Finite Group Databasebeta

← #6687616

Subgroups — #6687616

Order 512.

2060 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3229C211yesmaximal, characteristic, complemented
2C2×#3167C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33043C211yesmaximal, characteristic, complemented
6#30909C214yesmaximal, complemented
7#30705C214yesmaximal, complemented
8#30263C211yesmaximal, characteristic, complemented
9#29807C211yesmaximal, characteristic, complemented
10#28748C211yesmaximal, characteristic, complemented
11#28654C211yesmaximal, characteristic, complemented
12#26902C214yesmaximal, complemented
13#26624C214yesmaximal, complemented
14#25902C211yesmaximal, characteristic, complemented
15#25672C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18#22246C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3229—28no—
26#3167—28no—
27C2×#498C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#492C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#483C2214yes—
37C2×#475C2214yes—
38C2×#465C2214yes—
39C2×C4×SD16C2214yes—
40C2×#431C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42#2868C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2552—21no—
49#2545—21no—
50#2542C2212yes—
51#2538—21no—
52#2491—21no—
53#2491C2212yes—
54#2452—21no—
55#2452C2212yes—
56#2441—21no—
57#2441—21no—
58#2436—21no—
59#2432—21no—
60#2429C2212yes—
61#2429C2212yes—
62#2423—21no—
63#2423—21no—
64#2416—21no—
65#2416C2212yes—
66#2365C2212yes—
67#2361—21no—
68#2361C2212yes—
69#2354—21no—
70Q8×C4⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2065C2214yes—
75#2055C2214yes—
76#2043C2214yes—
77#2035C2214yes—
78#2024C2214yes—
79#2013C2214yes—
80#2013C2214yes—
81#2000C2214yes—
82#2000C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1981C2214yes—
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1933C2214yes—
92#1926C2214yes—
93#1923C2212yes—
94#1920C2214yes—
95#1919C2214yes—
96#1916C2212yes—
97#1892C2214yes—
98#1880C2214yes—
99#1877C2214yes—
100#1872C2214yes—
101#1869C2212yes—
102#1865C2214yes—
103#1850C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C22×SD16C2314yes—
112C22×SD16C2314yes—
113C23×C8C2312yes—
114#548—48no—
115#533—24no—
116#533—24no—
117#533—42no—
118#533—42no—
119#532—24no—
120#532—42no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2312yes—
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2312yes—
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133C2×#127C2311yescharacteristic
134C2×#125—21no—
135C2×#125—21no—
136C2×#124—22no—
137C2×#124—21no—
138C2×#124—21no—
139C2×#124—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—22no—
144C2×C22⋊Q8C2312yes—
145C2×C22⋊Q8C2312yes—
146C2×C22⋊Q8C2312yes—
147C2×C22⋊Q8C2312yes—
148C2×#121—22no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121—21no—
152C2×#121C2312yes—
153C2×#121C2312yes—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×C4×D4—22no—
161C2×C4×D4—21no—
162C2×C4×D4D411yescharacteristic
163C2×C4×D4D411yescharacteristic
164C2×C4×D4C2312yes—
165C2×C4×D4C2311yescharacteristic
166C2×#117—21no—
167C2×#117—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4C2312yes—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#498—24no—
173#498D418yescomplemented
174#492—24no—
175#492—42no—
176#487—24no—
177#487—24no—
178#487—24no—
179#487—42no—
180#486—24no—
181#483—216no—
182#475—216no—
183#465—216no—
184C4×SD16—216no—
185#431—24no—
186C2×#106C2314yes—
187C2×#106C2314yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C4×C8—24no—
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2312yes—
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207#399—22no—
208#399—22no—
209#398—22no—
210#398—22no—
211#396—22no—
212#396—22no—
213#396—22no—
214#396—22no—
215#394—22no—
216#394—22no—
217#393—22no—
218#393—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391C2312yes—
223#391C2312yes—
224#390—22no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390C2312yes—
230#390C2312yes—
231#390C2312yes—
232#389—22no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—22no—
241#389—22no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—22no—
251#386—22no—
252#386—22no—
253#385—22no—
254#385—22no—
255#384—22no—
256#384—21no—
257#384—21no—
258#384—21no—
259#384—21no—
260#384C2311yescharacteristic
261#384C2311yescharacteristic
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380C2312yes—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C43C2311yescharacteristic
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—82no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—82no—
302C22×Q8C2412yes—
303C22×Q8C2412yes—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4C2×D411yescharacteristic
309C22×D4C2412yes—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×SD16—28no—
319C2×SD16—44no—
320C2×SD16—44no—
321C2×SD16—44no—
322C2×SD16—44no—
323C2×SD16—44no—
324C22×C8—24no—
325C22×C8—42no—
