Finite Group Databasebeta

← C2×#13118535 #16030744

Subgroups — C2×#13118535 #16030744

Order 3328.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88198C211yesmaximal, characteristic, complemented
2C22×#88132C211yesmaximal, characteristic
3C23×#6101C211yesmaximal, characteristic
4#13118535C2116yesmaximal, direct product factor
5C2×#11718641C211yesmaximal, characteristic, complemented
6C2×#11718644C211yesmaximal, characteristic, complemented
7C2×#11718640C211yesmaximal, characteristic, complemented
8C2×#11718890C211yesmaximal, characteristic, complemented
9C2×#11718633C211yesmaximal, characteristic, complemented
10C2×#11718633C211yesmaximal, characteristic, complemented
11C2×#11718871C211yesmaximal, characteristic
12C2×#11718607C211yesmaximal, characteristic
13C2×#11718637C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic
16C22×C13×C22⋊Q8C211yesmaximal, characteristic
17C23×Q8×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C2×C13×C22⋊Q8—28no—
23C2×C13×C22⋊Q8C2218yes—
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×#88198—28no—
32C2×#88198C2218yescomplemented
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101—28no—
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2218yes—
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×C4×Dic13C2211yescharacteristic
49C22×C4×Dic13C2211yescharacteristic
50C2×#88132—28no—
51C2×#88132C2218yes—
52#11718890C2218yescomplemented
53#11718871C2218yes—
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718644C2218yescomplemented
63#11718641C2218yescomplemented
64#11718640C2218yescomplemented
65#11718637C2218yescomplemented
66#11718633C2218yescomplemented
67#11718633C2218yescomplemented
68#11718607C2218yes—
69#11718603C2218yes—
70C22⋊C4×Dic13C2218yes—
71C25×C13C2311yescharacteristic
72C22×Q8×C13—24no—
73C22×Q8×C13—24no—
74C22×Q8×C13—42no—
75C22×Q8×C13C2314yes—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—42no—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—42no—
91C23×Dic13Q818yescomplemented
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2314yes—
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2314yes—
101C23×Dic13C2311yescharacteristic
102C22×Dic26—24no—
103C22×Dic26—24no—
104C22×Dic26—42no—
105C22×Dic26C2314yes—
106C13×C22⋊Q8—232no—
107C2×C13×C4⋊C4—24no—
108C2×C13×C4⋊C4—24no—
109C2×C13×C4⋊C4—24no—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C4⋊C4C2314yes—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4D418yes—
115C2×C13×C22⋊C4C2314yes—
116C2×C13×C22⋊C4C2314yes—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13Q818yescomplemented
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121#88198—232no—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13C2314yes—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—24no—
130C2×#6101—24no—
131C2×#6101—24no—
132C2×#6101—24no—
133C2×#6101—232no—
134C2×#6101—42no—
135C2×#6101—42no—
136C2×#6101D418yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×#6101C2314yes—
149C2×C4×Dic13—24no—
150C2×C4×Dic13—24no—
151C2×C4×Dic13C2314yes—
152C2×C4×Dic13C2314yes—
153#88132—232no—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162C2×#2440—131nomaximal, Sylow
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13C2×D414yes—
168C24×C13C2×Q814yes—
169C24×C13C2×Q814yes—
170C24×C13C2412yes—
171C24×C13C2411yescharacteristic
172C2×Q8×C13—28no—
173C2×Q8×C13—28no—
174C2×Q8×C13—44no—
175C2×Q8×C13—416no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—28no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—28no—
