Finite Group Databasebeta

← C2×#72251201 #72315033

Subgroups — C2×#72251201 #72315033

Order 2048.

At least 8656 conjugacy classes of subgroups; only the 5000 normal subgroups are shown.

The subgroup lattice has 992 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123535C211yesmaximal, characteristic, complemented
2C2×#123560C211yesmaximal, characteristic, complemented
3C22×#11030C212yesmaximal, complemented
4C22×#11012C212yesmaximal, complemented
5C2×#123547C211yesmaximal, characteristic, complemented
6C22×#23407C211yesmaximal, characteristic, complemented
7C2×#6431766C211yesmaximal, characteristic, complemented
8C22×#23443C211yesmaximal, characteristic, complemented
9C2×#517415C211yesmaximal, characteristic, complemented
10C22×#10994C212yesmaximal, complemented
11#72251201C2116yesmaximal, direct product factor
12C23×#3003C212yesmaximal, complemented
13C26×D4C2211yescharacteristic
14C24×AGL(1,ℤ/8)C2212yes—
15C24×AGL(1,ℤ/8)C2212yes—
16C22×#3449C2211yescharacteristic, complemented
17C23×#525C2212yes—
18C22×#3003C22116yescomplemented
19C23×#407C2212yes—
20C23×#410C2212yescomplemented
21C22×#2896C2212yescomplemented
22C23×#421C2212yescomplemented
23C23×#418C2212yes—
24C23×#418C2212yes—
25C22×#2309C2211yescharacteristic
26C22×#2309C2211yescharacteristic
27C22×#2309C2211yescharacteristic
28C22×#2309C2211yescharacteristic
29C22×#2280C2211yescharacteristic
30C22×#2280C2211yescharacteristic
31C2×#23443C2218yescomplemented
32#6431766C2218yescomplemented
33C2×#23407C2218yescomplemented
34C23×#344C2212yescomplemented
35C22×#1742C2211yescharacteristic, complemented
36C22×#1740C2211yescharacteristic, complemented
37C22×#1733C2212yescomplemented
38C23×H(3,ℤ/4)C2212yescomplemented
39C2×#20335C2211yescharacteristic, complemented
40#517415C2218yescomplemented
41C2×#11030C22116yescomplemented
42C2×#11012C22116yescomplemented
43C2×#10994C22116yescomplemented
44#123560C2218yescomplemented
45#123547C2218yescomplemented
46#123535C2218yescomplemented
47C24×#41C2312yes—
48C25×D4D418yescomplemented
49C25×D4C2314yes—
50C25×D4C2311yescharacteristic
51C25×D4C2311yescharacteristic
52C26×C4C2311yescharacteristic
53C23×AGL(1,ℤ/8)D4116yescomplemented
54C23×AGL(1,ℤ/8)D418yescomplemented
55C23×AGL(1,ℤ/8)C2318yes—
56C23×AGL(1,ℤ/8)C2318yes—
57C24×SD16D414yescomplemented
58C24×D8D414yescomplemented
59C24×M16C2312yes—
60C24×M16C2312yes—
61C2×#3449C2314yescomplemented
62C22×#525D4116yes—
63C22×#525C2318yes—
64C23×#117C2312yes—
65C23×#117C2311yescharacteristic
66C23×#117C2311yescharacteristic
67C23×#117C2311yescharacteristic
68C23×#117C2311yescharacteristic
69C22×#421C2318yescomplemented
70C2×#2896C2318yescomplemented
71C22×#418D4116yescomplemented
72C22×#418D4116yescomplemented
73C22×#418C2318yes—
74C22×#418C2318yes—
75C22×#410C2318yescomplemented
76C22×#407D4116yescomplemented
77C22×#407C2318yes—
78C2×#2309D414yescomplemented
