Finite Group Databasebeta

← C2×#19137702 #25256271

Subgroups — C2×#19137702 #25256271

Order 11008.

3158 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
1C22×#13063311C211yesmaximal, characteristic
2#19137702C2116yesmaximal, direct product factor
3C2×#14582804C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582793C211yesmaximal, characteristic, complemented
6C2×#14582789C211yesmaximal, characteristic, complemented
7C2×#14582788C211yesmaximal, characteristic, complemented
8C2×#14582776C211yesmaximal, characteristic
9C2×#14582775C211yesmaximal, characteristic
10C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
13C2×#14582746C211yesmaximal, characteristic, complemented
14C2×#14582745C211yesmaximal, characteristic, complemented
15C2×#14582744C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063311C4116yescomplemented
22C2×#13063311C2218yes—
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582804C2218yescomplemented
38#14582803C2218yescomplemented
39#14582793C2218yescomplemented
40#14582789C2218yescomplemented
41#14582788C2218yescomplemented
42#14582776C2218yes—
43#14582775C2218yes—
44C22⋊C4×Dic43C2218yescomplemented
45C22⋊C4×Dic43C2218yescomplemented
46C4×(C2×D43)⋊C4C2218yescomplemented
47#14582746C2218yescomplemented
48#14582745C2218yescomplemented
49#14582744C2218yescomplemented
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#388C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×Dic86—42no—
70C22×Dic86—42no—
71C22×Dic86C2×C418yescomplemented
72C22×Dic86C2314yes—
73C22×C22⋊D43—42no—
74C22×C22⋊D43—42no—
75C22×C22⋊D43C2×C418yes—
76C22×C22⋊D43C2314yes—
77C23×Dic43—24no—
78C23×Dic43—24no—
79C23×Dic43—42no—
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2314yes—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—42no—
91C22×C4×D43C2314yes—
92#13063311C2×C4164yescomplemented
93C2×Dic43⋊C4—42no—
94C2×Dic43⋊C4C2314yes—
95C2×C22⋊Dic43—24no—
96C2×C22⋊Dic43C2×C418yescomplemented
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×(C2×D43)⋊C4—24no—
100C2×(C2×D43)⋊C4—24no—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4C2×C418yescomplemented
103C2×(C2×D43)⋊C4C2×C418yescomplemented
104C2×(C2×D43)⋊C4C2314yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×C4×Dic43—24no—
110C2×C4×Dic43—24no—
111C2×C4×Dic43—24no—
112C2×C4×Dic43—42no—
113C2×C4×Dic43—42no—
114C2×C4×Dic43C2×C418yescomplemented
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C2×C4×Dic43C2314yes—
118C2×C4×Dic43C2314yes—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C25×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—42no—
139C2×C4⋊C4×C43C2314yes—
140C2×C22⋊C4×C43—24no—
141C2×C22⋊C4×C43—42no—
142C2×C22⋊C4×C43C2×C418yescomplemented
143C2×C22⋊C4×C43C2314yes—
144C2×C22⋊C4×C43C2314yes—
145C2×C22⋊C4×C43C2314yes—
146C2×C42×C43—24no—
147C2×C42×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C22×C414yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43C22×C414yes—
166C23×D43C2412yes—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43C22×C414yes—
183C22×C4×C43C22×C414yes—
184C22×C4×C43#4114yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C2×C22⋊D43—416no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—44no—
194C2×C22⋊D43C22×C4116yes—
195C22×Dic43—28no—
196C22×Dic43—28no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—44no—
213C22×Dic43—416no—
214C22×Dic43C22×C414yes—
215C22×Dic43C22×C414yes—
216C22×Dic43C22×C414yes—
217C22×Dic43#4114yes—
