Finite Group Databasebeta

← #6343395

Subgroups — #6343395

Order 512.

3139 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34057C211yesmaximal, characteristic, complemented
4#17598C2116yesmaximal, complemented
5#17584C212yesmaximal, complemented
6#17582C212yesmaximal, complemented
7#17579C212yesmaximal, complemented
8#17578C212yesmaximal, complemented
9#17542C212yesmaximal, complemented
10C2×#1508C212yesmaximal, complemented
11#3520—24no—
12#3520—24no—
13#3520C418yescomplemented
14#3520C2218yes—
15C2×#556C411yescharacteristic, complemented
16C2×#554—21no—
17C2×#552C411yescharacteristic, complemented
18C2×#552C411yescharacteristic, complemented
19C2×#551—21no—
20C2×#551—21no—
21C2×D4×Q8C411yescharacteristic, complemented
22C2×#548C411yescharacteristic, complemented
23C2×#548C411yescharacteristic, complemented
24C2×#547C411yescharacteristic, complemented
25C2×#547C411yescharacteristic, complemented
26C2×#546—21no—
27C2×#542—21no—
28C2×#539—21no—
29C2×#539—21no—
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C2×#520—21no—
37C22×C4×D4C2211yescharacteristic
38#2975—21no—
39#2974C2218yescomplemented
40#2973—21no—
41#2973—21no—
42#2972—21no—
43D4×M16—24no—
44#2920C2212yes—
45C2×#407C2212yes—
46C2×#407C2212yes—
47#2318C2218yescomplemented
48#2315—21no—
49#2313—21no—
50#2312—21no—
51#2308—21no—
52#2290—24no—
53#2283C2212yes—
54#2280C2212yes—
55C2×C4×C22⋊C4C2212yes—
56#1521C2218yescomplemented
57#1520C2218yescomplemented
58#1518C2218yescomplemented
59#1516C2218yescomplemented
60#1515C2218yescomplemented
61#1513C2218yescomplemented
62#1512C2218yescomplemented
63#1511C2218yescomplemented
64#1508C2214yes—
65#1508C2214yes—
66#1508C2214yes—
67#1508C2218yescomplemented
68#1507C2214yes—
69#1504C2218yescomplemented
70#1501C2218yescomplemented
71C2×#328C2218yescomplemented
72C22×#41—21no—
73C22×#41C2×C411yescharacteristic
74C22×#41C2×C411yescharacteristic, complemented
75C23×Q8C2×C411yescharacteristic
76C23×Q8C2×C411yescharacteristic, complemented
77C23×D4D411yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C22×M16—22no—
81C22×M16—22no—
82#556—24no—
83#556C2×C418yescomplemented
84#554—28no—
85#554—28no—
86#552—24no—
87#552—24no—
88#552C2×C418yescomplemented
89#552C2×C418yescomplemented
90#551—28no—
91#551—28no—
92#551—28no—
93#551—28no—
94D4×Q8—24no—
95D4×Q8C2×C418yescomplemented
96#548—24no—
97#548—24no—
98#548C2×C418yescomplemented
99#548C2×C418yescomplemented
100#547—24no—
101#547—24no—
102#547C2×C418yescomplemented
103#547C2×C418yescomplemented
104#546—28no—
105#546—28no—
106#542—28no—
107#542—28no—
108#539—28no—
109#539—28no—
110#539—28no—
111#539—28no—
112#533—22no—
113#533—22no—
114#533C2×C414yescomplemented
115#533C2314yes—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8C2×C411yescharacteristic, complemented
118C2×C4⋊Q8C2×C411yescharacteristic, complemented
119#529—22no—
120#529—22no—
121#529C2×C414yescomplemented
122#529C2314yes—
123C2×#126—21no—
124C2×#126—21no—
125C2×#126—21no—
126C2×#126—21no—
127C2×#126—21no—
128C2×#125—21no—
129C2×#125—21no—
130C2×#125—21no—
131C2×#125C2×C411yescharacteristic, complemented
132C2×#124—21no—
133C2×#124—21no—
134C2×#124—21no—
135C2×#124C2×C411yescharacteristic, complemented
