Finite Group Databasebeta

← D3×#66151 #14482831

Subgroups — D3×#66151 #14482831

Order 1920.

3240 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×#713C211yesmaximal, characteristic, complemented
3#11756576C211yesmaximal, characteristic, complemented
4C3×#66151C211yesmaximal, characteristic, complemented
5D3×#4093C213yesmaximal, complemented
6D3×#4092C213yesmaximal, complemented
7#11755247C211yesmaximal, characteristic, complemented
8#11755234C213yesmaximal, complemented
9#11755230C213yesmaximal, complemented
10D3×Q8×Dic5C211yesmaximal, characteristic, complemented
11#11755131C211yesmaximal, characteristic, complemented
12D3×#4076C213yesmaximal, complemented
13C4×D3×C22⋊D5C213yesmaximal, complemented
14#11754544C213yesmaximal, complemented
15#11754344C213yesmaximal, complemented
16C2×#66151—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×#6821C2211yescharacteristic, complemented
19C2×C5×D3×Q8—28no—
20C2×C5×D3×Q8C2213yes—
21C2×C5×D3×Q8C2211yescharacteristic
22C2×C5×D3×Q8C2211yescharacteristic, complemented
23C2×C5×D3×Q8C2213yescomplemented
24C22×C4×C5×D3C2213yes—
25C22×C5×Dic6C2213yescomplemented
26C2×C3×#713C2211yescharacteristic, complemented
27C2×D3×C22⋊D5C2213yes—
28D3×#713—28no—
29C2×D3×D20C2213yes—
30C2×C4×D3×D5C2213yes—
31C2×#6773C2213yescomplemented
32C2×#6766C2213yescomplemented
33#91836C2213yescomplemented
34#91835C2213yescomplemented
35Q8×Dic15C2211yescharacteristic, complemented
36#91819C2213yescomplemented
37C4×#1220C2213yescomplemented
38C3×#4093C2213yescomplemented
39C3×#4092C2213yescomplemented
40C3×Q8×Dic5C2211yescharacteristic, complemented
41C3×#4076C2213yescomplemented
42C3×C4×C22⋊D5C2213yescomplemented
43#91569C2216yescomplemented
44#91556C2213yescomplemented
45D3×C22⋊Dic5C2211yescharacteristic
46Dic3×C22⋊D5C2213yescomplemented
47D3×#685C2216yes—
48D3×#685C2213yes—
49#91460C2213yescomplemented
50#91456C2213yescomplemented
51#91455C2216yescomplemented
52#91455C2216yescomplemented
53#91454C2216yescomplemented
54#91446C2213yescomplemented
55C4×#1203C2213yescomplemented
56#91441C2213yescomplemented
57C4×#1201C2213yescomplemented
58D3×C4⋊Dic5C2213yes—
59#91424C2216yescomplemented
60#91421C2216yescomplemented
61D3×#683C2213yes—
62C4×D3×Dic5C2213yes—
63#91383C2213yescomplemented
64#91375C2213yescomplemented
65#91368C2213yescomplemented
66#91359C2213yescomplemented
67#91344C2213yescomplemented
68Dic5×Dic6C2213yescomplemented
69D3×#548—51nomaximal, Hall
70C23×C5×Q8—31no—
71C22×#713—31no—
72#66151—33no—
73#66151—33no—
74#66151—31no—
75#66151—33no—
76#66151—33no—
77#66151—31no—
78#66151—31no—
79#66151D311yescharacteristic, direct product factor
80C2×#4093—33no—
