Finite Group Databasebeta

← C2×#19142604 #25302747

Subgroups — C2×#19142604 #25302747

Order 11008.

3322 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic, complemented
2C22×#13063298C211yesmaximal, characteristic, complemented
3#19142604C2116yesmaximal, direct product factor
4C2×#14582840C211yesmaximal, characteristic, complemented
5C2×#14582834C211yesmaximal, characteristic, complemented
6C2×#14582821C211yesmaximal, characteristic, complemented
7C2×#14582816C211yesmaximal, characteristic, complemented
8C2×#14582816C211yesmaximal, characteristic, complemented
9C2×#14582815C211yesmaximal, characteristic, complemented
10C2×#14582814C211yesmaximal, characteristic, complemented
11C2×#14582814C211yesmaximal, characteristic, complemented
12C2×#14582809C211yesmaximal, characteristic, complemented
13C2×#14582808C211yesmaximal, characteristic, complemented
14C2×#14582808C211yesmaximal, characteristic, complemented
15C2×#14582756C211yesmaximal, characteristic, complemented
16C2×C43×#396C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×C22⋊D43C2211yescharacteristic
21C23×C22⋊D43C2211yescharacteristic
22C23×C22⋊D43C2211yescharacteristic
23C23×C4×D43C2211yescharacteristic
24C2×#13063310—28no—
25C2×#13063310C2218yescomplemented
26C2×#13063298—28no—
27C2×#13063298C2218yescomplemented
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44#14582840C2218yescomplemented
45#14582834C2218yescomplemented
46#14582821C2218yescomplemented
47#14582816C2218yescomplemented
48#14582816C2218yescomplemented
49#14582815C2218yescomplemented
50#14582814C2218yescomplemented
51#14582814C2218yescomplemented
52#14582809C2218yescomplemented
53#14582808C2218yescomplemented
54#14582808C2218yescomplemented
55#14582756C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#396C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C24×D43C2311yescharacteristic
71C24×D43C2311yescharacteristic
72C22×D172—24no—
73C22×D172—24no—
74C22×D172—42no—
75C22×D172—42no—
76C22×D172—42no—
77C22×D172—42no—
78C22×D172—42no—
79C22×D172—42no—
80C22×D172—42no—
81C22×D172C2314yes—
82C22×D172C2314yes—
83C22×D172C2314yes—
84C22×C22⋊D43—24no—
85C22×C22⋊D43—24no—
86C22×C22⋊D43—42no—
87C22×C22⋊D43—42no—
88C22×C22⋊D43—42no—
89C22×C22⋊D43—42no—
90C22×C22⋊D43—42no—
91C22×C22⋊D43—42no—
92C22×C22⋊D43—42no—
93C22×C22⋊D43C2314yes—
94C22×C22⋊D43C2314yes—
95C22×C22⋊D43C2314yes—
96C23×Dic43C2311yescharacteristic
97C23×Dic43C2311yescharacteristic
98C23×Dic43C2311yescharacteristic
99C23×Dic43C2311yescharacteristic
100C23×Dic43C2311yescharacteristic
101C22×C4×D43—42no—
102C22×C4×D43—42no—
103C22×C4×D43D418yescomplemented
104C22×C4×D43C2314yes—
105#13063310—232no—
106#13063298—232no—
107C2×C4⋊Dic43—42no—
108C2×C4⋊Dic43C2314yes—
109C2×Dic43⋊C4—24no—
110C2×Dic43⋊C4—24no—
111C2×Dic43⋊C4—42no—
112C2×Dic43⋊C4C2314yes—
113C2×Dic43⋊C4C2314yes—
114C2×Dic43⋊C4C2314yes—
115C2×C22⋊Dic43—42no—
116C2×C22⋊Dic43C2314yes—
117C2×(C2×D43)⋊C4—24no—
