Finite Group Databasebeta

← C2×#19137501 #25255889

Subgroups — C2×#19137501 #25255889

Order 11008.

4198 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
3C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
4#19137501C2116yesmaximal, direct product factor
5C2×#14582796C211yesmaximal, characteristic, complemented
6C2×#14582794C211yesmaximal, characteristic, complemented
7C2×#14582774C211yesmaximal, characteristic, complemented
8C2×#14582773C211yesmaximal, characteristic, complemented
9C2×#14582770C211yesmaximal, characteristic, complemented
10C2×#14582763C211yesmaximal, characteristic, complemented
11C2×#14582757C211yesmaximal, characteristic, complemented
12C2×#14582756C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C22×C43⋊#95C211yesmaximal, characteristic, complemented
15C2×#95×D43C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C2×C4×C22⋊D43—28no—
24C2×C4×C22⋊D43C2218yes—
25C2×(C22⋊D43)⋊C4—28no—
26C2×(C22⋊D43)⋊C4C4116yescomplemented
27C2×(C22⋊D43)⋊C4C2218yes—
28C2×(C22⋊D43)⋊C4C2218yes—
29C22×C4⋊Dic43C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×C22⋊Dic43C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582796C2218yescomplemented
44#14582794C2218yescomplemented
45#14582774C2218yescomplemented
46#14582773C2218yescomplemented
47#14582770C2218yescomplemented
48#14582763C2218yescomplemented
49#14582757C2218yescomplemented
50#14582756C2218yescomplemented
51C4⋊C4×Dic43C2218yescomplemented
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2218yescomplemented
61#95×D43C2218yescomplemented
62C24×C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#385C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×C22⋊D43C2×C418yes—
72C22×C22⋊D43D418yes—
73C22×C22⋊D43Q818yes—
74C22×C22⋊D43C2314yes—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43—42no—
78C23×Dic43—42no—
79C23×Dic43—42no—
80C23×Dic43C2×C418yescomplemented
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2314yes—
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2314yes—
89C23×Dic43C2311yescharacteristic
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—24no—
93C22×C4×D43—24no—
94C22×C4×D43—42no—
95C22×C4×D43—42no—
96C22×C4×D43—42no—
97C22×C4×D43—42no—
98C22×C4×D43C2×C418yescomplemented
99C22×C4×D43C2314yes—
100C22×C4×D43C2314yes—
101C22×C4×D43C2314yes—
102C4×C22⋊D43—232no—
103(C22⋊D43)⋊C4—232no—
104(C22⋊D43)⋊C4C2×C4164yescomplemented
105C2×C4⋊Dic43—24no—
106C2×C4⋊Dic43—42no—
107C2×C4⋊Dic43C2314yes—
108C2×C4⋊Dic43C2314yes—
109C2×Dic43⋊C4—24no—
110C2×Dic43⋊C4—24no—
111C2×Dic43⋊C4—42no—
112C2×Dic43⋊C4—42no—
113C2×Dic43⋊C4C2×C418yescomplemented
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2314yes—
116C2×Dic43⋊C4C2314yes—
117C2×Dic43⋊C4C2314yes—
118C2×Dic43⋊C4C2314yes—
119C2×C22⋊Dic43—24no—
120C2×C22⋊Dic43C2314yes—
121C2×(C2×D43)⋊C4—24no—
122C2×(C2×D43)⋊C4—24no—
