Finite Group Databasebeta

← #6409508

Subgroups — #6409508

Order 512.

1407 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34913C211yesmaximal, characteristic
2#23319C212yesmaximal, complemented
3#23315C212yesmaximal, complemented
4#23254C211yesmaximal, characteristic, complemented
5#23253C211yesmaximal, characteristic, complemented
6#23209C211yesmaximal, characteristic, complemented
7#23204C211yesmaximal, characteristic, complemented
8#22822C211yesmaximal, characteristic, complemented
9#22800C212yesmaximal, complemented
10#22795C211yesmaximal, characteristic, complemented
11#22754C212yesmaximal, complemented
12#22721C211yesmaximal, characteristic, complemented
13D4×C4⋊C8C211yesmaximal, characteristic, complemented
14#22352C212yesmaximal, complemented
15#22342C212yesmaximal, complemented
16#22135C211yesmaximal, characteristic
17#22133C211yesmaximal, characteristic
18#22102C211yesmaximal, characteristic, complemented
19#22098C211yesmaximal, characteristic, complemented
20#21973C212yesmaximal, complemented
21#21928C212yesmaximal, complemented
22#20812C211yesmaximal, characteristic, complemented
23#20809C211yesmaximal, characteristic, complemented
24C2×#446C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×C8×D4C2211yescharacteristic
27C2×C8×D4C2211yescharacteristic
28C2×#433C2212yes—
29C2×#431C2212yes—
30C2×#431C2211yescharacteristic
31C2×#431C2211yescharacteristic
32C22×C4⋊C8C2212yes—
33#2578C412yes—
34#2577C412yes—
35#2576C412yes—
36#2575C412yes—
37#2514C411yescharacteristic
38#2508C411yescharacteristic
39#2495C411yescharacteristic
40#2489C411yescharacteristic
41#2454C411yescharacteristic
42#2447C411yescharacteristic
43#2427C411yescharacteristic
44#2420C411yescharacteristic
45#2401C2212yes—
46#2395C2212yes—
47C4×#125C2211yescharacteristic
48C4×#124C2211yescharacteristic
49C4×C22⋊Q8C2211yescharacteristic
50C4×#121C2211yescharacteristic
51#2295C2211yescharacteristic
52#2290C2212yes—
53#2283C2212yes—
54C42×D4C2211yescharacteristic
55C4×#117C2211yescharacteristic
56#1984C2211yescharacteristic
57#1984C2211yescharacteristic
58#1955C2212yes—
59#1954C2211yescharacteristic
60#1954C2211yescharacteristic
61#1954C2212yes—
62#1940C2212yes—
63#1939C2212yes—
64#1939C2212yes—
65#1939C2212yes—
66#1939C2212yes—
67#1939C2212yes—
68#1939C2211yescharacteristic
69#1939C2211yescharacteristic
70#1939C2211yescharacteristic
71#1939C2211yescharacteristic
72#1924C2212yes—
73#1924C2212yes—
74#1924C2212yes—
75#1924C2212yes—
76#1923C2212yes—
77#1923C2212yes—
78#1923C2212yes—
79#1923C2212yes—
80#1923C2212yes—
81#1923C2212yes—
82#1923C2212yes—
83#1923C2212yes—
84#1917C2212yes—
85#1917C2212yes—
86#1917C2212yes—
87#1917C2212yes—
88#1916C2212yes—
89#1916C2212yes—
90#1916C2212yes—
91#1916C2212yes—
92#1869C2212yes—
93#1869C2212yes—
94#1850C2212yes—
95#1850C2212yes—
96#1850C2212yes—
97#1850C2212yes—
98#1850C2212yes—
99#1850C2212yes—
100#1843C2212yes—
101#1843C2211yescharacteristic
102#1843C2211yescharacteristic
103#1842C2211yescharacteristic
104#1842C2211yescharacteristic
105#1832C2212yes—
106#1832C2211yescharacteristic
107#1832C2211yescharacteristic
108#1832C2212yes—
109#1798C2211yescharacteristic
110#1798C2211yescharacteristic
111#1798C2212yes—
112#1798C2211yescharacteristic
113#1798C2211yescharacteristic
114#1797C2212yes—
115#1797C2212yes—
116#1797C2211yescharacteristic
117#1797C2211yescharacteristic
118#1771C2212yes—
119#1770C2211yescharacteristic
120C8×C4⋊C4C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2212yes—
