Finite Group Databasebeta

← C2×#60275 #10574362

Subgroups — C2×#60275 #10574362

Order 512.

6624 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic
2#60275C2132yesmaximal, direct product factor
3C2×#2995C214yesmaximal, complemented
4C2×#2994C212yesmaximal, complemented
5C2×#2993C212yesmaximal, complemented
6C2×#2992C214yesmaximal, complemented
7C2×#2990C212yesmaximal, complemented
8C2×#2989C212yesmaximal, complemented
9C2×Q8×M16C211yesmaximal, characteristic, complemented
10C22×#446C211yesmaximal, characteristic, complemented
11C2×#2935C211yesmaximal, characteristic, complemented
12C2×#2935C212yesmaximal, complemented
13C2×#2932C212yesmaximal, complemented
14C2×#2931C211yesmaximal, characteristic, complemented
15C2×#2923C212yesmaximal, complemented
16C2×#2922C211yesmaximal, characteristic, complemented
17C2×#2906C211yesmaximal, characteristic, complemented
18C2×#2906C212yesmaximal, complemented
19C22×#131C2212yes—
20C22×#131C2212yes—
21C22×#131C2212yes—
22#3480C4116yes—
23#3480C22116yes—
24C2×#559C411yescharacteristic
25C2×#559C412yes—
26C2×#557C411yescharacteristic
27C2×#556C411yescharacteristic
28C2×#556C412yes—
29C2×#553C412yes—
30C2×#553C414yes—
31C2×#550C411yescharacteristic
32C2×#548C412yes—
33C2×#532C2211yescharacteristic
34C2×#532C2212yes—
35C2×#529C2214yes—
36C2×#529C2212yes—
37C2×C4×#41C2212yes—
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2212yes—
40C22×C4×Q8C2211yescharacteristic
41#2995C22164yescomplemented
42#2994C22132yescomplemented
43#2993C22132yescomplemented
44#2992C22164yescomplemented
45#2990C22132yescomplemented
46#2989C22132yescomplemented
47Q8×M16C22116yescomplemented
48C2×#446C2211yescharacteristic
49C2×#446C2211yescharacteristic
50C2×#446C2212yes—
51C2×#446C2211yescharacteristic
52C2×#446C2211yescharacteristic
53C2×#446C2212yes—
54C2×#446C2212yes—
55C2×#446C2214yes—
56C2×#446C22116yescomplemented
57C2×C8×Q8C2212yes—
58#2935C22116yescomplemented
59#2935C22132yescomplemented
60#2932C22132yescomplemented
61#2931C22116yescomplemented
62C2×#436C2212yes—
63C2×#436C2212yes—
64C2×#436C2214yes—
65C2×#436C2212yes—
66C2×#435C2214yes—
67C2×#435C2214yes—
68C2×#435C2214yes—
69C2×#435C2214yes—
70C2×#435C2214yes—
71C2×#435C2214yes—
72C2×#435C2214yes—
73C2×C8×D4C2212yes—
74C2×C8×D4C2212yes—
75C2×C8×D4C2212yes—
76C2×C8×D4C2214yes—
77#2923C22132yescomplemented
78#2922C22116yescomplemented
79C2×#433C2212yes—
80C2×#433C2214yes—
81C2×#433C2214yes—
82C2×#433C2212yes—
83C2×#432C2214yes—
84C2×#432C2214yes—
85C2×#431C2212yes—
86C2×#431C2212yes—
87#2906C22116yescomplemented
88#2906C22132yescomplemented