136#525—22no—
137#525—22no—
138#525—22no—
139#525—22no—
140#525C2×C414yes—
141#525C2×C414yescomplemented
142#525C2314yes—
143#525C2314yes—
144C2×#123—21no—
145C2×#123—21no—
146C2×#123—21no—
147C2×#123—21no—
148C2×#123—21no—
149C2×#123—21no—
150C2×#123—21no—
151C2×#123—21no—
152C2×#123—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8C2×C411yescharacteristic
168C2×C22⋊Q8C2×C411yescharacteristic
169C2×C22⋊Q8C2×C414yes—
170C2×C22⋊Q8C2×C411yescharacteristic
171C2×C22⋊Q8C2×C411yescharacteristic, complemented
172C2×C22⋊Q8C2×C411yescharacteristic, complemented
173C2×C22⋊Q8C2×C414yescomplemented
174C2×C22⋊Q8C2×C411yescharacteristic, complemented
175C2×C22⋊Q8C2311yescharacteristic
176C2×C22⋊Q8C2311yescharacteristic
177C2×C22⋊Q8C2311yescharacteristic
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×#121—21no—
181C2×#121—21no—
182C2×#121—21no—
183C2×#121C2×C411yescharacteristic
184C2×#121C2×C411yescharacteristic, complemented
185C2×#121C2311yescharacteristic
186C2×#120—21no—
187C2×#120—21no—
188#520—28no—
189#520—28no—
190C2×C4×Q8—21no—
191C2×C4×Q8—21no—
192C2×C4×Q8C2×C411yescharacteristic, complemented
193C2×C4×Q8C2×C411yescharacteristic, complemented
194C2×C4×Q8C2×C411yescharacteristic, complemented
195C2×C4×D4—21no—
196C2×C4×D4—21no—
197C2×C4×D4—21no—
198C2×C4×D4—21no—
199C2×C4×D4—21no—
200C2×C4×D4—21no—
201C2×C4×D4—21no—
202C2×C4×D4—21no—
203C2×C4×D4C2×C411yescharacteristic
204C2×C4×D4C2×C411yescharacteristic
205C2×C4×D4C2×C411yescharacteristic
206C2×C4×D4C2×C411yescharacteristic
207C2×C4×D4C2×C414yes—
208C2×C4×D4C2×C411yescharacteristic, complemented
209C2×C4×D4D411yescharacteristic
210C2×C4×D4D414yes—
211C2×C4×D4D411yescharacteristic
212C2×C4×D4D411yescharacteristic
213C2×C4×D4D411yescharacteristic
214C2×C4×D4D414yes—
215C2×C4×D4C2314yes—
216C2×#117—21no—
217C2×#117—22no—
218C2×#117—21no—
219C2×#117—21no—
220C2×#117—21no—
221C2×#117C2×C411yescharacteristic
222C2×#117C2×C411yescharacteristic, complemented
223C22×C4⋊C4—21no—
224C22×C4⋊C4—21no—
225C22×C4⋊C4—21no—
226C22×C4⋊C4C2×C411yescharacteristic
227C22×C4⋊C4C2×C411yescharacteristic, complemented
228C22×C4⋊C4D411yescharacteristic
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C22×C22⋊C4—22no—
232C22×C22⋊C4D411yescharacteristic
233C22×C22⋊C4D411yescharacteristic
234C22×C42—22no—
235C22×C42C2311yescharacteristic
236#436—28no—
237#435—28no—
238#435—28no—
239C8×D4—28no—
240#432—22no—
241#432C2314yes—
242#431—22no—
243#431C2314yes—
244#423—22no—
245#407—22no—
246#407—22no—
247#407—22no—
248#407—22no—
249#407C2314yes—
250#407C2314yes—
251#407C2314yes—
252C2×C22⋊C8—22no—
253C2×C22⋊C8—22no—
254C2×C22⋊C8C2314yes—
255C2×C22⋊C8C2314yes—
256C4×M16—22no—
257#388—28no—
258#387—28no—
259#386—28no—
260#385—28no—
261#383C2314yes—
262#382C2314yes—
263#381—22no—
264#381C2314yes—
265#380—22no—
266#380—22no—
267#380C2314yes—
268#379—22no—
269C4×C4⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—22no—
273C4×C22⋊C4C2314yes—
274C4×C22⋊C4C2314yes—
275#376—22no—
276C2×#95C2314yes—
277#328C23116yes—
278#328C23116yes—
279#328C23116yes—
280#327C23116yes—
281C25C2×D411yescharacteristic
282C25C2×D411yescharacteristic
