Finite Group Databasebeta

← C2×#20286281 #28259133

Subgroups — C2×#20286281 #28259133

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133247C211yesmaximal, characteristic, complemented
2C23×#11719925C211yesmaximal, characteristic, complemented
3C2×D4×Dic106C211yesmaximal, characteristic, complemented
4#20286281C2116yesmaximal, direct product factor
5C2×#16811018C211yesmaximal, characteristic, complemented
6C2×#16810879C211yesmaximal, characteristic, complemented
7C2×#16810850C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810833C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810779C211yesmaximal, characteristic, complemented
12C2×#16810778C211yesmaximal, characteristic, complemented
13C2×#16810761C211yesmaximal, characteristic, complemented
14C2×#16810728C211yesmaximal, characteristic, complemented
15C2×#16810695C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C2×#13133247—28no—
20C2×#13133247C2218yescomplemented
21C22×#11719925—28no—
22C22×#11719925C2211yescharacteristic
23C22×#11719925C2211yescharacteristic
24C22×#11719925C2211yescharacteristic
25C22×#11719925C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C22×#11719925C2211yescharacteristic
28C22×#11719925C2218yescomplemented
29C22×#11719923C2211yescharacteristic
30C22×#11719923C2211yescharacteristic
31C22×#11719923C2211yescharacteristic
32C22×#11719917C2211yescharacteristic
33C23×#88322C2211yescharacteristic
34D4×Dic106—24no—
35D4×Dic106C2218yescomplemented
36C2×#13133217C2211yescharacteristic
37C2×#13133216—21no—
38C2×#13133196C2211yescharacteristic
39C2×#13133196C2211yescharacteristic
40C2×#13133194—21no—
41C2×#13133194—21no—
42C2×C4×Dic106C2211yescharacteristic
43C2×D4×Dic53—21no—
44#16811018C2218yescomplemented
45#16810879C2218yescomplemented
46#16810850C2218yescomplemented
47#16810842C2218yescomplemented
48#16810833C2218yescomplemented
49#16810785C2218yescomplemented
50#16810779C2218yescomplemented
51#16810778C2218yescomplemented
52#16810761C2218yescomplemented
53#16810728C2218yescomplemented
54#16810695C2218yescomplemented
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×C22⋊#88322C2211yescharacteristic
64C2×C22⋊#88322C2211yescharacteristic
65C2×#13133128C2211yescharacteristic
66C22×#41×C53C2211yescharacteristic
67C23×Q8×C53C2211yescharacteristic
68C53×#548—24no—
69C53×#548C2218yes—
70C2×#124×C53—21no—
71C2×#124×C53C2211yescharacteristic
72C2×C22⋊Q8×C53—21no—
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×#121×C53—21no—
75C2×#121×C53C2211yescharacteristic
76C2×C4×Q8×C53C2211yescharacteristic
77C2×C4×D4×C53—21no—
78C2×C4×D4×C53C2211yescharacteristic
79C22×Dic106—24no—
80C22×Dic106—24no—
81C22×Dic106—22no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—21no—
85C22×Dic106—42no—
86C22×Dic106—42no—
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2314yes—
90C22×Dic106C2314yes—
91C22×Dic106C2311yescharacteristic
92C23×Dic53—21no—
93C23×Dic53—21no—
94#13133247—232no—
95C2×#11719925—232no—
96C2×#11719925—24no—
97C2×#11719925—24no—
98C2×#11719925—24no—
99C2×#11719925—24no—
100C2×#11719925—42no—
101C2×#11719925D418yescomplemented
102C2×#11719925C2314yes—