193C22×C4×C13—44no—
194C22×C4×C13—416no—
195C22×C4×C13C2×D414yes—
196C22×C4×C13C2×D414yes—
197C22×C4×C13C2×D414yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—232no—
213C22×Dic13—28no—
214C22×Dic13—28no—
215C22×Dic13—28no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—28no—
226C22×Dic13—44no—
227C22×Dic13—416no—
228C22×Dic13C2×D414yes—
229C22×Dic13C2×D414yes—
230C22×Dic13C2×Q814yes—
231C22×Dic13C2×Q814yes—
232C22×Dic13C2×Q814yes—
233C22×Dic13C2×Q814yes—
234C22×Dic13C2×Q8116yescomplemented
235C22×Dic13#4114yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C2×Dic26—28no—
245C2×Dic26—28no—
246C2×Dic26—44no—
247C2×Dic26—416no—
248C13×C4⋊C4—28no—
249C13×C4⋊C4—28no—
250C13×C4⋊C4—28no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4C2×D4116yes—
253C22⋊Dic13—28no—
254C22⋊Dic13C2×Q8116yescomplemented
255C4⋊Dic13—28no—
256#6101—28no—
257#6101—28no—
258#6101—28no—
259#6101—28no—
260#6101—28no—
261#6101—28no—
262#6101—28no—
263#6101—28no—
264#6101—28no—
265#6101—44no—
266#6101—44no—
267#6101C2×D4116yes—
268C4×Dic13—28no—
269C4×Dic13—28no—
270C22×C4⋊Q8—131no—
271C22×C22⋊Q8—131no—
272C22×C22⋊Q8D1311yescharacteristic
273C23×C4⋊C4—131no—
274#2440—1316no—
275C2×#398—131no—
276C2×#398—131no—
277C2×#395—131no—
278C2×#395—131no—
279C2×#389—131no—
280C2×#389—131no—
281C2×#385—131no—
282C2×#385—131no—
283C2×#384—131no—
284C2×#380—131no—
285C2×C4×C22⋊C4—131no—
286C23×C13—28no—
287C23×C13—28no—
288C23×C13—28no—
289C23×C13—28no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13C4⋊Q8116yescomplemented
297C23×C13C22×D414yes—
298C23×C13C22×D412yes—
299C23×C13C22×D412yes—
300C23×C13C22×Q814yes—
301C23×C13C22×Q814yes—
302C23×C13C22×Q812yes—
303C23×C13C22×Q812yes—
304C23×C13C2×#4112yes—
305C23×C13H(5,𝔽2)12yes—
306C23×C132−1+412yes—
307C23×C13C2511yescharacteristic
308Q8×C13—416no—
309C2×C4×C13—28no—
310C2×C4×C13—28no—
311C2×C4×C13—28no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—416no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13—44no—
331C2×C4×C13C22×D414yes—
332C2×C4×C13C22×D414yes—
333C2×C4×C13C22×D414yes—
334C2×Dic13—28no—
335C2×Dic13—28no—
336C2×Dic13—28no—
337C2×Dic13—28no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—232no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—416no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13C22⋊Q8116yescomplemented
361C2×Dic13C22×D414yes—
362C2×Dic13C22×D414yes—
363C2×Dic13C22×Q814yes—
364C2×Dic13C22×Q814yes—
365C2×Dic13C22×Q814yes—
366C2×Dic13C22×Q814yes—
367C2×Dic13C2×#4114yes—
368Dic26—416no—
369C23×Q8—131no—
370C23×Q8C2×D1311yescharacteristic
371C24×C4—131no—
372C24×C4—131no—
373C24×C4C2×D1311yescharacteristic
374C2×C4⋊Q8—138no—
375C2×C4⋊Q8—268no—
376C2×C22⋊Q8—28no—
377C2×C22⋊Q8—138no—
378C2×C22⋊Q8—268no—
379C2×C22⋊Q8C2×D1318yes—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—138no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4—131no—
394C22×C4⋊C4—268no—
395C22×C4⋊C4C2×D1311yescharacteristic
396C22×C4⋊C4C2×D1311yescharacteristic
397C22×C4⋊C4C2×D1311yescharacteristic
398C22×C22⋊C4—131no—
399C22×C22⋊C4—131no—
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C42—131no—
403C22×C42—131no—
404#398—138no—
405#398—138no—
406#395—138no—
407#395—138no—
408#389—138no—
409#389—138no—
410#385—138no—
411#385—138no—
412#384—138no—
413#380—138no—
414C4×C22⋊C4—138no—
415C2×#95—131no—
416C2×#95—131no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C22×C13—24no—
424C22×C13—24no—
425C22×C13—24no—
426C22×C13—232no—
427C22×C13—24no—
428C22×C13—24no—