81C2×#4092—33no—
82C2×Q8×Dic5—31no—
83C2×#4076—33no—
84C2×C4×C22⋊D5—33no—
85C23×C5×D3C2311yescharacteristic
86C22×D3×D5C2313yes—
87C2×C3×C5×Q8—24no—
88C2×C3×C5×Q8C2313yes—
89C2×C3×C5×Q8C2311yescharacteristic
90C22×C3×C4×C5C2313yes—
91C2×#1220C2313yes—
92#6821—24no—
93C2×D60C2313yes—
94C2×C4×D15C2313yes—
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⋊D5C2313yes—
110C3×#713—24no—
111C2×C3×D20C2313yes—
112C2×C3×C4×D5C2313yes—
113D3×C22⋊D5—212no—
114C2×#1203C2313yes—
115C2×#1202C2316yes—
116C2×#1201C2313yes—
117C2×#1200C2313yes—
118C2×D3×Dic5C2311yescharacteristic
119C2×D3×Dic5C2313yes—
120C2×D3×Dic5C2311yescharacteristic
121C2×D5×Dic3C2313yes—
122D3×D20—212no—
123C4×D3×D5—212no—
124#6773—212no—
125#6766—212no—
126#6719C2311yescharacteristic
127#6714C2316yes—
128#6714C2313yes—
129C4⋊Dic15C2313yes—
130#6712C2313yes—
131C4×Dic15C2313yes—
132C3×C22⋊Dic5C2311yescharacteristic
133C3×#685C2316yes—
134C3×#685C2313yes—
135C3×C4⋊Dic5C2313yes—
136C3×#683C2313yes—
137C3×C4×Dic5C2313yes—
138Dic3⋊Dic5C2316yes—
139#6669C2313yes—
140#6668C2313yes—
141#6667C2316yes—
142#6667C2313yes—
143(C2×D3)⋊Dic5C2311yescharacteristic
144(C2×D3)⋊Dic5C2311yescharacteristic
145#6665C2316yes—
146#6665C2313yes—
147Dic3×Dic5C2313yes—
148Dic3×Dic5C2313yes—
149C2×D3×#41—51no—
150C22×D3×Q8D511yescharacteristic, complemented
151C3×#548—51no—
152#5831—51no—
153#5817—51no—
154#5677—53no—
155D3×#124—53no—
156#5633—53no—
157D3×C22⋊Q8—53no—
158D3×#121—53no—
159#5598—53no—
160#5576—51no—
161C4×D3×Q8—51no—
162#5552—53no—
163C4×D3×D4—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—33no—
173C2×#713—31no—
174C2×#713—33no—
175C2×#713—33no—
176C2×#713—68no—
177C2×#713C2×D311yescharacteristic, complemented
178C22×D20—33no—
179C22×C4×D5—33no—
180C2×C22⋊Dic5—31no—
181#4093—33no—
182#4093—33no—
183#4093—36no—
184#4093—36no—
185#4093—33no—
186#4093C2×D313yescomplemented
187#4092—33no—
188#4092—33no—
189#4092—36no—
190#4092—33no—
191#4092—36no—
192#4092C2×D313yescomplemented
193Q8×Dic5—31no—
194Q8×Dic5—33no—
195Q8×Dic5—33no—
196Q8×Dic5C2×D311yescharacteristic, complemented
197#4076—33no—
198#4076—36no—
199#4076—33no—
200#4076—36no—
201#4076—33no—
202#4076C2×D313yescomplemented
203C4×C22⋊D5—33no—
204C4×C22⋊D5—33no—
205C4×C22⋊D5—33no—
206C4×C22⋊D5—33no—
207C4×C22⋊D5—33no—
208C4×C22⋊D5—33no—
209C4×C22⋊D5—33no—
210C4×C22⋊D5C2×D313yescomplemented
211C2×#685—33no—
212C2×#685—36no—
213C2×C4⋊Dic5—33no—
214C2×#683—33no—
215C2×C4×Dic5—33no—
216C2×#548—151noSylow
217C23×C3×C5C2411yescharacteristic
218C22×D15C2413yes—
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3#4114yescomplemented
222C22×C5×D3C2411yescharacteristic
