Finite Group Databasebeta

← C2×#19137136 #25255067

Subgroups — C2×#19137136 #25255067

Order 11008.

3790 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063311C211yesmaximal, characteristic
2C22×#13063290C211yesmaximal, characteristic, complemented
3C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
4#19137136C2116yesmaximal, direct product factor
5C2×#14582803C211yesmaximal, characteristic, complemented
6C2×#14582799C211yesmaximal, characteristic
7C2×#14582793C211yesmaximal, characteristic, complemented
8C2×#14582790C211yesmaximal, characteristic, complemented
9C2×#14582789C211yesmaximal, characteristic, complemented
10C2×#14582763C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582746C211yesmaximal, characteristic, complemented
14C2×#14582746C211yesmaximal, characteristic, complemented
15C2×C42×Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063311C4116yescomplemented
22C2×#13063311C2218yes—
23C2×#13063290—28no—
24C2×#13063290C2218yescomplemented
25C2×(C22⋊D43)⋊C4—28no—
26C2×(C22⋊D43)⋊C4C2218yes—
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43C22×C4×Dic43C2211yescharacteristic
44C22×C4×Dic43C2211yescharacteristic
45#14582803C2218yescomplemented
46#14582799C2218yes—
47#14582793C2218yescomplemented
48#14582790C2218yescomplemented
49#14582789C2218yescomplemented
50#14582763C2218yescomplemented
51C22⋊C4×Dic43C2218yescomplemented
52C22⋊C4×Dic43C2218yescomplemented
53#14582746C2218yescomplemented
54#14582746C2218yescomplemented
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C42×Dic43C2218yescomplemented
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C43×#388C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86C2×C418yescomplemented
74C22×Dic86C2314yes—
75C22×C22⋊D43—24no—
76C22×C22⋊D43—24no—
77C22×C22⋊D43C2×C418yes—
78C22×C22⋊D43C2314yes—
79C23×Dic43—24no—
80C23×Dic43—24no—
81C23×Dic43—24no—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2314yes—
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—24no—
93C22×C4×D43C2314yes—
94#13063311C2×C4164yescomplemented
95#13063290—232no—
96(C22⋊D43)⋊C4—232no—
97C2×Dic43⋊C4—24no—
98C2×Dic43⋊C4—24no—
99C2×Dic43⋊C4—24no—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×C22⋊Dic43—24no—
104C2×C22⋊Dic43C2×C418yescomplemented
105C2×C22⋊Dic43C2314yes—
106C2×C22⋊Dic43C2314yes—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4—24no—
110C2×(C2×D43)⋊C4C2×C418yescomplemented
111C2×(C2×D43)⋊C4C2×C418yescomplemented
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43—24no—
120C2×C4×Dic43—24no—
121C2×C4×Dic43—24no—
122C2×C4×Dic43—24no—
123C2×C4×Dic43C2×C418yescomplemented
124C2×C4×Dic43D418yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C25×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—24no—
147C2×C4⋊C4×C43C2314yes—
148C2×C22⋊C4×C43—24no—
149C2×C22⋊C4×C43—24no—
150C2×C22⋊C4×C43C2×C418yescomplemented
151C2×C22⋊C4×C43C2314yes—
152C2×C22⋊C4×C43C2314yes—
153C2×C22⋊C4×C43C2314yes—
154C2×C42×C43—24no—
155C2×C42×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43C22×C414yes—
165C24×C43C2412yes—
166C24×C43C2411yescharacteristic
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—22no—
173C23×D43C22×C414yes—
174C23×D43C2412yes—
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×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43C22×C414yes—
190C22×C4×C43C22×C414yes—
191C22×C4×C43C2×D414yes—
192C22×C4×C43#4114yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C2×C22⋊D43—232no—
200C2×C22⋊D43—28no—
201C2×C22⋊D43—28no—
202C2×C22⋊D43C22×C4116yes—
203C22×Dic43—28no—
204C22×Dic43—28no—
205C22×Dic43—28no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—416no—
219C22×Dic43C22×C414yes—
220C22×Dic43C22×C414yes—
221C22×Dic43C22×C414yes—
222C22×Dic43C2×D414yes—
