Finite Group Databasebeta

← Q8×#6790 #14482921

Subgroups — Q8×#6790 #14482921

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3C5×Q8×#67C211yesmaximal, characteristic, complemented
4C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
5#11755281C213yesmaximal, complemented
6Q8×#1203C211yesmaximal, characteristic, complemented
7Q8×#1202C211yesmaximal, characteristic, complemented
8Q8×#1200C211yesmaximal, characteristic, complemented
9#11755169C213yesmaximal, complemented
10#11755165C213yesmaximal, complemented
11#11755153C213yesmaximal, complemented
12C4×#6790C213yesmaximal
13#11754383C213yesmaximal, complemented
14#11754377C213yesmaximal, complemented
15#11754366C213yesmaximal, complemented
16D4×Q8×D5—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×Q8×D15—28no—
19C2×Q8×D15C2213yes—
20C2×Q8×D15C2211yescharacteristic
21C2×Q8×D15C2213yescomplemented
22C2×Q8×D15C2211yescharacteristic, complemented
23C22×C4×D15C2213yes—
24C22×Dic30C2213yescomplemented
25C2×C5×D3×Q8C2211yescharacteristic, complemented
26C2×C3×Q8×D5C2211yescharacteristic, complemented
27C2×#6790C2211yescharacteristic
28D3×Q8×D5—28no—
29C2×C4×D3×D5C2213yes—
30C2×D15⋊Q8C2213yes—
31C2×D3×Dic10C2213yescomplemented
32C2×D5×Dic6C2213yescomplemented
33C5×#946C2213yescomplemented
34C5×Q8×Dic3C2211yescharacteristic, complemented
35C5×#944C2213yescomplemented
36C4×C5×#67C2213yes—
37C5×#924C2213yescomplemented
38C3×#4092C2213yescomplemented
39C3×Q8×Dic5C2211yescharacteristic, complemented
40C3×#4090C2213yescomplemented
41C3×C4×C22⋊D5C2213yes—
42C3×#4070C2213yescomplemented
43#91576C2216yescomplemented
44#91561C2213yes—
45#67⋊Dic5C2213yes—
46#91559C2213yes—
47#91473C2213yes—
48C4×#1203C2213yes—
49C4×#1202C2213yes—
50#91437C2213yes—
51#91432C2216yescomplemented
52#91431C2216yescomplemented
53#91406C2213yes—
54#91404C2216yes—
55#91404C2213yes—
56C4×#1200C2213yes—
57#91396C2213yes—
58#91390C2213yescomplemented
59#91389C2213yescomplemented
60#91383C2213yescomplemented
61#91377C2216yescomplemented
62#91376C2213yescomplemented
63#91365C2213yescomplemented
64#91360C2213yescomplemented
65#91340C2213yescomplemented
66#91333C2213yescomplemented
67#91328C2216yescomplemented
68#91328C2216yescomplemented
69D3×D4×Q8—51nomaximal, Hall
70C22×Q8×D5—31no—
71C22×Q8×D5—31no—
72C5×D4×Q8—31no—
73Q8×C22⋊D5—31no—
74Q8×C22⋊D5D311yescharacteristic, complemented
75#66061—33no—
76D5×C4⋊Q8—33no—
77#65966—33no—
78#65966—33no—
79D5×C22⋊Q8—33no—
80D5×C22⋊Q8—33no—
81Q8×D20—31no—
82C4×Q8×D5—31no—
83C4×D4×D5—33no—
84D4×Dic10—33no—