326C22×C8—42no—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C4⋊Q8—24no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—42no—
341C4⋊Q8—44no—
342C4⋊Q8—44no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345C4⋊Q8C2×D414yes—
346C4⋊Q8C2×D414yes—
347#127—22no—
348#127—22no—
349#125—44no—
350#125—44no—
351#124—44no—
352#124—48no—
353#124—44no—
354#124—82no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—42no—
358C22⋊Q8—42no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—48no—
363C22⋊Q8—44no—
364C22⋊Q8—44no—
365#121—24no—
366#121—44no—
367#121—42no—
368#121—44no—
369#121—44no—
370#121—48no—
371#121—44no—
372C4×Q8—24no—
373C4×Q8—24no—
374C4×Q8—42no—
375C4×Q8—42no—
376C4×Q8—44no—
377C4×Q8—44no—
378C4×Q8—44no—
379C4×Q8—44no—
380C4×D4—24no—
381C4×D4—42no—
382C4×D4—44no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—48no—
386C4×D4SD1618yescomplemented
387#117—44no—
388#117—44no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C22⋊C4C2×D411yescharacteristic
445C2×C22⋊C4C2×D411yescharacteristic
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467#106—28no—
468#106C2×D4116yes—
469C4⋊C8—24no—
470C4⋊C8—42no—
471#103—28no—
472#103—28no—
473#103—28no—
474#103—44no—
475#103—44no—
476#103—44no—
477#102—28no—
478#102—44no—
479C22⋊C8—24no—
480C22⋊C8—42no—
481C22⋊C8—42no—
482C4×C8—24no—
483C4×C8—22no—
484C4×C8—22no—
485C4×C8—22no—
486C4×C8C2×D414yes—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501#95C2×D411yescharacteristic
502#95C2×D411yescharacteristic
503C24—22no—
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506#41—816no—
507C2×Q8—24no—
508C2×Q8—24no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—24no—
514C2×Q8—24no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8—44no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—44no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—82no—
527C2×Q8—816no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—82no—
546C2×D4C2×SD1614yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4C2×SD1614yes—
579C22×C4C2×SD1614yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C2511yescharacteristic
593SD16—416no—
594SD16—88no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—48no—
607C2×C8C22×D414yes—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—82no—
639C4⋊C4—82no—
640C4⋊C4—82no—
641C4⋊C4—82no—
642C4⋊C4C2×SD1614yes—
643C4⋊C4C22×D414yes—
644C4⋊C4C22×D414yes—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C22⋊C4—41no—
648C22⋊C4—41no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—82no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4C2×SD1614yes—
664C22⋊C4C2×SD1614yes—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—22no—
677C42—22no—
678C42—44no—
679C42—44no—
680C42—44no—
681C42—44no—
682C42C2×SD1614yes—
683C42C22×D412yes—
684C42H(5,𝔽2)12yes—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23C22×SD1612yes—
705C23C22×SD1612yes—
706C23C23×D411yescharacteristic
707Q8—48no—
708Q8—48no—
709Q8—44no—
710Q8—44no—
711Q8—44no—
712Q8—44no—
713Q8—88no—
714Q8—84no—
715D4—44no—
716D4—44no—
717D4—44no—
718D4—88no—
719D4—88no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4D4212yes—
780C2×C4D4212yes—
781C2×C4C22×SD1612yes—
782C2×C4C22×SD1612yes—
783C2×C4C22×SD1612yes—
784C2×C4C22×SD1612yes—
785C2×C4C22×SD1612yes—
786C2×C4#57512yes—
787C2×C4#57712yes—
788C2×C4#57812yes—
789C2×C4C23×D411yescharacteristic
790C2×C4C2×H(5,𝔽2)11yescharacteristic
791C2×C4#58512yes—
792C2×C4#58512yes—
793C8—24no—
794C8—42no—
795C8—42no—
796C8—42no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22#344911yescharacteristic
819C22C2×D4211yescharacteristic
820C22#350011yescharacteristic
821C22C23×SD1611yescharacteristic
822C22C2×#57511yescharacteristic
823C22C2×#57711yescharacteristic
824C22C2×#57811yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—44no—
836C4—44no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4#326914yes—
843C4D4×SD1614yes—
844C4#348712yes—
845C4#356212yes—
846C2—42no—
847C2—42no—
848C2—162no—
849C2#3768311yescharacteristic
850C2#6094111yescharacteristic
851C2#6100811yescharacteristic
852C2C2×#326911yescharacteristic
853C2C2×D4×SD1611yescharacteristic
854C2#6252611yescharacteristic
855C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3229C2semidirect
2. C2×#3167C2semidirect
3. #36134C2semidirect
5. #33043C2semidirect
6. #30909C2semidirect
7. #30705C2semidirect
8. #30263C2semidirect
9. #29807C2semidirect
10. #28748C2semidirect
11. #28654C2semidirect
12. #26902C2semidirect
13. #26624C2semidirect
14. #25902C2semidirect
15. #25672C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. #22246C2semidirect
19. #21101C2semidirect
173. #498D4semidirect
386. C4×D4SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#32292
C2×#31672
#361342
#361222
#330432
#309092
#307052
#302632
#298072
#287482
#286542
#269022
#266242
#259022
#256722
#255982
#255972
#222462
#211012