123C2×(C2×D43)⋊C4C2×C418yescomplemented
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×C4×Dic43—24no—
128C2×C4×Dic43—24no—
129C2×C4×Dic43C2×C418yescomplemented
130C2×C4×Dic43C2314yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C43⋊#95C2314yes—
140C43⋊#95C2314yes—
141C25×C43C2311yescharacteristic
142C23×C4×C43—24no—
143C23×C4×C43—24no—
144C23×C4×C43—42no—
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2314yes—
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43—24no—
153C2×C4⋊C4×C43—42no—
154C2×C4⋊C4×C43C2314yes—
155C2×C4⋊C4×C43C2314yes—
156C2×C22⋊C4×C43—24no—
157C2×C22⋊C4×C43C2×C418yescomplemented
158C2×C22⋊C4×C43C2314yes—
159C2×C22⋊C4×C43C2314yes—
160#95×C43C2314yes—
161#95×C43C2314yes—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43—22no—
165C24×C43—22no—
166C24×C43C22×C414yes—
167C24×C43C2×D414yes—
168C24×C43C2×Q814yes—
169C24×C43C2412yes—
170C24×C43C2411yescharacteristic
171C23×D43—22no—
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43C22×C414yes—
176C23×D43C2×D414yes—
177C23×D43C2×Q814yes—
178C23×D43C2412yes—
179C22×C4×C43—28no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—28no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—44no—
197C22×C4×C43—416no—
198C22×C4×C43C22×C414yes—
199C22×C4×C43C22×C414yes—
200C22×C4×C43#4114yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C2×C22⋊D43C4⋊C4164yescomplemented
208C2×C22⋊D43C22×C4116yes—
209C2×C22⋊D43C2×D4116yes—
210C2×C22⋊D43C2×Q8116yes—
211C22×Dic43—28no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—28no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43—416no—
229C22×Dic43—44no—
230C22×Dic43—44no—
231C22×Dic43—44no—
232C22×Dic43—416no—
233C22×Dic43C22×C414yes—
234C22×Dic43C22×C414yes—
235C22×Dic43C22×C414yes—
236C22×Dic43C22×C4116yescomplemented
237C22×Dic43C2×D414yes—
238C22×Dic43C2×Q814yes—
239C22×Dic43#4114yes—
240C22×Dic43C2412yes—
241C22×Dic43C2412yes—
242C22×Dic43C2412yes—
243C22×Dic43C2412yes—
244C22×Dic43C2412yes—
245C22×Dic43C2412yes—
246C22×Dic43C2412yes—
247C2×C4×D43—28no—
248C2×C4×D43—28no—
249C2×C4×D43—28no—
250C2×C4×D43—28no—
251C2×C4×D43—416no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—44no—
256C2×C4×D43—416no—
257C2×C4×D43—416no—
258C2×C4×D43C22×C4116yescomplemented
259C4⋊C4×C43—28no—
260C4⋊C4×C43—44no—
261C22⋊C4×C43—28no—
262C22⋊C4×C43C22×C4116yescomplemented
263C22⋊Dic43—28no—
264(C2×D43)⋊C4—28no—
265(C2×D43)⋊C4—28no—
266(C2×D43)⋊C4C22×C4116yescomplemented
267C4⋊Dic43—28no—
268C4⋊Dic43—44no—
269Dic43⋊C4—28no—
270Dic43⋊C4—28no—
271Dic43⋊C4—44no—
272Dic43⋊C4—44no—
273Dic43⋊C4C22×C4116yescomplemented
274C4×Dic43—28no—
275C4×Dic43—28no—
276C4×Dic43C22×C4116yescomplemented
277C23×C43—28no—
278C23×C43—28no—
279C23×C43—28no—
280C23×C43—28no—
281C23×C43—28no—
282C23×C43—28no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43C2×C4⋊C4116yes—
288C23×C43C23×C414yes—