103C2×#11719925C2314yes—
104C2×#11719925C2314yes—
105C2×#11719925C2314yes—
106C2×#11719925C2314yes—
107C2×#11719925C2314yes—
108C2×#11719923—24no—
109C2×#11719923—24no—
110C2×#11719923—42no—
111C2×#11719923C2314yes—
112C2×#11719923C2314yes—
113C2×#11719923C2314yes—
114C2×#11719917—24no—
115C2×#11719917C2314yes—
116C22×#88322—24no—
117C22×#88322C2311yescharacteristic
118C22×#88322C2311yescharacteristic
119C22×#88322C2311yescharacteristic
120C22×#88322C2314yes—
121C22×#88322C2311yescharacteristic
122#13133217—22no—
123#13133217C2314yes—
124#13133216—28no—
125#13133196—22no—
126#13133196—22no—
127#13133196C2314yes—
128#13133196C2314yes—
129#13133194—28no—
130#13133194—28no—
131C4×Dic106—22no—
132C4×Dic106C2314yes—
133D4×Dic53—28no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C4×Dic53—21no—
143#13133148C2314yes—
144C4⋊#88322C2314yes—
145#13133141C2314yes—
146#13133141C2314yes—
147#13133140C2314yes—
148#13133140C2314yes—
149#13133140C2314yes—
150#13133138C2314yes—
151C22⋊#88322C2314yes—
152C22⋊#88322C2314yes—
153#13133128C2314yes—
154C2×#41×C53—22no—
155C2×#41×C53—24no—
156C2×#41×C53—42no—
157C2×#41×C53C2314yes—
158C22×Q8×C53—21no—
159C22×Q8×C53—22no—
160C22×Q8×C53—24no—
161C22×Q8×C53—42no—
162C22×Q8×C53C2311yescharacteristic
163C22×Q8×C53C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53—21no—
166C22×D4×C53—21no—
167C22×D4×C53D411yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C23×C4×C53C2311yescharacteristic
173#124×C53—28no—
174#124×C53—22no—
175#124×C53C2314yes—
176C22⋊Q8×C53—28no—
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179#121×C53—28no—
180#121×C53—22no—
181#121×C53C2314yes—
182C4×Q8×C53—22no—
183C4×Q8×C53C2314yes—
184C4×D4×C53—28no—
185C4×D4×C53D414yes—
186C4×D4×C53C2314yes—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53—21no—
189C2×C4⋊C4×C53D411yescharacteristic
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C22⋊C4×C53—21no—
192C2×C22⋊C4×C53—21no—
193C2×C22⋊C4×C53—21no—
194C2×C22⋊C4×C53—21no—
195C2×C22⋊C4×C53D411yescharacteristic
196C2×C22⋊C4×C53D411yescharacteristic
197C2×C42×C53—21no—
198C2×C42×C53C2311yescharacteristic
199C24×C53—21no—
200C24×C53C2×D411yescharacteristic
201C24×C53C2×D411yescharacteristic
202#41×C53—28no—
203#41×C53—44no—
204#41×C53—48no—
205C2×Q8×C53—21no—
206C2×Q8×C53—24no—
207C2×Q8×C53—21no—
208C2×Q8×C53—22no—
209C2×Q8×C53—28no—
210C2×Q8×C53—22no—
211C2×Q8×C53—22no—
212C2×Q8×C53—44no—
213C2×Q8×C53—44no—
214C2×Q8×C53—48no—
215C2×Q8×C53C2×D414yes—
216C2×Q8×C53C2412yes—
217C2×Q8×C53C2412yes—
218C2×D4×C53—24no—
219C2×D4×C53—24no—
220C2×D4×C53—24no—
221C2×D4×C53—22no—
222C2×D4×C53—21no—
223C2×D4×C53—22no—
224C2×D4×C53—44no—
225C2×D4×C53—44no—
226C2×D4×C53C2×D414yes—
227C2×D4×C53C2412yes—
228C22×C4×C53—21no—
229C22×C4×C53—22no—
230C22×C4×C53—22no—
231C22×C4×C53—22no—
232C22×C4×C53—22no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—24no—
236C22×C4×C53—24no—
237C22×C4×C53—44no—
238C22×C4×C53—44no—
239C22×C4×C53C2×D411yescharacteristic
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D411yescharacteristic
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2×D412yes—
244C22×C4×C53C2×D412yes—
245C22×C4×C53C2412yes—
