Finite Group Databasebeta

← D3×Q8×C22⋊D5 #14482922

Subgroups — D3×Q8×C22⋊D5 #14482922

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×C5×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3Q8×#1220C211yesmaximal, characteristic, complemented
4C3×Q8×C22⋊D5C211yesmaximal, characteristic, complemented
5D3×#4092C213yesmaximal, complemented
6Q8×#1203C211yesmaximal, characteristic, complemented
7Q8×#1201C211yesmaximal, characteristic, complemented
8#11755235C213yesmaximal, complemented
9#11755229C213yesmaximal, complemented
10D3×Q8×Dic5C211yesmaximal, characteristic, complemented
11D3×#4090C213yesmaximal, complemented
12C4×D3×C22⋊D5C213yesmaximal
13#11754354C213yesmaximal, complemented
14D3×#4070C213yesmaximal, complemented
15Dic6×C22⋊D5C213yesmaximal, complemented
16C2×Q8×C22⋊D5—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×D3×Q8—28no—
20C2×C5×D3×Q8C2213yes—
21C2×C5×D3×Q8C2211yescharacteristic
22C2×C5×D3×Q8C2213yescomplemented
23C2×C5×D3×Q8C2211yescharacteristic, complemented
24C22×C4×C5×D3C2213yes—
25C22×C5×Dic6C2213yescomplemented
26C2×C3×Q8×D5C2211yescharacteristic, complemented
27C2×D3×C22⋊D5C2211yescharacteristic
28D3×Q8×D5—28no—
29C2×C4×D3×D5C2213yes—
30C2×D15⋊Q8C2213yescomplemented
31C2×D3×Dic10C2213yes—
32C2×D5×Dic6C2213yescomplemented
33#91835C2213yescomplemented
34Q8×Dic15C2211yescharacteristic, complemented
35#91833C2213yescomplemented
36C4×#1220C2213yes—
37#91813C2213yescomplemented
38C3×#4092C2213yescomplemented
39C3×Q8×Dic5C2211yescharacteristic, complemented
40C3×#4090C2213yescomplemented
41C3×C4×C22⋊D5C2213yes—
42C3×#4070C2213yescomplemented
43#91575C2216yescomplemented
44#91556C2213yes—
45D3×C22⋊Dic5C2213yes—
46Dic3×C22⋊D5C2213yes—
47D3×#685C2213yes—
48#91446C2213yes—
49C4×#1203C2213yes—
50#91441C2213yes—
51C4×#1201C2213yes—
52D3×C4⋊Dic5C2213yes—
53#91424C2216yescomplemented
54#91421C2216yescomplemented
55D3×#683C2216yes—
56D3×#683C2213yes—
57C4×D3×Dic5C2213yes—
58#91385C2213yescomplemented
59#91383C2213yescomplemented
60#91376C2213yescomplemented
61#91369C2213yescomplemented
62#91365C2213yescomplemented
63#91359C2213yescomplemented
64#91352C2216yescomplemented
65#91344C2213yescomplemented
66Dic5×Dic6C2213yescomplemented
67#91329C2216yescomplemented
68#91329C2216yescomplemented
69D3×D4×Q8—51nomaximal, Hall
70C23×C5×Q8—31no—
71C22×Q8×D5—31no—
72Q8×C22⋊D5—33no—
73Q8×C22⋊D5—31no—
74Q8×C22⋊D5—33no—
75Q8×C22⋊D5—33no—
76Q8×C22⋊D5—33no—
77Q8×C22⋊D5—31no—
78Q8×C22⋊D5—31no—
79Q8×C22⋊D5D311yescharacteristic, direct product factor
80C2×#4092—33no—
81C2×Q8×Dic5—31no—
82C2×#4090—33no—
83C2×C4×C22⋊D5—33no—
84C2×#4070—33no—
85C23×C5×D3C2311yescharacteristic
86C22×D3×D5C2311yescharacteristic