218C22×Dic43#4114yes—
219C22×Dic43#4114yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—28no—
228C2×C4×D43—28no—
229C2×C4×D43—44no—
230C2×C4×D43—416no—
231C2×Dic86—416no—
232C2×Dic86—44no—
233C2×Dic86—44no—
234C2×Dic86C22×C4116yescomplemented
235C4⋊C4×C43—44no—
236C22⋊C4×C43—28no—
237C22⋊C4×C43—44no—
238C22⋊C4×C43C22×C4116yescomplemented
239C42×C43—28no—
240C22⋊Dic43—28no—
241C22⋊Dic43C22×C4116yescomplemented
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—28no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4C22×C4116yescomplemented
246(C2×D43)⋊C4C22×C4116yescomplemented
247Dic43⋊C4—44no—
248C4×Dic43—28no—
249C4×Dic43—28no—
250C4×Dic43—28no—
251C4×Dic43—44no—
252C4×Dic43—44no—
253C4×Dic43C22×C4116yescomplemented
254C23×C43—28no—
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43C23×C414yes—
268C23×C43C23×C412yes—
269C23×C43C2×#4112yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43C2×#4112yes—
273C23×C43H(5,𝔽2)12yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C43C2511yescharacteristic
276C22×D43—28no—
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43C23×C414yes—
290C2×C4×C43—28no—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—44no—
309C2×C4×C43—44no—
310C2×C4×C43—44no—
311C2×C4×C43C23×C414yes—
312C2×C4×C43C23×C414yes—
313C2×C4×C43C2×#4114yes—
314C22⋊D43—416no—
315C2×Dic43—28no—
316C2×Dic43—28no—
317C2×Dic43—28no—
318C2×Dic43—28no—
319C2×Dic43—28no—
320C2×Dic43—28no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—416no—
337C2×Dic43—44no—
338C2×Dic43C23×C414yes—
339C2×Dic43C23×C414yes—
340C2×Dic43C23×C414yes—
341C2×Dic43C2×#4114yes—
342C2×Dic43C2×#4114yes—
343C2×Dic43C2×#4114yes—
344C4×D43—416no—
345Dic86—416no—
346C2×#2372—431nomaximal, Sylow
347C22×C43—24no—
348C22×C43—24no—
349C22×C43—24no—
350C22×C43—416no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43C4×#4114yes—
356C22×C43C4×#4114yes—
357C22×C43#51814yes—
358C22×C43#55114yes—
359C22×C43#55114yes—
360C22×C43#55514yes—
361C22×C43#55514yes—
362C22×C43C24×C411yescharacteristic
363C22×C43C22×#4111yescharacteristic
364C22×C43C22×#4111yescharacteristic
365C22×C43C22×#4111yescharacteristic
366C22×C43C22×#4111yescharacteristic
367C22×C43C2×H(5,𝔽2)11yescharacteristic
368C22×C43C2×H(5,𝔽2)11yescharacteristic
369C2×D43—24no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—416no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C4×C43—24no—
378C4×C43—24no—
379C4×C43—24no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383Dic43—24no—
384Dic43—24no—
385Dic43—24no—
386Dic43—24no—
387Dic43—24no—
388Dic43—24no—
389Dic43—42no—
390C22×#124—431no—
391#2372—4316no—
392C2×#391—431no—
393C2×#391—431no—
394C2×#388—431no—
395C2×#388—431no—
396C2×#388—431no—
397C2×#388D4311yescharacteristic, complemented
398C2×#386—431no—
399C2×#386—431no—
400C2×C4×C22⋊C4—431no—
401C2×C4×C22⋊C4—431no—
402C2×C4×C22⋊C4—431no—
403C2×C4×C22⋊C4—431no—
404C2×#376—431no—
405C2×#376—431no—
406C2×C43—44no—
407C2×C43#237218yescomplemented
408C2×C43C2×C4×#4111yescharacteristic
409C2×C43C2×C4×#4111yescharacteristic
410C2×C43C2×#51811yescharacteristic
411C2×C43C2×#55111yescharacteristic
412C2×C43C2×#55111yescharacteristic
413C2×C43C2×#55511yescharacteristic
414C2×C43C2×#55511yescharacteristic
415D43—44no—
416C23×Q8—431no—
417C23×D4—431no—
418C24×C4—431no—
419C24×C4—431no—
420C2×#124—438no—
421C2×#124—4316no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4C2×D4311yescharacteristic
424C22×C22⋊C4—431no—
425C22×C22⋊C4—431no—
