Finite Group Databasebeta

← C2×#13118078 #16029143

Subgroups — C2×#13118078 #16029143

Order 3328.

4134 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C22×#88180C211yesmaximal, characteristic, complemented
4#13118078C2116yesmaximal, direct product factor
5C2×#11718645C211yesmaximal, characteristic, complemented
6C2×#11718613C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718655C211yesmaximal, characteristic, complemented
9C2×#11718622C211yesmaximal, characteristic, complemented
10C2×#11718620C211yesmaximal, characteristic, complemented
11C2×#11718883C211yesmaximal, characteristic, complemented
12C2×#11718884C211yesmaximal, characteristic
13C2×C4×#6101C211yesmaximal, characteristic, complemented
14C2×C4×#6103C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C2×C4×D4×C13—28no—
24C2×C4×D4×C13C2218yescomplemented
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×C4×C22⋊D13—28no—
36C2×C4×C22⋊D13—28no—
37C2×C4×C22⋊D13C2218yescomplemented
38C2×C4×C22⋊D13C2218yescomplemented
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C2×#88180—28no—
44C2×#88180C2218yescomplemented
45C22×C4⋊Dic13C2211yescharacteristic
46C22×C4⋊Dic13C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×#6101C2211yescharacteristic
51C22×C4×Dic13C2211yescharacteristic
52C22×C4×Dic13C2211yescharacteristic
53C22×C4×Dic13C2211yescharacteristic
54#11718884C2218yes—
55#11718883C2218yescomplemented
56C4×C22⋊Dic13C2218yescomplemented
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63#11718655C2218yescomplemented
64#11718645C2218yescomplemented
65#11718622C2218yescomplemented
66#11718620C2218yescomplemented
67#11718613C2218yescomplemented
68#11718609C2218yescomplemented
69C4×#6103C2218yescomplemented
70C4×#6101C2218yescomplemented
71C25×C13C2311yescharacteristic
72C25×C13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13C2314yes—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13—24no—
82C23×C4×C13—24no—
83C23×C4×C13D418yescomplemented
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2314yes—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2314yes—
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C22×C22⋊D13—24no—
92C22×C22⋊D13—24no—
93C22×C22⋊D13—24no—
94C22×C22⋊D13—24no—
95C22×C22⋊D13—24no—
96C22×C22⋊D13—24no—
97C22×C22⋊D13C2314yes—
98C22×C22⋊D13C2314yes—
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C22×C4×D13—24no—
107C22×C4×D13—24no—
108C22×C4×D13—24no—
109C22×C4×D13C2314yes—
110C4×D4×C13—232no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4—24no—
115C2×C13×C22⋊C4C2314yes—
116C2×C13×C22⋊C4C2314yes—
117C2×C42×C13—24no—
118C2×C42×C13C2314yes—
119C2×C22⋊Dic13—24no—
120C2×C22⋊Dic13—24no—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13—24no—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131C4×C22⋊D13—232no—
132C4×C22⋊D13—232no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141#88180—232no—
142C2×C4⋊Dic13—24no—
143C2×C4⋊Dic13—24no—
144C2×C4⋊Dic13C2314yes—
145C2×C4⋊Dic13C2314yes—
146C2×#6101—24no—
147C2×#6101—24no—
148C2×#6101—24no—
149C2×#6101—24no—
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×C4×Dic13—24no—
155C2×C4×Dic13—24no—
156C2×C4×Dic13D418yescomplemented
157C2×C4×Dic13C2314yes—
158C2×C4×Dic13C2314yes—
159C2×C4×Dic13C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2392—131nomaximal, Sylow
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—22no—
178C24×C13—22no—
179C24×C13C2×D414yes—
180C24×C13#4114yes—
181C24×C13C2412yes—
182C24×C13C2412yes—
183C24×C13C2411yescharacteristic
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13—22no—
189C23×D13—22no—
190C23×D13#4114yes—
191C23×D13C2412yes—
192C2×D4×C13—232no—