79C2×#2309D414yescomplemented
80C2×#2309C2314yes—
81C2×#2309C2314yes—
82C2×#2309C2314yes—
83C2×#2309C2314yes—
84C22×#390D414yescomplemented
85C22×#390D414yescomplemented
86C2×#2280D414yes—
87C2×#2280C2314yes—
88C2×#2280C2314yes—
89C22×#381D412yes—
90C22×#379D412yes—
91C22×#344C2318yescomplemented
92C2×#1742C2314yescomplemented
93C2×#1740C2314yescomplemented
94C2×#1733C2318yescomplemented
95C22×H(3,ℤ/4)C2318yescomplemented
96#20335C2314yescomplemented
97C27C2×D411yescharacteristic
98C23×#41C2×D418yes—
99C23×#41C2×D418yes—
100C23×#41C2×D414yes—
101C23×#41C2414yes—
102C24×Q8C2×D412yes—
103C24×D4C2×D412yes—
104C24×D4C2×D414yes—
105C24×D4C2×D414yes—
106C24×D4C2×D414yes—
107C24×D4C2×D418yes—
108C24×D4C2×D414yes—
109C24×D4C2×D418yes—
110C24×D4C2×D418yes—
111C24×D4C2×D412yes—
112C24×D4C2×D412yes—
113C24×D4C2×D412yes—
114C24×D4C2×D412yes—
115C24×D4C2×D4116yescomplemented
116C24×D4#4114yes—
117C24×D4#4114yes—
118C24×D4C2412yes—
119C24×D4C2412yes—
120C25×C4C2×D414yes—
121C25×C4C2×D418yes—
122C25×C4C2×D411yescharacteristic
123C25×C4C2×D412yes—
124C25×C4C2×D418yes—
125C25×C4#4114yes—
126C25×C4C2412yes—
127C25×C4C2411yescharacteristic
128C22×AGL(1,ℤ/8)C2×D4132yescomplemented
129C23×SD16C2×D4116yescomplemented
130C23×D8C2×D4116yescomplemented
131C23×M16C2×D418yes—
132C23×M16C2×D418yes—
133C23×M16C2×D418yes—
134C23×M16C2×D418yes—
135C23×M16C2×D418yes—
136C23×M16C2×D414yes—
137C23×M16C2414yes—
138C23×M16C2414yes—
139C24×C8C2×D414yes—
140C2×#525C2×D4132yes—
141C22×#117C2×D412yes—
142C22×#117C2×D418yes—
143C22×#117C2×D418yes—
144C22×#117C2×D418yes—
145C22×#117C2×D412yes—
146C22×#117C2×D412yes—
147C22×#117C2×D412yes—
148C22×#117C2×D412yes—
149C22×#117C2×D412yes—
150C22×#117C2412yes—
151C22×#117C2414yes—
152C22×#117C2412yes—
153C22×#117C2412yes—
154C22×#117C2412yes—
155C23×C4⋊C4C2×D412yes—
156C23×C4⋊C4C2×D412yes—
157C23×C22⋊C4C2×D412yes—
158C23×C22⋊C4C2×D412yes—
159C23×C42C2×D412yes—
160C23×C42C2×D412yes—
161C2×#418C2×D4132yescomplemented
162C2×#418C2×D4132yescomplemented
163C2×#407C2×D4132yescomplemented
164C2×#390C2×D4116yescomplemented
165C2×#390C2×D4116yescomplemented
166C2×#381C2×D418yes—
167C2×#379C2×D418yes—
168C26#12014yes—
169C26#12114yes—
170C26#12714yes—
171C26C22×D412yes—
172C26C22×D411yescharacteristic
173C22×#41#120116yes—
174C22×#41C22×D418yes—
175C22×#41C22×D418yes—
176C23×Q8#12018yes—
177C23×Q8C22×D414yes—
178C23×D4#12018yes—
179C23×D4#120116yes—
180C23×D4#120132yes—
181C23×D4#120116yes—
182C23×D4#12018yes—
183C23×D4#12018yes—
184C23×D4#12014yes—
185C23×D4#12018yes—
186C23×D4#12014yes—
187C23×D4#12118yes—
188C23×D4#12118yes—
189C23×D4#12118yes—
190C23×D4#12118yes—
191C23×D4#121116yes—
192C23×D4#121132yes—
193C23×D4#121116yes—
194C23×D4#12718yes—
195C23×D4#12718yes—
196C23×D4#12718yes—
197C23×D4#12718yes—
198C23×D4C22×D414yes—
199C23×D4C22×D418yes—
200C23×D4C22×D418yes—