223C22×C5×D3C2411yescharacteristic
224C22×C3×D5C2413yes—
225C2×D3×D5—26no—
226C2×D3×D5—26no—
227C2×D3×D5—26no—
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C2×C3×C4×C5—26no—
231C2×C3×C4×C5C2413yes—
232C2×C3×C4×C5C2413yes—
233#1220—26no—
234C2×Dic15C2411yescharacteristic
235C2×Dic15C2413yes—
236C2×Dic15C2411yescharacteristic
237D60—26no—
238C4×D15—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⋊D5—26no—
250C2×C3×Dic5C2411yescharacteristic
251C2×C3×Dic5C2413yes—
252C2×C3×Dic5C2411yescharacteristic
253C3×D20—26no—
254C3×C4×D5—26no—
255#1203—26no—
256#1202—212no—
257#1201—26no—
258#1200—26no—
259D3×Dic5—22no—
260D3×Dic5—26no—
261D3×Dic5—22no—
262D5×Dic3—26no—
263C2×C3×#41—51no—
264C22×C3×Q8C2×D511yescharacteristic, complemented
265D3×#41—108no—
266C2×#239—51no—
267C2×D3×Q8—28no—
268C2×D3×Q8C2×D513yes—
269C2×D3×Q8C2×D511yescharacteristic
270C2×D3×Q8C2×D513yescomplemented
271C2×D3×Q8C2×D511yescharacteristic, complemented
272C2×#237—53no—
273C2×D3×D4—53no—
274C2×D3×D4—53no—
275C2×#235—53no—
276C22×C4×D3—53no—
277C22×C4×D3C2×D513yes—
278C22×Dic6C2×D513yescomplemented
279C3×#124—53no—
280C3×C22⋊Q8—53no—
281C3×#121—53no—
282C3×C4×Q8—51no—
283C3×C4×D4—53no—
284#947—53no—
285#946—53no—
286Q8×Dic3—51no—
287#939—56no—
288#938—53no—
289#936—53no—
290D4×Dic3—53no—
291#930—53no—
292C4×#67—53no—
293C4×#67—53no—
294#924—53no—
295#897—53no—
296#896—56no—
297#895—53no—
298#893—53no—
299D3×C4⋊C4—53no—
300D3×C4⋊C4—53no—
301#887—53no—
302#885—56no—
303#885—56no—
304#884—56no—
305#67⋊C4—53no—
306#67⋊C4—53no—
307D3×C22⋊C4—51no—
308D3×C22⋊C4—53no—
309D3×C22⋊C4—56no—
310#878—56no—
311#875—53no—
312C4×D12—53no—
313C42×D3—53no—
314C4×Dic6—53no—
315C24×C5—31no—
316C23×D5—33no—
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—33no—
336C2×C22⋊D5—33no—
337C2×C22⋊D5—33no—
338C2×C22⋊D5—612no—
339C2×C22⋊D5C22×D313yes—
340C22×Dic5—31no—
341C22×Dic5—31no—
342C22×Dic5—33no—
343#713—24no—
344#713—612no—
345#713—612no—
346#713—64no—
347C2×D20—36no—
348C2×D20—33no—
349C2×D20—612no—
350C2×D20C22×D313yes—
351C2×C4×D5—33no—
352C2×C4×D5—33no—
353C2×C4×D5—33no—
354C2×C4×D5—612no—
355C2×C4×D5C22×D313yes—
356C22⋊Dic5—31no—
357C22⋊Dic5—31no—
358C22⋊Dic5—31no—
359C22⋊Dic5C22×D311yescharacteristic
360#685—33no—
361#685—36no—
362#685—33no—
363#685—36no—
364#685—33no—
365#685—36no—
366#685C22×D313yes—
367#685C22×D316yes—
368C4⋊Dic5—33no—
369C4⋊Dic5—36no—
370C4⋊Dic5C22×D313yes—
371#683—33no—
372#683—33no—
373#683—33no—
374#683C22×D313yes—
375C4×Dic5—33no—
376C4×Dic5—33no—
377C4×Dic5—33no—
378C4×Dic5C22×D313yes—
379C22×#41—151no—
380C23×Q8—31no—
381#548—51no—
382#548—153no—
383#548—151no—
384#548—153no—
385#548—153no—