85C23×D15C2311yescharacteristic
86C22×D3×D5C2311yescharacteristic
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C22×Dic15C2313yes—
92Q8×D15—24no—
93Q8×D15—212no—
94Q8×D15—212no—
95Q8×D15D418yescomplemented
96C2×C4×D15—212no—
97C2×C4×D15C2313yes—
98C2×C4×D15C2313yes—
99C2×C4×D15C2313yes—
100C2×C4×D15C2313yes—
101C2×Dic30—212no—
102C2×Dic30C2316yes—
103C2×Dic30C2313yes—
104C2×Dic30C2313yes—
105C2×C5×#67C2311yescharacteristic
106C5×D3×Q8—24no—
107C2×C4×C5×D3C2313yes—
108C2×C5×Dic6C2313yes—
109C2×C3×C22⋊D5C2311yescharacteristic
110C3×Q8×D5—24no—
111C2×C3×C4×D5C2313yes—
112C2×C3×Dic10C2313yes—
113#6790Q818yesdirect product factor
114C2×#1204C2316yes—
115C2×#1203C2311yescharacteristic
116C2×#1202C2311yescharacteristic
117C2×#1200C2313yes—
118C2×#1200C2313yes—
119C2×#1200C2311yescharacteristic
120C2×D3×Dic5C2313yes—
121C2×D5×Dic3C2313yes—
122C4×D3×D5—212no—
123D15⋊Q8—212no—
124D3×Dic10—212no—
125D5×Dic6—212no—
126C5×#217C2313yes—
127C5×(C2×D3)⋊C4C2313yes—
128C5×C4⋊Dic3C2313yes—
129C5×Dic3⋊C4C2313yes—
130C5×Dic3⋊C4C2316yes—
131C4×C5×Dic3C2313yes—
132C3×C22⋊Dic5C2313yes—
133C3×#685C2313yes—
134C3×C4⋊Dic5C2313yes—
135C3×#683C2313yes—
136C3×#683C2316yes—
137C3×C4×Dic5C2313yes—
138Dic3⋊Dic5C2316yes—
139Dic3⋊Dic5C2313yes—
140#6669C2316yes—
141#6668C2316yes—
142#6668C2313yes—
143#6667C2313yes—
144#6667C2313yes—
145(C2×D3)⋊Dic5C2313yes—
146#6665C2313yes—
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C22×D3×Q8—51no—
150C22×D3×Q8—51no—
151C3×D4×Q8—51no—
152Q8×#67—51no—
153Q8×#67D511yescharacteristic, complemented
154#5727—53no—
155D3×C4⋊Q8—53no—
156#5632—53no—
157#5632—53no—
158D3×C22⋊Q8—53no—
159D3×C22⋊Q8—53no—
160Q8×D12—51no—
161C4×D3×Q8—51no—
162C4×D3×D4—53no—
163D4×Dic6—53no—
164C22×C5×Q8—31no—
165C22×C5×Q8C2×D311yescharacteristic, complemented
166C2×Q8×D5—31no—
167C2×Q8×D5—33no—
168C2×Q8×D5—33no—
169C2×Q8×D5—31no—
170C2×Q8×D5—33no—
171C2×Q8×D5—33no—
172C2×Q8×D5—68no—
173C2×Q8×D5—68no—
174C2×Q8×D5C2×D311yescharacteristic, complemented
175C2×D4×D5—31no—
176C22×C4×D5—33no—
177C22×C4×D5—33no—
178C22×Dic10—33no—
179C22×Dic10—33no—
180C5×C4⋊Q8—33no—
181C5×C22⋊Q8—33no—
182C5×C22⋊Q8—33no—
183C4×C5×Q8—31no—
184C4×C5×D4—33no—
185#4092—33no—
186#4092C2×D313yescomplemented
187Q8×Dic5C2×D311yescharacteristic, complemented
188#4090—33no—
189#4090C2×D313yescomplemented
190D4×Dic5—33no—
191C4×C22⋊D5—33no—
192C4×C22⋊D5C2×D313yes—
193#4070—33no—
194#4070C2×D313yescomplemented
195#4043—33no—
196#4043—33no—
197#4042—36no—
198#4042—36no—
199#4039—33no—
200D5×C4⋊C4—33no—
201D5×C4⋊C4—33no—