201C23×D4C22×D414yes—
202C23×D4C22×D414yes—
203C23×D4C22×D418yes—
204C23×D4C22×D418yes—
205C23×D4C22×D414yes—
206C23×D4C22×D414yes—
207C23×D4C2×#4114yes—
208C23×D4C2×#4114yes—
209C24×C4#120132yes—
210C24×C4#12014yes—
211C24×C4#12018yes—
212C24×C4#12014yes—
213C24×C4#121132yes—
214C24×C4#12114yes—
215C24×C4#12118yes—
216C24×C4#12714yes—
217C24×C4#12718yes—
218C24×C4C22×D414yes—
219C24×C4C22×D418yes—
220C24×C4C22×D412yes—
221C24×C4C22×D418yes—
222C24×C4C22×D412yes—
223C24×C4C22×D412yes—
224C24×C4C22×D414yes—
225C24×C4C22×D412yes—
226C24×C4C22×D414yes—
227C24×C4C22×D414yes—
228C24×C4C22×D414yes—
229C24×C4C22×D414yes—
230C24×C4C22×D411yescharacteristic
231C24×C4C22×D411yescharacteristic
232C24×C4C22×D411yescharacteristic
233C24×C4C22×D411yescharacteristic
234C24×C4C22×D411yescharacteristic
235C24×C4C2×#4114yes—
236C24×C4C2×#4112yes—
237C24×C4C2×#4112yes—
238C24×C4C2×#4112yes—
239C24×C4H(5,𝔽2)12yes—
240C24×C4H(5,𝔽2)14yes—
241C24×C4H(5,𝔽2)12yes—
242C24×C4H(5,𝔽2)14yes—
243C24×C4H(5,𝔽2)14yes—
244C24×C4H(5,𝔽2)14yes—
245C24×C4H(5,𝔽2)14yes—
246C24×C4C2511yescharacteristic
247C22×M16#120132yes—
248C22×M16#120116yes—
249C22×M16C22×D418yes—
250C22×M16C22×D418yes—
251C22×M16C22×D418yes—
252C22×M16C22×D418yes—
253C22×M16C22×D418yes—
254C23×C8#120116yes—
255C23×C8C22×D418yes—
256C2×#117#120132yes—
257C2×#117C22×D418yes—
258C2×#117C22×D418yes—
259C2×#117C22×D418yes—
260C22×C4⋊C4#12014yes—
261C22×C4⋊C4C22×D414yes—
262C22×C4⋊C4C22×D414yes—
263C22×C22⋊C4#12014yes—
264C22×C22⋊C4C22×D414yes—
265C22×C22⋊C4C22×D414yes—
266C22×C42#12014yes—
267C22×C42C22×D414yes—
268C22×C42C22×D414yes—
269C25#392116yes—
270C25C2×#12011yescharacteristic
271C25C2×#12014yes—
272C25C2×#12011yescharacteristic
273C25C2×#12012yes—
274C25C2×#12114yes—
275C25C2×#12112yes—
276C25#52512yes—
277C25C2×#12714yes—
278C25C2×#12712yes—
279C25#53412yes—
280C25#53512yes—
281C25D4212yes—
282C25D4214yes—
283C25D4212yes—
284C25D4214yes—
285C25D4214yes—
286C25C23×D411yescharacteristic
287C22×Q8C2×#12018yes—
288C22×D4#392116yes—
289C22×D4#392132yes—
290C22×D4#392132yes—
291C22×D4#392132yes—
292C22×D4#392116yes—
293C22×D4C2×#12018yes—
294C22×D4C2×#12018yes—
295C22×D4C2×#120116yes—
296C22×D4C2×#12018yes—
297C22×D4C2×#120116yes—
298C22×D4C2×#121116yes—
299C22×D4C2×#121116yes—
300C22×D4C2×#12118yes—
301C22×D4C2×#12118yes—
302C22×D4C2×#12718yes—
303C22×D4C2×#12718yes—
304C23×C4#392116yes—
305C23×C4#392132yes—
306C23×C4C2×#12014yes—
307C23×C4C2×#120116yes—
308C23×C4C2×#12018yes—
309C23×C4C2×#12014yes—
310C23×C4C2×#12018yes—
311C23×C4C2×#12014yes—
312C23×C4C2×#12018yes—
313C23×C4C2×#12014yes—
314C23×C4C2×#12014yes—
315C23×C4C2×#12014yes—
316C23×C4C2×#12018yes—
317C23×C4C2×#12014yes—
318C23×C4C2×#12018yes—
319C23×C4C2×#12011yescharacteristic
320C23×C4C2×#12011yescharacteristic
321C23×C4C2×#12012yes—
322C23×C4C2×#12011yescharacteristic
323C23×C4C2×#12012yes—