386#548—153no—
387#548—151no—
388#548—151no—
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—151no—
393C2×C4×D4—153no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5C2×#4112yescomplemented
397C22×C3×C5C2511yescharacteristic
398C2×D15—23no—
399C2×D15—23no—
400C2×D15—23no—
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3—28no—
404C2×C5×D3C22×D412yes—
405C2×C5×D3C2×#4112yes—
406C2×C5×D3C2×#4112yescomplemented
407C2×C5×D32−1+412yes—
408C2×C3×D5—23no—
409C2×C3×D5—23no—
410C2×C3×D5—23no—
411D3×D5—412no—
412C3×C4×C5—23no—
413C3×C4×C5C22×D416yes—
414Dic15—21no—
415Dic15—23no—
416Dic15—21no—
417C3×Dic5—21no—
418C3×Dic5—23no—
419C3×Dic5—21no—
420C5×Dic3—23no—
421C5×Dic3C22×D416yes—
422C23×D3—53no—
423C23×D3C22×D511yescharacteristic
424C3×#41—104no—
425C2×C3×Q8—24no—
426C2×C3×Q8C22×D513yes—
427C2×C3×Q8C22×D511yescharacteristic
428C2×C3×D4—53no—
429C2×C3×D4—53no—
430C22×C3×C4—53no—
431C22×C3×C4C22×D513yes—
432C2×#67—53no—
433C2×#67—53no—
434C2×#67—56no—
435C22×Dic3—53no—
436C22×Dic3C22×D513yes—
437#239—104no—
438D3×Q8—24no—
439D3×Q8—212no—
440D3×Q8—212no—
441D3×Q8C22⋊D518yescomplemented
442#237—1012no—
443D3×D4—1012no—
444D3×D4—1012no—
445#235—1012no—
446C2×D12—53no—
447C2×D12—53no—
448C2×C4×D3—212no—
449C2×C4×D3—51no—
450C2×C4×D3—53no—
451C2×C4×D3—51no—
452C2×C4×D3—53no—
453C2×C4×D3—53no—
454C2×C4×D3—1012no—
455C2×C4×D3C22×D513yes—
456C2×C4×D3C22×D513yes—
457C2×C4×D3C22×D513yes—
458C2×C4×D3C22×D513yes—
459C2×Dic6—212no—
460C2×Dic6C22×D513yes—
461C2×Dic6C22×D516yes—
462C2×Dic6C22×D513yes—
463C3×C4⋊C4—53no—
464C3×C4⋊C4—53no—
465C3×C22⋊C4—51no—
466C3×C22⋊C4—56no—
467C3×C22⋊C4—53no—
468C3×C42—53no—
469#217—51no—
470#217—56no—
471#217—53no—
472(C2×D3)⋊C4—51no—
473(C2×D3)⋊C4—51no—
474(C2×D3)⋊C4—56no—
475(C2×D3)⋊C4—53no—
476(C2×D3)⋊C4—53no—
477(C2×D3)⋊C4—56no—
478C4⋊Dic3—53no—
479C4⋊Dic3—53no—
480Dic3⋊C4—53no—
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—33no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—66no—
496C22×D5C23×D313yes—
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—26no—
513C22⋊D5—66no—
514C22⋊D5—66no—
515C22⋊D5—66no—
516C2×Dic5—31no—
517C2×Dic5—33no—
518C2×Dic5—31no—
519C2×Dic5—62no—
520C2×Dic5—62no—
521C2×Dic5—66no—
522C2×Dic5C23×D311yescharacteristic
523C2×Dic5C23×D313yes—
524C2×Dic5C23×D311yescharacteristic
525D20—26no—
526D20—612no—
527D20—66no—
528C4×D5—26no—
529C4×D5—66no—
530C4×D5—66no—
531C4×D5—66no—
532C2×#41—51no—
533C2×#41—153no—
534C2×#41—153no—
535C2×#41—151no—
536C2×#41—308no—
537C22×Q8—31no—
538C22×Q8—33no—
539C22×Q8—33no—
540C22×Q8—31no—
541C22×Q8—33no—
542C22×Q8—68no—
543C22×Q8D3×D511yescharacteristic, complemented