202D5×C4⋊C4—36no—
203#4034—36no—
204#4034—36no—
205#4033—33no—
206#4027—33no—
207#4027—33no—
208D5×C22⋊C4—33no—
209D5×C22⋊C4—33no—
210#4024—36no—
211#4024—36no—
212C4×D20—33no—
213C42×D5—33no—
214#4015—33no—
215C4×Dic10—33no—
216C2×D4×Q8—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15—22no—
219C22×D15—22no—
220C22×D15C2×Q814yescomplemented
221C22×D15C2411yescharacteristic
222C22×D15C2411yescharacteristic
223C22×C5×D3C2411yescharacteristic
224C22×C3×D5C2411yescharacteristic
225C2×D3×D5—22no—
226C2×D3×D5—22no—
227C2×D3×D5C2×Q814yescomplemented
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2413yes—
232C2×C3×C4×C5C2413yes—
233C2×Dic15—26no—
234C2×Dic15C2413yes—
235C2×Dic15C2413yes—
236C4×D15—26no—
237C4×D15—26no—
238C4×D15—26no—
239C4×D15C2×D4112yes—
240Dic30—26no—
241Dic30—212no—
242Dic30C2×D4112yescomplemented
243C5×#67C2×Q814yescomplemented
244C2×C5×Dic3C2413yes—
245C2×C5×Dic3C2413yes—
246C2×C5×Dic3C2411yescharacteristic
247C4×C5×D3—26no—
248C5×Dic6—26no—
249C3×C22⋊D5C2×Q814yescomplemented
250C2×C3×Dic5C2413yes—
251C2×C3×Dic5C2413yes—
252C2×C3×Dic5C2411yescharacteristic
253C3×C4×D5—26no—
254C3×Dic10—26no—
255#1204—212no—
256#1203C2×Q814yescomplemented
257#1202C2×Q814yescomplemented
258#1200—26no—
259#1200—26no—
260#1200C2×Q814yescomplemented
261D3×Dic5—26no—
262D5×Dic3—26no—
263C22×C3×Q8—51no—
264C22×C3×Q8C2×D511yescharacteristic, complemented
265C2×D3×Q8—51no—
266C2×D3×Q8—53no—
267C2×D3×Q8—53no—
268C2×D3×Q8—51no—
269C2×D3×Q8—53no—
270C2×D3×Q8—53no—
271C2×D3×Q8—108no—
272C2×D3×Q8—108no—
273C2×D3×Q8C2×D511yescharacteristic, complemented
274C2×D3×D4—51no—
275C22×C4×D3—53no—
276C22×C4×D3—53no—
277C22×Dic6—53no—
278C22×Dic6—53no—
279C3×C4⋊Q8—53no—
280C3×C22⋊Q8—53no—
281C3×C22⋊Q8—53no—
282C3×C4×Q8—51no—
283C3×C4×D4—53no—
284#946—53no—
285#946C2×D513yescomplemented
286Q8×Dic3C2×D511yescharacteristic, complemented
287#944—53no—
288#944C2×D513yescomplemented
289D4×Dic3—53no—
290C4×#67—53no—
291C4×#67C2×D513yes—
292#924—53no—
293#924C2×D513yescomplemented
294#897—53no—
295#897—53no—
296#896—56no—
297#896—56no—
298#893—53no—
299D3×C4⋊C4—53no—
300D3×C4⋊C4—53no—
301D3×C4⋊C4—56no—
302#888—56no—
303#888—56no—
304#887—53no—
305#67⋊C4—53no—
306#67⋊C4—53no—
307D3×C22⋊C4—53no—
308D3×C22⋊C4—53no—
309#878—56no—
310#878—56no—
311C4×D12—53no—
312C42×D3—53no—
313#869—53no—
314C4×Dic6—53no—
315C23×D5—31no—
316C23×D5—31no—
317C2×C5×Q8—24no—
318C2×C5×Q8—33no—
319C2×C5×Q8—64no—
320C2×C5×Q8C22×D313yes—
321C2×C5×Q8C22×D311yescharacteristic
322C2×C5×D4—31no—