193C2×D4×C13—28no—
194C2×D4×C13—28no—
195C2×D4×C13—28no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—232no—
201C22×C4×C13—28no—
202C22×C4×C13—28no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—22no—
209C22×C4×C13—28no—
210C22×C4×C13—28no—
211C22×C4×C13—28no—
212C22×C4×C13—416no—
213C22×C4×C13C2×D414yes—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2×D414yes—
216C22×C4×C13C2×D4116yescomplemented
217C22×C4×C13#4114yes—
218C22×C4×C13#4114yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C2×C22⋊D13—232no—
225C2×C22⋊D13—232no—
226C2×C22⋊D13—28no—
227C2×C22⋊D13—28no—
228C2×C22⋊D13—28no—
229C2×C22⋊D13—28no—
230C2×C22⋊D13—28no—
231C2×C22⋊D13—28no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13C2×D414yes—
251C22×Dic13C2×D414yes—
252C22×Dic13#4114yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2412yes—
260C2×C4×D13—28no—
261C2×C4×D13—28no—
262C2×C4×D13—28no—
263C2×C4×D13—416no—
264C13×C4⋊C4—28no—
265C13×C22⋊C4—28no—
266C13×C22⋊C4—28no—
267C42×C13—28no—
268C22⋊Dic13—28no—
269C22⋊Dic13—28no—
270C22⋊Dic13—28no—
271C22⋊Dic13—28no—
272C22⋊Dic13—28no—
273C22⋊Dic13—28no—
274#6103—28no—
275#6103—28no—
276#6103—28no—
277#6103—28no—
278C4⋊Dic13—28no—
279C4⋊Dic13—28no—
280#6101—28no—
281#6101—28no—
282#6101—28no—
283#6101—28no—
284C4×Dic13—28no—
285C4×Dic13—28no—
286C4×Dic13C2×D4116yescomplemented
287C22×C4×D4—131no—
288C22×C4×D4—131no—
289C22×C4×D4D1311yescharacteristic, complemented
290C22×#117—131no—
291#2392—1316no—
292C2×#398—131no—
293C2×#397—131no—
294C2×#396—131no—
295C2×#396—131no—
296C2×#394—131no—
297C2×#394—131no—
298C2×#394—131no—
299C2×#392—131no—
300C2×C4×C4⋊C4—131no—
301C2×C4×C22⋊C4—131no—
302C2×C4×C22⋊C4—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—44no—
322C23×C13—44no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13C22×D414yes—
330C23×C13C22×D412yes—
331C23×C13C22×D412yes—
332C23×C13C2×#4114yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13C2×#4112yes—
337C23×C13C2×#4112yes—
338C23×C13C2511yescharacteristic
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13C2×#4114yes—
353D4×C13—232no—
354C2×C4×C13—28no—
355C2×C4×C13—28no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—232no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—44no—
368C2×C4×C13—44no—
369C2×C4×C13—416no—
370C2×C4×C13#121116yes—
371C2×C4×C13C22×D414yes—
372C2×C4×C13C22×D414yes—
373C2×C4×C13C22×D414yes—
374C2×C4×C13C2×#4114yes—
375C2×C4×C13C2×#4114yes—
376C22⋊D13—232no—
377C22⋊D13—232no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—28no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—44no—
400C2×Dic13—44no—
401C2×Dic13—44no—
402C2×Dic13—44no—
403C2×Dic13C22×D414yes—
404C2×Dic13C22×D414yes—
405C2×Dic13C2×#4114yes—
406C4×D13—416no—
407C23×D4—131no—
408C23×D4—131no—
409C23×D4C2×D1311yescharacteristic
410C24×C4—131no—
411C24×C4C2×D1311yescharacteristic
412C24×C4C2×D1311yescharacteristic
413C2×C4×D4—28no—
414C2×C4×D4—138no—
415C2×C4×D4—138no—
416C2×C4×D4—268no—
417C2×C4×D4—268no—
418C2×C4×D4C2×D1318yescomplemented
419C2×#117—138no—
420C2×#117—268no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4C2×D1311yescharacteristic
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4C2×D1311yescharacteristic
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C42—131no—
441C22×C42—131no—
442C22×C42—131no—
443C22×C42C2×D1311yescharacteristic
444#398—138no—
445#397—138no—
446#396—138no—
447#396—138no—
448#394—138no—
449#394—138no—
450#394—138no—
451#392—138no—
452C4×C4⋊C4—138no—
453C4×C22⋊C4—138no—
454C4×C22⋊C4—138no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—416no—
468C22×C13—416no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13C2×#12114yes—
