Finite Group Databasebeta

← C2×C4×#13063311 #25255066

Subgroups — C2×C4×#13063311 #25255066

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×C4×Dic86C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D43C211yesmaximal, characteristic
4C4×#13063311C2116yesmaximal, direct product factor
5C2×#14582803C211yesmaximal, characteristic, complemented
6C2×#14582799C211yesmaximal, characteristic
7C2×#14582792C211yesmaximal, characteristic, complemented
8C2×#14582791C211yesmaximal, characteristic, complemented
9C2×#14582788C211yesmaximal, characteristic, complemented
10C2×#14582787C211yesmaximal, characteristic, complemented
11C2×#14582763C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C2×C42×Dic43C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063311C4116yesdirect product factor
21C2×#13063311C2218yes—
22C2×C4×Dic86—28no—
23C2×C4×Dic86C2218yescomplemented
24C2×C4×C22⋊D43—28no—
25C2×C4×C22⋊D43C2218yes—
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
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#14582792C2218yescomplemented
48#14582791C2218yescomplemented
49#14582788C2218yescomplemented
50#14582787C2218yescomplemented
51#14582763C2218yescomplemented
52C4×(C2×D43)⋊C4C2218yescomplemented
53C4×(C2×D43)⋊C4C2218yescomplemented
54C4×C22⋊Dic43C2218yescomplemented
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C42×Dic43C2218yescomplemented
62C24×C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C4×C22⋊C4×C43C2218yescomplemented
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×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43C2314yes—
90#13063311C2×C4164yesdirect product factor
91C4×Dic86—232no—
92C4×C22⋊D43—232no—
93C2×C4⋊Dic43—24no—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4—24no—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×C22⋊Dic43—24no—
102C2×C22⋊Dic43—24no—
103C2×C22⋊Dic43C2×C418yescomplemented
104C2×C22⋊Dic43C2314yes—
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×Dic43C2×C418yescomplemented
123C2×C4×Dic43D418yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C25×C43C2311yescharacteristic
138C23×C4×C43—24no—
139C23×C4×C43—24no—
140C23×C4×C43—24no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2314yes—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—24no—
149C2×C22⋊C4×C43C2×C418yescomplemented
150C2×C22⋊C4×C43C2314yes—
151C2×C22⋊C4×C43C2314yes—
152C2×C42×C43—24no—
153C2×C42×C43—24no—
154C2×C42×C43C2314yes—
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—28no—
176C22×C4×C43—28no—
177C22×C4×C43—28no—
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×C43—22no—
190C22×C4×C43—416no—
191C22×C4×C43C22×C414yes—
192C22×C4×C43C22×C414yes—
193C22×C4×C43C2×D414yes—
194C22×C4×C43#4114yes—
195C22×C4×C43#4114yes—
196C22×C4×C43#4114yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
203C2×C22⋊D43—232no—
204C2×C22⋊D43—28no—
205C2×C22⋊D43—28no—
206C2×C22⋊D43C22×C4116yes—
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—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43C22×C414yes—
222C22×Dic43C22×C414yes—
223C22×Dic43C22×C414yes—
224C22×Dic43C2×D414yes—
225C22×Dic43C2×D414yes—
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
243C22⋊C4×C43—28no—
244C22⋊C4×C43C22×C4116yescomplemented
245C42×C43—28no—
246C42×C43—28no—
247C22⋊Dic43—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
255C4⋊Dic43—28no—
256Dic43⋊C4—28no—
257Dic43⋊C4—28no—
258Dic43⋊C4—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—22no—