323C22×C4×C5—33no—
324C22×C4×C5C22×D313yes—
325C2×C22⋊D5—31no—
326C2×C22⋊D5C22×D311yescharacteristic
327C22×Dic5—33no—
328C22×Dic5—33no—
329Q8×D5—24no—
330Q8×D5—38no—
331Q8×D5—612no—
332Q8×D5—612no—
333Q8×D5—612no—
334Q8×D5—612no—
335Q8×D5—64no—
336D4×D5—38no—
337C2×D20—31no—
338C2×C4×D5—33no—
339C2×C4×D5—31no—
340C2×C4×D5—33no—
341C2×C4×D5—33no—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—33no—
346C2×C4×D5—612no—
347C2×C4×D5—612no—
348C2×C4×D5C22×D313yes—
349C2×Dic10—33no—
350C2×Dic10—33no—
351C2×Dic10—36no—
352C2×Dic10—36no—
353C2×Dic10—612no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4—33no—
358C5×C4⋊C4—36no—
359C5×C22⋊C4—33no—
360C5×C22⋊C4—33no—
361C42×C5—33no—
362C22⋊Dic5—33no—
363C22⋊Dic5C22×D313yes—
364#685—33no—
365#685—33no—
366#685—33no—
367#685C22×D313yes—
368C4⋊Dic5—33no—
369C4⋊Dic5—36no—
370C4⋊Dic5C22×D313yes—
371#683—36no—
372#683—33no—
373#683—36no—
374#683C22×D316yes—
375#683C22×D313yes—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5C22×D313yes—
379C23×Q8—151no—
380C23×Q8—151no—
381D4×Q8—31no—
382D4×Q8—51no—
383D4×Q8—153no—
384D4×Q8—153no—
385D4×Q8—151no—
386D4×Q8—151no—
387D4×Q8—153no—
388D4×Q8—153no—
389C2×C4⋊Q8—153no—
390C2×C22⋊Q8—153no—
391C2×C22⋊Q8—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5C22×Q812yescomplemented
397C22×C3×C5C2511yescharacteristic
398C2×D15—21no—
399C2×D15—21no—
400C2×D15—28no—
401C2×D15C22×D412yes—
402C2×D15C22×Q812yes—
403C2×D15C22×Q812yescomplemented
404C2×D152−1+412yes—
405C2×C5×D3—21no—
406C2×C5×D3—21no—
407C2×C5×D3C22×Q812yescomplemented
408C2×C3×D5—21no—
409C2×C3×D5—21no—
410C2×C3×D5C22×Q812yescomplemented
411D3×D5—28no—
412C3×C4×C5—23no—
413C3×C4×C5C22×D416yes—
414Dic15—23no—
415Dic15C22×D416yes—
416C3×Dic5—23no—
417C3×Dic5—23no—
418C3×Dic5C22×Q812yescomplemented
419C5×Dic3—23no—
420C5×Dic3—23no—
421C5×Dic3C22×Q812yescomplemented
422C23×D3—51no—
423C23×D3—51no—
424C2×C3×Q8—24no—
425C2×C3×Q8—53no—
426C2×C3×Q8—104no—
427C2×C3×Q8C22×D513yes—
428C2×C3×Q8C22×D511yescharacteristic
429C2×C3×D4—51no—
430C22×C3×C4—53no—
431C22×C3×C4C22×D513yes—
432C2×#67—51no—
433C2×#67C22×D511yescharacteristic
434C22×Dic3—53no—
435C22×Dic3—53no—
436D3×Q8—24no—
437D3×Q8—58no—
438D3×Q8—1012no—
439D3×Q8—1012no—
440D3×Q8—1012no—
441D3×Q8—1012no—
442D3×Q8—104no—
443D3×D4—58no—
444C2×D12—51no—
445C2×C4×D3—53no—
446C2×C4×D3—51no—
447C2×C4×D3—53no—
448C2×C4×D3—53no—
449C2×C4×D3—53no—
450C2×C4×D3—53no—
451C2×C4×D3—53no—
452C2×C4×D3—53no—
453C2×C4×D3—1012no—
454C2×C4×D3—1012no—
455C2×C4×D3C22×D513yes—
456C2×Dic6—53no—