89C2×#424C2214yes—
90C2×#424C2214yes—
91C2×#424C2214yes—
92C2×#424C2211yescharacteristic
93C2×#424C2212yes—
94C2×#424C2211yescharacteristic
95C2×#423C2211yescharacteristic
96C2×#423C2212yes—
97C2×#423C2214yes—
98C2×#423C2212yes—
99C22×C4⋊C8C2212yes—
100C22×C4⋊C8C2211yescharacteristic
101C22×C4⋊C8C2212yes—
102C22×C4⋊C8C2214yes—
103C2×#408C2211yescharacteristic
104C2×#408C2211yescharacteristic
105C2×#408C2212yes—
106C2×#408C2212yes—
107C2×C4×M16C2211yescharacteristic
108C2×C4×M16C2212yes—
109C22×#97C2212yes—
110C22×C4×C8C2211yescharacteristic
111C22×#41C2×C412yes—
112C22×#41C2311yescharacteristic
113C22×#41C2312yes—
114C23×Q8C2×C411yescharacteristic
115C2×#131—48no—
116C2×#131—48no—
117C2×#131—48no—
118C2×#131C23116yes—
119C2×#131C23116yes—
120C2×#131C23116yes—
121C22×M16C2311yescharacteristic
122C22×M16C2311yescharacteristic
123C22×M16C2312yes—
124C22×M16C2314yes—
125C22×M16C2314yes—
126C22×M16C2314yes—
127C23×C8C2311yescharacteristic
128C23×C8C2311yescharacteristic
129C23×C8C2312yes—
130C23×C8C2314yes—
131C23×C8C2314yes—
132C23×C8C2314yes—
133#559C2×C4116yes—
134#559C2×C4132yes—
135#557C2×C4116yes—
136#556C2×C4116yes—
137#556C2×C4132yes—
138#553C2×C4132yes—
139#553C2×C4164yes—
140#550C2×C4116yes—
141#548C2×C4132yes—
142#532C2×C418yes—
143#532C2×C4116yes—
144#532C2318yes—
145#532C23116yes—
146C2×C4⋊Q8C2×C411yescharacteristic
147C2×C4⋊Q8C2×C412yes—
148C2×#127C2×C411yescharacteristic
149C2×#127C2×C412yes—
150#529C2×C4132yes—
151#529C2×C4116yes—
152#529C23132yes—
153#529C23116yes—
154C2×#126C2×C414yes—
155C2×#126C2×C414yes—
156C2×#126C2×C414yes—
157C2×#125C2×C414yes—
158C2×#125C2×C412yes—
159C2×#124C2×C412yes—
160C2×#124C2×C414yes—
161C2×#124C2×C412yes—
162C2×#124C2×C412yes—
163C2×#124C2×C412yes—
164C2×#123C2×C414yes—
165C2×#123C2×C414yes—
166C2×#123C2×C414yes—
167C2×C22⋊Q8C2×C412yes—
168C2×C22⋊Q8C2×C414yes—
169C2×#121C2×C412yes—
170C2×#121C2×C414yes—
171C2×#121C2×C412yes—
172C2×#121C2×C414yes—
173C2×#121C2×C412yes—
174C2×#121C2×C414yes—
175C4×#41C2×C418yes—
176C4×#41C2×C4116yes—
177C4×#41C2×C4116yes—
178C4×#41C23116yes—
179C4×#41C2318yes—
180C4×#41C23116yes—
181C2×C4×Q8C2×C411yescharacteristic
182C2×C4×Q8C2×C411yescharacteristic
183C2×C4×Q8C2×C412yes—
184C2×C4×Q8C2×C418yes—
185C2×C4×Q8C2×C412yes—
186C2×C4×Q8C2×C411yescharacteristic
187C2×C4×Q8C2×C412yes—
188C2×C4×Q8C2×C411yescharacteristic
189C2×C4×Q8C2×C412yes—
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2318yes—
194C2×C4×D4C2×C412yes—
195C2×C4×D4C2×C414yes—
196C2×C4×D4C2×C411yescharacteristic
197C2×C4×D4C2×C412yes—
198C2×C4×D4C2×C412yes—
199C2×C4×D4C2×C414yes—
200C2×C4×D4C2×C412yes—