544C22×D4—153no—
545C22×D4—153no—
546C23×C4—33no—
547C23×C4—153no—
548#124—53no—
549#124—153no—
550#124—156no—
551#124—156no—
552#124—153no—
553#124—153no—
554C22⋊Q8—53no—
555C22⋊Q8—156no—
556C22⋊Q8—156no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—53no—
561#121—156no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—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×C22⋊C4—153no—
581C2×C22⋊C4—156no—
582C2×C22⋊C4—151no—
583C2×C42—153no—
584C2×C3×C5—22no—
585C2×C3×C5C23×D411yescharacteristic
586C2×C3×C5C22×#4111yescharacteristic
587C2×C3×C5C2×2−1+411yescharacteristic
588D15—43no—
589C3×D5—43no—
590C5×D3—22no—
591C5×D3#54814yescomplemented
592C23×C3—53no—
593C23×C3C23×D511yescharacteristic
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—53no—
597C22×D3—106no—
598C22×D3—106no—
599C22×D3—106no—
600C22×D3#71314yescomplemented
601C22×D3C23×D511yescharacteristic
602C22×D3C23×D511yescharacteristic
603C3×Q8—26no—
604C3×Q8C2×C22⋊D514yescomplemented
605C3×D4—106no—
606C3×D4—106no—
607C2×C3×C4—26no—
608C2×C3×C4—51no—
609C2×C3×C4—53no—
610C2×C3×C4—51no—
611C2×C3×C4—106no—
612C2×C3×C4C23×D513yes—
613C2×C3×C4C23×D513yes—
614#67—106no—
615#67—106no—
616#67—1012no—
617C2×Dic3—26no—
618C2×Dic3—51no—
619C2×Dic3—53no—
620C2×Dic3—51no—
621C2×Dic3—106no—
622C2×Dic3C23×D513yes—
623C2×Dic3C23×D513yes—
624D12—106no—
625D12—106no—
626C4×D3—26no—
627C4×D3—26no—
628C4×D3—26no—
629C4×D3—106no—
630C4×D3—102no—
631C4×D3—102no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3C2×C22⋊D5112yes—
635Dic6—26no—
636Dic6—212no—
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×C5D3×#4112yescomplemented
648C22×C5C24×D311yescharacteristic
649C2×D5—23no—
650C2×D5—23no—
651C2×D5—23no—
652C2×D5—63no—
653C2×D5—63no—
654C2×D5—63no—
655C2×D5—1212no—
656C4×C5—23no—
657C4×C5—36no—
658C4×C5—63no—
659C4×C5C2×D3×D416yes—
660Dic5—21no—
661Dic5—23no—
662Dic5—21no—
663Dic5—61no—
664Dic5—63no—
665Dic5—61no—
666C24—31no—
667C24—153no—
668#41—104no—
669#41—3012no—
670#41—3012no—
671#41—304no—
672C2×Q8—24no—
673C2×Q8—38no—
674C2×Q8—33no—
675C2×Q8—36no—
676C2×Q8—33no—
677C2×Q8—612no—
678C2×Q8—612no—
679C2×Q8—612no—
680C2×Q8—64no—
681C2×Q8C2×D3×D513yes—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—53no—
684C2×D4—53no—
685C2×D4—156no—
686C2×D4—153no—
687C2×D4—153no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—3012no—
691C2×D4—3012no—
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—151no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4C2×D3×D513yes—
707C4⋊C4—53no—
708C4⋊C4—53no—
709C4⋊C4—153no—
710C4⋊C4—153no—
711C4⋊C4—156no—
712C4⋊C4—153no—
713C4⋊C4—153no—
714C22⋊C4—51no—
715C22⋊C4—53no—