457C2×Dic6—53no—
458C2×Dic6—56no—
459C2×Dic6—56no—
460C2×Dic6—1012no—
461C2×Dic6—1012no—
462C2×Dic6C22×D513yes—
463C3×C4⋊C4—53no—
464C3×C4⋊C4—56no—
465C3×C4⋊C4—53no—
466C3×C22⋊C4—53no—
467C3×C22⋊C4—53no—
468C3×C42—53no—
469#217—53no—
470#217C22×D513yes—
471(C2×D3)⋊C4—53no—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4C22×D513yes—
475C4⋊Dic3—53no—
476C4⋊Dic3—56no—
477C4⋊Dic3C22×D513yes—
478Dic3⋊C4—56no—
479Dic3⋊C4—56no—
480Dic3⋊C4—53no—
481Dic3⋊C4C22×D516yes—
482Dic3⋊C4C22×D513yes—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3C22×D513yes—
486C23×C5—31no—
487C23×C5C23×D311yescharacteristic
488C22×D5—31no—
489C22×D5—34no—
490C22×D5—31no—
491C22×D5—34no—
492C22×D5—62no—
493C22×D5—62no—
494C22×D5—62no—
495C22×D5—62no—
496C22×D5C23×D311yescharacteristic
497C5×Q8—26no—
498C5×Q8—66no—
499C5×Q8D3×D414yescomplemented
500C5×D4—34no—
501C2×C4×C5—26no—
502C2×C4×C5—31no—
503C2×C4×C5—33no—
504C2×C4×C5—33no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D313yes—
508C22⋊D5—34no—
509C22⋊D5D3×Q814yescomplemented
510C2×Dic5—33no—
511C2×Dic5—33no—
512C2×Dic5—66no—
513C2×Dic5—66no—
514C2×Dic5C23×D313yes—
515C2×Dic5C23×D313yes—
516C2×Dic5C23×D311yescharacteristic
517D20—34no—
518C4×D5—26no—
519C4×D5—312no—
520C4×D5—34no—
521C4×D5—66no—
522C4×D5—66no—
523C4×D5—66no—
524C4×D5—66no—
525C4×D5—66no—
526C4×D5—66no—
527Dic10—26no—
528Dic10—312no—
529Dic10—612no—
530Dic10—612no—
531Dic10—66no—
532C22×Q8—31no—
533C22×Q8—51no—
534C22×Q8—153no—
535C22×Q8—153no—
536C22×Q8—153no—
537C22×Q8—151no—
538C22×Q8—153no—
539C22×Q8—153no—
540C22×Q8—151no—
541C22×Q8—153no—
542C22×Q8—308no—
543C22×Q8—308no—
544C22×Q8D3×D511yescharacteristic, complemented
545C22×D4—151no—
546C23×C4—153no—
547C23×C4—153no—
548C4⋊Q8—33no—
549C4⋊Q8—53no—
550C4⋊Q8—153no—
551C4⋊Q8—153no—
552C4⋊Q8—156no—
553C4⋊Q8—156no—
554C22⋊Q8—33no—
555C22⋊Q8—33no—
556C22⋊Q8—53no—
557C22⋊Q8—53no—
558C22⋊Q8—156no—
559C22⋊Q8—156no—
560C22⋊Q8—156no—
561C22⋊Q8—156no—
562C22⋊Q8—153no—
563C22⋊Q8—153no—
564C22⋊Q8—153no—
565C22⋊Q8—153no—
566C4×Q8—31no—
567C4×Q8—51no—
568C4×Q8—153no—
569C4×Q8—153no—
570C4×D4—33no—
571C4×D4—53no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C2×C4⋊C4—153no—
579C2×C4⋊C4—153no—
580C2×C4⋊C4—156no—
581C2×C22⋊C4—153no—
582C2×C22⋊C4—153no—
583C2×C42—153no—
584C2×C3×C5—22no—
585C2×C3×C5C23×D411yescharacteristic
586C2×C3×C5C23×Q811yescharacteristic
587C2×C3×C5C2×2−1+411yescharacteristic
588D15—22no—
589D15D4×Q814yescomplemented
590C3×D5—22no—
591C5×D3—22no—
592C23×C3—51no—
593C23×C3C23×D511yescharacteristic