123C8×C4⋊C4C2211yescharacteristic
124#1768C2212yes—
125#1768C2212yes—
126#1768C2212yes—
127#1767C2211yescharacteristic
128C4×C4⋊C8C2211yescharacteristic
129C4×C4⋊C8C2211yescharacteristic
130C4×C4⋊C8C2211yescharacteristic
131C4×C4⋊C8C2211yescharacteristic
132C4×C4⋊C8C2211yescharacteristic
133#1752C2212yes—
134C8×C22⋊C4C2212yes—
135C23×C8C2312yes—
136C23×C8C2312yes—
137C2×#125C2×C411yescharacteristic
138C2×#124C2×C411yescharacteristic
139C2×C22⋊Q8C2×C411yescharacteristic
140C2×#121C2×C411yescharacteristic
141C2×C4×Q8C2311yescharacteristic
142C2×C4×D4C2×C411yescharacteristic
143C2×C4×D4C2×C411yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×C4×D4C2312yes—
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150#446—42no—
151C8×Q8—42no—
152C8×D4—42no—
153C8×D4—42no—
154#433—44no—
155#431—42no—
156#431—42no—
157#431—44no—
158C2×C4⋊C8—44no—
159C2×C4⋊C8C2311yescharacteristic
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×#97C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208C2×C4×C8C2312yes—
209#401C2×C412yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#400C2×C412yes—
213#400C2×C412yes—
214#399C2×C412yes—
215#398C2×C412yes—
216#397C2×C412yes—
217#397C2×C412yes—
218#397C2×C412yes—
219#397C2×C412yes—
220#397C2×C412yes—
221#397C2×C412yes—
222#396C2×C412yes—
223#394C2×C412yes—
224#394C2×C412yes—
225#391C2×C411yescharacteristic
226#391C2×C411yescharacteristic
227#391C2×C411yescharacteristic
228#391C2×C411yescharacteristic
229#390C2×C411yescharacteristic
230#390C2×C411yescharacteristic
231#389C2×C411yescharacteristic
232#389C2×C411yescharacteristic
233#389C2×C411yescharacteristic
234#389C2×C411yescharacteristic
235#389C2×C411yescharacteristic
236#389C2×C411yescharacteristic
237#388C2×C412yes—
238#388C2×C412yes—
239#388C2×C412yes—
240#388C2×C412yes—
241#388C2×C412yes—
242#387C2×C412yes—
243#387C2×C412yes—
244#387C2×C412yes—
245#387C2×C412yes—
246#387C2×C412yes—
247#387C2×C412yes—
248#387C2×C412yes—
249#386C2×C412yes—
250#386C2×C412yes—
251#386C2×C412yes—
252#385C2×C412yes—
253#385C2×C412yes—
254#385C2×C412yes—
255#383C2×C412yes—
256#383C2×C412yes—
257#382C2×C411yescharacteristic
258#382C2×C412yes—
259#382C2×C412yes—
260#382C2×C411yescharacteristic
261#381C2×C412yes—
262#381C2×C412yes—
263#380C2×C412yes—
264#380C2×C412yes—
265#380C2×C411yescharacteristic
266#380C2×C411yescharacteristic
267C4×C4⋊C4C2×C411yescharacteristic
268C4×C4⋊C4C2×C411yescharacteristic
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2×C411yescharacteristic
272C4×C4⋊C4C2×C411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C22⋊C4C2×C412yes—
280C4×C22⋊C4C2×C411yescharacteristic
281C4×C22⋊C4C2×C412yes—
282C4×C22⋊C4C2×C411yescharacteristic
283C4×C22⋊C4C2×C411yescharacteristic
284C4×C22⋊C4C2×C411yescharacteristic
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2312yes—
288C4×C22⋊C4C2312yes—
289C4×C22⋊C4C2312yes—
290#376C2311yescharacteristic
291#376C2311yescharacteristic
292#376C2312yes—
293C43C2311yescharacteristic
294C43C2311yescharacteristic
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2311yescharacteristic
302#336C2311yescharacteristic
303#336C2312yes—
304#336C2312yes—
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2311yescharacteristic
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319C22×Q8C22×C411yescharacteristic
320C22×D4C22×C411yescharacteristic
321C22×D4C22×C412yes—
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C412yes—