246C22×C4×C53C2412yes—
247C22×C4×C53C2411yescharacteristic
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—24no—
253C22×Dic53—24no—
254C22×Dic53—44no—
255C22×Dic53—44no—
256C2×Dic106—21no—
257C2×Dic106—22no—
258C2×Dic106—22no—
259C2×Dic106—22no—
260C2×Dic106—22no—
261C2×Dic106—22no—
262C2×Dic106—28no—
263C2×Dic106—28no—
264C2×Dic106—24no—
265C2×Dic106—24no—
266C2×Dic106—21no—
267C2×Dic106—21no—
268C2×Dic106—44no—
269C2×Dic106—44no—
270C2×Dic106—48no—
271C2×Dic106—48no—
272C2×Dic106—44no—
273C2×Dic106—44no—
274C2×Dic106C2×D414yes—
275C2×Dic106C2412yes—
276C2×Dic106C2412yes—
277C2×Dic106C2412yes—
278C4⋊C4×C53—24no—
279C4⋊C4×C53—24no—
280C4⋊C4×C53—21no—
281C4⋊C4×C53C2×D414yes—
282C4⋊C4×C53C2412yes—
283C22⋊C4×C53—24no—
284C22⋊C4×C53—24no—
285C22⋊C4×C53—24no—
286C22⋊C4×C53—24no—
287C22⋊C4×C53C2×D414yes—
288C22⋊C4×C53C2×D414yes—
289C42×C53—24no—
290C42×C53C2×D412yes—
291C42×C53C2412yes—
292C22⋊Dic53—24no—
293C22⋊Dic53—24no—
294#11719925—28no—
295#11719925—28no—
296#11719925—28no—
297#11719925—28no—
298#11719925—44no—
299#11719925C2×D4116yescomplemented
300#11719923—28no—
301#11719923—28no—
302#11719923—44no—
303C4⋊Dic53—24no—
304C4⋊Dic53—24no—
305C4⋊Dic53—21no—
306C4⋊Dic53C2412yes—
307#11719919—24no—
308#11719919—24no—
309#11719919—24no—
310C4×Dic53—24no—
311#11719917—28no—
312C2×#88322—22no—
313C2×#88322—22no—
314C2×#88322—22no—
315C2×#88322—28no—
316C2×#88322C2×D414yes—
317C2×#88322C2412yes—
318C2×#88322C2412yes—
319C2×#88322C2412yes—
320C2×#88322C2412yes—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—42no—
328C23×C53—42no—
329C23×C53—42no—
330C23×C53#13714yescomplemented
331C23×C53C22×D412yes—
332C23×C53C22×D412yes—
333C23×C53C22×D411yescharacteristic
334Q8×C53—24no—
335Q8×C53—22no—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—48no—
339Q8×C53—42no—
340Q8×C53C22×D414yes—
341D4×C53—28no—
342D4×C53—22no—
343D4×C53—22no—
344D4×C53—48no—
345D4×C53—48no—
346D4×C53—42no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—24no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—24no—
354C2×C4×C53—24no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—48no—
362C2×C4×C53—48no—
363C2×C4×C53—42no—
364C2×C4×C53—42no—
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D412yes—
367C2×C4×C53C22×D412yes—
368C2×C4×C53C22×D412yes—
369C2×C4×C53C22×D412yes—
370C2×C4×C53C22×D411yescharacteristic
371C2×C4×C53H(5,𝔽2)12yes—
372C2×C4×C53C2511yescharacteristic
373C2×Dic53—24no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—48no—
379C2×Dic53—48no—
380C2×Dic53—42no—
381C2×Dic53—42no—
382C2×Dic53—42no—
383Dic106—24no—
384Dic106—22no—
385Dic106—22no—
386Dic106—22no—
387Dic106—22no—
388Dic106—22no—
389Dic106—48no—
390Dic106—48no—
391Dic106—42no—
392Dic106—42no—
393Dic106C22×D414yes—
394#88322—22no—
395#88322—22no—
396#88322—22no—
397#88322C22×D414yes—
398C2×#3270—531nomaximal, Sylow
399C22×C53—22no—
400C22×C53—28no—
401C22×C53—22no—
402C22×C53—22no—
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—44no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—84no—
410C22×C53D4212yes—
411C22×C53C2×#13712yes—
412C22×C53C2×#13714yescomplemented
413C22×C53#57812yes—