324C23×C4C2×#12012yes—
325C23×C4C2×#12012yes—
326C23×C4C2×#12011yescharacteristic
327C23×C4C2×#12114yes—
328C23×C4C2×#121116yes—
329C23×C4C2×#12112yes—
330C23×C4C2×#12112yes—
331C23×C4C2×#12112yes—
332C23×C4C2×#12112yes—
333C23×C4C2×#12112yes—
334C23×C4C2×#12114yes—
335C23×C4C2×#12114yes—
336C23×C4C2×#12118yes—
337C23×C4C2×#12118yes—
338C23×C4#52512yes—
339C23×C4#52512yes—
340C23×C4#52512yes—
341C23×C4#52512yes—
342C23×C4#52512yes—
343C23×C4C2×#12714yes—
344C23×C4C2×#12712yes—
345C23×C4C2×#12712yes—
346C23×C4C2×#12712yes—
347C23×C4C2×#12712yes—
348C23×C4C2×#12712yes—
349C23×C4#53418yes—
350C23×C4#53414yes—
351C23×C4#53414yes—
352C23×C4#53418yes—
353C23×C4#53414yes—
354C23×C4#53418yes—
355C23×C4#53414yes—
356C23×C4#53414yes—
357C23×C4#53414yes—
358C23×C4#53414yes—
359C23×C4#53414yes—
360C23×C4#53418yes—
361C23×C4#53414yes—
362C23×C4#53414yes—
363C23×C4#53412yes—
364C23×C4#53411yescharacteristic
365C23×C4#53412yes—
366C23×C4#53412yes—
367C23×C4#53412yes—
368C23×C4#53411yescharacteristic
369C23×C4#53518yes—
370C23×C4#53514yes—
371C23×C4#53514yes—
372C23×C4#53514yes—
373C23×C4#53518yes—
374C23×C4#53518yes—
375C23×C4#53518yes—
376C23×C4#53514yes—
377C23×C4#53512yes—
378C23×C4#53512yes—
379C23×C4#53512yes—
380C23×C4#53512yes—
381C23×C4#53512yes—
382C23×C4#53814yes—
383C23×C4#53814yes—
384C23×C4#53818yes—
385C23×C4#53818yes—
386C23×C4D4214yes—
387C23×C4D4214yes—
388C23×C4D4214yes—
389C23×C4D4214yes—
390C23×C4D4214yes—
391C23×C4D4214yes—
392C23×C4D4214yes—
393C23×C4D4218yes—
394C23×C4D4214yes—
395C23×C4D4214yes—
396C23×C4D4218yes—
397C23×C4D4214yes—
398C23×C4D4212yes—
399C23×C4D4214yes—
400C23×C4D4212yes—
401C23×C4D4218yes—
402C23×C4D4218yes—
403C23×C4D4214yes—
404C23×C4D4212yes—
405C23×C4D4214yes—
406C23×C4D4212yes—
407C23×C4D4214yes—
408C23×C4D4214yes—
409C23×C4D4212yes—
410C23×C4D4214yes—
411C23×C4D4214yes—
412C23×C4D4212yes—
413C23×C4D4218yes—
414C23×C4D4214yes—
415C23×C4D4214yes—
416C23×C4D4218yes—
417C23×C4D4214yes—
418C23×C4D4214yes—
419C23×C4D4214yes—
420C23×C4D4214yes—
421C23×C4D4214yes—
422C23×C4D4214yes—
423C23×C4D4214yes—
424C23×C4D4214yes—
425C23×C4D4214yes—
426C23×C4D4214yes—
427C23×C4#54614yes—
428C23×C4#54614yes—
429C23×C4#54618yes—
430C23×C4#54614yes—
431C23×C4#54614yes—
432C23×C4#54618yes—
433C23×C4#54618yes—
434C23×C4#54618yes—
435C23×C4#54618yes—
436C23×C4#54618yes—
437C23×C4#54614yes—
438C23×C4#54618yes—
439C23×C4#54614yes—
440C23×C4#54618yes—
441C23×C4#54614yes—
442C23×C4#54614yes—
443C23×C4#56014yes—
444C23×C4#56018yes—
445C23×C4#56014yes—
446C23×C4#56018yes—
447C23×C4H(3,𝔽4)14yes—
448C23×C4H(3,𝔽4)14yes—
449C23×C4C23×D411yescharacteristic
450C23×C4C23×D412yes—
451C23×C4C23×D412yes—
452C23×C4C23×D412yes—
453C23×C4C23×D412yes—
454C23×C4C23×D412yes—
455C23×C4C23×D412yes—
456C23×C4C23×D411yescharacteristic
457C23×C4C23×D411yescharacteristic
458C23×C4C22×#4111yescharacteristic