324C23×C4C22×C412yes—
325C23×C4C22×C411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2412yes—
328C22×C8—42no—
329C22×C8—42no—
330C22×C8—42no—
331C22×C8—42no—
332C22×C8—42no—
333C22×C8—42no—
334C22×C8C2411yescharacteristic
335C22×C8C2411yescharacteristic
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2411yescharacteristic
339C22×C8C2411yescharacteristic
340C22×C8C2412yes—
341C22×C8C2411yescharacteristic
342C22×C8C2411yescharacteristic
343C22×C8C2412yes—
344C22×C8C2411yescharacteristic
345C22×C8C2411yescharacteristic
346#125—24no—
347#124—24no—
348C22⋊Q8—24no—
349#121—24no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—42no—
357C4×D4—42no—
358#117—22no—
359#117—22no—
360#117—41no—
361#117—41no—
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C411yescharacteristic
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C412yes—
368C2×C4⋊C4C22×C411yescharacteristic
369C2×C4⋊C4C22×C412yes—
370C2×C4⋊C4C22×C412yes—
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C412yes—
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C412yes—
378C2×C4⋊C4C22×C412yes—
379C2×C4⋊C4C22×C412yes—
380C2×C4⋊C4C22×C412yes—
381C2×C4⋊C4C22×C411yescharacteristic
382C2×C22⋊C4C22×C411yescharacteristic
383C2×C22⋊C4C22×C411yescharacteristic
384C2×C22⋊C4C22×C412yes—
385C2×C22⋊C4C22×C412yes—
386C2×C22⋊C4C22×C412yes—
387C2×C22⋊C4C22×C412yes—
388C2×C22⋊C4C22×C412yes—
389C2×C22⋊C4C22×C412yes—
390C2×C22⋊C4C22×C412yes—
391C2×C22⋊C4C22×C411yescharacteristic
392C2×C22⋊C4C22×C411yescharacteristic
393C2×C22⋊C4C22×C412yes—
394C2×C22⋊C4C22×C412yes—
395C2×C22⋊C4C22×C412yes—
396C2×C22⋊C4C22×C412yes—
397C2×C22⋊C4C22×C412yes—
398C2×C22⋊C4C22×C412yes—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C412yes—
408C2×C42C22×C412yes—
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2412yes—
419C2×C42C2412yes—
420C2×C42C2411yescharacteristic
421C2×C42C2412yes—
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C4⋊C8—22no—
425C4⋊C8—24no—
426C4⋊C8—22no—
427C4⋊C8—24no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—42no—
435C4⋊C8—42no—
436C4⋊C8—41no—
437C4⋊C8—42no—
438C4⋊C8—41no—
439C4⋊C8—41no—
440C4⋊C8—41no—
441C4⋊C8—42no—
442C4⋊C8—42no—
443C4⋊C8—42no—
444C4⋊C8—41no—
445C4⋊C8—41no—
446C4⋊C8—41no—
447C4⋊C8—41no—
448C4⋊C8—42no—
449C4⋊C8—42no—
450C22⋊C8—42no—
451C22⋊C8—42no—
452C22⋊C8—41no—
453C22⋊C8—41no—
454C22⋊C8—41no—
455C22⋊C8—41no—
456C22⋊C8—42no—
457C22⋊C8—42no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460C22⋊C8—42no—
461C22⋊C8—42no—
462#97—42no—
463#97—42no—
464#97—42no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—42no—
470C4×C8—42no—
471C4×C8—42no—
472C4×C8—42no—
473C4×C8—42no—
474#95C22×C411yescharacteristic
475#95C22×C411yescharacteristic
476#95C22×C411yescharacteristic
477#95C22×C411yescharacteristic
478#95C22×C411yescharacteristic
479#95C22×C411yescharacteristic
480#95C22×C411yescharacteristic
481#95C22×C411yescharacteristic
482#95C22×C412yes—
483#95C22×C412yes—
484#95C22×C412yes—
485#95C22×C412yes—
486#95C22×C412yes—
487#95C22×C412yes—
488#95C22×C412yes—
489#95C22×C412yes—
490#95C22×C412yes—
491#95C22×C412yes—
492#95C22×C412yes—
493#95C22×C412yes—
494#95C22×C412yes—
495#95C22×C412yes—
496#95C22×C412yes—
497#95C22×C412yes—
498#95C22×C412yes—
499#95C22×C412yes—
500#95C22×C412yes—
501#95C22×C412yes—
502#95C22×C412yes—
503#95C22×C412yes—
504#95C22×C412yes—
505#95C22×C412yes—
506C24C23×C411yescharacteristic
