Finite Group Databasebeta

← C2×#19142668 #25303130

Subgroups — C2×#19142668 #25303130

Order 11008.

2502 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063320C211yesmaximal, characteristic, complemented
2C22×#13063318C211yesmaximal, characteristic, complemented
3#19142668C2116yesmaximal, direct product factor
4C2×#14582832C211yesmaximal, characteristic, complemented
5C2×#14582831C211yesmaximal, characteristic, complemented
6C2×#14582830C211yesmaximal, characteristic, complemented
7C2×#14582823C211yesmaximal, characteristic, complemented
8C2×#14582822C211yesmaximal, characteristic, complemented
9C2×#14582822C211yesmaximal, characteristic, complemented
10C2×#14582821C211yesmaximal, characteristic, complemented
11C2×#14582821C211yesmaximal, characteristic, complemented
12C2×#14582815C211yesmaximal, characteristic
13C2×#14582814C211yesmaximal, characteristic
14C2×#14582814C211yesmaximal, characteristic
15C2×#14582768C211yesmaximal, characteristic, complemented
16C2×C43×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C2×#13063320—28no—
19C2×#13063320C2218yescomplemented
20C2×#13063318—28no—
21C2×#13063318C2218yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×C22⋊Dic43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
44#14582832C2218yescomplemented
45#14582831C2218yescomplemented
46#14582830C2218yescomplemented
47#14582823C2218yescomplemented
48#14582822C2218yescomplemented
49#14582822C2218yescomplemented
50#14582821C2218yescomplemented
51#14582821C2218yescomplemented
52#14582815C2218yes—
53#14582814C2218yes—
54#14582814C2218yes—
55#14582768C2218yescomplemented
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
70C22×C22⋊D43—42no—
71C22×C22⋊D43—42no—
72C22×C22⋊D43—42no—
73C22×C22⋊D43C2314yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81#13063320—232no—
82#13063318—232no—
83C2×C4⋊Dic43—24no—
84C2×C4⋊Dic43—24no—
85C2×C4⋊Dic43—42no—
86C2×C4⋊Dic43—42no—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2314yes—
91C2×Dic43⋊C4—24no—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—42no—
95C2×Dic43⋊C4—42no—
96C2×Dic43⋊C4—42no—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4—42no—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×C22⋊Dic43—24no—
108C2×C22⋊Dic43—24no—
109C2×C22⋊Dic43—42no—
110C2×C22⋊Dic43C2314yes—
111C2×C22⋊Dic43C2314yes—
112C2×C22⋊Dic43C2314yes—
113C2×(C2×D43)⋊C4—24no—
114C2×(C2×D43)⋊C4—24no—
115C2×(C2×D43)⋊C4—24no—
116C2×(C2×D43)⋊C4—42no—
117C2×(C2×D43)⋊C4—42no—
118C2×(C2×D43)⋊C4—42no—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×C4×Dic43D418yescomplemented
126C2×C4×Dic43C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C25×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43—24no—
140C2×C4⋊C4×C43—42no—
141C2×C4⋊C4×C43—42no—
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C4⋊C4×C43C2314yes—
145C2×C22⋊C4×C43—24no—
146C2×C22⋊C4×C43—42no—
147C2×C22⋊C4×C43—42no—
148C2×C22⋊C4×C43C2314yes—
149C2×C22⋊C4×C43C2314yes—
150C2×C22⋊C4×C43C2314yes—
151#95×C43C2314yes—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43C2412yes—
160C24×C43C2411yescharacteristic
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43C2412yes—
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×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43C2×D414yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C2×C22⋊D43—44no—
194C2×C22⋊D43—44no—
195C2×C22⋊D43—44no—
196C2×C22⋊D43—416no—
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—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43C2×D414yes—
217C22×Dic43C2×D414yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C4⋊C4×C43—28no—
226C4⋊C4×C43—44no—
227C4⋊C4×C43—44no—
228C22⋊C4×C43—28no—
229C22⋊C4×C43—44no—
230C22⋊C4×C43—44no—
231C22⋊Dic43—28no—
232C22⋊Dic43—28no—
233C22⋊Dic43—44no—
234(C2×D43)⋊C4—28no—
235(C2×D43)⋊C4—28no—
236(C2×D43)⋊C4—28no—
237(C2×D43)⋊C4—44no—
238(C2×D43)⋊C4—44no—
239(C2×D43)⋊C4—44no—
240C4⋊Dic43—28no—
241C4⋊Dic43—28no—
242C4⋊Dic43—44no—
243C4⋊Dic43—44no—
244Dic43⋊C4—28no—
245Dic43⋊C4—28no—
246Dic43⋊C4—28no—
247Dic43⋊C4—44no—
248Dic43⋊C4—44no—
249Dic43⋊C4—44no—
250Dic43⋊C4—44no—
251Dic43⋊C4—44no—
252C4×Dic43C2×D4116yescomplemented
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—44no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43C22×D412yes—
268C23×C43H(5,𝔽2)12yes—