716C22⋊C4—56no—
717C22⋊C4—153no—
718C22⋊C4—156no—
719C22⋊C4—153no—
720C22⋊C4—156no—
721C22⋊C4—151no—
722C22⋊C4—151no—
723C22⋊C4—151no—
724C22⋊C4—153no—
725C22⋊C4—156no—
726C42—53no—
727C42—153no—
728C42—153no—
729C42—153no—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—103no—
734C22×C3—103no—
735C22×C3—103no—
736C22×C3C2×#71312yescomplemented
737C22×C3C24×D511yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—28no—
741C2×D3—103no—
742C2×D3—103no—
743C2×D3—103no—
744C2×D3—2012no—
745C2×D3C2×#71312yes—
746C2×D3C2×#71312yescomplemented
747C2×D3#414712yes—
748C2×D3C22×C22⋊D512yes—
749C3×C4—23no—
750C3×C4—103no—
751C3×C4—101no—
752C3×C4—101no—
753C3×C4C22×C22⋊D516yes—
754Dic3—23no—
755Dic3—103no—
756Dic3—101no—
757Dic3—101no—
758Dic3C22×C22⋊D516yes—
759C2×C5—22no—
760C2×C5—34no—
761C2×C5—62no—
762C2×C5C22×D3×D411yescharacteristic
763C2×C5C2×D3×#4111yescharacteristic
764C2×C5D3×2−1+411yescharacteristic
765D5—43no—
766D5—123no—
767C23—31no—
768C23—34no—
769C23—31no—
770C23—53no—
771C23—62no—
772C23—62no—
773C23—153no—
774C23—306no—
775C23—306no—
776C23—306no—
777C23C22×D3×D511yescharacteristic
778Q8—26no—
779Q8—312no—
780Q8—612no—
781Q8—66no—
782Q8D3×C22⋊D514yescomplemented
783D4—106no—
784D4—106no—
785D4—3012no—
786D4—306no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—26no—
791C2×C4—33no—
792C2×C4—312no—
793C2×C4—33no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—51no—
797C2×C4—66no—
798C2×C4—66no—
799C2×C4—66no—
800C2×C4—66no—
801C2×C4—106no—
802C2×C4—151no—
803C2×C4—153no—
804C2×C4—151no—
805C2×C4—306no—
806C2×C4—306no—
807C2×C4—302no—
808C2×C4—306no—
809C2×C4—302no—
810C2×C4—306no—
811C2×C4C22×D3×D513yes—
812C2×C4C22×D3×D513yes—
813C2×C3—22no—
814C2×C3—203no—
815C2×C3C22×#71311yescharacteristic
816C2×C3C2×#414711yescharacteristic
817C2×C3C23×C22⋊D511yescharacteristic
818D3—22no—
819D3—203no—
820D3#6615114yesdirect product factor
821C5D3×#54811yescharacteristic, complemented, Sylow
822C22—21no—
823C22—21no—
824C22—32no—
825C22—32no—
826C22—32no—
827C22—32no—
828C22—68no—
829C22—61no—
830C22—61no—
831C22—103no—
832C22—103no—
833C22—103no—
834C22—303no—
835C22—303no—
836C22—303no—
837C22—6012no—
838C22D3×#71312yescomplemented
839C22C23×D3×D511yescharacteristic
840C4—23no—
841C4—36no—
842C4—63no—
843C4—101no—
844C4—103no—
845C4—101no—
846C4—301no—
847C4—303no—
848C4—301no—
849C4C2×D3×C22⋊D516yes—
850C3C2×#6615111yescharacteristic, complemented, Sylow
851C2—22no—
852C2—34no—
853C2—62no—
854C2—203no—
855C2—603no—
856C2C2×D3×#71311yescharacteristic
857C2D3×#414711yescharacteristic
858C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC22×C3×C5×Q8C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#548