459C23×C4C22×#4111yescharacteristic
460C23×C4C22×#4111yescharacteristic
461C23×C4C2×H(5,𝔽2)12yes—
462C23×C4C2×H(5,𝔽2)12yes—
463C23×C4C2×H(5,𝔽2)12yes—
464C23×C4C2×H(5,𝔽2)12yes—
465C23×C4C2×H(5,𝔽2)12yes—
466C23×C4C2×H(5,𝔽2)12yes—
467C2×M16C2×#120116yes—
468C22×C8C2×#120116yes—
469#117C2×#120116yes—
470C24C2×#39218yes—
471C24C2×#39214yes—
472C24#240314yes—
473C24#240312yes—
474C24#240312yes—
475C24#240311yescharacteristic
476C24#240312yes—
477C24#240314yes—
478C24#240312yes—
479C24#240312yes—
480C24#240318yes—
481C24#240311yescharacteristic
482C24#240414yes—
483C24#241014yes—
484C24#241014yes—
485C24#241018yes—
486C24#242414yes—
487C24#242414yes—
488C24#242418yes—
489C24#243314yes—
490C24#243312yes—
491C24#243312yes—
492C24#243312yes—
493C24#243314yes—
494C24#243318yes—
495C24#243312yes—
496C24#243312yes—
497C24#243312yes—
498C24#253914yes—
499C24#261714yes—
500C24#266914yes—
501C24#266914yes—
502C24#266918yes—
503C24#266918yes—
504C24#267914yes—
505C24#267914yes—
506C24#284712yes—
507C24#284712yes—
508C24C22×#12011yescharacteristic
509C24C22×#12011yescharacteristic
510C24C22×#12111yescharacteristic
511C24C2×#52511yescharacteristic
512C24C22×#12711yescharacteristic
513C24C2×#53411yescharacteristic
514C24C2×#53511yescharacteristic
515C24C2×D4212yes—
516C24C2×D4212yes—
517C24C2×D4212yes—
518C24C2×D4212yes—
519C2×D4C2×#392116yes—
520C2×D4C2×#392116yes—
521C22×C4C2×#39218yes—
522C22×C4C2×#39214yes—
523C22×C4C2×#39212yes—
524C22×C4C2×#39214yes—
525C22×C4C2×#39214yes—
526C22×C4C2×#39214yes—
527C22×C4C2×#39212yes—
528C22×C4#240314yes—
529C22×C4#240314yes—
530C22×C4#240312yes—
531C22×C4#240311yescharacteristic
532C22×C4#240311yescharacteristic
533C22×C4#240312yes—
534C22×C4#240312yes—
535C22×C4#240312yes—
536C22×C4#240312yes—
537C22×C4#240314yes—
538C22×C4#240314yes—
539C22×C4#240314yes—
540C22×C4#240314yes—
541C22×C4#240314yes—
542C22×C4#240314yes—
543C22×C4#240314yes—
544C22×C4#240314yes—
545C22×C4#240318yes—
546C22×C4#240318yes—
547C22×C4#240318yes—
548C22×C4#240318yes—
549C22×C4#240318yes—
550C22×C4#240318yes—
551C22×C4#240318yes—
552C22×C4#240314yes—
553C22×C4#240314yes—
554C22×C4#240314yes—
555C22×C4#240314yes—
556C22×C4#240318yes—
557C22×C4#240318yes—
558C22×C4#240414yes—
559C22×C4#240412yes—
560C22×C4#240414yes—
561C22×C4#240412yes—
562C22×C4#240414yes—
563C22×C4#240414yes—
564C22×C4#240818yes—
565C22×C4#240818yes—
566C22×C4#240818yes—
567C22×C4#240818yes—
568C22×C4#240818yes—
569C22×C4#240818yes—
570C22×C4#240818yes—
571C22×C4#240818yes—
572C22×C4#240818yes—
573C22×C4#240818yes—
574C22×C4#240818yes—
575C22×C4#240818yes—
576C22×C4#241014yes—
577C22×C4#241014yes—
578C22×C4#241018yes—
579C22×C4#241018yes—
580C22×C4#241018yes—
581C22×C4#241018yes—
582C22×C4#241014yes—
583C22×C4#241014yes—
584C22×C4#241018yes—
585C22×C4#241018yes—
586C22×C4#241018yes—
587C22×C4#241018yes—
588C22×C4#241018yes—