289C23×C43C23×C412yes—
290C23×C43C22×D414yes—
291C23×C43C22×D412yes—
292C23×C43C22×Q814yes—
293C23×C43C22×Q812yes—
294C23×C43C2×#4112yes—
295C23×C43C2×#4112yes—
296C23×C43H(5,𝔽2)12yes—
297C23×C43H(5,𝔽2)12yes—
298C23×C43C2511yescharacteristic
299C22×D43—28no—
300C22×D43—28no—
301C22×D43—28no—
302C22×D43—28no—
303C22×D43—28no—
304C22×D43—28no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43C2×C4⋊C4116yes—
310C22×D43C23×C414yes—
311C22×D43C22×D414yes—
312C22×D43C22×Q814yes—
313C2×C4×C43—28no—
314C2×C4×C43—28no—
315C2×C4×C43—28no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—416no—
332C2×C4×C43—44no—
333C2×C4×C43—44no—
334C2×C4×C43—44no—
335C2×C4×C43C23×C414yes—
336C2×C4×C43C23×C414yes—
337C2×C4×C43C2×#4114yes—
338C22⋊D43C2×C4⋊C4164yescomplemented
339C2×Dic43—28no—
340C2×Dic43—28no—
341C2×Dic43—28no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—416no—
358C2×Dic43—416no—
359C2×Dic43—44no—
360C2×Dic43—44no—
361C2×Dic43—44no—
362C2×Dic43C2×C4⋊C4116yes—
363C2×Dic43C23×C414yes—
364C2×Dic43C23×C414yes—
365C2×Dic43C23×C414yes—
366C2×Dic43C22×D414yes—
367C2×Dic43C22×Q814yes—
368C2×Dic43C2×#4114yes—
369C4×D43—416no—
370C4×D43—416no—
371C4×D43—416no—
372C2×#2349—431nomaximal, Sylow
373C22×C43—232no—
374C22×C43—24no—
375C22×C43—24no—
376C22×C43—24no—
377C22×C43—24no—
378C22×C43—24no—
379C22×C43—24no—
380C22×C43C22×C4⋊C418yes—
381C22×C43C22×C4⋊C414yes—
382C22×C43C4×#4114yes—
383C22×C43#51814yes—
384C22×C43#54614yes—
385C22×C43#54614yes—
386C22×C43#55414yes—
387C22×C43#55414yes—
388C22×C43C24×C411yescharacteristic
389C22×C43C23×D411yescharacteristic
390C22×C43C23×Q811yescharacteristic
391C22×C43C22×#4111yescharacteristic
392C22×C43C22×#4111yescharacteristic
393C22×C43C2×H(5,𝔽2)11yescharacteristic
394C22×C43C2×H(5,𝔽2)11yescharacteristic
395C2×D43—232no—
396C2×D43—24no—
397C2×D43—24no—
398C2×D43—24no—
399C2×D43—24no—
400C2×D43—24no—
401C2×D43—24no—
402C2×D43C22×C4⋊C418yes—
403C4×C43—24no—
404C4×C43—24no—
405C4×C43—24no—
406C4×C43—42no—
407C4×C43—42no—
408C4×C43—42no—
409Dic43—24no—
410Dic43—24no—
411Dic43—24no—
412Dic43—42no—
413Dic43—42no—
414Dic43—42no—
415Dic43C22×C4⋊C418yes—
416C22×C4×D4—431no—
417C22×C4×D4—431no—
418C22×C4×D4—431no—
419#2349—4316no—
420C2×#389—431no—
421C2×#389—431no—
422C2×#385—431no—
423C2×#385—431no—
424C2×#385—431no—
425C2×#385D4311yescharacteristic, complemented
426C2×#382—431no—
427C2×#380—431no—
428C2×#380—431no—
429C2×C4×C4⋊C4—431no—
430C22×#95—431no—
431C22×#95—431no—
432C2×C43—28no—
433C2×C43#234918yescomplemented
434C2×C43C23×C4⋊C411yescharacteristic
435C2×C43C2×C4×#4111yescharacteristic
436C2×C43C2×#51811yescharacteristic
437C2×C43C2×#54611yescharacteristic
438C2×C43C2×#54611yescharacteristic
439C2×C43C2×#55411yescharacteristic
440C2×C43C2×#55411yescharacteristic
441D43—28no—
442C23×D4—431no—
443C24×C4—431no—
444C24×C4—431no—
445C24×C4—431no—
446C24×C4—431no—