507C24C23×C412yes—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×D4—24no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4#13114yes—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C23×C412yes—
542C22×C4C23×C411yescharacteristic
543C22×C4C23×C412yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C412yes—
546C22×C4C23×C412yes—
547C22×C4C23×C411yescharacteristic
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C412yes—
554C22×C4C23×C412yes—
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C23×C412yes—
560C22×C4C23×C411yescharacteristic
561C22×C4C2511yescharacteristic
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—21no—
589C2×C8—22no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—84no—
599C2×C8—84no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—42no—
619C4⋊C4#13114yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C42—24no—
638C42—24no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—21no—
646C42—22no—
647C42—22no—
648C42—21no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—22no—
659C42—41no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42H(5,𝔽2)12yes—
664C42H(5,𝔽2)12yes—
665C422−1+412yes—
666C422−1+412yes—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23C2×#13114yes—
681C23C24×C411yescharacteristic
682Q8—44no—
683D4—28no—
684D4—84no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—48no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4#52012yes—
751C2×C4#52012yes—
752C2×C4#52012yes—
753C2×C4#52012yes—
754C2×C4C2×#13114yes—
755C2×C4C2×#13112yes—
756C2×C4C2×#13112yes—
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C2×C4C2×H(5,𝔽2)11yescharacteristic
759C2×C4C2×2−1+411yescharacteristic
760C2×C4C2×2−1+411yescharacteristic
761C2×C4#58511yescharacteristic
762C2×C4#58511yescharacteristic
763C8—41no—
764C8—41no—
765C8—42no—
766C8—42no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C8—41no—
773C8—42no—
774C8—42no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22C2×#52011yescharacteristic
790C22C2×#52011yescharacteristic
791C22#342811yescharacteristic
792C22C22×#13111yescharacteristic
793C22C22×#13111yescharacteristic
794C22#357311yescharacteristic
795C22#357311yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—41no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4#299414yes—
816C4#354611yescharacteristic
817C4#354711yescharacteristic
818C4#355411yescharacteristic
819C4#355511yescharacteristic
820C2—44no—
821C2—81no—
822C2#3438311yescharacteristic
823C2C2×#299411yescharacteristic
824C2#6026711yescharacteristic
825C2#6027111yescharacteristic
826C2#6027111yescharacteristic
827C2#6029811yescharacteristic
828C2#6030111yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#121C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #23319C2semidirect
3. #23315C2semidirect
4. #23254C2semidirect
5. #23253C2semidirect
6. #23209C2semidirect
7. #23204C2semidirect
8. #22822C2semidirect
9. #22800C2semidirect
10. #22795C2semidirect
11. #22754C2semidirect
12. #22721C2semidirect
13. D4×C4⋊C8C2semidirect
14. #22352C2semidirect
15. #22342C2semidirect
18. #22102C2semidirect
19. #22098C2semidirect
20. #21973C2semidirect
21. #21928C2semidirect
22. #20812C2semidirect
23. #20809C2semidirect

Maximal subgroups

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

subgroupindex
#349132
#233192
#233152
#232542
#232532
#232092
#232042
#228222
#228002
#227952
#227542
#227212
D4×C4⋊C82
#223522
#223422
#221352
#221332
#221022
#220982
#219732
#219282
#208122
#208092