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C2×#1220C2311yescharacteristic
92Q8×D15—24no—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C22×C5×Dic3C2313yes—
96C5×D3×Q8—24no—
97C5×D3×Q8—212no—
98C5×D3×Q8—212no—
99C5×D3×Q8D418yescomplemented
100C2×C4×C5×D3—212no—
101C2×C4×C5×D3C2313yes—
102C2×C4×C5×D3C2313yes—
103C2×C4×C5×D3C2313yes—
104C2×C4×C5×D3C2313yes—
105C2×C5×Dic6—212no—
106C2×C5×Dic6C2316yes—
107C2×C5×Dic6C2313yes—
108C2×C5×Dic6C2313yes—
109C2×C3×C22⋊D5C2311yescharacteristic
110C3×Q8×D5—24no—
111C2×C3×C4×D5C2313yes—
112C2×C3×Dic10C2313yes—
113D3×C22⋊D5Q818yesdirect product factor
114C2×#1204C2316yes—
115C2×#1203C2311yescharacteristic
116C2×#1201C2311yescharacteristic
117C2×#1200C2313yes—
118C2×D3×Dic5C2313yes—
119C2×D3×Dic5C2313yes—
120C2×D3×Dic5C2311yescharacteristic
121C2×D5×Dic3C2313yes—
122C4×D3×D5—212no—
123D15⋊Q8—212no—
124D3×Dic10—212no—
125D5×Dic6—212no—
126#6719C2313yes—
127#6714C2313yes—
128C4⋊Dic15C2313yes—
129#6712C2316yes—
130#6712C2313yes—
131C4×Dic15C2313yes—
132C3×C22⋊Dic5C2313yes—
133C3×#685C2313yes—
134C3×C4⋊Dic5C2313yes—
135C3×#683C2313yes—
136C3×#683C2316yes—
137C3×C4×Dic5C2313yes—
138Dic3⋊Dic5C2316yes—
139#6669C2316yes—
140#6669C2313yes—
141#6668C2316yes—
142#6668C2313yes—
143#6667C2313yes—
144(C2×D3)⋊Dic5C2313yes—
145(C2×D3)⋊Dic5C2313yes—
146#6665C2313yes—
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C22×D3×Q8—51no—
150C22×D3×Q8D511yescharacteristic, complemented
151C3×D4×Q8—51no—
152Q8×#67—51no—
153Q8×#67—51no—
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×Q8—33no—
166C22×C5×Q8—33no—
167C22×C5×Q8—31no—
168C22×C5×Q8—33no—
169C22×C5×Q8—68no—
170C22×C5×Q8C2×D311yescharacteristic, complemented
171C23×C4×C5—33no—
172C22×C22⋊D5—31no—
173C2×Q8×D5—31no—
174C2×Q8×D5—33no—
175C2×Q8×D5—33no—
176C2×Q8×D5—68no—
177C2×Q8×D5C2×D311yescharacteristic, complemented
178C22×C4×D5—33no—
179C22×Dic10—33no—
180C2×C22⋊Dic5—33no—
181#4092—33no—
182#4092—33no—
183#4092—36no—
184#4092—33no—
185#4092—36no—
186#4092C2×D313yescomplemented
187Q8×Dic5—31no—
188Q8×Dic5—33no—
189Q8×Dic5—33no—
190Q8×Dic5C2×D311yescharacteristic, complemented
191#4090—33no—
192#4090—33no—
193#4090—36no—
194#4090—36no—
195#4090—33no—
196#4090C2×D313yescomplemented
197C4×C22⋊D5—33no—
198C4×C22⋊D5—33no—
199C4×C22⋊D5—33no—
200C4×C22⋊D5—33no—
201C4×C22⋊D5—33no—
202C4×C22⋊D5—33no—
203C4×C22⋊D5—33no—
204C4×C22⋊D5C2×D313yes—
205C2×#685—33no—
206C2×C4⋊Dic5—33no—
207#4070—33no—
208#4070—33no—
209#4070—36no—
210#4070—33no—
211#4070—36no—
212#4070C2×D313yescomplemented
213C2×#683—36no—
214C2×#683—33no—
215C2×C4×Dic5—33no—
216C2×D4×Q8—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15C2411yescharacteristic