283C2×#41—28no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—48no—
287C2×#41—82no—
288C2×#41—82no—
289C2×#41C22×C414yes—
290C2×#41C22×C414yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—82no—
297C22×Q8—82no—
298C22×Q8C22×C411yescharacteristic
299C22×Q8C22×C411yescharacteristic
300C22×Q8C22×C411yescharacteristic
301C22×Q8C22×C414yes—
302C22×Q8C22×C414yes—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—44no—
309C22×D4C22⋊C411yescharacteristic
310C22×D4C22⋊C411yescharacteristic
311C22×D4C22⋊C411yescharacteristic
312C22×D4C22⋊C411yescharacteristic
313C22×D4C22⋊C414yes—
314C22×D4C22×C411yescharacteristic
315C22×D4C2×D414yes—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—24no—
324C23×C4—82no—
325C23×C4—82no—
326C23×C4C22×C411yescharacteristic
327C23×C4C22×C411yescharacteristic
328C23×C4C22×C411yescharacteristic
329C23×C4C22×C411yescharacteristic
330C23×C4C22×C412yes—
331C23×C4C22×C412yes—
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D411yescharacteristic
334C23×C4C2×D412yes—
335C23×C4C2×D412yes—
336C23×C4C2×D412yes—
337C23×C4C2×D412yes—
338C23×C4C2×D411yescharacteristic
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2411yescharacteristic
345C23×C4C2412yes—
346C23×C4C2412yes—
347C2×M16—24no—
348C2×M16—24no—
349C2×M16—24no—
350C2×M16—84no—
351C2×M16—84no—
352C22×C8—24no—
353C22×C8—24no—
354C4⋊Q8—28no—
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4⋊Q8C22×C414yes—
358C4⋊Q8C22×C414yes—
359#126—28no—
360#126—28no—
361#126—28no—
362#126—28no—
363#126—24no—
364#126—24no—
365#125—28no—
366#125—28no—
367#125—24no—
368#125—22no—
369#125—24no—
370#125C22×C414yes—
371#124—28no—
372#124—28no—
373#124—28no—
374#124—22no—
375#124C22×C414yes—
376#123—28no—
377#123—28no—
378#123—24no—
379#123—24no—
380#123—24no—
381#123—24no—
382#123—24no—
383#123—24no—
384#123—28no—
385#123—28no—
386#123—28no—
387#123—28no—
388C22⋊Q8—24no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—24no—
392C22⋊Q8—24no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—24no—
396C22⋊Q8—24no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—24no—
406C22⋊Q8—24no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410C22⋊Q8—28no—
411C22⋊Q8—28no—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C22⋊Q8—28no—
415C22⋊Q8C22×C412yes—
416C22⋊Q8C22×C412yes—
417C22⋊Q8C22×C414yes—
418C22⋊Q8C22×C414yes—
419C22⋊Q8C22×C414yes—
420C22⋊Q8C22×C412yes—
421C22⋊Q8C22×C414yes—
422C22⋊Q8C22×C414yes—
423C22⋊Q8C22×C414yes—
424C22⋊Q8C2412yes—
425C22⋊Q8C2412yes—
426C22⋊Q8C2412yes—
427#121—28no—
428#121—28no—
429#121—28no—
430#121—22no—
431#121—22no—
432#121—21no—
433#121—21no—
434#121C22×C414yes—
435#121C22×C414yes—
436#121C22×C412yes—
437#121C2412yes—
438#120—24no—
439#120—24no—
440#120—24no—
441#120—24no—
442C4×Q8—28no—
443C4×Q8—24no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—24no—
448C4×Q8C22×C414yes—
449C4×Q8C22×C414yes—
450C4×Q8C22×C414yes—
451C4×D4—28no—
452C4×D4—24no—
453C4×D4—24no—
454C4×D4—24no—
455C4×D4—24no—
456C4×D4—24no—
457C4×D4—24no—
458C4×D4—24no—
459C4×D4—24no—
460C4×D4—24no—
461C4×D4—24no—
462C4×D4—28no—
463C4×D4—28no—
464C4×D4—22no—
465C4×D4C22⋊C414yes—
466C4×D4C22⋊C414yes—
467C4×D4C22⋊C414yes—
468C4×D4C22⋊C414yes—
469C4×D4C22⋊C414yes—