447C24×C4—431no—
448C24×C4C2×D4311yescharacteristic
449C2×C4×D4—438no—
450C2×C4×D4—438no—
451C2×C4×D4—438no—
452C2×C4×D4—4316no—
453C2×C4×D4—868no—
454C2×C4×D4—868no—
455C22×C4⋊C4—431no—
456C22×C4⋊C4—431no—
457C22×C4⋊C4—431no—
458C22×C4⋊C4—431no—
459C22×C4⋊C4—431no—
460C22×C4⋊C4—431no—
461C22×C4⋊C4—431no—
462C22×C4⋊C4C2×D4311yescharacteristic
463C22×C4⋊C4C2×D4311yescharacteristic
464C22×C22⋊C4—431no—
465C22×C22⋊C4—431no—
466C22×C22⋊C4—431no—
467C22×C22⋊C4—431no—
468C22×C22⋊C4C2×D4311yescharacteristic
469C22×C22⋊C4C2×D4311yescharacteristic
470C22×C42—431no—
471C22×C42—431no—
472C22×C42—431no—
473#389—438no—
474#389—438no—
475#385—438no—
476#385—438no—
477#385—438no—
478#385C2×D4318yescomplemented
479#382—438no—
480#380—438no—
481#380—438no—
482C4×C4⋊C4—438no—
483C2×#95—438no—
484C2×#95—431no—
485C2×#95—431no—
486C2×#95—431no—
487C2×#95—431no—
488C2×#95—431no—
489C2×#95—431no—
490C2×#95—431no—
491C2×#95—431no—
492C2×#95—438no—
493C2×#95C2×D4311yescharacteristic
494C2×#95C2×D4311yescharacteristic
495C43C2×#234911yescharacteristic, complemented, Sylow
496C25—431no—
497C25C22×D4311yescharacteristic
498C22×D4—438no—
499C22×D4—438no—
500C22×D4—438no—
501C22×D4—434no—
502C23×C4—24no—
503C23×C4—24no—
504C23×C4—42no—
505C23×C4—431no—
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—438no—
510C23×C4—434no—
511C23×C4—438no—
512C23×C4—434no—
513C23×C4—431no—
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—434no—
517C23×C4—434no—
518C23×C4—434no—
519C23×C4—864no—
520C23×C4—864no—
521C23×C4—864no—
522C23×C4—864no—
523C23×C4—864no—
524C23×C4—864no—
525C23×C4—1722no—
526C23×C4—1722no—
527C23×C4—1722no—
528C23×C4—1722no—
529C23×C4—1722no—
530C23×C4—1722no—
531C23×C4—1722no—
532C23×C4C22×D4311yescharacteristic
533C23×C4C22×D4311yescharacteristic
534C23×C4C22×D4311yescharacteristic
535C23×C4C22×D4314yes—
536C23×C4C22×D4311yescharacteristic
537C23×C4C22×D4311yescharacteristic
538C23×C4C22×D4311yescharacteristic
539C4×D4—4364no—
540C4×D4—8632no—
541C4×D4—8632no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—42no—
544C2×C4⋊C4—438no—
545C2×C4⋊C4—434no—
546C2×C4⋊C4—434no—
547C2×C4⋊C4—434no—
548C2×C4⋊C4—434no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—434no—
551C2×C4⋊C4—434no—
552C2×C4⋊C4—864no—
553C2×C4⋊C4—864no—
554C2×C4⋊C4—864no—
555C2×C4⋊C4—1722no—
556C2×C4⋊C4—1722no—
557C2×C4⋊C4—1722no—
558C2×C4⋊C4C22×D4314yes—
559C2×C4⋊C4C22×D4314yes—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—438no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—434no—
564C2×C22⋊C4—434no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4—864no—
567C2×C22⋊C4—864no—
568C2×C22⋊C4—864no—
569C2×C22⋊C4C4×D4318yescomplemented
570C2×C22⋊C4C22×D4314yes—
571C2×C22⋊C4C22×D4314yes—
572C2×C42—438no—
573C2×C42—434no—
574C2×C42—434no—
575C2×C42—434no—
576C2×C42—864no—
577C2×C42—864no—
578#95—434no—
579#95—434no—