589C22×C4#241018yes—
590C22×C4#241018yes—
591C22×C4#241018yes—
592C22×C4#241018yes—
593C22×C4#241018yes—
594C22×C4#241018yes—
595C22×C4#241018yes—
596C22×C4#241018yes—
597C22×C4#241018yes—
598C22×C4#241014yes—
599C22×C4#241014yes—
600C22×C4#241018yes—
601C22×C4#242418yes—
602C22×C4#242418yes—
603C22×C4#242418yes—
604C22×C4#242418yes—
605C22×C4#242414yes—
606C22×C4#242414yes—
607C22×C4#242414yes—
608C22×C4#242414yes—
609C22×C4#242418yes—
610C22×C4#242418yes—
611C22×C4#242414yes—
612C22×C4#242414yes—
613C22×C4#242418yes—
614C22×C4#243314yes—
615C22×C4#243314yes—
616C22×C4#243318yes—
617C22×C4#243318yes—
618C22×C4#243318yes—
619C22×C4#243314yes—
620C22×C4#243314yes—
621C22×C4#243318yes—
622C22×C4#243318yes—
623C22×C4#243318yes—
624C22×C4#243314yes—
625C22×C4#243314yes—
626C22×C4#243318yes—
627C22×C4#243312yes—
628C22×C4#243312yes—
629C22×C4#243312yes—
630C22×C4#243312yes—
631C22×C4#243312yes—
632C22×C4#243312yes—
633C22×C4#253912yes—
634C22×C4#253914yes—
635C22×C4#253912yes—
636C22×C4#253914yes—
637C22×C4#253914yes—
638C22×C4#253914yes—
639C22×C4#261318yes—
640C22×C4#261318yes—
641C22×C4#261318yes—
642C22×C4#261318yes—
643C22×C4#261318yes—
644C22×C4#261318yes—
645C22×C4#261714yes—
646C22×C4#261712yes—
647C22×C4#261714yes—
648C22×C4#261714yes—
649C22×C4#261714yes—
650C22×C4#261712yes—
651C22×C4#266818yes—
652C22×C4#266818yes—
653C22×C4#266818yes—
654C22×C4#266818yes—
655C22×C4#266818yes—
656C22×C4#266818yes—
657C22×C4#266914yes—
658C22×C4#266914yes—
659C22×C4#266918yes—
660C22×C4#266918yes—
661C22×C4#266918yes—
662C22×C4#266914yes—
663C22×C4#266914yes—
664C22×C4#266918yes—
665C22×C4#266918yes—
666C22×C4#266918yes—
667C22×C4#266918yes—
668C22×C4#266914yes—
669C22×C4#266914yes—
670C22×C4#266914yes—
671C22×C4#266914yes—
672C22×C4#266918yes—
673C22×C4#266914yes—
674C22×C4#266914yes—
675C22×C4#266918yes—
676C22×C4#266918yes—
677C22×C4#267018yes—
678C22×C4#267018yes—
679C22×C4#267018yes—
680C22×C4#267018yes—
681C22×C4#267018yes—
682C22×C4#267018yes—
683C22×C4#267818yes—
684C22×C4#267818yes—
685C22×C4#267818yes—
686C22×C4#267818yes—
687C22×C4#267818yes—
688C22×C4#267818yes—
689C22×C4#267818yes—
690C22×C4#267818yes—
691C22×C4#267818yes—
692C22×C4#267818yes—
693C22×C4#267818yes—
694C22×C4#267818yes—
695C22×C4#267914yes—
696C22×C4#267914yes—
697C22×C4#267914yes—
698C22×C4#267914yes—
699C22×C4#267914yes—
700C22×C4#267914yes—
701C22×C4#267914yes—
702C22×C4#267914yes—
703C22×C4#267914yes—
704C22×C4#267914yes—
705C22×C4#281218yes—
706C22×C4#281218yes—
707C22×C4#284618yes—
708C22×C4#284618yes—
709C22×C4#284712yes—
710C22×C4#284712yes—
711C22×C4C22×#12012yes—
712C22×C4C22×#12012yes—
713C22×C4C22×#12012yes—
714C22×C4C22×#12012yes—
715C22×C4C22×#12012yes—
716C22×C4C22×#12012yes—
717C22×C4C22×#12012yes—
718C22×C4C22×#12011yescharacteristic
719C22×C4C22×#12011yescharacteristic
720C22×C4C22×#12111yescharacteristic