269C23×C43H(5,𝔽2)12yes—
270C23×C43H(5,𝔽2)12yes—
271C23×C432−1+412yes—
272C23×C432−1+412yes—
273C23×C432−1+412yes—
274C23×C43C2511yescharacteristic
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—44no—
283C22×D43—44no—
284C22×D43—44no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C2×C4×C43—28no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
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—44no—
308C2×C4×C43—44no—
309C2×C4×C43—44no—
310C2×C4×C43—44no—
311C2×C4×C43—44no—
312C2×C4×C43C22×D414yes—
313C22⋊D43—416no—
314C2×Dic43—28no—
315C2×Dic43—28no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
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—44no—
336C2×Dic43—44no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43C22×D414yes—
341C2×Dic43C22×D414yes—
342C2×#2823—431nomaximal, Sylow
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—88no—
351C22×C43#53714yes—
352C22×C43#53714yes—
353C22×C43#53714yes—
354C22×C43#56014yes—
355C22×C43#56314yes—
356C22×C43#56314yes—
357C22×C43#56314yes—
358C22×C43C23×D411yescharacteristic
359C22×C43C2×H(5,𝔽2)11yescharacteristic
360C22×C43C2×H(5,𝔽2)11yescharacteristic
361C22×C43C2×H(5,𝔽2)11yescharacteristic
362C22×C43C2×2−1+411yescharacteristic
363C22×C43C2×2−1+411yescharacteristic
364C22×C43C2×2−1+411yescharacteristic
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—88no—
373C4×C43—24no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43—42no—
379Dic43—24no—
380Dic43—24no—
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386C22×#126—431no—
387C22×#126—431no—
388#2823—4316no—
389C2×#398—431no—
390C2×#398—431no—
391C2×#398—431no—
392C2×#396—431no—
393C2×#396—431no—
394C2×#396—431no—
395C2×#396—431no—
396C2×#396—431no—
397C2×#396D4311yescharacteristic, complemented
398C2×#394—431no—
399C2×#394—431no—
400C2×#394—431no—
401C2×#384—431no—
402C2×C43—82no—
403C2×C43#282318yescomplemented
404C2×C43C2×#53711yescharacteristic
405C2×C43C2×#53711yescharacteristic
406C2×C43C2×#53711yescharacteristic
407C2×C43C2×#56011yescharacteristic
408C2×C43C2×#56311yescharacteristic
409C2×C43C2×#56311yescharacteristic
410C2×C43C2×#56311yescharacteristic
411D43—82no—
412C23×D4—431no—
413C2×#126—438no—
414C2×#126—438no—
415C2×#126—868no—
416C2×#126—868no—
417C22×C4⋊C4—431no—
418C22×C4⋊C4—431no—
419C22×C4⋊C4—431no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4C2×D4311yescharacteristic
430C22×C4⋊C4C2×D4311yescharacteristic
431C22×C4⋊C4C2×D4311yescharacteristic
432C22×C22⋊C4—431no—
433C22×C22⋊C4—431no—
434C22×C22⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—431no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4—431no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4—431no—
441C22×C22⋊C4C2×D4311yescharacteristic
442C22×C22⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4C2×D4311yescharacteristic
444C22×C42—431no—
445#398—438no—
446#398—438no—
447#398—438no—
448#396—438no—
449#396—438no—
450#396—438no—
451#396—438no—
452#396—438no—
453#396C2×D4318yescomplemented
454#394—438no—
455#394—438no—
456#394—438no—
457#384—438no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95C2×D4311yescharacteristic
464C43C2×#282311yescharacteristic, complemented, Sylow
465C25—431no—
466C25C22×D4311yescharacteristic
467C22×D4—434no—
468C22×D4—1722no—
469C22×D4—1722no—
470C22×D4—1722no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C23×C4C22×D4311yescharacteristic
484#126—8632no—
485#126—8632no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—434no—
490C2×C4⋊C4—434no—
491C2×C4⋊C4—434no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—434no—
496C2×C4⋊C4—434no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—434no—
501C2×C4⋊C4—864no—
502C2×C4⋊C4—864no—
503C2×C4⋊C4—864no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—864no—
506C2×C4⋊C4—1722no—
507C2×C4⋊C4—1722no—
508C2×C4⋊C4—1722no—
509C2×C4⋊C4—1722no—
510C2×C4⋊C4—1722no—
511C2×C4⋊C4—1722no—
512C2×C4⋊C4—1722no—
513C2×C4⋊C4C22×D4314yes—
514C2×C4⋊C4C22×D4314yes—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—434no—
523C2×C22⋊C4—434no—
524C2×C22⋊C4—434no—
525C2×C22⋊C4—434no—
526C2×C22⋊C4—434no—
527C2×C22⋊C4—434no—
528C2×C22⋊C4—864no—
529C2×C22⋊C4—864no—
530C2×C22⋊C4—864no—
531C2×C22⋊C4—864no—
532C2×C22⋊C4—864no—
533C2×C22⋊C4—1722no—
534C2×C22⋊C4—1722no—
535C2×C22⋊C4—1722no—
536C2×C22⋊C4—1722no—