580#95—434no—
581#95—434no—
582#95—434no—
583#95—434no—
584#95—434no—
585#95—434no—
586#95C22×D4314yes—
587#95C22×D4314yes—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—434no—
593C24—434no—
594C24—434no—
595C24—432no—
596C24—862no—
597C24—862no—
598C24—862no—
599C24—862no—
600C24C2×C4×D4314yes—
601C24D4×D4314yes—
602C24Q8×D4314yes—
603C24C23×D4312yes—
604C24C23×D4311yescharacteristic
605C2×D4—4364no—
606C2×D4—4316no—
607C2×D4—4316no—
608C2×D4—4316no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—28no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—44no—
627C22×C4—416no—
628C22×C4—434no—
629C22×C4—434no—
630C22×C4—434no—
631C22×C4—432no—
632C22×C4—434no—
633C22×C4—434no—
634C22×C4—434no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—4316no—
639C22×C4—4316no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—868no—
644C22×C4—868no—
645C22×C4—868no—
646C22×C4—868no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—868no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—862no—
662C22×C4—862no—
663C22×C4—868no—
664C22×C4—17216no—
665C22×C4—1724no—
666C22×C4—1724no—
667C22×C4—1724no—
668C22×C4—1724no—
669C22×C4—17216no—
670C22×C4—17216no—
671C22×C4—17216no—
672C22×C4—1724no—
673C22×C4—1724no—
674C22×C4—1724no—
675C22×C4—17216no—
676C22×C4C2×C4×D4314yes—
677C22×C4C2×C4×D4314yes—
678C22×C4#1062190014yes—
679C22×C4C23×D4312yes—
680C22×C4C23×D4312yes—
681C22×C4C23×D4312yes—
682C22×C4C23×D4312yes—
683C22×C4C23×D4312yes—
684C22×C4C23×D4312yes—
685C4⋊C4—28no—
686C4⋊C4—44no—
687C4⋊C4—4316no—
688C4⋊C4—868no—
689C4⋊C4—868no—
690C4⋊C4—868no—
691C4⋊C4—1724no—
692C4⋊C4—1724no—
693C4⋊C4—1724no—
694C22⋊C4—28no—
695C22⋊C4—4316no—
696C22⋊C4—868no—
697C22⋊C4—868no—
698C22⋊C4—868no—
699C22⋊C4C2×C4×D43116yescomplemented
700C42—4316no—
701C42—868no—
702C42—868no—
703C23—28no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—28no—
712C23—28no—
713C23—4316no—
714C23—434no—
715C23—434no—
716C23—434no—
717C23—868no—
718C23—868no—
719C23—868no—
720C23—868no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—868no—
726C23—868no—
727C23C4⋊C4×D43116yes—
728C23C22×C4×D4314yes—
729C23C22×C4×D4312yes—
730C23C2×D4×D4314yes—
731C23C2×D4×D4312yes—
732C23C2×Q8×D4314yes—
733C23C2×Q8×D4312yes—
734C23#41×D4312yes—
735C23C2×#1062190012yes—
736C23#1306337012yes—
737C23#1306337112yes—
738C23C24×D4311yescharacteristic
739D4—4364no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—4316no—
763C2×C4—434no—
764C2×C4—434no—
765C2×C4—434no—
766C2×C4—434no—
767C2×C4—434no—
768C2×C4—434no—
769C2×C4—868no—
770C2×C4—868no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—868no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—17216no—
788C2×C4—17216no—
789C2×C4—17216no—
790C2×C4—17216no—
791C2×C4—17216no—
792C2×C4—1724no—
793C2×C4—1724no—
794C2×C4—1724no—
795C2×C4C22×C4×D4314yes—
796C2×C4C22×C4×D4314yes—