223C22×Dic43C2×D414yes—
224C22×Dic43#4114yes—
225C22×Dic43#4114yes—
226C22×Dic43#4114yes—
227C22×Dic43#4114yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—28no—
236C2×C4×D43—28no—
237C2×C4×D43—28no—
238C2×C4×D43—416no—
239C2×Dic86—232no—
240C2×Dic86—28no—
241C2×Dic86—28no—
242C2×Dic86C22×C4116yescomplemented
243C4⋊C4×C43—28no—
244C22⋊C4×C43—28no—
245C22⋊C4×C43—28no—
246C22⋊C4×C43C22×C4116yescomplemented
247C42×C43—28no—
248C22⋊Dic43—28no—
249C22⋊Dic43C22×C4116yescomplemented
250(C2×D43)⋊C4—28no—
251(C2×D43)⋊C4—28no—
252(C2×D43)⋊C4—28no—
253(C2×D43)⋊C4C22×C4116yescomplemented
254(C2×D43)⋊C4C22×C4116yescomplemented
255Dic43⋊C4—28no—
256Dic43⋊C4—28no—
257Dic43⋊C4—28no—
258C4×Dic43—28no—
259C4×Dic43—28no—
260C4×Dic43—28no—
261C4×Dic43—28no—
262C4×Dic43—28no—
263C4×Dic43—28no—
264C4×Dic43C22×C4116yescomplemented
265C4×Dic43C2×D4116yes—
266C23×C43—28no—
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43C23×C414yes—
280C23×C43C23×C412yes—
281C23×C43C22×D412yes—
282C23×C43C2×#4112yes—
283C23×C43C2×#4112yes—
284C23×C43C2×#4112yes—
285C23×C43C2×#4112yes—
286C23×C43C2×#4112yes—
287C23×C43C2511yescharacteristic
288C22×D43—28no—
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43—44no—
300C22×D43—44no—
301C22×D43C23×C414yes—
302C2×C4×C43—28no—
303C2×C4×C43—28no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—44no—
321C2×C4×C43—44no—
322C2×C4×C43C23×C414yes—
323C2×C4×C43C23×C414yes—
324C2×C4×C43C22×D414yes—
325C2×C4×C43C2×#4114yes—
326C22⋊D43—232no—
327C2×Dic43—28no—
328C2×Dic43—28no—
329C2×Dic43—28no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—44no—
343C2×Dic43—44no—
344C2×Dic43—416no—
345C2×Dic43C4×D4116yes—
346C2×Dic43#124116yescomplemented
347C2×Dic43C23×C414yes—
348C2×Dic43C23×C414yes—
349C2×Dic43C23×C414yes—
350C2×Dic43C22×D414yes—
351C2×Dic43C22×D414yes—
352C2×Dic43C2×#4114yes—
353C2×Dic43C2×#4114yes—
354C2×Dic43C2×#4114yes—
355C2×Dic43C2×#4114yes—
356C4×D43—416no—
357Dic86—232no—
358C2×C4×#124—431nomaximal, Sylow
359C22×C43—24no—
360C22×C43—24no—
361C22×C43—24no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—416no—
367C22×C43C2×C4×D414yes—
368C22×C43C4×#4114yes—
369C22×C43C4×#4114yes—
370C22×C43C2×#12414yes—
371C22×C43#52914yes—
372C22×C43#52914yes—
373C22×C43#53214yes—
374C22×C43C24×C411yescharacteristic
375C22×C43C23×D411yescharacteristic
376C22×C43C22×#4111yescharacteristic
377C22×C43C22×#4111yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C22×#4111yescharacteristic
380C22×C43C22×#4111yescharacteristic
381C2×D43—24no—
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—416no—
389C4×C43—24no—
390C4×C43—24no—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—42no—
394C4×C43—42no—
395Dic43—24no—
396Dic43—24no—
397Dic43—24no—
398Dic43—42no—
399Dic43—42no—
400Dic43C2×C4×D418yes—
401Dic43C2×#12418yescomplemented
402C22×#124—431no—
403C22×C4×Q8—431no—
404C22×C4×D4—431no—
405C4×#124—4316no—
406C2×#391—431no—
407C2×#390—431no—
408C2×#388—431no—
409C2×#388—431no—
410C2×#388—431no—
411C2×#388D4311yescharacteristic, complemented
412C2×#382—431no—
413C2×C4×C22⋊C4—431no—
414C2×C4×C22⋊C4—431no—
415C2×C4×C22⋊C4—431no—
416C2×C4×C22⋊C4—431no—
417C2×C43—431no—
418C2×C43—44no—
419C2×C43C4×#12418yescomplemented
420C2×C43C22×C4×D411yescharacteristic
421C2×C43C2×C4×#4111yescharacteristic
422C2×C43C2×C4×#4111yescharacteristic
423C2×C43C22×#12411yescharacteristic
424C2×C43C2×#52911yescharacteristic
425C2×C43C2×#52911yescharacteristic
426C2×C43C2×#53211yescharacteristic
427D43—44no—
428C23×Q8—431no—
429C23×D4—431no—
430C24×C4—431no—
431C24×C4—431no—
432C2×#124—438no—
433C2×#124—4316no—
434C2×C4×Q8—438no—
435C2×C4×Q8—868no—
436C2×C4×D4—438no—
437C2×C4×D4—868no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4C2×D4311yescharacteristic
442C22×C22⋊C4—431no—