470C4×D4C22⋊C414yes—
471C4×D4C22⋊C414yes—
472C4×D4C22⋊C414yes—
473C4×D4C22×C414yes—
474C4×D4C22×C414yes—
475C4×D4C22×C414yes—
476C4×D4C22×C414yes—
477C4×D4C22×C414yes—
478C4×D4C2×D414yes—
479C4×D4C2×D414yes—
480C4×D4C2×D414yes—
481C4×D4C2×D414yes—
482#117—24no—
483#117—22no—
484#117—22no—
485#117—24no—
486#117—28no—
487#117—28no—
488#117—24no—
489#117—24no—
490#117—84no—
491#117C22×C414yes—
492#117C22×C414yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—28no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4C22⋊C411yescharacteristic
522C2×C4⋊C4C22⋊C411yescharacteristic
523C2×C4⋊C4C22⋊C411yescharacteristic
524C2×C4⋊C4C22⋊C411yescharacteristic
525C2×C4⋊C4C22⋊C414yes—
526C2×C4⋊C4C22×C411yescharacteristic
527C2×C4⋊C4C22×C411yescharacteristic
528C2×C4⋊C4C22×C414yes—
529C2×C4⋊C4C22×C411yescharacteristic
530C2×C4⋊C4C22×C414yes—
531C2×C4⋊C4C22×C411yescharacteristic
532C2×C4⋊C4C2×D414yes—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—48no—
559C2×C22⋊C4C22⋊C411yescharacteristic
560C2×C22⋊C4C22⋊C411yescharacteristic
561C2×C22⋊C4C22⋊C411yescharacteristic
562C2×C22⋊C4C22⋊C411yescharacteristic
563C2×C22⋊C4C22⋊C411yescharacteristic
564C2×C22⋊C4C22⋊C411yescharacteristic
565C2×C22⋊C4C22⋊C411yescharacteristic
566C2×C22⋊C4C22⋊C411yescharacteristic
567C2×C22⋊C4C22⋊C414yes—
568C2×C22⋊C4C22⋊C414yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C42—21no—
572C2×C42—21no—
573C2×C42—21no—
574C2×C42—21no—
575C2×C42—21no—
576C2×C42—24no—
577C2×C42—24no—
578C2×C42—84no—
579C2×C42C22×C411yescharacteristic
580C2×C42C22×C411yescharacteristic
581C2×C42C22×C412yes—
582C2×C42C2×D412yes—
583C2×C42C2×D411yescharacteristic
584C2×C42C2×D411yescharacteristic
585C2×C42C2×D412yes—
586C2×C42C2412yes—
587C4⋊C8—24no—
588C4⋊C8—24no—
589C22⋊C8—24no—
590C22⋊C8—24no—
591C22⋊C8—24no—
592C22⋊C8—24no—
593C22⋊C8—24no—
594C22⋊C8C2418yes—
595#97—24no—
596C4×C8—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95C2418yes—
603C24—24no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—81no—
609C24—81no—
610C24C2×C22⋊C411yescharacteristic
611C24C2×C22⋊C411yescharacteristic
612C24C2×C22⋊C412yes—
613C24C2×C22⋊C411yescharacteristic
614C24C2×C22⋊C412yes—
615C24C2×C22⋊C411yescharacteristic
616C24C22×D411yescharacteristic
617C24C22×D412yes—
618C24C22×D412yes—
619#41—432no—
620#41—84no—
621#41—84no—
622#41—84no—
623#41—84no—
624C2×Q8—24no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—24no—
629C2×Q8—24no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8—42no—
633C2×Q8—44no—
634C2×Q8—84no—
635C2×Q8—84no—
636C2×Q8—82no—
637C2×Q8—82no—
638C2×Q8—84no—
639C2×Q8—84no—
640C2×Q8C23×C412yes—
641C2×Q8C23×C412yes—
642C2×Q8C23×C412yes—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—48no—
656C2×D4—48no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—82no—
661C2×D4—82no—
662C2×D4C2×C22⋊C414yes—
663C2×D4C2×C22⋊C414yes—
664C2×D4C2×C22⋊C414yes—
665C2×D4C2×C22⋊C414yes—
666C2×D4C23×C412yes—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—28no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—48no—
697C22×C4—82no—
698C22×C4—82no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4—82no—
706C22×C4—82no—
707C22×C4—84no—
708C22×C4—84no—