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—44no—
318C2×C4×C43—44no—
319C2×C4×C43—416no—
320C2×C4×C43#124116yescomplemented
321C2×C4×C43C23×C414yes—
322C2×C4×C43C23×C414yes—
323C2×C4×C43C22×D414yes—
324C2×C4×C43C2×#4114yes—
325C2×C4×C43C2×#4114yes—
326C2×C4×C43C2×#4114yes—
327C22⋊D43—232no—
328C2×Dic43—28no—
329C2×Dic43—28no—
330C2×Dic43—28no—
331C2×Dic43—28no—
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—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—44no—
347C2×Dic43—44no—
348C2×Dic43C4×D4116yes—
349C2×Dic43C23×C414yes—
350C2×Dic43C23×C414yes—
351C2×Dic43C23×C414yes—
352C2×Dic43C22×D414yes—
353C2×Dic43C22×D414yes—
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—42no—
393C4×C43—42no—
394C4×C43C2×#12418yescomplemented
395Dic43—24no—
396Dic43—24no—
397Dic43—24no—
398Dic43—24no—
399Dic43—42no—
400Dic43—42no—
401Dic43C2×C4×D418yes—
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×#388—431no—
412C2×#382—431no—
413C2×C4×C22⋊C4—431no—
414C2×C4×C22⋊C4—431no—
415C2×C4×C22⋊C4—431no—
416C2×C4×C22⋊C4D4311yescharacteristic, complemented
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×C4C2×D4311yescharacteristic
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⋊C4—431no—
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⋊C4—431no—
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×C42C2×D4311yescharacteristic
460C22×C42C2×D4311yescharacteristic
461#391—438no—
462#390—438no—
463#388—438no—
464#388—438no—
465#388—438no—
466#388—438no—
467#382—438no—
468C4×C22⋊C4—438no—
469C4×C22⋊C4—438no—
470C4×C22⋊C4—438no—
471C4×C22⋊C4C2×D4318yescomplemented
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—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—434no—
503C23×C4—864no—
504C23×C4—864no—
505C23×C4—864no—
506C23×C4C22×D4311yescharacteristic
507C23×C4C22×D4311yescharacteristic
508C23×C4C22×D4314yes—
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513#124—4364no—
514C4×Q8—8632no—
515C4×D4—8632no—
516C2×C4⋊C4—434no—
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⋊C4—864no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—438no—
526C2×C22⋊C4—434no—
527C2×C22⋊C4—438no—
528C2×C22⋊C4—438no—
529C2×C22⋊C4—434no—
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⋊C4—864no—
541C2×C22⋊C4C4×D4318yescomplemented
542C2×C22⋊C4C22×D4314yes—
543C2×C22⋊C4C22×D4314yes—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—438no—
547C2×C42—438no—
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×C42C22×D4314yes—
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—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—416no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—434no—
618C22×C4—434no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
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—868no—
640C22×C4—868no—
641C22×C4—868no—
642C22×C4—17216no—
643C22×C4C2×C4×D4314yes—
644C22×C4C2×C4×D4314yes—
645C22×C4#1062189814yes—
646C22×C4#1062189814yes—
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—868no—
656C4⋊C4—868no—
657C4⋊C4—868no—
658C4⋊C4—868no—
659C22⋊C4—28no—
660C22⋊C4—4316no—
661C22⋊C4—4316no—
662C22⋊C4—4316no—
663C22⋊C4—868no—
664C22⋊C4—868no—
665C22⋊C4—868no—
666C22⋊C4—868no—
667C22⋊C4—868no—
668C22⋊C4C2×C4×D43116yescomplemented
669C42—28no—
670C42—28no—
671C42—4316no—
672C42—4316no—
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—
710C23C2×#1062190012yes—
711C23C2×#1062189812yes—
712C23C2×#1062189812yes—
713C23C24×D4311yescharacteristic
714Q8—8632no—