201C2×C4×D4C2×C414yes—
202C2×C4×D4C2×C411yescharacteristic
203C2×C4×D4C2×C412yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×#117C2×C412yes—
209C2×#117C2×C414yes—
210C2×#117C2311yescharacteristic
211C2×#117C2314yes—
212C2×#117C2312yes—
213C22×C4⋊C4C2×C411yescharacteristic
214C22×C4⋊C4C2×C412yes—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2314yes—
219#446C2318yes—
220#446C2318yes—
221#446C23116yes—
222#446C2318yes—
223#446C2318yes—
224#446C23116yes—
225#446C23116yes—
226#446C23132yes—
227C8×Q8C23116yes—
228#436C23116yes—
229#436C23116yes—
230#436C23116yes—
231#436C23132yes—
232#435C23132yes—
233#435C23132yes—
234#435C23132yes—
235#435C23132yes—
236#435C23132yes—
237#435C23132yes—
238#435C23132yes—
239C8×D4C23116yes—
240C8×D4C23116yes—
241C8×D4C23116yes—
242C8×D4C23132yes—
243#433C23116yes—
244#433C23116yes—
245#433C23132yes—
246#433C23132yes—
247#432C23132yes—
248#432C23132yes—
249#431C23116yes—
250#431C23116yes—
251#424C2318yes—
252#424C23116yes—
253#424C23132yes—
254#424C23132yes—
255#424C23132yes—
256#424C2318yes—
257#423C2318yes—
258#423C23116yes—
259#423C23132yes—
260#423C23116yes—
261C2×C4⋊C8C2312yes—
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2312yes—
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2312yes—
266C2×C4⋊C8C2312yes—
267C2×C4⋊C8C2314yes—
268C2×C4⋊C8C2314yes—
269C2×C4⋊C8C2314yes—
270C2×C4⋊C8C2312yes—
271C2×C4⋊C8C2312yes—
272C2×C4⋊C8C2312yes—
273C2×C4⋊C8C23116yes—
274C2×C4⋊C8C2318yes—
275C2×C4⋊C8C23116yes—
276C2×C4⋊C8C23132yes—
277C2×C4⋊C8C2312yes—
278C2×C4⋊C8C2312yes—
279C2×C4⋊C8C2314yes—
280C2×C4⋊C8C2312yes—
281C2×C4⋊C8C2312yes—
282#408C2318yes—
283#408C2318yes—
284#408C23116yes—
285#408C23116yes—
286C2×C22⋊C8C2312yes—
287C2×C22⋊C8C2312yes—
288C2×C22⋊C8C2312yes—
289C2×C22⋊C8C2312yes—
290C2×C22⋊C8C2314yes—
291C2×C22⋊C8C2314yes—
292C2×C22⋊C8C2314yes—
293C2×C22⋊C8C2314yes—
294C4×M16C2318yes—
295C4×M16C23116yes—
296C2×#97C2312yes—
297C2×#97C2312yes—
298C2×#97C2312yes—
299C2×#97C2312yes—
300C2×#97C23116yes—
301C2×#97C2314yes—
302C2×#97C2312yes—
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2318yes—
308C2×C4×C8C2312yes—
309C2×C4×C8C2314yes—
310C2×#41—28no—
311C2×#41—24no—
312C2×#41—24no—
313C2×#41—28no—
314C2×#41—48no—
315C2×#41C22×C414yes—
316C2×#41C22×C418yes—
317C2×#41C22×C4116yes—
318C2×#41C2414yes—
319C2×#41C2418yes—
320C22×Q8—44no—
321C22×Q8C22×C411yescharacteristic
322C22×Q8C22×C411yescharacteristic
323C22×Q8C22×C412yes—
324C22×Q8C22×C411yescharacteristic
325C22×Q8C22×C412yes—
326C22×Q8C22×C418yes—
327C22×D4C22×C412yes—
328C22×D4C22×C414yes—
329C22×D4C22×C411yescharacteristic