709C22×C4—82no—
710C22×C4—82no—
711C22×C4—82no—
712C22×C4—82no—
713C22×C4C2×C22⋊C411yescharacteristic
714C22×C4C2×C22⋊C411yescharacteristic
715C22×C4C2×C22⋊C412yes—
716C22×C4C2×C22⋊C412yes—
717C22×C4C2×C22⋊C412yes—
718C22×C4C2×C22⋊C412yes—
719C22×C4C2×C22⋊C411yescharacteristic
720C22×C4C2×C22⋊C411yescharacteristic
721C22×C4C2×C22⋊C411yescharacteristic
722C22×C4C2×C22⋊C411yescharacteristic
723C22×C4C2×C22⋊C412yes—
724C22×C4C2×C22⋊C412yes—
725C22×C4C2×C22⋊C411yescharacteristic
726C22×C4C2×C22⋊C411yescharacteristic
727C22×C4C2×C22⋊C412yes—
728C22×C4C2×C22⋊C412yes—
729C22×C4C2×C22⋊C412yes—
730C22×C4C2×C22⋊C412yes—
731C22×C4C2×C22⋊C412yes—
732C22×C4C2×C22⋊C412yes—
733C22×C4C23×C411yescharacteristic
734C22×C4C23×C411yescharacteristic
735C22×C4C23×C412yes—
736C22×C4C23×C412yes—
737C22×C4C23×C412yes—
738C22×C4C23×C412yes—
739C22×C4C22×D412yes—
740C22×C4C22×D411yescharacteristic
741C22×C4C22×D411yescharacteristic
742C22×C4C22×D412yes—
743C22×C4C22×D412yes—
744C22×C4C22×D412yes—
745C22×C4C22×D411yescharacteristic
746C22×C4C22×D412yes—
747C22×C4C22×D412yes—
748C22×C4C22×D412yes—
749C22×C4C22×D412yes—
750C22×C4C2511yescharacteristic
751M16—48no—
752M16—84no—
753M16—84no—
754C2×C8—28no—
755C2×C8—84no—
756C2×C8—84no—
757C4⋊C4—22no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—21no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—22no—
765C4⋊C4—22no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—21no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—84no—
784C4⋊C4—84no—
785C4⋊C4C2×C22⋊C414yes—
786C4⋊C4C2×C22⋊C414yes—
787C4⋊C4C2×C22⋊C414yes—
788C4⋊C4C2×C22⋊C414yes—
789C4⋊C4C23×C412yes—
790C4⋊C4C23×C412yes—
791C4⋊C4C23×C412yes—
792C4⋊C4C23×C412yes—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—24no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—24no—
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—22no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—84no—
817C22⋊C4—84no—
818C22⋊C4C2×C22⋊C414yes—
819C22⋊C4C2×C22⋊C414yes—
820C22⋊C4C2×C22⋊C414yes—
821C22⋊C4C2×C22⋊C414yes—
822C22⋊C4C2×C22⋊C414yes—
823C22⋊C4C2×C22⋊C414yes—
824C22⋊C4C2×C22⋊C414yes—
825C22⋊C4C2×C22⋊C414yes—
826C42—24no—
827C42—24no—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—48no—
832C42—84no—
833C42C2×C22⋊C412yes—
834C42C2×C22⋊C412yes—
835C42C2×C22⋊C412yes—
836C42C2×C22⋊C412yes—
837C42C23×C412yes—
838C42C23×C412yes—
839C42C22×D412yes—
840C42C22×D412yes—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—24no—
845C23—22no—
846C23—24no—
847C23—22no—
848C23—24no—
849C23—22no—
850C23—22no—
851C23—41no—
852C23—41no—
853C23—42no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—41no—
859C23—41no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—41no—
865C23—41no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—88no—
872C23—88no—
873C23#42114yes—
874C23C22×C22⋊C412yes—
875C23C22×C22⋊C412yes—
876C23C22×C22⋊C411yescharacteristic
877C23C22×C22⋊C412yes—
878C23C22×C22⋊C412yes—
879C23C22×C22⋊C411yescharacteristic
880C23C23×D411yescharacteristic
881Q8—42no—
882Q8—42no—
883Q8—42no—
884Q8—48no—
885Q8—42no—
886Q8—42no—
887Q8—42no—
888Q8—84no—
889Q8—84no—
890D4—28no—
891D4—28no—
892D4—44no—
893D4—44no—
894D4—42no—