429C22×C13—24no—
430C22×C13C2×C22⋊Q814yes—
431C22×C13C2×C4⋊Q814yes—
432C22×C13C2×C4⋊Q818yescomplemented
433C22×C13#54414yes—
434C22×C13D4214yes—
435C22×C13#54714yes—
436C22×C13D4×Q814yes—
437C22×C13#55414yes—
438C22×C13C23×D411yescharacteristic
439C22×C13C23×D411yescharacteristic
440C22×C13C23×Q811yescharacteristic
441C22×C13C23×Q811yescharacteristic
442C22×C13C22×#4111yescharacteristic
443C22×C13C2×H(5,𝔽2)11yescharacteristic
444C22×C13C2×2−1+411yescharacteristic
445C4×C13—24no—
446C4×C13—24no—
447C4×C13—24no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451Dic13—24no—
452Dic13—24no—
453Dic13—24no—
454Dic13—24no—
455Dic13—42no—
456Dic13—42no—
457Dic13—42no—
458Dic13C2×C22⋊Q818yescomplemented
459C25C22×D1311yescharacteristic
460C22×Q8—24no—
461C22×Q8—24no—
462C22×Q8—42no—
463C22×Q8—134no—
464C22×Q8—264no—
465C22×Q8—264no—
466C22×Q8—522no—
467C22×Q8C22×D1314yes—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—42no—
471C23×C4—131no—
472C23×C4—138no—
473C23×C4—134no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4—134no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—264no—
485C23×C4—264no—
486C23×C4—522no—
487C23×C4C22×D1311yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C23×C4C22×D1314yes—
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C4⋊Q8—2632no—
495C22⋊Q8—232no—
496C22⋊Q8—2632no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—138no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—134no—
509C2×C4⋊C4—134no—
510C2×C4⋊C4—134no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—2632no—
515C2×C4⋊C4—264no—
516C2×C4⋊C4—264no—
517C2×C4⋊C4—264no—
518C2×C4⋊C4—264no—
519C2×C4⋊C4—264no—
520C2×C4⋊C4—264no—
521C2×C4⋊C4—264no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—264no—
524C2×C4⋊C4—264no—
525C2×C4⋊C4—522no—
526C2×C4⋊C4—522no—
527C2×C4⋊C4C22×D1314yes—
528C2×C4⋊C4C22×D1314yes—
529C2×C4⋊C4C22×D1314yes—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—138no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—264no—
535C2×C22⋊C4C22⋊D1318yes—
536C2×C22⋊C4C22×D1314yes—
537C2×C22⋊C4C22×D1314yes—
538C2×C42—134no—
539C2×C42—134no—
540C2×C42—264no—
541C2×C42—264no—
542#95—134no—
543#95—134no—
544#95—134no—
545#95—134no—
546#95—134no—
547#95—134no—
548#95—134no—
549#95—134no—
550C2×C13—28no—
551C2×C13#244018yescomplemented
552C2×C13C22×C22⋊Q811yescharacteristic
553C2×C13C22×C4⋊Q811yescharacteristic
554C2×C13C2×#54411yescharacteristic
555C2×C13C2×D4211yescharacteristic
556C2×C13C2×#54711yescharacteristic
557C2×C13C2×D4×Q811yescharacteristic
558C2×C13C2×#55411yescharacteristic
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24Q8×D1314yes—
564C24Q8×D1314yes—
565C24C2×C22⋊D1314yes—
566C24C23×D1312yes—
567C24C23×D1311yescharacteristic
568C2×Q8—28no—
569C2×Q8—28no—
570C2×Q8—44no—
571C2×Q8—416no—
572C2×Q8—268no—
573C2×Q8—268no—
574C2×Q8—524no—
575C2×Q8—5216no—
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—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—44no—
594C22×C4—416no—
595C22×C4—134no—
596C22×C4—134no—
597C22×C4—134no—
598C22×C4—132no—
599C22×C4—134no—
600C22×C4—134no—
601C22×C4—134no—
602C22×C4—134no—
603C22×C4—1316no—
604C22×C4—132no—
605C22×C4—132no—
606C22×C4—132no—
607C22×C4—132no—
608C22×C4—132no—
609C22×C4—132no—
610C22×C4—132no—
611C22×C4—268no—
612C22×C4—2632no—
613C22×C4—268no—
614C22×C4—268no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—268no—
633C22×C4—524no—
634C22×C4—5216no—
635C22×C4D4×D1314yes—
636C22×C4C2×C22⋊D1314yes—
637C22×C4C2×C22⋊D1314yes—
638C22×C4C23×D1312yes—