330C22×D4C22×C412yes—
331C22×D4C22×C412yes—
332C22×D4C22×C414yes—
333C22×D4C22×C414yes—
334C22×D4C22×C412yes—
335C23×C4C22×C411yescharacteristic
336C23×C4C22×C412yes—
337C23×C4C22×C411yescharacteristic
338C23×C4C22×C412yes—
339C23×C4C22×C412yes—
340C23×C4C22×C414yes—
341C23×C4C22×C412yes—
342C23×C4C22×C414yes—
343C23×C4C2414yes—
344C23×C4C2412yes—
345C23×C4C2411yescharacteristic
346#131—432no—
347#131—432no—
348#131—432no—
349C2×M16—24no—
350C2×M16—28no—
351C2×M16—24no—
352C2×M16—48no—
353C2×M16—48no—
354C2×M16—48no—
355C2×M16C2418yes—
356C2×M16C2414yes—
357C2×M16C2414yes—
358C2×M16C24116yes—
359C2×M16C24116yes—
360C2×M16C24116yes—
361C22×C8—24no—
362C22×C8—28no—
363C22×C8—24no—
364C22×C8—48no—
365C22×C8—48no—
366C22×C8—48no—
367C22×C8C2414yes—
368C22×C8C2418yes—
369C22×C8C2414yes—
370C22×C8C2411yescharacteristic
371C22×C8C2412yes—
372C22×C8C2412yes—
373C22×C8C2414yes—
374C22×C8C2412yes—
375C22×C8C2411yescharacteristic
376C22×C8C2411yescharacteristic
377C22×C8C2411yescharacteristic
378C22×C8C2412yes—
379C22×C8C24116yes—
380C22×C8C24116yes—
381C22×C8C24116yes—
382C4⋊Q8C22×C418yes—
383C4⋊Q8C22×C4116yes—
384#127C22×C418yes—
385#127C22×C4116yes—
386#126C22×C4132yes—
387#126C22×C4132yes—
388#126C22×C4132yes—
389#125C22×C4132yes—
390#125C22×C4116yes—
391#124C22×C4116yes—
392#124C22×C4132yes—
393#124C22×C4116yes—
394#124C22×C4116yes—
395#124C22×C4116yes—
396#123C22×C4132yes—
397#123C22×C4132yes—
398#123C22×C4132yes—
399C22⋊Q8C22×C4116yes—
400C22⋊Q8C22×C4132yes—
401#121C22×C4116yes—
402#121C22×C4132yes—
403#121C22×C4116yes—
404#121C22×C4132yes—
405#121C22×C4116yes—
406#121C22×C4132yes—
407C4×Q8C22×C414yes—
408C4×Q8C22×C414yes—
409C4×Q8C22×C418yes—
410C4×Q8C22×C418yes—
411C4×Q8C22×C418yes—
412C4×Q8C22×C4116yes—
413C4×Q8C22×C4116yes—
414C4×Q8C22×C418yes—
415C4×Q8C22×C4116yes—
416C4×Q8C22×C418yes—
417C4×Q8C22×C4116yes—
418C4×Q8C2414yes—
419C4×Q8C2414yes—
420C4×Q8C2418yes—
421C4×D4C22×C4116yes—
422C4×D4C22×C4132yes—
423C4×D4C22×C418yes—
424C4×D4C22×C4116yes—
425C4×D4C22×C4116yes—
426C4×D4C22×C4132yes—
427C4×D4C22×C4116yes—
428C4×D4C22×C4132yes—
429C4×D4C22×C418yes—
430C4×D4C22×C4116yes—
431C4×D4C22×C418yes—
432C4×D4C22×C4116yes—
433C4×D4C22×C418yes—
434C4×D4C22×C4116yes—
435C4×D4C2418yes—
436C4×D4C24116yes—
437C4×D4C2418yes—
438C4×D4C24116yes—
439#117C22×C4116yes—
440#117C22×C4132yes—
441#117C22×C414yes—
442#117C22×C4116yes—
443#117C22×C418yes—
444#117C2414yes—
445#117C2418yes—
446#117C24116yes—
447C2×C4⋊C4C22×C412yes—
448C2×C4⋊C4C22×C411yescharacteristic
449C2×C4⋊C4C22×C412yes—
450C2×C4⋊C4C22×C411yescharacteristic
451C2×C4⋊C4C22×C412yes—