118C2×(C2×D43)⋊C4—24no—
119C2×(C2×D43)⋊C4—24no—
120C2×(C2×D43)⋊C4—24no—
121C2×(C2×D43)⋊C4—42no—
122C2×(C2×D43)⋊C4—42no—
123C2×(C2×D43)⋊C4—42no—
124C2×(C2×D43)⋊C4—42no—
125C2×(C2×D43)⋊C4—42no—
126C2×(C2×D43)⋊C4—42no—
127C2×(C2×D43)⋊C4—42no—
128C2×(C2×D43)⋊C4C2314yes—
129C2×(C2×D43)⋊C4C2314yes—
130C2×(C2×D43)⋊C4C2314yes—
131C2×(C2×D43)⋊C4C2314yes—
132C2×(C2×D43)⋊C4C2314yes—
133C2×(C2×D43)⋊C4C2314yes—
134C2×(C2×D43)⋊C4C2314yes—
135C2×(C2×D43)⋊C4C2314yes—
136C2×(C2×D43)⋊C4C2314yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×(C2×D43)⋊C4C2314yes—
139C43⋊#95C2314yes—
140C43⋊#95C2314yes—
141C43⋊#95C2314yes—
142C43⋊#95C2314yes—
143C43⋊#95C2314yes—
144C25×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43—24no—
152C2×C4⋊C4×C43—42no—
153C2×C4⋊C4×C43—42no—
154C2×C4⋊C4×C43C2314yes—
155C2×C4⋊C4×C43C2314yes—
156C2×C4⋊C4×C43C2314yes—
157C2×C22⋊C4×C43—24no—
158C2×C22⋊C4×C43—42no—
159C2×C22⋊C4×C43—42no—
160C2×C22⋊C4×C43C2314yes—
161C2×C22⋊C4×C43C2314yes—
162C2×C22⋊C4×C43C2314yes—
163#95×C43C2314yes—
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—22no—
167C24×C43—22no—
168C24×C43—22no—
169C24×C43—22no—
170C24×C43—22no—
171C24×C43C2412yes—
172C24×C43C2411yescharacteristic
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—22no—
176C23×D43—22no—
177C23×D43—22no—
178C23×D43—22no—
179C23×D43—22no—
180C23×D43—22no—
181C23×D43—22no—
182C23×D43—22no—
183C23×D43—22no—
184C23×D43—22no—
185C23×D43—22no—
186C23×D43—22no—
187C23×D43—22no—
188C23×D43—22no—
189C23×D43—22no—
190C23×D43—22no—
191C23×D43—22no—
192C23×D43—22no—
193C23×D43C2×D414yes—
194C23×D43C2412yes—
195C23×D43C2412yes—
196C23×D43C2412yes—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43C2×D414yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2412yes—
221C2×C22⋊D43—28no—
222C2×C22⋊D43—28no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43—44no—
226C2×C22⋊D43—44no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—416no—
231C2×C22⋊D43—416no—
232C2×C22⋊D43—416no—
233C22×Dic43—22no—
234C22×Dic43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—22no—
239C22×Dic43—22no—
240C22×Dic43—22no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—22no—
244C22×Dic43—22no—
245C22×Dic43—22no—
246C22×Dic43—22no—
247C22×Dic43C2×D414yes—
248C22×Dic43C2412yes—
249C22×Dic43C2412yes—
250C22×Dic43C2412yes—
251C22×Dic43C2412yes—
252C22×Dic43C2412yes—
253C2×D172—28no—
254C2×D172—28no—
255C2×D172—44no—
256C2×D172—44no—
257C2×D172—44no—
258C2×D172—44no—
259C2×D172—44no—
260C2×D172—44no—
261C2×D172—44no—
262C2×D172—416no—
263C2×D172—416no—
264C2×D172—416no—
265C2×C4×D43—416no—
266C2×C4×D43—44no—
267C2×C4×D43—44no—
268C2×C4×D43C2×D4116yescomplemented
269C4⋊C4×C43—28no—
270C4⋊C4×C43—44no—
271C4⋊C4×C43—44no—
272C22⋊C4×C43—28no—
273C22⋊C4×C43—44no—
274C22⋊C4×C43—44no—
275C22⋊Dic43—44no—
276(C2×D43)⋊C4—28no—
277(C2×D43)⋊C4—28no—
278(C2×D43)⋊C4—28no—
279(C2×D43)⋊C4—28no—
280(C2×D43)⋊C4—44no—
281(C2×D43)⋊C4—44no—