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3C2×Q814yescomplemented
222C22×C5×D3C2411yescharacteristic
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—
233#1220C2×Q814yescomplemented
234C2×Dic15C2413yes—
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237C4×D15—26no—
238Dic30—26no—
239C2×C5×Dic3—26no—
240C2×C5×Dic3C2413yes—
241C2×C5×Dic3C2413yes—
242C4×C5×D3—26no—
243C4×C5×D3—26no—
244C4×C5×D3—26no—
245C4×C5×D3C2×D4112yes—
246C5×Dic6—26no—
247C5×Dic6—212no—
248C5×Dic6C2×D4112yescomplemented
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#1201C2×Q814yescomplemented
258#1200—26no—
259D3×Dic5—26no—
260D3×Dic5—26no—
261D3×Dic5C2×Q814yescomplemented
262D5×Dic3—26no—
263C22×C3×Q8—51no—
264C22×C3×Q8C2×D511yescharacteristic, complemented
265C2×D3×Q8—28no—
266C2×D3×Q8—51no—
267C2×D3×Q8—53no—
268C2×D3×Q8—53no—
269C2×D3×Q8—108no—
270C2×D3×Q8C2×D513yes—
271C2×D3×Q8C2×D511yescharacteristic
272C2×D3×Q8C2×D513yescomplemented
273C2×D3×Q8C2×D511yescharacteristic, complemented
274C2×D3×D4—51no—
275C22×C4×D3—53no—
276C22×C4×D3C2×D513yes—
277C22×Dic6—53no—
278C22×Dic6C2×D513yescomplemented
279C3×C4⋊Q8—53no—
280C3×C22⋊Q8—53no—
281C3×C22⋊Q8—53no—
282C3×C4×Q8—51no—
283C3×C4×D4—53no—
284#946—53no—
285#946—53no—
286Q8×Dic3—51no—
287#944—53no—
288#944—53no—
289D4×Dic3—53no—
290C4×#67—53no—
291C4×#67—53no—
292#924—53no—
293#924—53no—
294#897—53no—
295#897—53no—
296#896—56no—
297#896—56no—
298#893—53no—
299D3×C4⋊C4—53no—
300D3×C4⋊C4—56no—
301D3×C4⋊C4—53no—
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—
315C24×C5—31no—
316C23×D5—31no—
317C2×C5×Q8—24no—
318C2×C5×Q8—38no—
319C2×C5×Q8—33no—
320C2×C5×Q8—36no—
321C2×C5×Q8—33no—
322C2×C5×Q8—612no—
323C2×C5×Q8—612no—
324C2×C5×Q8—612no—
325C2×C5×Q8—64no—
326C2×C5×Q8C22×D313yes—
327C2×C5×Q8C22×D311yescharacteristic
328C22×C4×C5—33no—
329C22×C4×C5—33no—
330C22×C4×C5—33no—
331C22×C4×C5—33no—
332C22×C4×C5—33no—
333C22×C4×C5—612no—
334C22×C4×C5C22×D313yes—
335C2×C22⋊D5—31no—
336C2×C22⋊D5—31no—
337C2×C22⋊D5—38no—
338C2×C22⋊D5—31no—
339C2×C22⋊D5C22×D311yescharacteristic
340C22×Dic5—31no—
341C22×Dic5—33no—
342C22×Dic5—33no—
343Q8×D5—24no—
344Q8×D5—612no—
345Q8×D5—612no—
346Q8×D5—64no—
347C2×C4×D5—33no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—612no—
351C2×C4×D5C22×D313yes—
352C2×Dic10—33no—
353C2×Dic10—36no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C22⋊Dic5—33no—
357C22⋊Dic5—33no—
358C22⋊Dic5—33no—
359C22⋊Dic5C22×D313yes—
360#685—33no—
361#685—33no—
362#685—33no—
363#685C22×D313yes—
364C4⋊Dic5—33no—
365C4⋊Dic5—36no—
366C4⋊Dic5C22×D313yes—
367#683—36no—
368#683—33no—
369#683—36no—
370#683—33no—
371#683—36no—
372#683—33no—
373#683C22×D316yes—