895D4—44no—
896D4—48no—
897D4—44no—
898D4—48no—
899D4—42no—
900D4—84no—
901D4—84no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—84no—
961C2×C4—84no—
962C2×C4—84no—
963C2×C4—84no—
964C2×C4—816no—
965C2×C4C22×C22⋊C412yes—
966C2×C4C22×C22⋊C412yes—
967C2×C4C22×C22⋊C412yes—
968C2×C4C22×C22⋊C412yes—
969C2×C4C22×C22⋊C411yescharacteristic
970C2×C4C22×C22⋊C412yes—
971C2×C4C22×C22⋊C412yes—
972C2×C4C22×C22⋊C412yes—
973C2×C4C22×C22⋊C412yes—
974C2×C4C22×C22⋊C411yescharacteristic
975C2×C4C24×C411yescharacteristic
976C2×C4C23×D411yescharacteristic
977C8—48no—
978C22—21no—
979C22—21no—
980C22—22no—
981C22—21no—
982C22—22no—
983C22—21no—
984C22—21no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—21no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—21no—
994C22—22no—
995C22—22no—
996C22—44no—
997C22—48no—
998C22—44no—
999C22—44no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—84no—
1004C22—82no—
1005C22—82no—
1006C22—84no—
1007C22—84no—
1008C22—84no—
1009C22C2×#42112yes—
1010C22C2×#42114yes—
1011C22C23×C22⋊C411yescharacteristic
1012C22#358612yes—
1013C4—21no—
1014C4—21no—
1015C4—21no—
1016C4—22no—
1017C4—22no—
1018C4—22no—
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—22no—
1023C4—22no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—88no—
1032C4#288312yes—
1033C2—22no—
1034C2—22no—
1035C2—24no—
1036C2—42no—
1037C2—42no—
1038C2—41no—
1039C2—42no—
1040C2—82no—
1041C2C2×#288311yescharacteristic
1042C2#6008811yescharacteristic
1043C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3520C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. #34057C2semidirect
4. #17598C2semidirect
5. #17584C2semidirect
6. #17582C2semidirect
7. #17579C2semidirect
8. #17578C2semidirect
9. #17542C2semidirect
10. C2×#1508C2semidirect
13. #3520C4semidirect
15. C2×#556C4semidirect
17. C2×#552C4semidirect
18. C2×#552C4semidirect
21. C2×D4×Q8C4semidirect
22. C2×#548C4semidirect
23. C2×#548C4semidirect
24. C2×#547C4semidirect
25. C2×#547C4semidirect
39. #2974C22semidirect
47. #2318C22semidirect
56. #1521C22semidirect
57. #1520C22semidirect
58. #1518C22semidirect
59. #1516C22semidirect
60. #1515C22semidirect
61. #1513C22semidirect
62. #1512C22semidirect
63. #1511C22semidirect
67. #1508C22semidirect
69. #1504C22semidirect
70. #1501C22semidirect
71. C2×#328C22semidirect
74. C22×#41C2×C4semidirect
76. C23×Q8C2×C4semidirect
83. #556C2×C4semidirect
88. #552C2×C4semidirect
89. #552C2×C4semidirect
95. D4×Q8C2×C4semidirect
98. #548C2×C4semidirect
99. #548C2×C4semidirect
102. #547C2×C4semidirect
103. #547C2×C4semidirect
114. #533C2×C4semidirect
117. C2×C4⋊Q8C2×C4semidirect
118. C2×C4⋊Q8C2×C4semidirect
121. #529C2×C4semidirect
131. C2×#125C2×C4semidirect
135. C2×#124C2×C4semidirect
141. #525C2×C4semidirect
171. C2×C22⋊Q8C2×C4semidirect
172. C2×C22⋊Q8C2×C4semidirect
173. C2×C22⋊Q8C2×C4semidirect
174. C2×C22⋊Q8C2×C4semidirect
184. C2×#121C2×C4semidirect
192. C2×C4×Q8C2×C4semidirect
193. C2×C4×Q8C2×C4semidirect
194. C2×C4×Q8C2×C4semidirect
208. C2×C4×D4C2×C4semidirect
222. C2×#117C2×C4semidirect
227. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
#602302
#340572
#175982
#175842
#175822
#175792
#175782
#175422
C2×#15082