797C2×C4C2×#1062190014yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—232no—
804C22—24no—
805C22—438no—
806C22—864no—
807C22—864no—
808C22—864no—
809C22—864no—
810C22—864no—
811C22—8632no—
812C22—864no—
813C22C2×C4⋊C4×D4318yes—
814C22C2×C4⋊C4×D4314yes—
815C22C4×#1062190014yes—
816C22#1458337114yes—
817C22#1458353614yes—
818C22#1458354114yes—
819C22#1458360314yes—
820C22#1458360714yes—
821C22C23×C4×D4311yescharacteristic
822C22C22×D4×D4311yescharacteristic
823C22C22×Q8×D4311yescharacteristic
824C22C2×#41×D4311yescharacteristic
825C22C22×#1062190011yescharacteristic
826C22C2×#1306337011yescharacteristic
827C22C2×#1306337111yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—438no—
835C4—864no—
836C4—864no—
837C4—864no—
838C4—1722no—
839C4—1722no—
840C4—1722no—
841C2—28no—
842C2—868no—
843C2#1913750118yesdirect product factor
844C2C22×C4⋊C4×D4311yescharacteristic
845C2C2×C4×#1062190011yescharacteristic
846C2C2×#1458337111yescharacteristic
847C2C2×#1458353611yescharacteristic
848C2C2×#1458354111yescharacteristic
849C2C2×#1458360311yescharacteristic
850C2C2×#1458360711yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2349
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. #19137501C2direct (N × H)
5. C2×#14582796C2semidirect
6. C2×#14582794C2semidirect
7. C2×#14582774C2semidirect
8. C2×#14582773C2semidirect
9. C2×#14582770C2semidirect
10. C2×#14582763C2semidirect
11. C2×#14582757C2semidirect
12. C2×#14582756C2semidirect
13. C2×C4⋊C4×Dic43C2semidirect
14. C22×C43⋊#95C2semidirect
15. C2×#95×D43C2semidirect
16. C2×C43×#385C2semidirect
26. C2×(C22⋊D43)⋊C4C4semidirect
43. #14582796C22semidirect
44. #14582794C22semidirect
45. #14582774C22semidirect
46. #14582773C22semidirect
47. #14582770C22semidirect
48. #14582763C22semidirect
49. #14582757C22semidirect
50. #14582756C22semidirect
51. C4⋊C4×Dic43C22semidirect
60. C2×C43⋊#95C22semidirect
61. #95×D43C22semidirect
67. C43×#385C22semidirect
80. C23×Dic43C2×C4semidirect
98. C22×C4×D43C2×C4semidirect
104. (C22⋊D43)⋊C4C2×C4semidirect
113. C2×Dic43⋊C4C2×C4semidirect
123. C2×(C2×D43)⋊C4C2×C4semidirect
129. C2×C4×Dic43C2×C4semidirect
157. C2×C22⋊C4×C43C2×C4semidirect
207. C2×C22⋊D43C4⋊C4semidirect
236. C22×Dic43C22×C4semidirect
258. C2×C4×D43C22×C4semidirect
262. C22⋊C4×C43C22×C4semidirect
266. (C2×D43)⋊C4C22×C4semidirect
273. Dic43⋊C4C22×C4semidirect
276. C4×Dic43C22×C4semidirect
338. C22⋊D43C2×C4⋊C4semidirect
425. C2×#385D43semidirect
433. C2×C43#2349semidirect
478. #385C2×D43semidirect
495. C43C2×#2349semidirect
569. C2×C22⋊C4C4×D43semidirect
699. C22⋊C4C2×C4×D43semidirect
843. C2#19137501direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×(C22⋊D43)⋊C42
#191375012
C2×#145827962
C2×#145827942
C2×#145827742
C2×#145827732
C2×#145827702
C2×#145827632
C2×#145827572
C2×#145827562
C2×C4⋊C4×Dic432
C22×C43⋊#952
C2×#95×D432
C2×C43×#3852
C2×#234943