426C22×C22⋊C4—431no—
427C22×C22⋊C4—431no—
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4C2×D4311yescharacteristic
432C22×C22⋊C4C2×D4311yescharacteristic
433C22×C22⋊C4C2×D4311yescharacteristic
434C22×C42—431no—
435C22×C42—431no—
436C22×C42—431no—
437C22×C42—431no—
438C22×C42—431no—
439C22×C42—431no—
440C22×C42C2×D4311yescharacteristic
441#391—438no—
442#391—438no—
443#388—438no—
444#388—438no—
445#388—438no—
446#388C2×D4318yescomplemented
447#386—438no—
448#386—438no—
449C4×C22⋊C4—438no—
450C4×C22⋊C4—438no—
451C4×C22⋊C4—438no—
452C4×C22⋊C4—438no—
453#376—438no—
454#376—438no—
455C2×#95—431no—
456C2×#95—431no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C2×#95C2×D4311yescharacteristic
466C2×#95C2×D4311yescharacteristic
467C43C2×#237211yescharacteristic, complemented, Sylow
468C25—431no—
469C25C22×D4311yescharacteristic
470C22×Q8—438no—
471C22×Q8—434no—
472C22×Q8—1722no—
473C22×Q8—1722no—
474C22×D4—438no—
475C22×D4—434no—
476C22×D4—1722no—
477C22×D4—1722no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—434no—
486C23×C4—434no—
487C23×C4—864no—
488C23×C4—864no—
489C23×C4—864no—
490C23×C4—864no—
491C23×C4—1722no—
492C23×C4—1722no—
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C23×C4C22×D4311yescharacteristic
499#124—4364no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—1722no—
503C2×C4⋊C4C22×D4314yes—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—438no—
507C2×C22⋊C4—434no—
508C2×C22⋊C4—438no—
509C2×C22⋊C4—438no—
510C2×C22⋊C4—434no—
511C2×C22⋊C4—434no—
512C2×C22⋊C4—434no—
513C2×C22⋊C4—434no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—864no—
517C2×C22⋊C4—864no—
518C2×C22⋊C4—864no—
519C2×C22⋊C4—1722no—
520C2×C22⋊C4C4×D4318yescomplemented
521C2×C22⋊C4C22×D4314yes—
522C2×C22⋊C4C22×D4314yes—
523C2×C22⋊C4C22×D4314yes—
524C2×C42—24no—
525C2×C42—438no—
526C2×C42—434no—
527C2×C42—434no—
528C2×C42—434no—
529C2×C42—434no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—864no—
533C2×C42—864no—
534C2×C42—864no—
535C2×C42—1722no—
536C2×C42—1722no—
537C2×C42C22×D4314yes—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548#95C22×D4314yes—
549#95C22×D4314yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—434no—
557C24—432no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24C2×C4×D4314yes—
565C24C23×D4312yes—
566C24C23×D4311yescharacteristic
567C2×Q8—4316no—
568C2×Q8—17216no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×D4—4316no—
572C2×D4—17216no—
573C2×D4—1724no—
574C2×D4—1724no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—434no—
591C22×C4—434no—
592C22×C4—434no—
593C22×C4—434no—
594C22×C4—434no—
595C22×C4—434no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—868no—
604C22×C4—868no—
605C22×C4—868no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—868no—
622C22×C4—1724no—
623C22×C4—17216no—
624C22×C4—1724no—
625C22×C4—17216no—
626C22×C4C2×C4×D4314yes—
627C22×C4C2×C4×D4314yes—
628C22×C4#1062190014yes—
629C22×C4C23×D4312yes—
630C22×C4C23×D4312yes—
631C22×C4C23×D4312yes—
632C22×C4C23×D4312yes—
633C22×C4C23×D4312yes—
634C22×C4C23×D4312yes—
635C4⋊C4—44no—
636C4⋊C4—1724no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—4316no—
640C22⋊C4—4316no—
641C22⋊C4—4316no—
642C22⋊C4—868no—
643C22⋊C4—868no—
644C22⋊C4—868no—
645C22⋊C4—1724no—
646C22⋊C4C2×C4×D43116yescomplemented
647C42—28no—
648C42—4316no—
649C42—868no—
650C42—868no—
651C42—868no—
652C42—1724no—
653C42—1724no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—434no—