594C22×D3—51no—
595C22×D3—54no—
596C22×D3—51no—
597C22×D3—54no—
598C22×D3—102no—
599C22×D3—102no—
600C22×D3—102no—
601C22×D3—102no—
602C22×D3C23×D511yescharacteristic
603C3×Q8—26no—
604C3×Q8—106no—
605C3×Q8D4×D514yescomplemented
606C3×D4—54no—
607C2×C3×C4—26no—
608C2×C3×C4—51no—
609C2×C3×C4—53no—
610C2×C3×C4—53no—
611C2×C3×C4—106no—
612C2×C3×C4C23×D513yes—
613C2×C3×C4C23×D513yes—
614#67—54no—
615#67Q8×D514yescomplemented
616C2×Dic3—53no—
617C2×Dic3—53no—
618C2×Dic3—106no—
619C2×Dic3—106no—
620C2×Dic3C23×D513yes—
621C2×Dic3C23×D513yes—
622C2×Dic3C23×D511yescharacteristic
623D12—54no—
624C4×D3—26no—
625C4×D3—512no—
626C4×D3—54no—
627C4×D3—106no—
628C4×D3—106no—
629C4×D3—106no—
630C4×D3—106no—
631C4×D3—106no—
632C4×D3—106no—
633Dic6—26no—
634Dic6—512no—
635Dic6—1012no—
636Dic6—1012no—
637Dic6—106no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—32no—
641C22×C5—61no—
642C22×C5—61no—
643C22×C5C2×D3×Q812yescomplemented
644C22×C5C24×D311yescharacteristic
645C2×D5—21no—
646C2×D5—21no—
647C2×D5—32no—
648C2×D5—32no—
649C2×D5—32no—
650C2×D5—32no—
651C2×D5—68no—
652C2×D5—68no—
653C2×D5—61no—
654C2×D5—61no—
655C2×D5C2×D3×Q812yescomplemented
656C4×C5—23no—
657C4×C5—32no—
658C4×C5—63no—
659C4×C5—63no—
660C4×C5C2×D3×D416yes—
661Dic5—23no—
662Dic5—23no—
663Dic5—36no—
664Dic5—63no—
665Dic5C2×D3×Q812yescomplemented
666C24—151no—
667C24—151no—
668C2×Q8—24no—
669C2×Q8—33no—
670C2×Q8—53no—
671C2×Q8—64no—
672C2×Q8—104no—
673C2×Q8—156no—
674C2×Q8—158no—
675C2×Q8—153no—
676C2×Q8—156no—
677C2×Q8—153no—
678C2×Q8—3012no—
679C2×Q8—3012no—
680C2×Q8—3012no—
681C2×Q8—3012no—
682C2×Q8—3012no—
683C2×Q8—3012no—
684C2×Q8—304no—
685C2×Q8C2×D3×D513yes—
686C2×Q8C2×D3×D511yescharacteristic
687C2×D4—31no—
688C2×D4—51no—
689C2×D4—151no—
690C2×D4—151no—
691C2×D4—158no—
692C22×C4—33no—
693C22×C4—53no—
694C22×C4—151no—
695C22×C4—153no—
696C22×C4—153no—
697C22×C4—153no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—153no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—3012no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—33no—
708C4⋊C4—33no—
709C4⋊C4—36no—
710C4⋊C4—53no—
711C4⋊C4—53no—
712C4⋊C4—56no—
713C4⋊C4—153no—
714C4⋊C4—153no—
715C4⋊C4—156no—
716C4⋊C4—156no—
717C4⋊C4—156no—
718C22⋊C4—33no—
719C22⋊C4—33no—
720C22⋊C4—53no—
721C22⋊C4—53no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—153no—
725C22⋊C4—153no—
726C42—33no—
727C42—53no—
728C42—153no—
729C42—153no—
730C3×C5C2×D4×Q811yescharacteristic, complemented, Hall
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—52no—