282(C2×D43)⋊C4—44no—
283(C2×D43)⋊C4—44no—
284(C2×D43)⋊C4—44no—
285(C2×D43)⋊C4—44no—
286(C2×D43)⋊C4—44no—
287C4⋊Dic43—44no—
288Dic43⋊C4—28no—
289Dic43⋊C4—28no—
290Dic43⋊C4—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—44no—
299C23×C43—44no—
300C23×C43—44no—
301C23×C43—44no—
302C23×C43—44no—
303C23×C43—44no—
304C23×C43—44no—
305C23×C43C22×D412yes—
306C23×C43H(5,𝔽2)12yes—
307C23×C43H(5,𝔽2)12yes—
308C23×C43H(5,𝔽2)12yes—
309C23×C43H(5,𝔽2)12yes—
310C23×C43H(5,𝔽2)12yes—
311C23×C432−1+412yes—
312C23×C43C2511yescharacteristic
313C22×D43—28no—
314C22×D43—28no—
315C22×D43—28no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—44no—
337C22×D43—44no—
338C22×D43—44no—
339C22×D43—44no—
340C22×D43—44no—
341C22×D43—44no—
342C22×D43—44no—
343C22×D43—44no—
344C22×D43—44no—
345C22×D43—44no—
346C22×D43—44no—
347C22×D43—44no—
348C22×D43—44no—
349C22×D43—44no—
350C22×D43—44no—
351C22×D43—44no—
352C22×D43—44no—
353C22×D43—44no—
354C22×D43C22×D414yes—
355C2×C4×C43—28no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—44no—
374C2×C4×C43—44no—
375C2×C4×C43—44no—
376C2×C4×C43—44no—
377C2×C4×C43—44no—
378C2×C4×C43C22×D414yes—
379C22⋊D43—416no—
380C22⋊D43—416no—
381C22⋊D43—416no—
382C2×Dic43—28no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—44no—
398C2×Dic43—44no—
399C2×Dic43—44no—
400C2×Dic43—44no—
401C2×Dic43C22×D414yes—
402D172—416no—
403D172—416no—
404D172—416no—
405C4×D43—416no—
406C2×#2813—431nomaximal, Sylow
407C22×C43—42no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—88no—
415C22×C43#53414yes—
416C22×C43#53514yes—
417C22×C43#53714yes—
418C22×C43#56014yes—
419C22×C43#56014yes—
420C22×C43#56214yes—
421C22×C43#56214yes—
422C22×C43C23×D411yescharacteristic
423C22×C43C2×H(5,𝔽2)11yescharacteristic
424C22×C43C2×H(5,𝔽2)11yescharacteristic
425C22×C43C2×H(5,𝔽2)11yescharacteristic
426C22×C43C2×H(5,𝔽2)11yescharacteristic
427C22×C43C2×H(5,𝔽2)11yescharacteristic
428C22×C43C2×2−1+411yescharacteristic
429C2×D43—24no—
430C2×D43—24no—
431C2×D43—24no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—416no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43—42no—
451C2×D43—88no—
452C2×D43—88no—
453C4×C43—24no—
454C4×C43—42no—
455C4×C43—42no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43—42no—
459Dic43—24no—
460Dic43—42no—
461Dic43—42no—
462Dic43—42no—
463Dic43—42no—
464C22×#123—431no—
465C22×#121—431no—
466#2813—4316no—
467C2×#400—431no—
468C2×#399—431no—
469C2×#396—431no—
470C2×#396D4311yescharacteristic, complemented
471C2×#394—431no—
472C2×#394—431no—
473C2×#394—431no—
474C2×#394—431no—
475C2×#394—431no—
476C2×#392—431no—
477C2×#392—431no—
478C2×#392—431no—
479C2×#380—431no—
480C2×C43—82no—
481C2×C43#281318yescomplemented
482C2×C43C2×#53411yescharacteristic
483C2×C43C2×#53511yescharacteristic
484C2×C43C2×#53711yescharacteristic
485C2×C43C2×#56011yescharacteristic
486C2×C43C2×#56011yescharacteristic
487C2×C43C2×#56211yescharacteristic