668C23—868no—
669C23—868no—
670C23—868no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—1724no—
678C23—1724no—
679C23—1724no—
680C23—1724no—
681C23C22×C4×D4314yes—
682C23C22×C4×D4312yes—
683C23#41×D4312yes—
684C23#41×D4312yes—
685C23#41×D4312yes—
686C23C2×#1062190012yes—
687C23#1306337012yes—
688C23#1306337112yes—
689C23C24×D4311yescharacteristic
690Q8—17216no—
691D4—17216no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—434no—
714C2×C4—434no—
715C2×C4—434no—
716C2×C4—434no—
717C2×C4—434no—
718C2×C4—434no—
719C2×C4—868no—
720C2×C4—868no—
721C2×C4—868no—
722C2×C4—868no—
723C2×C4—868no—
724C2×C4—868no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—17216no—
741C2×C4—17216no—
742C2×C4—1724no—
743C2×C4C22×C4×D4314yes—
744C2×C4C22×C4×D4314yes—
745C2×C4C2×#1062190014yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—17216no—
762C22C4×#1062190014yes—
763C22#1458336714yes—
764C22#1458337114yes—
765C22#1458357214yes—
766C22#1458357414yes—
767C22#1458361114yes—
768C22#1458361314yes—
769C22C23×C4×D4311yescharacteristic
770C22C2×#41×D4311yescharacteristic
771C22C2×#41×D4311yescharacteristic
772C22C2×#41×D4311yescharacteristic
773C22C22×#1062190011yescharacteristic
774C22C2×#1306337011yescharacteristic
775C22C2×#1306337111yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—864no—
784C4—864no—
785C4—864no—
786C4—864no—
787C4—864no—
788C4—1722no—
789C2—44no—
790C2—1724no—
791C2#1913770218yesdirect product factor
792C2C2×C4×#1062190011yescharacteristic
793C2C2×#1458336711yescharacteristic
794C2C2×#1458337111yescharacteristic
795C2C2×#1458357211yescharacteristic
796C2C2×#1458357411yescharacteristic
797C2C2×#1458361111yescharacteristic
798C2C2×#1458361311yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2372
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #19137702C2direct (N × H)
3. C2×#14582804C2semidirect
4. C2×#14582803C2semidirect
5. C2×#14582793C2semidirect
6. C2×#14582789C2semidirect
7. C2×#14582788C2semidirect
10. C2×C22⋊C4×Dic43C2semidirect
11. C2×C22⋊C4×Dic43C2semidirect
12. C2×C4×(C2×D43)⋊C4C2semidirect
13. C2×#14582746C2semidirect
14. C2×#14582745C2semidirect
15. C2×#14582744C2semidirect
16. C2×C43×#388C2semidirect
21. C2×#13063311C4semidirect
37. #14582804C22semidirect
38. #14582803C22semidirect
39. #14582793C22semidirect
40. #14582789C22semidirect
41. #14582788C22semidirect
44. C22⋊C4×Dic43C22semidirect
45. C22⋊C4×Dic43C22semidirect
46. C4×(C2×D43)⋊C4C22semidirect
47. #14582746C22semidirect
48. #14582745C22semidirect
49. #14582744C22semidirect
65. C43×#388C22semidirect
71. C22×Dic86C2×C4semidirect
92. #13063311C2×C4semidirect
96. C2×C22⋊Dic43C2×C4semidirect
102. C2×(C2×D43)⋊C4C2×C4semidirect
103. C2×(C2×D43)⋊C4C2×C4semidirect
114. C2×C4×Dic43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
234. C2×Dic86C22×C4semidirect
238. C22⋊C4×C43C22×C4semidirect
241. C22⋊Dic43C22×C4semidirect
245. (C2×D43)⋊C4C22×C4semidirect
246. (C2×D43)⋊C4C22×C4semidirect
253. C4×Dic43C22×C4semidirect
397. C2×#388D43semidirect
407. C2×C43#2372semidirect
446. #388C2×D43semidirect
467. C43C2×#2372semidirect
520. C2×C22⋊C4C4×D43semidirect
646. C22⋊C4C2×C4×D43semidirect
791. C2#19137702direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633112
#191377022
C2×#145828042
C2×#145828032
C2×#145827932
C2×#145827892
C2×#145827882
C2×#145827762
C2×#145827752
C2×C22⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×#145827452
C2×#145827442
C2×C43×#3882
C2×#237243