639C22×C4C23×D1312yes—
640C22×C4C23×D1312yes—
641C22×C4C23×D1312yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—1316no—
648C4⋊C4—268no—
649C4⋊C4—268no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—268no—
653C4⋊C4—268no—
654C4⋊C4—268no—
655C4⋊C4—268no—
656C4⋊C4—268no—
657C4⋊C4—268no—
658C4⋊C4—524no—
659C4⋊C4—524no—
660C22⋊C4—28no—
661C22⋊C4—1316no—
662C22⋊C4—268no—
663C22⋊C4C2×C22⋊D13116yes—
664C42—268no—
665C42—268no—
666C13C2×#244011yescharacteristic, complemented, Sylow
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23#88198116yescomplemented
678C23C2×D4×D1312yes—
679C23#8825112yes—
680C23C2×Q8×D1314yes—
681C23C2×Q8×D1314yes—
682C23C2×Q8×D1312yes—
683C23C2×Q8×D1312yes—
684C23#41×D1312yes—
685C23#8825712yes—
686C23C22×C22⋊D1314yes—
687C23C22×C22⋊D1312yes—
688C23C24×D1311yescharacteristic
689Q8—416no—
690Q8—5216no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
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—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—1316no—
714C2×C4—134no—
715C2×C4—134no—
716C2×C4—134no—
717C2×C4—134no—
718C2×C4—134no—
719C2×C4—134no—
720C2×C4—134no—
721C2×C4—2632no—
722C2×C4—268no—
723C2×C4—268no—
724C2×C4—268no—
725C2×C4—268no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—5216no—
744C2×C4—524no—
745C2×C4—524no—
746C2×C4—524no—
747C2×C4C2×D4×D1314yes—
748C2×C4C22×C22⋊D1314yes—
749C2×C4C22×C22⋊D1314yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22#1171932814yes—
758C22D13×C22⋊Q814yes—
759C22#1171933714yes—
760C22#1171934114yes—
761C22D4×C22⋊D1314yes—
762C22C2×#8819814yes—
763C22C2×#8819818yescomplemented
764C22#1171952914yes—
765C22C22×D4×D1311yescharacteristic
766C22C2×#8825111yescharacteristic
767C22C22×Q8×D1311yescharacteristic
768C22C22×Q8×D1311yescharacteristic
769C22C2×#41×D1311yescharacteristic
770C22C2×#8825711yescharacteristic
771C22C23×C22⋊D1311yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—138no—
779C4—264no—
780C4—264no—
781C4—264no—
782C4—264no—
783C4—522no—
784C4—522no—
785C4—522no—
786C2—28no—
787C2#1311853518yesdirect product factor
788C2C2×D13×C22⋊Q811yescharacteristic
789C2C22×#8819811yescharacteristic
790C2C2×#1171932811yescharacteristic
791C2C2×D4×C22⋊D1311yescharacteristic
792C2C2×#1171952911yescharacteristic
793C2C2×#1171933711yescharacteristic
794C2C2×#1171934111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2440
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#88198C2semidirect
4. #13118535C2direct (N × H)
5. C2×#11718641C2semidirect
6. C2×#11718644C2semidirect
7. C2×#11718640C2semidirect
8. C2×#11718890C2semidirect
9. C2×#11718633C2semidirect
10. C2×#11718633C2semidirect
13. C2×#11718637C2semidirect
32. C2×#88198C22semidirect
52. #11718890C22semidirect
62. #11718644C22semidirect
63. #11718641C22semidirect
64. #11718640C22semidirect
65. #11718637C22semidirect
66. #11718633C22semidirect
67. #11718633C22semidirect
91. C23×Dic13Q8semidirect
118. C2×C22⋊Dic13Q8semidirect
234. C22×Dic13C2×Q8semidirect
254. C22⋊Dic13C2×Q8semidirect
296. C23×C13C4⋊Q8semidirect
360. C2×Dic13C22⋊Q8semidirect
432. C22×C13C2×C4⋊Q8semidirect
458. Dic13C2×C22⋊Q8semidirect
551. C2×C13#2440semidirect
666. C13C2×#2440semidirect
677. C23#88198semidirect
763. C22C2×#88198semidirect
787. C2#13118535direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881982
C22×#881322
C23×#61012
#131185352
C2×#117186412
C2×#117186442
C2×#117186402
C2×#117188902
C2×#117186332
C2×#117188712
C2×#117186072
C2×#117186372
C2×#117186032
C2×C22⋊C4×Dic132
C22×C13×C22⋊Q82
C2×#244013