414C22×C53C23×D411yescharacteristic
415C4×C53—22no—
416C4×C53—22no—
417C4×C53—24no—
418C4×C53—22no—
419C4×C53—22no—
420C4×C53—42no—
421C4×C53—42no—
422C4×C53D4212yes—
423C4×C53C23×D411yescharacteristic
424C4×C53C2×H(5,𝔽2)11yescharacteristic
425Dic53—24no—
426Dic53—42no—
427Dic53—42no—
428Dic53—42no—
429C22×#137—531no—
430C23×Q16—531no—
431C2×D4×Q8—531no—
432C2×#548D5311yescharacteristic
433#3270—5316no—
434C2×#497—531no—
435C2×#470—531no—
436C2×#465—531no—
437C2×#464—531no—
438C2×#462—531no—
439C2×#452—531no—
440C2×#451—531no—
441C2×#451—531no—
442C2×#448—531no—
443C2×#441—531no—
444C2×#435—531no—
445C2×C53—24no—
446C2×C53—42no—
447C2×C53—82no—
448C2×C53#327014yescomplemented
449C2×C53C2×D4211yescharacteristic
450C2×C53C22×#13711yescharacteristic
451C2×C53C2×#57811yescharacteristic
452C22×#41C2×D5311yescharacteristic
453C23×Q8—531no—
454C23×Q8—531no—
455C23×Q8C2×D5311yescharacteristic
456C2×#137—538no—
457C2×#137—1068no—
458C22×Q16—531no—
459C22×Q16—531no—
460C22×Q16—531no—
461C22×Q16—531no—
462C22×Q16—531no—
463C22×Q16—538no—
464C22×Q16—531no—
465C22×Q16—1068no—
466C22×SD16—531no—
467C22×SD16—531no—
468C22×SD16—531no—
469C22×M16—531no—
470C23×C8—531no—
471D4×Q8—538no—
472D4×Q8—1064no—
473#548—24no—
474#548C2×D5318yes—
475C2×C4⋊Q8—531no—
476C2×C4⋊Q8—1061no—
477C2×#124—21no—
478C2×#124C2×D5311yescharacteristic
479C2×C22⋊Q8—21no—
480C2×C22⋊Q8—531no—
481C2×C22⋊Q8—531no—
482C2×C22⋊Q8—1061no—
483C2×C22⋊Q8—1061no—
484C2×C22⋊Q8C2×D5311yescharacteristic
485C2×#121—21no—
486C2×#121C2×D5311yescharacteristic
487C2×C4×Q8—531no—
488C2×C4×Q8C2×D5311yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4—1061no—
491C2×C4×D4C2×D5311yescharacteristic
492#497—538no—
493#470—538no—
494#465—538no—
495#464—538no—
496#462—538no—
497#452—538no—
498#451—538no—
499#451—538no—
500#448—538no—
501#441—538no—
502#435—538no—
503C2×#106—531no—
504C2×C4⋊C8—531no—
505C2×#103—531no—
506C2×#103—531no—
507C2×#103—531no—
508C2×#103—531no—
509C2×#103—531no—
510C2×#102—531no—
511C2×C22⋊C8—531no—
512C2×C22⋊C8—531no—
513C2×#97—531no—
514C53C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—22no—
516C2×#41—24no—
517C2×#41—42no—
518C2×#41C22×D5314yes—
519C22×Q8—21no—
520C22×Q8—22no—
521C22×Q8—24no—
522C22×Q8—42no—
523C22×Q8—531no—
524C22×Q8—531no—
525C22×Q8—531no—
526C22×Q8—534no—
527C22×Q8—534no—
528C22×Q8—1064no—
529C22×Q8—1064no—
530C22×Q8—1061no—
531C22×Q8—1061no—
532C22×Q8—1062no—
533C22×Q8—1062no—
534C22×Q8—2122no—
535C22×Q8—2122no—
536C22×Q8C22×D5311yescharacteristic
537C22×Q8C22×D5314yes—
538C22×Q8C22×D5311yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C22⋊D5311yescharacteristic
542C22×D4C22×D5311yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—1061no—
546C23×C4—1061no—
547C23×C4C22×D5311yescharacteristic
548C23×C4C22×D5311yescharacteristic
549#137—10632no—
550C2×Q16—538no—
551C2×Q16—534no—
552C2×Q16—534no—
553C2×Q16—534no—
554C2×Q16—534no—
555C2×Q16—534no—
556C2×Q16—534no—
557C2×Q16—1064no—
558C2×Q16—10632no—
559C2×Q16—1064no—
560C2×Q16—1064no—
561C2×Q16—1064no—
562C2×Q16—2122no—
563C2×SD16—534no—
564C2×SD16—534no—
565C2×SD16—534no—
566C2×SD16—1064no—
567C2×SD16—1064no—
