⋊C4—434no—
418C22×C4⋊C4—864no—
419C22×C4⋊C4—864no—
420C22×C4⋊C4—864no—
421C22×C4⋊C4—864no—
422C22×C4⋊C4—864no—
423C2×#95—24no—
424C2×#95—434no—
425C2×#95—434no—
426C2×#95—434no—
427C2×#95—434no—
428C2×#95—864no—
429C2×#95—864no—
430C2×#95—864no—
431C2×#95—864no—
432C2×#95C2×D4314yes—
433C43C2×#144111yescharacteristic, complemented, Sylow
434C25C22×D4311yescharacteristic
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—434no—
452C23×C4—434no—
453C23×C4—434no—
454C23×C4—432no—
455C23×C4—434no—
456C23×C4—434no—
457C23×C4—434no—
458C23×C4—432no—
459C23×C4—432no—
460C23×C4—432no—
461C23×C4—862no—
462C23×C4—862no—
463C23×C4—862no—
464C23×C4—862no—
465C23×C4—862no—
466C23×C4—862no—
467C23×C4—862no—
468C23×C4—862no—
469C23×C4—862no—
470C23×C4—862no—
471C23×C4—862no—
472C23×C4—862no—
473C23×C4—862no—
474C23×C4—862no—
475C23×C4—862no—
476C23×C4—862no—
477C23×C4—862no—
478C23×C4—862no—
479C23×C4—862no—
480C23×C4—862no—
481C23×C4—862no—
482C23×C4—862no—
483C23×C4Dic8614yes—
484C23×C4Dic8614yes—
485C23×C4C4×D4314yes—
486C23×C4D17214yes—
487C23×C4C22⋊D4314yes—
488C23×C4C22×D4312yes—
489C23×C4C22×D4312yes—
490C23×C4C22×D4312yes—
491C2×C4⋊C4—4316no—
492C2×C4⋊C4—868no—
493C2×C4⋊C4—868no—
494C2×C4⋊C4—8632no—
495C2×C4⋊C4—868no—
496C2×C4⋊C4—868no—
497C2×C4⋊C4—8632no—
498C2×C4⋊C4—868no—
499#95—28no—
500#95—868no—
501#95—868no—
502#95—868no—
503#95—868no—
504C24C2×Dic8612yes—
505C24C2×Dic8612yes—
506C24C2×C4×D4312yes—
507C24C2×D17212yes—
508C24#1062189812yes—
509C24#1062189812yes—
510C24D4×D4312yes—
511C24D4×D4312yes—
512C24D4×D4312yes—
513C24#1062190012yes—
514C24#1062190012yes—
515C24#1062190012yes—
516C24Q8×D4312yes—
517C24#1062190212yes—
518C24C2×C22⋊D4312yes—
519C24C23×D4311yescharacteristic
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—4316no—
557C22×C4—434no—
558C22×C4—434no—
559C22×C4—434no—
560C22×C4—434no—
561C22×C4—434no—
562C22×C4—434no—
563C22×C4—868no—
564C22×C4—868no—
565C22×C4—868no—
566C22×C4—868no—
567C22×C4—868no—
568C22×C4—868no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—868no—
574C22×C4—868no—
575C22×C4—868no—
576C22×C4—868no—
577C22×C4—868no—
578C22×C4—868no—
579C22×C4—868no—
580C22×C4—868no—
581C22×C4—868no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—1724no—
601C22×C4—1724no—
602C22×C4—1724no—
603C22×C4—1724no—
604C22×C4—1724no—
605C22×C4—1724no—
606C22×C4—1724no—
607C22×C4—1724no—
608C22×C4—1724no—
609C22×C4—1724no—
610C22×C4—1724no—
611C22×C4—1724no—
612C22×C4Dic43⋊C4116yescomplemented
613C22×C4C2×Dic8614yes—
614C22×C4C2×Dic8614yes—
615C22×C4C2×C4×D4314yes—
616C22×C4C2×D17214yes—
617C22×C4C2×C22⋊D4314yes—
618C4⋊C4—8632no—
619C4⋊C4—8632no—
620C23C22⋊C4×D4314yes—
621C23C2×Dic43⋊C414yes—
622C23#1306328114yes—
623C23#1306328714yes—
624C23C4×D17214yes—
625C23#1306329014yes—
626C23C4×Dic8614yes—
627C23#1306329514yes—
628C23#1306329614yes—
629C23#1306329714yes—
630C23#1306329714yes—
631C23#1306329814yes—
632C23#1306329914yes—
633C23#1306330014yes—
634C23#1306330114yes—
635C23#1306330214yes—
636C23#1306330214yes—
637C23#1306330214yes—
638C23#1306330214yes—
639C23#1306330314yes—
640C23#1306330414yes—
641C23#1306330514yes—
642C23#1306330714yes—
643C23#1306330914yes—
644C23#1306331014yes—
645C23#1306331114yes—
646C23#1306331514yes—
647C23#1306331614yes—
648C23#1306331614yes—
649C23#1306331714yes—
650C23#1306331814yes—
651C23#1306332014yes—
652C23#1306332414yes—
653C23#1306332414yes—
654C23#1306332514yes—
655C23C22×C4×D4311yescharacteristic
656C23C2×D4×D4311yescharacteristic
657C23C2×D4×D4311yescharacteristic
658C23C2×D4×D4311yescharacteristic
659C23C22×C22⋊D4311yescharacteristic
660C23C22×D17211yescharacteristic
661C23C2×Q8×D4311yescharacteristic
662C23C22×Dic8611yescharacteristic
663C23C22×Dic8611yescharacteristic
664C23C2×#1062190011yescharacteristic