488C2×C43C2×#56211yescharacteristic
489D43—44no—
490D43—82no—
491D43—82no—
492C23×D4—431no—
493C23×D4—431no—
494C23×D4—431no—
495C23×D4—431no—
496C23×D4—431no—
497C23×D4—431no—
498C24×C4—431no—
499C2×#123—438no—
500C2×#123—868no—
501C2×#121—438no—
502C2×#121—868no—
503C22×C4⋊C4—431no—
504C22×C4⋊C4—431no—
505C22×C4⋊C4—431no—
506C22×C4⋊C4—431no—
507C22×C4⋊C4C2×D4311yescharacteristic
508C22×C4⋊C4C2×D4311yescharacteristic
509C22×C4⋊C4C2×D4311yescharacteristic
510C22×C22⋊C4—431no—
511C22×C22⋊C4—431no—
512C22×C22⋊C4—431no—
513C22×C22⋊C4—431no—
514C22×C22⋊C4—431no—
515C22×C22⋊C4—431no—
516C22×C22⋊C4—431no—
517C22×C22⋊C4—431no—
518C22×C22⋊C4—431no—
519C22×C22⋊C4—431no—
520C22×C22⋊C4—431no—
521C22×C22⋊C4—431no—
522C22×C22⋊C4C2×D4311yescharacteristic
523C22×C22⋊C4C2×D4311yescharacteristic
524C22×C22⋊C4C2×D4311yescharacteristic
525#400—438no—
526#399—438no—
527#396—438no—
528#396C2×D4318yescomplemented
529#394—438no—
530#394—438no—
531#394—438no—
532#394—438no—
533#394—438no—
534#392—438no—
535#392—438no—
536#392—438no—
537#380—438no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95C2×D4311yescharacteristic
544C43C2×#281311yescharacteristic, complemented, Sylow
545C25—431no—
546C25—431no—
547C25—431no—
548C25C22×D4311yescharacteristic
549C22×D4—434no—
550C22×D4—434no—
551C22×D4—434no—
552C22×D4—434no—
553C22×D4—434no—
554C22×D4—434no—
555C22×D4—864no—
556C22×D4—864no—
557C22×D4—864no—
558C22×D4—864no—
559C22×D4—1722no—
560C22×D4—1722no—
561C22×D4—1722no—
562C22×D4—1722no—
563C22×D4—1722no—
564C22×D4—1722no—
565C22×D4—1722no—
566C22×D4—1722no—
567C22×D4—1722no—
568C22×D4—1722no—
569C22×D4—1722no—
570C22×D4—1722no—
571C22×D4—1722no—
572C22×D4—1722no—
573C23×C4—431no—
574C23×C4—438no—
575C23×C4—434no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—1722no—
581C23×C4—1722no—
582C23×C4C22×D4311yescharacteristic
583C23×C4C22×D4311yescharacteristic
584C23×C4C22×D4311yescharacteristic
585C23×C4C22×D4311yescharacteristic
586C23×C4C22×D4311yescharacteristic
587C23×C4C22×D4311yescharacteristic
588#123—8632no—
589#121—8632no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—42no—
593C2×C4⋊C4—434no—
594C2×C4⋊C4—434no—
595C2×C4⋊C4—434no—
596C2×C4⋊C4—434no—
597C2×C4⋊C4—864no—
598C2×C4⋊C4—864no—
599C2×C4⋊C4—1722no—
600C2×C4⋊C4—1722no—
601C2×C4⋊C4C22×D4314yes—
602C2×C4⋊C4C22×D4314yes—
603C2×C4⋊C4C22×D4314yes—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—434no—
608C2×C22⋊C4—434no—
609C2×C22⋊C4—434no—
610C2×C22⋊C4—434no—
611C2×C22⋊C4—434no—
612C2×C22⋊C4—434no—
613C2×C22⋊C4—434no—
614C2×C22⋊C4—434no—
615C2×C22⋊C4—434no—
616C2×C22⋊C4—434no—
617C2×C22⋊C4—434no—
618C2×C22⋊C4—434no—
619C2×C22⋊C4—864no—
620C2×C22⋊C4—864no—
621C2×C22⋊C4—864no—
622C2×C22⋊C4—864no—
623C2×C22⋊C4—1722no—
624C2×C22⋊C4—1722no—
625C2×C22⋊C4—1722no—
626C2×C22⋊C4—1722no—
627C2×C22⋊C4—1722no—
628C2×C22⋊C4—1722no—
629C2×C22⋊C4—1722no—
630C2×C22⋊C4—1722no—
631C2×C22⋊C4C22×D4314yes—
632C2×C22⋊C4C22×D4314yes—