443C22×C22⋊C4—431no—
444C22×C22⋊C4—431no—
445C22×C22⋊C4—431no—
446C22×C22⋊C4—431no—
447C22×C22⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4C2×D4311yescharacteristic
450C22×C22⋊C4C2×D4311yescharacteristic
451C22×C22⋊C4C2×D4311yescharacteristic
452C22×C42—431no—
453C22×C42—431no—
454C22×C42—431no—
455C22×C42—431no—
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#391—438no—
462#390—438no—
463#388—438no—
464#388—438no—
465#388—438no—
466#388C2×D4318yescomplemented
467#382—438no—
468C4×C22⋊C4—438no—
469C4×C22⋊C4—438no—
470C4×C22⋊C4—438no—
471C4×C22⋊C4—438no—
472C2×#95—431no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95C2×D4311yescharacteristic
479C2×#95C2×D4311yescharacteristic
480C43—438no—
481C43C2×C4×#12411yescharacteristic, complemented, Sylow
482C25—431no—
483C25C22×D4311yescharacteristic
484C22×Q8—438no—
485C22×Q8—434no—
486C22×Q8—864no—
487C22×Q8—864no—
488C22×D4—438no—
489C22×D4—434no—
490C22×D4—864no—
491C22×D4—864no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—434no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—434no—
501C23×C4—864no—
502C23×C4—864no—
503C23×C4—864no—
504C23×C4—864no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4C22×D4311yescharacteristic
508C23×C4C22×D4311yescharacteristic
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513#124—4364no—
514C4×Q8—8632no—
515C4×D4—8632no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—434no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—864no—
521C2×C4⋊C4—864no—
522C2×C4⋊C4—864no—
523C2×C4⋊C4C22×D4314yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—438no—
527C2×C22⋊C4—434no—
528C2×C22⋊C4—438no—
529C2×C22⋊C4—438no—
530C2×C22⋊C4—434no—
531C2×C22⋊C4—434no—
532C2×C22⋊C4—434no—
533C2×C22⋊C4—434no—
534C2×C22⋊C4—434no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—864no—
537C2×C22⋊C4—864no—
538C2×C22⋊C4—864no—
539C2×C22⋊C4—864no—
540C2×C22⋊C4C4×D4318yescomplemented
541C2×C22⋊C4C22×D4314yes—
542C2×C22⋊C4C22×D4314yes—
543C2×C22⋊C4C22×D4314yes—
544C2×C42—24no—
545C2×C42—438no—
546C2×C42—438no—
547C2×C42—434no—
548C2×C42—434no—
549C2×C42—434no—
550C2×C42—434no—
551C2×C42—434no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—864no—
556C2×C42—864no—
557C2×C42—864no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42—864no—
561C2×C42C22×D4314yes—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95C22×D4314yes—
569#95C22×D4314yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—434no—
577C24—432no—
578C24—862no—
579C24—862no—
580C24—862no—
581C24—862no—
582C24—862no—
583C24—862no—
584C24C2×C4×D4314yes—
585C24C23×D4312yes—
586C24C23×D4311yescharacteristic
587C2×Q8—4316no—
588C2×Q8—868no—
589C2×Q8—8632no—
590C2×Q8—868no—
591C2×D4—4316no—
592C2×D4—868no—
593C2×D4—8632no—
594C2×D4—868no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—434no—
610C22×C4—434no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—434no—
615C22×C4—432no—
616C22×C4—432no—
617C22×C4—434no—
618C22×C4—434no—
619C22×C4—434no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—868no—
626C22×C4—868no—
627C22×C4—868no—
628C22×C4—868no—
629C22×C4—868no—
630C22×C4—868no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—17216no—
644C22×C4—17216no—
645C22×C4C2×C4×D4314yes—
646C22×C4C2×C4×D4314yes—
647C22×C4D4×D4314yes—
648C22×C4#1062190014yes—
649C22×C4C23×D4312yes—
650C22×C4C23×D4312yes—
651C22×C4C23×D4312yes—
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C4⋊C4—28no—
656C4⋊C4—868no—
657C4⋊C4—868no—
658C4⋊C4—868no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—4316no—
662C22⋊C4—4316no—
663C22⋊C4—4316no—
664C22⋊C4—868no—
665C22⋊C4—868no—
666C22⋊C4—868no—
667C22⋊C4—868no—
668C22⋊C4C2×C4×D43116yescomplemented
669C42—28no—
670C42—4316no—
671C42—4316no—