734C22×C3—101no—
735C22×C3—101no—
736C22×C3C2×Q8×D512yescomplemented
737C22×C3C24×D511yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—52no—
741C2×D3—52no—
742C2×D3—52no—
743C2×D3—52no—
744C2×D3—108no—
745C2×D3—108no—
746C2×D3—101no—
747C2×D3—101no—
748C2×D3C2×Q8×D512yescomplemented
749C3×C4—23no—
750C3×C4—52no—
751C3×C4—103no—
752C3×C4—103no—
753C3×C4C2×D4×D516yes—
754Dic3—23no—
755Dic3—23no—
756Dic3—56no—
757Dic3—103no—
758Dic3C2×Q8×D512yescomplemented
759C2×C5—22no—
760C2×C5—62no—
761C2×C5C22×D3×D411yescharacteristic
762C2×C5C22×D3×Q811yescharacteristic
763C2×C5D3×2−1+411yescharacteristic
764D5—22no—
765D5—34no—
766D5—62no—
767C23—31no—
768C23—51no—
769C23—154no—
770C23—151no—
771C23—154no—
772C23—151no—
773C23—302no—
774C23—302no—
775C23—302no—
776C23—302no—
777C23C22×D3×D511yescharacteristic
778Q8—26no—
779Q8—66no—
780Q8—106no—
781Q8—1512no—
782Q8—3012no—
783Q8—3012no—
784Q8—306no—
785Q8#679014yesdirect product factor
786D4—34no—
787D4—54no—
788D4—154no—
789D4—154no—
790C2×C4—26no—
791C2×C4—31no—
792C2×C4—33no—
793C2×C4—33no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—53no—
797C2×C4—66no—
798C2×C4—106no—
799C2×C4—154no—
800C2×C4—153no—
801C2×C4—1512no—
802C2×C4—153no—
803C2×C4—306no—
804C2×C4—306no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4C22×D3×D513yes—
812C2×C4C22×D3×D513yes—
813C2×C3—22no—
814C2×C3—102no—
815C2×C3C22×D4×D511yescharacteristic
816C2×C3C22×Q8×D511yescharacteristic
817C2×C3D5×2−1+411yescharacteristic
818D3—22no—
819D3—54no—
820D3—102no—
821C5D3×D4×Q811yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—32no—
825C22—52no—
826C22—61no—
827C22—61no—
828C22—101no—
829C22—101no—
830C22—152no—
831C22—152no—
832C22—152no—
833C22—152no—
834C22—308no—
835C22—308no—
836C22—301no—
837C22—301no—
838C22D3×Q8×D512yescomplemented
839C22C23×D3×D511yescharacteristic
840C4—23no—
841C4—32no—
842C4—52no—
843C4—63no—
844C4—63no—
845C4—103no—
846C4—103no—
847C4—156no—
848C4—303no—
849C4C2×#679016yes—
850C3D4×Q8×D511yescharacteristic, complemented, Sylow
851C2—22no—
852C2—62no—
853C2—102no—
854C2—154no—
855C2—302no—
856C2C2×D3×Q8×D511yescharacteristic
857C2#1175704711yescharacteristic
858C2C22×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
prime radicalC2×#6790C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×D4×Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D15C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. C5×Q8×#67C2semidirect
4. C3×Q8×C22⋊D5C2semidirect
5. #11755281C2semidirect
6. Q8×#1203C2semidirect