665C23C2×#1062190011yescharacteristic
666C23C2×#1062190011yescharacteristic
667C23C2×#1062189811yescharacteristic
668C23C2×#1062189811yescharacteristic
669C23C2×#1062190211yescharacteristic
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—232no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—416no—
684C2×C4—416no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—438no—
694C2×C4—864no—
695C2×C4—864no—
696C2×C4—864no—
697C2×C4—864no—
698C2×C4—864no—
699C2×C4—864no—
700C2×C4—8632no—
701C2×C4—864no—
702C2×C4—864no—
703C2×C4—864no—
704C2×C4—864no—
705C2×C4—864no—
706C2×C4—864no—
707C2×C4—864no—
708C2×C4—864no—
709C2×C4—864no—
710C2×C4—17216no—
711C2×C4—17216no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—17216no—
725C2×C4C2×Dic43⋊C418yescomplemented
726C22#1458275718yes—
727C22#1458277718yes—
728C22#1458278218yes—
729C22#1458278418yes—
730C22#1458279518yes—
731C22#1458279718yes—
732C22#1458280318yes—
733C22#1458281518yes—
734C22#1458282018yes—
735C22#1458282118yes—
736C22#1458282218yes—
737C22#1458283118yes—
738C22#1458283218yes—
739C22#1458283318yes—
740C22#1458284118yes—
741C22C2×C22⋊C4×D4311yescharacteristic
742C22C22×Dic43⋊C411yescharacteristic
743C22C2×#1306328111yescharacteristic
744C22C2×#1306328711yescharacteristic
745C22C2×C4×D17211yescharacteristic
746C22C2×#1306329011yescharacteristic
747C22C2×C4×Dic8611yescharacteristic
748C22C2×#1306329511yescharacteristic
749C22C2×#1306329611yescharacteristic
750C22C2×#1306329711yescharacteristic
751C22C2×#1306329711yescharacteristic
752C22C2×#1306329811yescharacteristic
753C22C2×#1306329911yescharacteristic
754C22C2×#1306330011yescharacteristic
755C22C2×#1306330111yescharacteristic
756C22C2×#1306330211yescharacteristic
757C22C2×#1306330211yescharacteristic
758C22C2×#1306330211yescharacteristic
759C22C2×#1306330211yescharacteristic
760C22C2×#1306330311yescharacteristic
761C22C2×#1306330411yescharacteristic
762C22C2×#1306330511yescharacteristic
763C22C2×#1306330711yescharacteristic
764C22C2×#1306330911yescharacteristic
765C22C2×#1306331011yescharacteristic
766C22C2×#1306331111yescharacteristic
767C22C2×#1306331511yescharacteristic
768C22C2×#1306331611yescharacteristic
769C22C2×#1306331611yescharacteristic
770C22C2×#1306331711yescharacteristic
771C22C2×#1306331811yescharacteristic
772C22C2×#1306332011yescharacteristic
773C22C2×#1306332411yescharacteristic
774C22C2×#1306332411yescharacteristic
775C22C2×#1306332511yescharacteristic
776C4—28no—
777C4—44no—
778C4—44no—
779C4—868no—
780C4—1724no—
781C4—1724no—
782C4—1724no—
783C2#19132847116yesdirect product factor
784C2C2×#1458275711yescharacteristic
785C2C2×#1458277711yescharacteristic
786C2C2×#1458278211yescharacteristic
787C2C2×#1458278411yescharacteristic
788C2C2×#1458279511yescharacteristic
789C2C2×#1458279711yescharacteristic
790C2C2×#1458280311yescharacteristic
791C2C2×#1458281511yescharacteristic
792C2C2×#1458282011yescharacteristic
793C2C2×#1458282111yescharacteristic
794C2C2×#1458282211yescharacteristic
795C2C2×#1458283111yescharacteristic
796C2C2×#1458283211yescharacteristic
797C2C2×#1458283311yescharacteristic
798C2C2×#1458284111yescharacteristic
subgroupG/H
centerC25C22×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC22×#95×C43C2
socle, prime radicalC25×C43C23
cosocleC24×C43C24
hypercenterC22×#95D43
hypocenterC43C2×#1441
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
7. #19132847C2direct (N × H)
15. C22×C4⋊Dic43C4semidirect
69. C2×C4⋊Dic43C2×C4semidirect
156. C22×C4×C43C4⋊C4semidirect
293. C2×C4×C43C2×C4⋊C4semidirect
392. C2×C43#1441semidirect
433. C43C2×#1441semidirect
612. C22×C4Dic43⋊C4semidirect
725. C2×C4C2×Dic43⋊C4semidirect
783. C2#19132847direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic432
C23×Dic43⋊C42
C22×C43⋊#952
#191328472
C22×#95×C432
C2×#144143