633C2×C22⋊C4C22×D4314yes—
634#95—434no—
635#95—434no—
636#95—434no—
637#95—434no—
638#95—434no—
639#95C22×D4314yes—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—434no—
648C24—432no—
649C24—432no—
650C24—432no—
651C24—862no—
652C24—862no—
653C24—862no—
654C24—862no—
655C24—862no—
656C24—862no—
657C24—862no—
658C24—862no—
659C24—862no—
660C24—862no—
661C24—862no—
662C24—862no—
663C24—862no—
664C24—862no—
665C24—862no—
666C24—862no—
667C24—862no—
668C24—862no—
669C24—862no—
670C24—862no—
671C24C23×D4312yes—
672C24C23×D4311yescharacteristic
673C2×D4—868no—
674C2×D4—868no—
675C2×D4—868no—
676C2×D4—868no—
677C2×D4—1724no—
678C2×D4—1724no—
679C2×D4—1724no—
680C2×D4—1724no—
681C2×D4—1724no—
682C2×D4—1724no—
683C2×D4—1724no—
684C2×D4—17216no—
685C2×D4—17216no—
686C2×D4—17216no—
687C2×D4—1724no—
688C2×D4—1724no—
689C2×D4—1724no—
690C2×D4—1724no—
691C2×D4—1724no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4—17216no—
695C2×D4—17216no—
696C2×D4—17216no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—434no—
715C22×C4—432no—
716C22×C4—4316no—
717C22×C4—432no—
718C22×C4—432no—
719C22×C4—432no—
720C22×C4—432no—
721C22×C4—862no—
722C22×C4—862no—
723C22×C4—862no—
724C22×C4—862no—
725C22×C4—862no—
726C22×C4—862no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—862no—
732C22×C4—862no—
733C22×C4—862no—
734C22×C4—862no—
735C22×C4—17216no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4314yes—
739C22×C4C23×D4312yes—
740C22×C4C23×D4312yes—
741C22×C4C23×D4312yes—
742C22×C4C23×D4312yes—
743C22×C4C23×D4312yes—
744C22×C4C23×D4312yes—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—868no—
749C4⋊C4—868no—
750C4⋊C4—1724no—
751C4⋊C4—1724no—
752C22⋊C4—28no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—868no—
756C22⋊C4—868no—
757C22⋊C4—868no—
758C22⋊C4—868no—
759C22⋊C4—1724no—
760C22⋊C4—1724no—
761C22⋊C4—1724no—
762C22⋊C4—1724no—
763C22⋊C4—1724no—
764C22⋊C4—1724no—
765C22⋊C4—1724no—
766C22⋊C4—1724no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—434no—
782C23—868no—
783C23—868no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—868no—
791C23—862no—
792C23—862no—
793C23—862no—
794C23—862no—
795C23—862no—
796C23—862no—
797C23—862no—
798C23—862no—
799C23—862no—
800C23—862no—
801C23—862no—
802C23—862no—
803C23—862no—
804C23—862no—
805C23—1724no—
806C23—1724no—
807C23—1724no—
808C23—1724no—
809C23—1724no—
810C23—1724no—
811C23—1724no—
812C23—1724no—
813C23—1724no—
814C23—1724no—
815C23—1724no—
816C23—1724no—
817C23—1724no—
818C23—1724no—
819C23—1724no—
820C23—1724no—
821C23—1724no—
822C23—1724no—
823C23C2×D4×D4312yes—
824C23#1306337012yes—
825C23#1306337012yes—
826C23#1306337112yes—
827C23#1306337112yes—
828C23#1306337112yes—
829C23#1306337312yes—
830C23C24×D4311yescharacteristic
831D4—17216no—
832D4—17216no—
833D4—17216no—
834D4—17216no—
835D4—17216no—
836D4—17216no—
837C2×C4—28no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—434no—