452C2×C4⋊C4C22×C412yes—
453C2×C4⋊C4C22×C412yes—
454C2×C4⋊C4C22×C418yes—
455C2×C4⋊C4C22×C4116yes—
456C2×C4⋊C4C22×C414yes—
457C2×C4⋊C4C22×C412yes—
458C2×C4⋊C4C22×C411yescharacteristic
459C2×C4⋊C4C22×C411yescharacteristic
460C2×C4⋊C4C22×C412yes—
461C2×C4⋊C4C22×C414yes—
462C2×C4⋊C4C22×C414yes—
463C2×C4⋊C4C22×C412yes—
464C2×C4⋊C4C22×C412yes—
465C2×C4⋊C4C22×C414yes—
466C2×C22⋊C4C22×C414yes—
467C2×C22⋊C4C22×C414yes—
468C2×C22⋊C4C22×C414yes—
469C2×C22⋊C4C22×C412yes—
470C2×C22⋊C4C22×C412yes—
471C2×C22⋊C4C22×C414yes—
472C2×C22⋊C4C22×C412yes—
473C2×C22⋊C4C22×C414yes—
474C2×C22⋊C4C22×C414yes—
475C2×C22⋊C4C22×C414yes—
476C2×C22⋊C4C22×C414yes—
477C2×C42C22×C412yes—
478C2×C42C22×C414yes—
479C2×C42C22×C414yes—
480C2×C42C22×C412yes—
481C2×C42C22×C411yescharacteristic
482C2×C42C22×C412yes—
483C2×C42C22×C412yes—
484C2×C42C22×C411yescharacteristic
485C2×C42C22×C414yes—
486C2×C42C22×C418yes—
487C2×C42C22×C418yes—
488C2×C42C22×C4116yes—
489C2×C42C2414yes—
490C2×C42C2418yes—
491C2×C42C2418yes—
492C2×C42C24116yes—
493C2×C42C2412yes—
494C2×C42C2412yes—
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2412yes—
498C4⋊C8C2418yes—
499C4⋊C8C2414yes—
500C4⋊C8C2418yes—
501C4⋊C8C2414yes—
502C4⋊C8C2418yes—
503C4⋊C8C2418yes—
504C4⋊C8C24116yes—
505C4⋊C8C24116yes—
506C4⋊C8C24116yes—
507C4⋊C8C2418yes—
508C4⋊C8C2418yes—
509C4⋊C8C2418yes—
510C4⋊C8C2418yes—
511C4⋊C8C2418yes—
512C4⋊C8C24116yes—
513C4⋊C8C2418yes—
514C4⋊C8C2418yes—
515C22⋊C8C2418yes—
516C22⋊C8C2418yes—
517C22⋊C8C2418yes—
518C22⋊C8C2418yes—
519C22⋊C8C24116yes—
520C22⋊C8C24116yes—
521C22⋊C8C24116yes—
522C22⋊C8C24116yes—
523#97C2418yes—
524#97C2418yes—
525#97C2418yes—
526#97C2418yes—
527#97C24116yes—
528#97C2418yes—
529C4×C8C2414yes—
530C4×C8C2414yes—
531C4×C8C2414yes—
532C4×C8C2414yes—
533C4×C8C2418yes—
534C4×C8C24116yes—
535C24C23×C412yes—
536C24C23×C414yes—
537C24C23×C411yescharacteristic
538#41—232no—
539#41—216no—
540#41—216no—
541#41—28no—
542#41—28no—
543#41—216no—
544#41—432no—
545C2×Q8—24no—
546C2×Q8—28no—
547C2×Q8—24no—
548C2×Q8—24no—
549C2×Q8—44no—
550C2×Q8—416no—
551C2×Q8C23×C414yes—
552C2×Q8C23×C414yes—
553C2×Q8C23×C418yes—
554C2×Q8C23×C414yes—
555C2×Q8C23×C418yes—
556C2×D4—28no—
557C2×D4—216no—
558C2×D4—24no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—48no—
562C2×D4—44no—
563C2×D4—48no—
564C2×D4C23×C418yes—
565C2×D4C23×C4116yes—
566C2×D4C23×C414yes—
567C2×D4C23×C418yes—
568C2×D4C23×C418yes—
569C2×D4C23×C4116yes—
570C2×D4C23×C4116yes—
571C2×D4C23×C418yes—
572C22×C4—24no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—28no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4C23×C412yes—