721C22×C4C22×#12111yescharacteristic
722C22×C4C22×#12112yes—
723C22×C4C22×#12112yes—
724C22×C4C22×#12112yes—
725C22×C4C2×#52511yescharacteristic
726C22×C4C2×#52511yescharacteristic
727C22×C4C22×#12711yescharacteristic
728C22×C4C22×#12711yescharacteristic
729C22×C4C2×#53411yescharacteristic
730C22×C4C2×#53411yescharacteristic
731C22×C4C2×#53412yes—
732C22×C4C2×#53412yes—
733C22×C4C2×#53412yes—
734C22×C4C2×#53412yes—
735C22×C4C2×#53412yes—
736C22×C4C2×#53412yes—
737C22×C4C2×#53412yes—
738C22×C4C2×#53412yes—
739C22×C4C2×#53412yes—
740C22×C4C2×#53512yes—
741C22×C4C2×#53512yes—
742C22×C4C2×#53512yes—
743C22×C4C2×#53512yes—
744C22×C4C2×#53512yes—
745C22×C4C2×#53512yes—
746C22×C4C2×#53511yescharacteristic
747C22×C4C2×#53511yescharacteristic
748C22×C4C2×#53812yes—
749C22×C4C2×#53812yes—
750C22×C4C2×#53812yes—
751C22×C4C2×D4212yes—
752C22×C4C2×D4212yes—
753C22×C4C2×D4212yes—
754C22×C4C2×D4212yes—
755C22×C4C2×D4212yes—
756C22×C4C2×D4212yes—
757C22×C4C2×D4212yes—
758C22×C4C2×D4212yes—
759C22×C4C2×D4212yes—
760C22×C4C2×D4212yes—
761C22×C4C2×D4212yes—
762C22×C4C2×D4212yes—
763C22×C4C2×D4212yes—
764C22×C4C2×D4212yes—
765C22×C4C2×D4212yes—
766C22×C4C2×D4212yes—
767C22×C4C2×D4212yes—
768C22×C4C2×D4212yes—
769C22×C4C2×D4212yes—
770C22×C4C2×D4212yes—
771C22×C4C2×#54612yes—
772C22×C4C2×#54612yes—
773C22×C4C2×#54612yes—
774C22×C4C2×#54612yes—
775C22×C4C2×#54612yes—
776C22×C4C2×#54612yes—
777C22×C4C2×#54612yes—
778C22×C4C2×#54612yes—
779C22×C4C2×#54612yes—
780C22×C4C2×#54612yes—
781C22×C4C2×#54612yes—
782C22×C4C2×#54612yes—
783C22×C4C2×#56012yes—
784C22×C4C2×#56012yes—
785C22×C4C2×#56012yes—
786C22×C4C2×H(3,𝔽4)12yes—
787C23#1471518yes—
788C23#1471518yes—
789C23#1471614yes—
790C23#1471614yes—
791C23#1471614yes—
792C23#1471612yes—
793C23#1471614yes—
794C23#1471614yes—
795C23#1471612yes—
796C23#1525718yes—
797C23#1525718yes—
798C23#1525814yes—
799C23#1525814yes—
800C23#1525812yes—
801C23#1525814yes—
802C23#1525814yes—
803C23#1525814yes—
804C23#1525812yes—
805C23#1526718yes—
806C23#1526718yes—
807C23#1594714yes—
808C23#1594712yes—
809C23#1594712yes—
810C23#1624918yes—
811C23#1624918yes—
812C23#2388218yes—
813C23C22×#39211yescharacteristic
814C23C2×#261711yescharacteristic
815C23C2×#240312yes—
816C23C2×#240311yescharacteristic
817C23C2×#240311yescharacteristic
818C23C2×#240312yes—
819C23C2×#240311yescharacteristic
820C23C2×#241012yes—
821C23C2×#241012yes—
822C23C2×#242412yes—
823C23C2×#242412yes—
824C23C2×#243311yescharacteristic
825C23C2×#243311yescharacteristic
826C23C2×#243311yescharacteristic
827C23C2×#243312yes—
828C23C2×#243312yes—
829C23C2×#240411yescharacteristic
830C23C2×#253911yescharacteristic
831C23C2×#284711yescharacteristic
832C23C2×#266912yes—
833C23C2×#266912yes—
834C23C2×#266912yes—
835C23C2×#267912yes—
836C2×C4#1471518yes—
837C2×C4#1471518yes—
838C2×C4#1471518yes—
839C2×C4#1471518yes—