374#683C22×D313yes—
375C4×Dic5—33no—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5C22×D313yes—
379C23×Q8—31no—
380C23×Q8—151no—
381D4×Q8—51no—
382D4×Q8—153no—
383D4×Q8—151no—
384D4×Q8—153no—
385D4×Q8—153no—
386D4×Q8—153no—
387D4×Q8—151no—
388D4×Q8—151no—
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×D15C22×Q812yescomplemented
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3—28no—
404C2×C5×D3C22×D412yes—
405C2×C5×D3C22×Q812yes—
406C2×C5×D3C22×Q812yescomplemented
407C2×C5×D32−1+412yes—
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—
415Dic15—23no—
416Dic15C22×Q812yescomplemented
417C3×Dic5—23no—
418C3×Dic5—23no—
419C3×Dic5C22×Q812yescomplemented
420C5×Dic3—23no—
421C5×Dic3C22×D416yes—
422C23×D3—51no—
423C23×D3C22×D511yescharacteristic
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×#67—51no—
434C22×Dic3—53no—
435C22×Dic3C22×D513yes—
436D3×Q8—24no—
437D3×Q8—212no—
438D3×Q8—212no—
439D3×Q8—104no—
440D3×Q8—1012no—
441D3×Q8—1012no—
442D3×Q8C22⋊D518yesdirect product factor
443D3×D4—58no—
444C2×D12—51no—
445C2×C4×D3—212no—
446C2×C4×D3—51no—
447C2×C4×D3—53no—
448C2×C4×D3—53no—
449C2×C4×D3—53no—
450C2×C4×D3—53no—
451C2×C4×D3—1012no—
452C2×C4×D3C22×D513yes—
453C2×C4×D3C22×D513yes—
454C2×C4×D3C22×D513yes—
455C2×C4×D3C22×D513yes—
456C2×Dic6—212no—
457C2×Dic6—53no—
458C2×Dic6—56no—
459C2×Dic6—1012no—
460C2×Dic6C22×D513yes—
461C2×Dic6C22×D516yes—
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#217—53no—
471(C2×D3)⋊C4—53no—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—53no—
475C4⋊Dic3—53no—
476C4⋊Dic3—53no—
477C4⋊Dic3—56no—
478Dic3⋊C4—56no—
479Dic3⋊C4—53no—
480Dic3⋊C4—56no—
481Dic3⋊C4—53no—
482Dic3⋊C4—56no—
483C4×Dic3—53no—
484C4×Dic3—53no—
485C4×Dic3—53no—
486C23×C5—31no—
487C23×C5—34no—
488C23×C5—31no—
489C23×C5—62no—
490C23×C5—62no—
491C23×C5C23×D311yescharacteristic
492C22×D5—31no—
493C22×D5—34no—
494C22×D5—62no—
495C22×D5—62no—
496C22×D5C23×D311yescharacteristic
497C5×Q8—26no—
498C5×Q8—312no—
499C5×Q8—612no—
500C5×Q8—66no—
501C5×Q8D3×D414yescomplemented
502C2×C4×C5—26no—
503C2×C4×C5—33no—
504C2×C4×C5—312no—
505C2×C4×C5—33no—
506C2×C4×C5—66no—
507C2×C4×C5—66no—
508C2×C4×C5—66no—
509C2×C4×C5—66no—
510C2×C4×C5C23×D313yes—
511C2×C4×C5C23×D313yes—
512C22⋊D5—34no—
513C22⋊D5—34no—
514C22⋊D5—34no—
515C22⋊D5D3×Q814yesdirect product factor
516C2×Dic5—31no—
517C2×Dic5—34no—
518C2×Dic5—33no—
519C2×Dic5—33no—
520C2×Dic5—66no—
521C2×Dic5—66no—
522C2×Dic5C23×D313yes—
523C2×Dic5C23×D313yes—
524C2×Dic5C23×D311yescharacteristic
525C4×D5—26no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5—66no—
529Dic10—26no—
530Dic10—612no—
531Dic10—66no—
532C22×Q8—31no—
533C22×Q8—33no—
534C22×Q8—33no—