478C22×C13#52514yes—
479C22×C13#52514yes—
480C22×C13#52514yes—
481C22×C13#52914yes—
482C22×C13#52914yes—
483C22×C13#53214yes—
484C22×C13C23×D411yescharacteristic
485C22×C13C23×D411yescharacteristic
486C22×C13C22×#4111yescharacteristic
487C22×C13C22×#4111yescharacteristic
488C22×C13C22×#4111yescharacteristic
489C22×C13C22×#4111yescharacteristic
490C22×C13C22×#4111yescharacteristic
491C2×D13—24no—
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—416no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C4×C13—24no—
500C4×C13—24no—
501C4×C13—42no—
502C4×C13—42no—
503C4×C13C2×#12118yes—
504Dic13—24no—
505Dic13—24no—
506Dic13—24no—
507Dic13—42no—
508Dic13—42no—
509Dic13—42no—
510Dic13—42no—
511C25—131no—
512C25C22×D1311yescharacteristic
513C25C22×D1311yescharacteristic
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—134no—
518C22×D4—134no—
519C22×D4—264no—
520C22×D4—264no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4C22×D1314yes—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—134no—
539C23×C4—264no—
540C23×C4—264no—
541C23×C4—264no—
542C23×C4C22⋊D1318yescomplemented
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1314yes—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1314yes—
549C23×C4C22×D1311yescharacteristic
550C4×D4—232no—
551C4×D4—2632no—
552C4×D4—2632no—
553#117—2632no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—134no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—134no—
561C2×C4⋊C4—264no—
562C2×C4⋊C4—264no—
563C2×C4⋊C4—264no—
564C2×C4⋊C4—264no—
565C2×C4⋊C4—264no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4C22×D1314yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—264no—
584C2×C22⋊C4—264no—
585C2×C22⋊C4—264no—
586C2×C22⋊C4—264no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4C22×D1314yes—
591C2×C22⋊C4C22×D1314yes—
592C2×C42—24no—
593C2×C42—138no—
594C2×C42—134no—
595C2×C42—134no—
596C2×C42—134no—
597C2×C42—264no—
598C2×C42—264no—
599C2×C42C22×D1314yes—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606C2×C13—44no—
607C2×C13—44no—
608C2×C13#239218yescomplemented
609C2×C13C22×#12111yescharacteristic
610C2×C13C2×#52511yescharacteristic
611C2×C13C2×#52511yescharacteristic
612C2×C13C2×#52511yescharacteristic
613C2×C13C2×#52911yescharacteristic
614C2×C13C2×#52911yescharacteristic
615C2×C13C2×#53211yescharacteristic
616D13—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—134no—
630C24—132no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24#612714yes—
638C24C2×C22⋊D1314yes—
639C24C23×D1312yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×D4—232no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—268no—
647C2×D4—268no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—2632no—
651C2×D4—2632no—
652C2×D4—268no—
653C2×D4—268no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—232no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—416no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—134no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—268no—
700C22×C4—268no—
701C22×C4—268no—
702C22×C4—5216no—
703C22×C4#612714yes—
704C22×C4D4×D1314yes—
705C22×C4#612914yes—
706C22×C4C2×C22⋊D1314yes—
707C22×C4C2×C22⋊D1314yes—
708C22×C4C2×C22⋊D13116yescomplemented
709C22×C4C23×D1312yes—
710C22×C4C23×D1312yes—
711C22×C4C23×D1312yes—
712C22×C4C23×D1312yes—
713C22×C4C23×D1312yes—
714C4⋊C4—28no—
715C4⋊C4—268no—
716C4⋊C4—268no—
717C4⋊C4—268no—
718C4⋊C4—268no—
719C4⋊C4—268no—
720C4⋊C4—268no—
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—268no—
724C22⋊C4—268no—
725C22⋊C4—268no—
726C22⋊C4—268no—
727C22⋊C4—268no—
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C42—28no—