568C2×SD16—2122no—
569C2×M16—534no—
570C2×M16—1064no—
571C22×C8—531no—
572C22×C8—531no—
573C22×C8—534no—
574C22×C8—531no—
575C22×C8—531no—
576C22×C8—1064no—
577C4⋊Q8—534no—
578C4⋊Q8—1068no—
579C4⋊Q8—1062no—
580#124—28no—
581#124—22no—
582#124C22×D5314yes—
583C22⋊Q8—22no—
584C22⋊Q8—28no—
585C22⋊Q8—534no—
586C22⋊Q8—534no—
587C22⋊Q8—1062no—
588C22⋊Q8—1062no—
589C22⋊Q8—1068no—
590C22⋊Q8—1068no—
591C22⋊Q8C22×D5314yes—
592#121—28no—
593#121—22no—
594#121C22×D5314yes—
595C4×Q8—22no—
596C4×Q8—534no—
597C4×Q8—1062no—
598C4×Q8C22×D5314yes—
599C4×D4—28no—
600C4×D4—1068no—
601C4×D4C22⋊D5314yes—
602C4×D4C22×D5314yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—531no—
606C2×C4⋊C4—1061no—
607C2×C4⋊C4—1061no—
608C2×C4⋊C4—1061no—
609C2×C4⋊C4—1061no—
610C2×C4⋊C4—1061no—
611C2×C4⋊C4C22⋊D5311yescharacteristic
612C2×C4⋊C4C22×D5311yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—1061no—
618C2×C22⋊C4—1061no—
619C2×C22⋊C4C22⋊D5311yescharacteristic
620C2×C22⋊C4C22⋊D5311yescharacteristic
621C2×C42—21no—
622C2×C42—1061no—
623C2×C42C22×D5311yescharacteristic
624#106—534no—
625C4⋊C8—534no—
626#103—534no—
627#103—534no—
628#103—534no—
629#103—534no—
630#103—534no—
631#102—534no—
632C22⋊C8—534no—
633C22⋊C8—534no—
634#97—534no—
635C24—21no—
636C24C2×C22⋊D5311yescharacteristic
637C24C2×C22⋊D5311yescharacteristic
638#41—28no—
639#41—44no—
640#41—48no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—28no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—44no—
649C2×Q8—44no—
650C2×Q8—48no—
651C2×Q8—534no—
652C2×Q8—532no—
653C2×Q8—532no—
654C2×Q8—532no—
655C2×Q8—1068no—
656C2×Q8—1068no—
657C2×Q8—1061no—
658C2×Q8—1064no—
659C2×Q8—1064no—
660C2×Q8—1061no—
661C2×Q8—1061no—
662C2×Q8—1062no—
663C2×Q8—1062no—
664C2×Q8—1062no—
665C2×Q8—1062no—
666C2×Q8—1062no—
667C2×Q8—2124no—
668C2×Q8—2124no—
669C2×Q8—2124no—
670C2×Q8—2124no—
671C2×Q8—2128no—
672C2×Q8—2128no—
673C2×Q8D4×D5314yes—
674C2×Q8C23×D5312yes—
675C2×Q8C23×D5312yes—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4C2×C22⋊D5314yes—
685C2×D4C23×D5312yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—24no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—1061no—
698C22×C4—1064no—
699C22×C4—1064no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1061no—
703C22×C4—2124no—
704C22×C4—2124no—
705C22×C4C2×C22⋊D5312yes—
706C22×C4C2×C22⋊D5312yes—
707C22×C4C2×C22⋊D5311yescharacteristic
708C22×C4C2×C22⋊D5311yescharacteristic
709C22×C4C2×C22⋊D5311yescharacteristic
710C22×C4C2×C22⋊D5311yescharacteristic
711C22×C4C23×D5312yes—
712C22×C4C23×D5312yes—
713C22×C4C23×D5311yescharacteristic
714Q16—5316no—
715Q16—1068no—
716Q16—1068no—
717Q16—1068no—
718Q16—1068no—
719Q16—2124no—
720SD16—1068no—
721SD16—1068no—
722SD16—2124no—
723M16—1068no—
724C2×C8—534no—
725C2×C8—532no—
726C2×C8—532no—
727C2×C8—532no—
728C2×C8—532no—
729C2×C8—1068no—
730C2×C8—1062no—
731C2×C8—1062no—
732C2×C8—1062no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—532no—
737C4⋊C4—1061no—
738C4⋊C4—1064no—
739C4⋊C4—1064no—
740C4⋊C4—1064no—
741C4⋊C4—1064no—
742C4⋊C4—1064no—
743C4⋊C4C2×C22⋊D5314yes—
744C4⋊C4C23×D5312yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4C2×C22⋊D5314yes—