861C2×C4—868no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—17216no—
877C2×C4—1724no—
878C2×C4—1724no—
879C2×C4—1724no—
880C2×C4—1724no—
881C2×C4C2×D4×D4314yes—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—88no—
890C22—864no—
891C22—864no—
892C22—864no—
893C22—3448no—
894C22—3448no—
895C22—1722no—
896C22—1722no—
897C22—1722no—
898C22—1722no—
899C22—1722no—
900C22—1722no—
901C22—1722no—
902C22—1722no—
903C22—1722no—
904C22—1722no—
905C22—1722no—
906C22—1722no—
907C22—1722no—
908C22—1722no—
909C22—1722no—
910C22—1722no—
911C22—1722no—
912C22—1722no—
913C22—17216no—
914C22#1458345714yes—
915C22#1458346514yes—
916C22#1458347914yes—
917C22#1458363714yes—
918C22#1458364014yes—
919C22#1458364514yes—
920C22#1458364514yes—
921C22C22×D4×D4311yescharacteristic
922C22C2×#1306337011yescharacteristic
923C22C2×#1306337011yescharacteristic
924C22C2×#1306337111yescharacteristic
925C22C2×#1306337111yescharacteristic
926C22C2×#1306337111yescharacteristic
927C22C2×#1306337311yescharacteristic
928C4—24no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—864no—
935C4—1722no—
936C4—1722no—
937C4—1722no—
938C4—1722no—
939C2—82no—
940C2—3442no—
941C2—3442no—
942C2—1724no—
943C2#1914260418yesdirect product factor
944C2C2×#1458345711yescharacteristic
945C2C2×#1458346511yescharacteristic
946C2C2×#1458347911yescharacteristic
947C2C2×#1458363711yescharacteristic
948C2C2×#1458364011yescharacteristic
949C2C2×#1458364511yescharacteristic
950C2C2×#1458364511yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#396C2
socleC24×C43C24
hypercenterC2×#396D43
hypocenterC43C2×#2813
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13063310C2semidirect
2. C22×#13063298C2semidirect
3. #19142604C2direct (N × H)
4. C2×#14582840C2semidirect
5. C2×#14582834C2semidirect
6. C2×#14582821C2semidirect
7. C2×#14582816C2semidirect
8. C2×#14582816C2semidirect
9. C2×#14582815C2semidirect
10. C2×#14582814C2semidirect
11. C2×#14582814C2semidirect
12. C2×#14582809C2semidirect
13. C2×#14582808C2semidirect
14. C2×#14582808C2semidirect
15. C2×#14582756C2semidirect
16. C2×C43×#396C2semidirect
25. C2×#13063310C22semidirect
27. C2×#13063298C22semidirect
44. #14582840C22semidirect
45. #14582834C22semidirect
46. #14582821C22semidirect
47. #14582816C22semidirect
48. #14582816C22semidirect
49. #14582815C22semidirect
50. #14582814C22semidirect
51. #14582814C22semidirect
52. #14582809C22semidirect
53. #14582808C22semidirect
54. #14582808C22semidirect
55. #14582756C22semidirect
67. C43×#396C22semidirect
103. C22×C4×D43D4semidirect
268. C2×C4×D43C2×D4semidirect
470. C2×#396D43semidirect
481. C2×C43#2813semidirect
528. #396C2×D43semidirect
544. C43C2×#2813semidirect
943. C2#19142604direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633102
C22×#130632982
#191426042
C2×#145828402
C2×#145828342
C2×#145828212
C2×#145828162
C2×#145828152
C2×#145828142
C2×#145828092
C2×#145828082
C2×#145827562
C2×C43×#3962
C2×#281343