535C22×Q8—31no—
536C22×Q8—33no—
537C22×Q8—51no—
538C22×Q8—68no—
539C22×Q8—153no—
540C22×Q8—153no—
541C22×Q8—153no—
542C22×Q8—151no—
543C22×Q8—308no—
544C22×Q8D3×D511yescharacteristic, complemented
545C22×D4—151no—
546C23×C4—33no—
547C23×C4—153no—
548C4⋊Q8—53no—
549C4⋊Q8—153no—
550C4⋊Q8—156no—
551C4⋊Q8—156no—
552C4⋊Q8—153no—
553C4⋊Q8—153no—
554C22⋊Q8—53no—
555C22⋊Q8—53no—
556C22⋊Q8—156no—
557C22⋊Q8—156no—
558C22⋊Q8—156no—
559C22⋊Q8—153no—
560C22⋊Q8—156no—
561C22⋊Q8—153no—
562C22⋊Q8—153no—
563C22⋊Q8—153no—
564C22⋊Q8—153no—
565C22⋊Q8—153no—
566C4×Q8—51no—
567C4×Q8—153no—
568C4×Q8—153no—
569C4×Q8—151no—
570C4×D4—53no—
571C4×D4—153no—
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—
589C3×D5—22no—
590C5×D3—22no—
591C5×D3D4×Q814yescomplemented
592C23×C3—51no—
593C23×C3C23×D511yescharacteristic
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—51no—
597C22×D3—54no—
598C22×D3—102no—
599C22×D3—102no—
600C22×D3Q8×D514yescomplemented
601C22×D3C23×D511yescharacteristic
602C22×D3C23×D511yescharacteristic
603C3×Q8—26no—
604C3×Q8—106no—
605C3×Q8C2×C22⋊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#67—54no—
616C2×Dic3—26no—
617C2×Dic3—51no—
618C2×Dic3—53no—
619C2×Dic3—53no—
620C2×Dic3—106no—
621C2×Dic3C23×D513yes—
622C2×Dic3C23×D513yes—
623D12—54no—
624C4×D3—26no—
625C4×D3—26no—
626C4×D3—26no—
627C4×D3—54no—
628C4×D3—106no—
629C4×D3—106no—
630C4×D3—106no—
631C4×D3—106no—
632C4×D3C2×C22⋊D5112yes—
633Dic6—26no—
634Dic6—212no—
635Dic6—106no—
636Dic6—1012no—
637Dic6C2×C22⋊D5112yescomplemented
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—32no—
641C22×C5—32no—
642C22×C5—32no—
643C22×C5—32no—
644C22×C5—68no—
645C22×C5—61no—
646C22×C5—61no—
647C22×C5C2×D3×Q812yescomplemented
648C22×C5C24×D311yescharacteristic
649C2×D5—21no—
650C2×D5—21no—
651C2×D5—32no—
652C2×D5—68no—
653C2×D5—61no—
654C2×D5—61no—
655C2×D5C2×D3×Q812yescomplemented
656C4×C5—23no—
657C4×C5—36no—
658C4×C5—63no—
659C4×C5C2×D3×D416yes—
660Dic5—23no—
661Dic5—23no—
662Dic5—32no—
663Dic5—63no—
664Dic5—63no—
665Dic5C2×D3×Q812yescomplemented
666C24—31no—
667C24—151no—
668C2×Q8—24no—
669C2×Q8—38no—
670C2×Q8—33no—
671C2×Q8—36no—
672C2×Q8—33no—
673C2×Q8—53no—
674C2×Q8—612no—
675C2×Q8—612no—
676C2×Q8—612no—
677C2×Q8—64no—
678C2×Q8—104no—
679C2×Q8—156no—
680C2×Q8—153no—
681C2×Q8—3012no—
682C2×Q8—3012no—
683C2×Q8—3012no—
684C2×Q8—304no—
685C2×Q8C2×D3×D513yes—
686C2×Q8C2×D3×D511yescharacteristic
687C2×D4—51no—
688C2×D4—151no—
689C2×D4—158no—
690C2×D4—151no—
691C2×D4—151no—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—33no—
695C22×C4—33no—
696C22×C4—33no—
697C22×C4—53no—
698C22×C4—612no—
699C22×C4—153no—
700C22×C4—153no—