734C42—1316no—
735C42—268no—
736C42—268no—
737C13C2×#239211yescharacteristic, complemented, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—134no—
765C23—268no—
766C23—268no—
767C23—268no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23C2×#612714yes—
779C23C2×#612712yes—
780C23C2×#612712yes—
781C23C2×D4×D1312yes—
782C23C2×#612912yes—
783C23#41×D1312yes—
784C23#41×D1312yes—
785C23C22×C22⋊D1314yes—
786C23C22×C22⋊D1312yes—
787C23C24×D1311yescharacteristic
788D4—232no—
789D4—2632no—
790D4—2632no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—232no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—416no—
807C2×C4—134no—
808C2×C4—134no—
809C2×C4—134no—
810C2×C4—268no—
811C2×C4—268no—
812C2×C4—268no—
813C2×C4—262no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—524no—
832C2×C4—524no—
833C2×C4—524no—
834C2×C4—524no—
835C2×C4—5216no—
836C2×C4#88193116yes—
837C2×C4C2×#612714yes—
838C2×C4C2×D4×D1314yes—
839C2×C4C2×#612914yes—
840C2×C4C22×C22⋊D1314yes—
841C2×C4C22×C22⋊D1314yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—416no—
850C22—416no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—264no—
859C22—264no—
860C22—264no—
861C22—522no—
862C22—5216no—
863C22—522no—
864C22—522no—
865C22—522no—
866C22#1171924314yes—
867C22#1171925214yes—
868C22#1171925314yes—
869C22#1171926214yes—
870C22#1171949614yes—
871C22C2×#8819314yes—
872C22#1171953314yes—
873C22C22×#612711yescharacteristic
874C22C22×#612711yescharacteristic
875C22C22×D4×D1311yescharacteristic
876C22C22×#612911yescharacteristic
877C22C2×#41×D1311yescharacteristic
878C22C2×#41×D1311yescharacteristic
879C22C23×C22⋊D1311yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—264no—
885C4—264no—
886C4—264no—
887C4—522no—
888C4—522no—
889C4—522no—
890C4—522no—
891C4C2×#8819318yes—
892C2—44no—
893C2—44no—
894C2—524no—
895C2#1311807818yesdirect product factor
896C2C22×#8819311yescharacteristic
897C2C2×#1171953311yescharacteristic
898C2C2×#1171925211yescharacteristic
899C2C2×#1171949611yescharacteristic
900C2C2×#1171924311yescharacteristic
901C2C2×#1171926211yescharacteristic
902C2C2×#1171925311yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2392
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D13C2semidirect
2. C22×C4×C22⋊D13C2semidirect
3. C22×#88180C2semidirect
4. #13118078C2direct (N × H)
5. C2×#11718645C2semidirect
6. C2×#11718613C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718655C2semidirect
9. C2×#11718622C2semidirect
10. C2×#11718620C2semidirect
11. C2×#11718883C2semidirect
13. C2×C4×#6101C2semidirect
14. C2×C4×#6103C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
16. C22×C4×D4×C13C2semidirect
24. C2×C4×D4×C13C22semidirect
37. C2×C4×C22⋊D13C22semidirect
38. C2×C4×C22⋊D13C22semidirect
44. C2×#88180C22semidirect
55. #11718883C22semidirect
56. C4×C22⋊Dic13C22semidirect
63. #11718655C22semidirect
64. #11718645C22semidirect
65. #11718622C22semidirect
66. #11718620C22semidirect
67. #11718613C22semidirect
68. #11718609C22semidirect
69. C4×#6103C22semidirect
70. C4×#6101C22semidirect
83. C23×C4×C13D4semidirect
156. C2×C4×Dic13D4semidirect
216. C22×C4×C13C2×D4semidirect
286. C4×Dic13C2×D4semidirect
289. C22×C4×D4D13semidirect
418. C2×C4×D4C2×D13semidirect
542. C23×C4C22⋊D13semidirect
608. C2×C13#2392semidirect
708. C22×C4C2×C22⋊D13semidirect
737. C13C2×#2392semidirect
895. C2#13118078direct (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⋊D132
C22×#881802
#131180782
C2×#117186452
C2×#117186132
C2×#117186092
C2×#117186552
C2×#117186222
C2×#117186202
C2×#117188832
C2×#117188842
C2×C4×#61012
C2×C4×#61032
C2×C4×C22⋊Dic132
C22×C4×D4×C132
C2×#239213