715D4—8632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
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—44no—
732C2×C4—44no—
733C2×C4—416no—
734C2×C4—4316no—
735C2×C4—434no—
736C2×C4—434no—
737C2×C4—434no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—868no—
743C2×C4—868no—
744C2×C4—868no—
745C2×C4—868no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
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—1724no—
761C2×C4—1724no—
762C2×C4—17216no—
763C2×C4#13063311116yesdirect product factor
764C2×C4C22×C4×D4314yes—
765C2×C4C22×C4×D4314yes—
766C2×C4C2×D4×D4314yes—
767C2×C4C2×#1062190014yes—
768C2×C4C2×#1062189814yes—
769C2×C4C2×#1062189814yes—
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—
788C22C4×#1062189814yes—
789C22C2×#1306331114yes—
790C22#1458342714yes—
791C22#1458342914yes—
792C22#1458344614yes—
793C22C23×C4×D4311yescharacteristic
794C22C22×D4×D4311yescharacteristic
795C22C2×#41×D4311yescharacteristic
796C22C2×#41×D4311yescharacteristic
797C22C22×#1062190011yescharacteristic
798C22C22×#1062189811yescharacteristic
799C22C22×#1062189811yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—438no—
806C4—864no—
807C4—864no—
808C4—864no—
809C4—864no—
810C4—1722no—
811C4—1722no—
812C4C2×#1306331118yesdirect product factor
813C2—44no—
814C2—1724no—
815C2C4×#1306331118yesdirect product factor
816C2C2×C4×D4×D4311yescharacteristic
817C2C2×C4×#1062190011yescharacteristic
818C2C2×C4×#1062189811yescharacteristic
819C2C22×#1306331111yescharacteristic
820C2C2×#1458342711yescharacteristic
821C2C2×#1458342911yescharacteristic
822C2C2×#1458344611yescharacteristic
subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×#124
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic86C2semidirect
4. C4×#13063311C2direct (N × H)
5. C2×#14582803C2semidirect
7. C2×#14582792C2semidirect
8. C2×#14582791C2semidirect
9. C2×#14582788C2semidirect
10. C2×#14582787C2semidirect
11. C2×#14582763C2semidirect
12. C2×C4×(C2×D43)⋊C4C2semidirect
13. C2×C4×(C2×D43)⋊C4C2semidirect
14. C2×C4×C22⋊Dic43C2semidirect
15. C2×C42×Dic43C2semidirect
16. C2×C4×C22⋊C4×C43C2semidirect
20. C2×#13063311C4direct (N × H)
23. C2×C4×Dic86C22semidirect
45. #14582803C22semidirect
47. #14582792C22semidirect
48. #14582791C22semidirect
49. #14582788C22semidirect
50. #14582787C22semidirect
51. #14582763C22semidirect
52. C4×(C2×D43)⋊C4C22semidirect
53. C4×(C2×D43)⋊C4C22semidirect
54. C4×C22⋊Dic43C22semidirect
61. C42×Dic43C22semidirect
67. C4×C22⋊C4×C43C22semidirect
73. C22×Dic86C2×C4semidirect
90. #13063311C2×C4direct (N × H)
103. C2×C22⋊Dic43C2×C4semidirect
110. C2×(C2×D43)⋊C4C2×C4semidirect
111. C2×(C2×D43)⋊C4C2×C4semidirect
122. C2×C4×Dic43C2×C4semidirect
149. C2×C22⋊C4×C43C2×C4semidirect
242. C2×Dic86C22×C4semidirect
244. C22⋊C4×C43C22×C4semidirect
249. C22⋊Dic43C22×C4semidirect
253. (C2×D43)⋊C4C22×C4semidirect
254. (C2×D43)⋊C4C22×C4semidirect
264. C4×Dic43C22×C4semidirect
320. C2×C4×C43#124semidirect
394. C4×C43C2×#124semidirect
416. C2×C4×C22⋊C4D43semidirect
419. C2×C43C4×#124semidirect
471. C4×C22⋊C4C2×D43semidirect
481. C43C2×C4×#124semidirect
541. C2×C22⋊C4C4×D43semidirect
668. C22⋊C4C2×C4×D43semidirect
763. C2×C4#13063311direct (N × H)
812. C4C2×#13063311direct (N × H)
815. C2C4×#13063311direct (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×C4×Dic862
C22×C4×C22⋊D432
C4×#130633112
C2×#145828032
C2×#145827992
C2×#145827922
C2×#145827912
C2×#145827882
C2×#145827872
C2×#145827632
C2×C4×(C2×D43)⋊C42
C2×C4×C22⋊Dic432
C2×C42×Dic432
C2×C4×C22⋊C4×C432
C2×C4×#12443