701C22×C4—151no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—53no—
708C4⋊C4—53no—
709C4⋊C4—56no—
710C4⋊C4—153no—
711C4⋊C4—153no—
712C4⋊C4—156no—
713C4⋊C4—156no—
714C4⋊C4—156no—
715C4⋊C4—153no—
716C4⋊C4—153no—
717C4⋊C4—156no—
718C22⋊C4—53no—
719C22⋊C4—53no—
720C22⋊C4—153no—
721C22⋊C4—153no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—153no—
725C22⋊C4—153no—
726C42—53no—
727C42—153no—
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—28no—
741C2×D3—52no—
742C2×D3—101no—
743C2×D3—101no—
744C2×D3—108no—
745C2×D3C2×Q8×D512yes—
746C2×D3C2×Q8×D512yescomplemented
747C2×D3#414712yes—
748C2×D3C22×C22⋊D512yes—
749C3×C4—23no—
750C3×C4—52no—
751C3×C4—103no—
752C3×C4—103no—
753C3×C4C22×C22⋊D516yes—
754Dic3—23no—
755Dic3—52no—
756Dic3—103no—
757Dic3—103no—
758Dic3C22×C22⋊D516yes—
759C2×C5—22no—
760C2×C5—34no—
761C2×C5—62no—
762C2×C5C22×D3×D411yescharacteristic
763C2×C5C22×D3×Q811yescharacteristic
764C2×C5D3×2−1+411yescharacteristic
765D5—22no—
766D5—62no—
767C23—31no—
768C23—34no—
769C23—31no—
770C23—51no—
771C23—62no—
772C23—62no—
773C23—154no—
774C23—151no—
775C23—302no—
776C23—302no—
777C23C22×D3×D511yescharacteristic
778Q8—26no—
779Q8—312no—
780Q8—612no—
781Q8—66no—
782Q8—106no—
783Q8—3012no—
784Q8—306no—
785Q8D3×C22⋊D514yesdirect product factor
786D4—54no—
787D4—154no—
788D4—154no—
789D4—154no—
790C2×C4—26no—
791C2×C4—33no—
792C2×C4—312no—
793C2×C4—33no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—53no—
797C2×C4—66no—
798C2×C4—66no—
799C2×C4—66no—
800C2×C4—66no—
801C2×C4—106no—
802C2×C4—154no—
803C2×C4—151no—
804C2×C4—153no—
805C2×C4—153no—
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×Q8×D511yescharacteristic
816C2×C3C2×#414711yescharacteristic
817C2×C3C23×C22⋊D511yescharacteristic
818D3—22no—
819D3—102no—
820D3Q8×C22⋊D514yesdirect product factor
821C5D3×D4×Q811yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—32no—
825C22—32no—
826C22—32no—
827C22—32no—
828C22—52no—
829C22—68no—
830C22—61no—
831C22—61no—
832C22—101no—
833C22—101no—
834C22—152no—
835C22—308no—
836C22—301no—
837C22—301no—
838C22D3×Q8×D512yescomplemented
839C22C23×D3×D511yescharacteristic
840C4—23no—
841C4—36no—
842C4—52no—
843C4—63no—
844C4—103no—
845C4—103no—
846C4—152no—
847C4—303no—
848C4—303no—
849C4C2×D3×C22⋊D516yes—
850C3C2×Q8×C22⋊D511yescharacteristic, complemented, Sylow
851C2—22no—
852C2—34no—
853C2—62no—
854C2—102no—
855C2—302no—
856C2C2×D3×Q8×D511yescharacteristic
857C2D3×#414711yescharacteristic
858C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
prime radicalC2×D3×C22⋊D5C22
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×C5×D3×Q8C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. Q8×#1220C2semidirect