7. Q8×#1202C2semidirect
8. Q8×#1200C2semidirect
9. #11755169C2semidirect
10. #11755165C2semidirect
11. #11755153C2semidirect
13. #11754383C2semidirect
14. #11754377C2semidirect
15. #11754366C2semidirect
17. C22×C3×C5×Q8C22semidirect
21. C2×Q8×D15C22semidirect
22. C2×Q8×D15C22semidirect
24. C22×Dic30C22semidirect
25. C2×C5×D3×Q8C22semidirect
26. C2×C3×Q8×D5C22semidirect
31. C2×D3×Dic10C22semidirect
32. C2×D5×Dic6C22semidirect
33. C5×#946C22semidirect
34. C5×Q8×Dic3C22semidirect
35. C5×#944C22semidirect
37. C5×#924C22semidirect
38. C3×#4092C22semidirect
39. C3×Q8×Dic5C22semidirect
40. C3×#4090C22semidirect
42. C3×#4070C22semidirect
43. #91576C22semidirect
51. #91432C22semidirect
52. #91431C22semidirect
58. #91390C22semidirect
59. #91389C22semidirect
60. #91383C22semidirect
61. #91377C22semidirect
62. #91376C22semidirect
63. #91365C22semidirect
64. #91360C22semidirect
65. #91340C22semidirect
66. #91333C22semidirect
67. #91328C22semidirect
68. #91328C22semidirect
74. Q8×C22⋊D5D3semidirect
95. Q8×D15D4semidirect
113. #6790Q8direct (N × H)
153. Q8×#67D5semidirect
165. C22×C5×Q8C2×D3semidirect
174. C2×Q8×D5C2×D3semidirect
186. #4092C2×D3semidirect
187. Q8×Dic5C2×D3semidirect
189. #4090C2×D3semidirect
194. #4070C2×D3semidirect
220. C22×D15C2×Q8semidirect
227. C2×D3×D5C2×Q8semidirect
229. C3×C5×Q8C2×D4semidirect
242. Dic30C2×D4semidirect
243. C5×#67C2×Q8semidirect
249. C3×C22⋊D5C2×Q8semidirect
256. #1203C2×Q8semidirect
257. #1202C2×Q8semidirect
260. #1200C2×Q8semidirect
264. C22×C3×Q8C2×D5semidirect
273. C2×D3×Q8C2×D5semidirect
285. #946C2×D5semidirect
286. Q8×Dic3C2×D5semidirect
288. #944C2×D5semidirect
293. #924C2×D5semidirect
396. C22×C3×C5C22×Q8semidirect
403. C2×D15C22×Q8semidirect
407. C2×C5×D3C22×Q8semidirect
410. C2×C3×D5C22×Q8semidirect
418. C3×Dic5C22×Q8semidirect
421. C5×Dic3C22×Q8semidirect
499. C5×Q8D3×D4semidirect
509. C22⋊D5D3×Q8semidirect
544. C22×Q8D3×D5semidirect
589. D15D4×Q8semidirect
605. C3×Q8D4×D5semidirect
615. #67Q8×D5semidirect
643. C22×C5C2×D3×Q8semidirect
655. C2×D5C2×D3×Q8semidirect
665. Dic5C2×D3×Q8semidirect
730. C3×C5C2×D4×Q8semidirect
736. C22×C3C2×Q8×D5semidirect
748. C2×D3C2×Q8×D5semidirect
758. Dic3C2×Q8×D5semidirect
785. Q8#6790direct (N × H)
821. C5D3×D4×Q8semidirect
838. C22D3×Q8×D5semidirect
850. C3D4×Q8×D5semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C2×D3×Q8×D52
C5×Q8×#672
C3×Q8×C22⋊D52
#117552812
Q8×#12032
Q8×#12022
Q8×#12002
#117551692
#117551652
#117551532
C4×#67902
#117543832
#117543772
#117543662
D4×Q8×D53
D3×D4×Q85