752C22⋊C4C2×C22⋊D5314yes—
753C42—24no—
754C42—1064no—
755C42C2×C22⋊D5312yes—
756C42C23×D5312yes—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23#1313324714yescomplemented
767C23C22×C22⋊D5312yes—
768C23C22×C22⋊D5312yes—
769C23C22×C22⋊D5311yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—48no—
775Q8—42no—
776Q8—534no—
777Q8—1062no—
778Q8—1064no—
779Q8—1062no—
780Q8—1062no—
781Q8—1062no—
782Q8—1062no—
783Q8—2128no—
784Q8—2128no—
785Q8—2122no—
786Q8—2122no—
787Q8C2×D4×D5314yes—
788D4—28no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—42no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—1062no—
813C2×C4—1064no—
814C2×C4—1062no—
815C2×C4—1062no—
816C2×C4—1062no—
817C2×C4—2128no—
818C2×C4—2128no—
819C2×C4—2122no—
820C2×C4—2122no—
821C2×C4—2122no—
822C2×C4C2×D4×D5312yes—
823C2×C4C22×C22⋊D5312yes—
824C2×C4C22×C22⋊D5312yes—
825C2×C4C22×C22⋊D5312yes—
826C2×C4C22×C22⋊D5312yes—
827C2×C4C22×C22⋊D5311yescharacteristic
828C2×C4#1313326212yes—
829C2×C4C24×D5311yescharacteristic
830C8—534no—
831C8—1062no—
832C8—1062no—
833C8—1062no—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—84no—
845C22D4×C22⋊D5312yes—
846C22C2×#1313324712yes—
847C22C2×#1313324714yescomplemented
848C22#1681143812yes—
849C22C23×C22⋊D5311yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—1064no—
858C4—2122no—
859C4—2122no—
860C4—2122no—
861C4D4×C22⋊D5312yes—
862C4C22×D4×D5311yescharacteristic
863C4C2×#1313326211yescharacteristic
864C2—24no—
865C2—42no—
866C2—82no—
867C2#2028628114yesdirect product factor
868C2C2×D4×C22⋊D5311yescharacteristic
869C2C22×#1313324711yescharacteristic
870C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC2×C53×#548C2
socleC23×C53C22×D4
hypercenterC2×#548D53
hypocenterC53C2×#3270
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13133247C2semidirect
2. C23×#11719925C2semidirect
3. C2×D4×Dic106C2semidirect
4. #20286281C2direct (N × H)
5. C2×#16811018C2semidirect
6. C2×#16810879C2semidirect
7. C2×#16810850C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810833C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810779C2semidirect
12. C2×#16810778C2semidirect
13. C2×#16810761C2semidirect
14. C2×#16810728C2semidirect
15. C2×#16810695C2semidirect
20. C2×#13133247C22semidirect
28. C22×#11719925C22semidirect
35. D4×Dic106C22semidirect
44. #16811018C22semidirect
45. #16810879C22semidirect
46. #16810850C22semidirect
47. #16810842C22semidirect
48. #16810833C22semidirect
49. #16810785C22semidirect
50. #16810779C22semidirect
51. #16810778C22semidirect
52. #16810761C22semidirect
53. #16810728C22semidirect
54. #16810695C22semidirect
101. C2×#11719925D4semidirect
299. #11719925C2×D4semidirect
330. C23×C53#137semidirect
412. C22×C53C2×#137semidirect
448. C2×C53#3270semidirect
514. C53C2×#3270semidirect
766. C23#13133247semidirect
847. C22C2×#13133247semidirect
867. C2#20286281direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332472
C23×#117199252
C2×D4×Dic1062
#202862812
C2×#168110182
C2×#168108792
C2×#168108502
C2×#168108422
C2×#168108332
C2×#168107852
C2×#168107792
C2×#168107782
C2×#168107612
C2×#168107282
C2×#168106952
C2×C53×#5482
C2×#327053