537C2×C22⋊C4C22×D4314yes—
538C2×C22⋊C4C22×D4314yes—
539C2×C22⋊C4C22×D4314yes—
540C2×C42—438no—
541C2×C42—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95C22×D4314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—432no—
556C24—862no—
557C24—862no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24C23×D4312yes—
564C24C23×D4311yescharacteristic
565C2×D4—1724no—
566C2×D4—1724no—
567C2×D4—1724no—
568C2×D4—17216no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
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—434no—
587C22×C4—434no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
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×C4D4×D4314yes—
615C22×C4C23×D4312yes—
616C22×C4C23×D4312yes—
617C22×C4C23×D4312yes—
618C22×C4C23×D4312yes—
619C22×C4C23×D4312yes—
620C22×C4C23×D4312yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—868no—
625C4⋊C4—868no—
626C4⋊C4—868no—
627C4⋊C4—868no—
628C4⋊C4—868no—
629C4⋊C4—1724no—
630C4⋊C4—1724no—
631C4⋊C4—1724no—
632C4⋊C4—1724no—
633C4⋊C4—1724no—
634C4⋊C4—1724no—
635C4⋊C4—1724no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—868no—
640C22⋊C4—868no—
641C22⋊C4—868no—
642C22⋊C4—868no—
643C22⋊C4—868no—
644C22⋊C4—1724no—
645C22⋊C4—1724no—
646C22⋊C4—1724no—
647C22⋊C4—1724no—
648C42—4316no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—862no—
664C23—862no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—1724no—
671C23—1724no—
672C23—1724no—
673C23—1724no—
674C23—1724no—
675C23—1724no—
676C23—1724no—
677C23C2×D4×D4312yes—
678C23#1306337012yes—
679C23#1306337012yes—
680C23#1306337112yes—
681C23#1306337212yes—
682C23#1306337212yes—
683C23#1306337312yes—
684C23C24×D4311yescharacteristic
685D4—17216no—
686C2×C4—22no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—434no—
710C2×C4—434no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—868no—
716C2×C4—868no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—1724no—
733C2×C4—1724no—
734C2×C4—1724no—
735C2×C4—1724no—
736C2×C4—1724no—
737C2×C4C2×D4×D4314yes—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—3448no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22#1458347614yes—
755C22#1458347814yes—
756C22#1458347914yes—
757C22#1458363714yes—
758C22#1458365014yes—
759C22#1458365014yes—
760C22#1458365114yes—
761C22C22×D4×D4311yescharacteristic
762C22C2×#1306337011yescharacteristic
763C22C2×#1306337011yescharacteristic
764C22C2×#1306337111yescharacteristic
765C22C2×#1306337211yescharacteristic
766C22C2×#1306337211yescharacteristic
767C22C2×#1306337311yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—864no—
775C4—864no—
776C4—1722no—
777C4—1722no—
778C4—1722no—
779C4—1722no—
780C4—1722no—
781C2—82no—
782C2—3442no—
783C2#1914266818yesdirect product factor
784C2C2×#1458347611yescharacteristic
785C2C2×#1458347811yescharacteristic
786C2C2×#1458347911yescharacteristic
787C2C2×#1458363711yescharacteristic
788C2C2×#1458365011yescharacteristic
789C2C2×#1458365011yescharacteristic
790C2C2×#1458365111yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#396C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#396D43
hypocenterC43C2×#2823
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13063320C2semidirect
2. C22×#13063318C2semidirect
3. #19142668C2direct (N × H)
4. C2×#14582832C2semidirect
5. C2×#14582831C2semidirect
6. C2×#14582830C2semidirect
7. C2×#14582823C2semidirect
8. C2×#14582822C2semidirect
9. C2×#14582822C2semidirect
10. C2×#14582821C2semidirect
11. C2×#14582821C2semidirect
15. C2×#14582768C2semidirect
16. C2×C43×#396C2semidirect
19. C2×#13063320C22semidirect
21. C2×#13063318C22semidirect
44. #14582832C22semidirect
45. #14582831C22semidirect
46. #14582830C22semidirect
47. #14582823C22semidirect
48. #14582822C22semidirect
49. #14582822C22semidirect
50. #14582821C22semidirect
51. #14582821C22semidirect
55. #14582768C22semidirect
67. C43×#396C22semidirect
125. C2×C4×Dic43D4semidirect
252. C4×Dic43C2×D4semidirect
397. C2×#396D43semidirect
403. C2×C43#2823semidirect
453. #396C2×D43semidirect
464. C43C2×#2823semidirect
783. C2#19142668direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633202
C22×#130633182
#191426682
C2×#145828322
C2×#145828312
C2×#145828302
C2×#145828232
C2×#145828222
C2×#145828212
C2×#145828152
C2×#145828142
C2×#145827682
C2×C43×#3962
C2×#282343