672C42—868no—
673C42—868no—
674C42—868no—
675C42—868no—
676C42—868no—
677C42—868no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—434no—
692C23—868no—
693C23—868no—
694C23—868no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—1724no—
702C23—1724no—
703C23—1724no—
704C23—1724no—
705C23C22×C4×D4314yes—
706C23C22×C4×D4312yes—
707C23C2×D4×D4312yes—
708C23#41×D4312yes—
709C23#41×D4312yes—
710C23#41×D4312yes—
711C23#41×D4312yes—
712C23C2×#1062190012yes—
713C23C24×D4311yescharacteristic
714Q8—8632no—
715D4—8632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—4316no—
737C2×C4—4316no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—434no—
744C2×C4—434no—
745C2×C4—434no—
746C2×C4—434no—
747C2×C4—868no—
748C2×C4—868no—
749C2×C4—868no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—17216no—
763C2×C4—17216no—
764C2×C4—1724no—
765C2×C4—1724no—
766C2×C4C22×C4×D4314yes—
767C2×C4C22×C4×D4314yes—
768C2×C4C2×D4×D4314yes—
769C2×C4C2×#1062190014yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—864no—
779C22—864no—
780C22—864no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—17216no—
786C22C4×D4×D4314yes—
787C22C4×#1062190014yes—
788C22#1458336714yes—
789C22#124×D4314yes—
790C22#1458342614yes—
791C22#1458343214yes—
792C22#1458344414yes—
793C22C23×C4×D4311yescharacteristic
794C22C22×D4×D4311yescharacteristic
795C22C2×#41×D4311yescharacteristic
796C22C2×#41×D4311yescharacteristic
797C22C2×#41×D4311yescharacteristic
798C22C2×#41×D4311yescharacteristic
799C22C22×#1062190011yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—438no—
807C4—438no—
808C4—864no—
809C4—864no—
810C4—864no—
811C4—1722no—
812C4—1722no—
813C2—44no—
814C2—1724no—
815C2#1913713618yesdirect product factor
816C2C2×C4×D4×D4311yescharacteristic
817C2C2×C4×#1062190011yescharacteristic
818C2C2×#1458336711yescharacteristic
819C2C2×#124×D4311yescharacteristic
820C2C2×#1458342611yescharacteristic
821C2C2×#1458343211yescharacteristic
822C2C2×#1458344411yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×C4×#124
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#13063290C2semidirect
4. #19137136C2direct (N × H)
5. C2×#14582803C2semidirect
7. C2×#14582793C2semidirect
8. C2×#14582790C2semidirect
9. C2×#14582789C2semidirect
10. C2×#14582763C2semidirect
11. C2×C22⋊C4×Dic43C2semidirect
12. C2×C22⋊C4×Dic43C2semidirect
13. C2×#14582746C2semidirect
14. C2×#14582746C2semidirect
15. C2×C42×Dic43C2semidirect
16. C2×C43×#388C2semidirect
21. C2×#13063311C4semidirect
24. C2×#13063290C22semidirect
45. #14582803C22semidirect
47. #14582793C22semidirect
48. #14582790C22semidirect
49. #14582789C22semidirect
50. #14582763C22semidirect
51. C22⋊C4×Dic43C22semidirect
52. C22⋊C4×Dic43C22semidirect
53. #14582746C22semidirect
54. #14582746C22semidirect
61. C42×Dic43C22semidirect
67. C43×#388C22semidirect
73. C22×Dic86C2×C4semidirect
94. #13063311C2×C4semidirect
104. C2×C22⋊Dic43C2×C4semidirect
110. C2×(C2×D43)⋊C4C2×C4semidirect
111. C2×(C2×D43)⋊C4C2×C4semidirect
123. C2×C4×Dic43C2×C4semidirect
150. C2×C22⋊C4×C43C2×C4semidirect
242. C2×Dic86C22×C4semidirect
246. C22⋊C4×C43C22×C4semidirect
249. C22⋊Dic43C22×C4semidirect
253. (C2×D43)⋊C4C22×C4semidirect
254. (C2×D43)⋊C4C22×C4semidirect
264. C4×Dic43C22×C4semidirect
346. C2×Dic43#124semidirect
401. Dic43C2×#124semidirect
411. C2×#388D43semidirect
419. C2×C43C4×#124semidirect
466. #388C2×D43semidirect
481. C43C2×C4×#124semidirect
540. C2×C22⋊C4C4×D43semidirect
668. C22⋊C4C2×C4×D43semidirect
815. C2#19137136direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633112
C22×#130632902
C22×(C22⋊D43)⋊C42
#191371362
C2×#145828032
C2×#145827992
C2×#145827932
C2×#145827902
C2×#145827892
C2×#145827632
C2×C22⋊C4×Dic432
C2×#145827462
C2×C42×Dic432
C2×C43×#3882
C2×C4×#12443