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×#713C2semidirect
3. #11756576C2semidirect
4. C3×#66151C2semidirect
5. D3×#4093C2semidirect
6. D3×#4092C2semidirect
7. #11755247C2semidirect
8. #11755234C2semidirect
9. #11755230C2semidirect
10. D3×Q8×Dic5C2semidirect
11. #11755131C2semidirect
12. D3×#4076C2semidirect
13. C4×D3×C22⋊D5C2semidirect
14. #11754544C2semidirect
15. #11754344C2semidirect
17. C22×C3×C5×Q8C22semidirect
18. C2×#6821C22semidirect
22. C2×C5×D3×Q8C22semidirect
23. C2×C5×D3×Q8C22semidirect
25. C22×C5×Dic6C22semidirect
26. C2×C3×#713C22semidirect
31. C2×#6773C22semidirect
32. C2×#6766C22semidirect
33. #91836C22semidirect
34. #91835C22semidirect
35. Q8×Dic15C22semidirect
36. #91819C22semidirect
37. C4×#1220C22semidirect
38. C3×#4093C22semidirect
39. C3×#4092C22semidirect
40. C3×Q8×Dic5C22semidirect
41. C3×#4076C22semidirect
42. C3×C4×C22⋊D5C22semidirect
43. #91569C22semidirect
44. #91556C22semidirect
46. Dic3×C22⋊D5C22semidirect
49. #91460C22semidirect
50. #91456C22semidirect
51. #91455C22semidirect
52. #91455C22semidirect
53. #91454C22semidirect
54. #91446C22semidirect
55. C4×#1203C22semidirect
56. #91441C22semidirect
57. C4×#1201C22semidirect
59. #91424C22semidirect
60. #91421C22semidirect
63. #91383C22semidirect
64. #91375C22semidirect
65. #91368C22semidirect
66. #91359C22semidirect
67. #91344C22semidirect
68. Dic5×Dic6C22semidirect
79. #66151D3direct (N × H)
99. C5×D3×Q8D4semidirect
150. C22×D3×Q8D5semidirect
170. C22×C5×Q8C2×D3semidirect
177. C2×#713C2×D3semidirect
186. #4093C2×D3semidirect
192. #4092C2×D3semidirect
196. Q8×Dic5C2×D3semidirect
202. #4076C2×D3semidirect
210. C4×C22⋊D5C2×D3semidirect
221. C22×C5×D3#41semidirect
229. C3×C5×Q8C2×D4semidirect
248. C5×Dic6C2×D4semidirect
264. C22×C3×Q8C2×D5semidirect
270. C2×D3×Q8C2×D5semidirect
271. C2×D3×Q8C2×D5semidirect
278. C22×Dic6C2×D5semidirect
396. C22×C3×C5C2×#41semidirect
406. C2×C5×D3C2×#41semidirect
441. D3×Q8C22⋊D5semidirect
501. C5×Q8D3×D4semidirect
543. C22×Q8D3×D5semidirect
591. C5×D3#548semidirect
600. C22×D3#713semidirect
604. C3×Q8C2×C22⋊D5semidirect
637. Dic6C2×C22⋊D5semidirect
647. C22×C5D3×#41semidirect
730. C3×C5C2×#548semidirect
736. C22×C3C2×#713semidirect
746. C2×D3C2×#713semidirect
782. Q8D3×C22⋊D5semidirect
820. D3#66151direct (N × H)
821. C5D3×#548semidirect
838. C22D3×#713semidirect
850. C3C2×#66151semidirect

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×#7132
#117565762
C3×#661512
D3×#40932
D3×#40922
#117552472
#117552342
#117552302
D3×Q8×Dic52
#117551312
D3×#40762
C4×D3×C22⋊D52
#117545442
#117543442
C2×#661513
D3×#5485