4. C3×Q8×C22⋊D5C2semidirect
5. D3×#4092C2semidirect
6. Q8×#1203C2semidirect
7. Q8×#1201C2semidirect
8. #11755235C2semidirect
9. #11755229C2semidirect
10. D3×Q8×Dic5C2semidirect
11. D3×#4090C2semidirect
13. #11754354C2semidirect
14. D3×#4070C2semidirect
15. Dic6×C22⋊D5C2semidirect
17. C22×C3×C5×Q8C22semidirect
18. C2×Q8×D15C22semidirect
22. C2×C5×D3×Q8C22semidirect
23. C2×C5×D3×Q8C22semidirect
25. C22×C5×Dic6C22semidirect
26. C2×C3×Q8×D5C22semidirect
30. C2×D15⋊Q8C22semidirect
32. C2×D5×Dic6C22semidirect
33. #91835C22semidirect
34. Q8×Dic15C22semidirect
35. #91833C22semidirect
37. #91813C22semidirect
38. C3×#4092C22semidirect
39. C3×Q8×Dic5C22semidirect
40. C3×#4090C22semidirect
42. C3×#4070C22semidirect
43. #91575C22semidirect
53. #91424C22semidirect
54. #91421C22semidirect
58. #91385C22semidirect
59. #91383C22semidirect
60. #91376C22semidirect
61. #91369C22semidirect
62. #91365C22semidirect
63. #91359C22semidirect
64. #91352C22semidirect
65. #91344C22semidirect
66. Dic5×Dic6C22semidirect
67. #91329C22semidirect
68. #91329C22semidirect
79. Q8×C22⋊D5D3direct (N × H)
99. C5×D3×Q8D4semidirect
113. D3×C22⋊D5Q8direct (N × H)
150. C22×D3×Q8D5semidirect
170. C22×C5×Q8C2×D3semidirect
177. C2×Q8×D5C2×D3semidirect
186. #4092C2×D3semidirect
190. Q8×Dic5C2×D3semidirect
196. #4090C2×D3semidirect
212. #4070C2×D3semidirect
221. C22×C5×D3C2×Q8semidirect
227. C2×D3×D5C2×Q8semidirect
229. C3×C5×Q8C2×D4semidirect
233. #1220C2×Q8semidirect
248. C5×Dic6C2×D4semidirect
249. C3×C22⋊D5C2×Q8semidirect
256. #1203C2×Q8semidirect
257. #1201C2×Q8semidirect
261. D3×Dic5C2×Q8semidirect
264. C22×C3×Q8C2×D5semidirect
272. C2×D3×Q8C2×D5semidirect
273. C2×D3×Q8C2×D5semidirect
278. C22×Dic6C2×D5semidirect
396. C22×C3×C5C22×Q8semidirect
400. C2×D15C22×Q8semidirect
406. C2×C5×D3C22×Q8semidirect
410. C2×C3×D5C22×Q8semidirect
416. Dic15C22×Q8semidirect
419. C3×Dic5C22×Q8semidirect
442. D3×Q8C22⋊D5direct (N × H)
501. C5×Q8D3×D4semidirect
515. C22⋊D5D3×Q8direct (N × H)
544. C22×Q8D3×D5semidirect
591. C5×D3D4×Q8semidirect
600. C22×D3Q8×D5semidirect
605. C3×Q8C2×C22⋊D5semidirect
637. Dic6C2×C22⋊D5semidirect
647. C22×C5C2×D3×Q8semidirect
655. C2×D5C2×D3×Q8semidirect
665. Dic5C2×D3×Q8semidirect
730. C3×C5C2×D4×Q8semidirect
736. C22×C3C2×Q8×D5semidirect
746. C2×D3C2×Q8×D5semidirect
785. Q8D3×C22⋊D5direct (N × H)
820. D3Q8×C22⋊D5direct (N × H)
821. C5D3×D4×Q8semidirect
838. C22D3×Q8×D5semidirect
850. C3C2×Q8×C22⋊D5semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×Q82
C2×D3×Q8×D52
Q8×#12202
C3×Q8×C22⋊D52
D3×#40922
Q8×#12032
Q8×#12012
#117552352
#117552292
D3×Q8×Dic52
D3×#40902
C4×D3×C22⋊D52
#117543542
D3×#40702
Dic6×C22⋊D52
C2×Q8×C22⋊D53
D3×D4×Q85