585C22×C4C23×C411yescharacteristic
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C23×C414yes—
591C22×C4C23×C414yes—
592C22×C4C23×C418yes—
593C22×C4C23×C411yescharacteristic
594C22×C4C23×C412yes—
595C22×C4C23×C412yes—
596C22×C4C23×C411yescharacteristic
597C22×C4C23×C414yes—
598C22×C4C23×C418yes—
599C22×C4C23×C414yes—
600C22×C4C23×C418yes—
601C22×C4C23×C418yes—
602C22×C4C23×C4116yes—
603C22×C4C23×C418yes—
604C22×C4C23×C4116yes—
605C22×C4C23×C411yescharacteristic
606C22×C4C23×C412yes—
607C22×C4C23×C411yescharacteristic
608C22×C4H(5,𝔽2)14yes—
609C22×C42−1+414yes—
610C22×C4C2514yes—
611C22×C4C2518yes—
612C22×C4C2512yes—
613C22×C4C2511yescharacteristic
614M16—216no—
615M16—28no—
616M16—28no—
617M16—416no—
618M16—416no—
619M16—416no—
620C2×C8—22no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—22no—
624C2×C8—28no—
625C2×C8—216no—
626C2×C8—28no—
627C2×C8—24no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—28no—
631C2×C8—24no—
632C2×C8—416no—
633C2×C8—416no—
634C2×C8—416no—
635C2×C8C2514yes—
636C2×C8C2512yes—
637C2×C8C2512yes—
638C2×C8C2512yes—
639C2×C8C2512yes—
640C2×C8C2514yes—
641C2×C8C2518yes—
642C2×C8C2514yes—
643C2×C8C2514yes—
644C4⋊C4C23×C418yes—
645C4⋊C4C23×C414yes—
646C4⋊C4C23×C418yes—
647C4⋊C4C23×C414yes—
648C4⋊C4C23×C418yes—
649C4⋊C4C23×C418yes—
650C4⋊C4C23×C418yes—
651C4⋊C4C23×C4116yes—
652C4⋊C4C23×C418yes—
653C4⋊C4C23×C414yes—
654C4⋊C4C23×C414yes—
655C4⋊C4C23×C418yes—
656C4⋊C4C23×C4116yes—
657C4⋊C4C23×C418yes—
658C4⋊C4C23×C4116yes—
659C4⋊C4C23×C418yes—
660C4⋊C4C23×C4116yes—
661C22⋊C4C23×C4116yes—
662C22⋊C4C23×C4116yes—
663C22⋊C4C23×C4116yes—
664C22⋊C4C23×C418yes—
665C22⋊C4C23×C418yes—
666C22⋊C4C23×C4116yes—
667C22⋊C4C23×C418yes—
668C22⋊C4C23×C4116yes—
669C22⋊C4C23×C4116yes—
670C22⋊C4C23×C4116yes—
671C22⋊C4C23×C4116yes—
672C42C23×C414yes—
673C42C23×C414yes—
674C42C23×C412yes—
675C42C23×C412yes—
676C42C23×C414yes—
677C42C23×C418yes—
678C42C23×C4116yes—
679C42C23×C4116yes—
680C42C23×C418yes—
681C42C23×C414yes—
682C42C23×C418yes—
683C42C23×C418yes—
684C42C23×C414yes—
685C42C2512yes—
686C42C2512yes—
687C42C2514yes—
688C42C2514yes—
689C42C2514yes—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—28no—
694C23—24no—
695C23—28no—
696C23—24no—
697C23—28no—
698C23#52014yes—
699C23C24×C414yes—
700C23C24×C418yes—
701C23C24×C412yes—
702C23C24×C411yescharacteristic
703Q8—28no—
704Q8—216no—
705Q8—28no—
706Q8—28no—
707Q8—48no—
708D4—216no—
709D4—232no—
710D4—28no—
711D4—216no—
712D4—216no—
713D4—416no—
714D4—48no—
715D4—416no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—216no—
733C2×C4—28no—
734C2×C4—216no—
735C2×C4—48no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—48no—
739C2×C4—48no—
740C2×C4—416no—
741C2×C4#52014yes—
742C2×C4#52018yes—
743C2×C4#56814yes—
744C2×C4C24×C414yes—
745C2×C4C24×C414yes—
746C2×C4C24×C412yes—
747C2×C4C24×C414yes—
748C2×C4C24×C414yes—
749C2×C4C24×C414yes—
750C2×C4C24×C418yes—
751C2×C4C24×C412yes—
752C2×C4C24×C414yes—
753C2×C4C24×C414yes—
754C2×C4C24×C412yes—
755C2×C4C24×C411yescharacteristic
756C2×C4C24×C412yes—
757C2×C4C24×C412yes—
758C2×C4C2×H(5,𝔽2)12yes—
759C2×C4C2×H(5,𝔽2)14yes—
760C2×C4C2×2−1+412yes—
761C2×C4C2×2−1+414yes—
762C2×C4C2611yescharacteristic
763C8—22no—
764C8—24no—
765C8—24no—
766C8—22no—
767C8—28no—
768C8—24no—
769C8—22no—
770C8—22no—
771C8—24no—
772C22—22no—
773C22—22no—
774C22—28no—
775C22—24no—
776C22—28no—
777C22—24no—
778C22—28no—
779C22—24no—
780C22—28no—
781C22—48no—
782C22—416no—
783C22C2×#52014yes—
784C22C2×#52012yes—
785C22C2×#56812yes—
786C22#357312yes—
787C22C25×C411yescharacteristic
788C4—24no—
789C4—22no—
790C4—24no—
791C4—24no—
792C4—24no—
793C4—22no—
794C4—24no—
795C4—22no—
796C4—24no—
797C4—28no—
798C4—24no—
799C4C2×#52012yes—
800C4C2×#52014yes—
801C4C2×#56814yes—
802C4C22×H(5,𝔽2)11yescharacteristic
803C4C22×2−1+411yescharacteristic
804C2—24no—
805C2—44no—
806C2—48no—
807C2#6027514yesdirect product factor
808C2C22×#52011yescharacteristic
809C2C22×#56811yescharacteristic
810C2C2×#357311yescharacteristic
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, cosocleC2×C4C26
socleC23C24×C4
prime radicalC2×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60275C2direct (N × H)
3. C2×#2995C2semidirect
4. C2×#2994C2semidirect
5. C2×#2993C2semidirect
6. C2×#2992C2semidirect
7. C2×#2990C2semidirect
8. C2×#2989C2semidirect
9. C2×Q8×M16C2semidirect
10. C22×#446C2semidirect
11. C2×#2935C2semidirect
12. C2×#2935C2semidirect
13. C2×#2932C2semidirect
14. C2×#2931C2semidirect
15. C2×#2923C2semidirect
16. C2×#2922C2semidirect
17. C2×#2906C2semidirect
18. C2×#2906C2semidirect
41. #2995C22semidirect
42. #2994C22semidirect
43. #2993C22semidirect
44. #2992C22semidirect
45. #2990C22semidirect
46. #2989C22semidirect
47. Q8×M16C22semidirect
56. C2×#446C22semidirect
58. #2935C22semidirect
59. #2935C22semidirect
60. #2932C22semidirect
61. #2931C22semidirect
77. #2923C22semidirect
78. #2922C22semidirect
87. #2906C22semidirect
88. #2906C22semidirect
807. C2#60275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34802
#602752
C2×#29952
C2×#29942
C2×#29932
C2×#29922
C2×#29902
C2×#29892
C2×Q8×M162
C22×#4462
C2×#29352
C2×#29322
C2×#29312
C2×#29232
C2×#29222
C2×#29062