840C2×C4#1471518yes—
841C2×C4#1471518yes—
842C2×C4#1471518yes—
843C2×C4#1471518yes—
844C2×C4#1471518yes—
845C2×C4#1471518yes—
846C2×C4#1471614yes—
847C2×C4#1471614yes—
848C2×C4#1471612yes—
849C2×C4#1471614yes—
850C2×C4#1471612yes—
851C2×C4#1471614yes—
852C2×C4#1471614yes—
853C2×C4#1525718yes—
854C2×C4#1525718yes—
855C2×C4#1525718yes—
856C2×C4#1525718yes—
857C2×C4#1525718yes—
858C2×C4#1525718yes—
859C2×C4#1525718yes—
860C2×C4#1525718yes—
861C2×C4#1525718yes—
862C2×C4#1525718yes—
863C2×C4#1525814yes—
864C2×C4#1525814yes—
865C2×C4#1525814yes—
866C2×C4#1525812yes—
867C2×C4#1525812yes—
868C2×C4#1525814yes—
869C2×C4#1525814yes—
870C2×C4#1526718yes—
871C2×C4#1526718yes—
872C2×C4#1526718yes—
873C2×C4#1526718yes—
874C2×C4#1526718yes—
875C2×C4#1526718yes—
876C2×C4#1526718yes—
877C2×C4#1526718yes—
878C2×C4#1526718yes—
879C2×C4#1526718yes—
880C2×C4#1594712yes—
881C2×C4#1594712yes—
882C2×C4#1594714yes—
883C2×C4#1624918yes—
884C2×C4#1624918yes—
885C2×C4#1624918yes—
886C2×C4#1624918yes—
887C2×C4#1624918yes—
888C2×C4#1624918yes—
889C2×C4#1624918yes—
890C2×C4#1624918yes—
891C2×C4#1624918yes—
892C2×C4#1624918yes—
893C2×C4C22×#39211yescharacteristic
894C2×C4C22×#39211yescharacteristic
895C2×C4C2×#261312yes—
896C2×C4C2×#261312yes—
897C2×C4C2×#261312yes—
898C2×C4C2×#261711yescharacteristic
899C2×C4C2×#261711yescharacteristic
900C2×C4C2×#240312yes—
901C2×C4C2×#240312yes—
902C2×C4C2×#240312yes—
903C2×C4C2×#240312yes—
904C2×C4C2×#240312yes—
905C2×C4C2×#240312yes—
906C2×C4C2×#240312yes—
907C2×C4C2×#241012yes—
908C2×C4C2×#241012yes—
909C2×C4C2×#241012yes—
910C2×C4C2×#241012yes—
911C2×C4C2×#241012yes—
912C2×C4C2×#241012yes—
913C2×C4C2×#241012yes—
914C2×C4C2×#241012yes—
915C2×C4C2×#241012yes—
916C2×C4C2×#241012yes—
917C2×C4C2×#242412yes—
918C2×C4C2×#242412yes—
919C2×C4C2×#242412yes—
920C2×C4C2×#242412yes—
921C2×C4C2×#240812yes—
922C2×C4C2×#240812yes—
923C2×C4C2×#240812yes—
924C2×C4C2×#240812yes—
925C2×C4C2×#240812yes—
926C2×C4C2×#240812yes—
927C2×C4C2×#243312yes—
928C2×C4C2×#243312yes—
929C2×C4C2×#243312yes—
930C2×C4C2×#243312yes—
931C2×C4C2×#240411yescharacteristic
932C2×C4C2×#240411yescharacteristic
933C2×C4C2×#253911yescharacteristic
934C2×C4C2×#253911yescharacteristic
935C2×C4C2×#284612yes—
936C2×C4C2×#281212yes—
937C2×C4C2×#266812yes—
938C2×C4C2×#266812yes—
939C2×C4C2×#266812yes—
940C2×C4C2×#266912yes—
941C2×C4C2×#266912yes—
942C2×C4C2×#266912yes—
943C2×C4C2×#266912yes—
944C2×C4C2×#266912yes—
945C2×C4C2×#266912yes—
946C2×C4C2×#267012yes—
947C2×C4C2×#267012yes—
948C2×C4C2×#267012yes—
949C2×C4C2×#267812yes—
950C2×C4C2×#267812yes—
951C2×C4C2×#267812yes—
952C2×C4C2×#267812yes—
953C2×C4C2×#267812yes—
954C2×C4C2×#267812yes—
955C2×C4C2×#267912yes—
956C2×C4C2×#267912yes—
957C22#15668418yes—
958C22#15668414yes—
959C22#15668414yes—
960C22#39424918yes—
961C22#41777418yes—
962C22#44949618yes—
963C22C2×#1471512yes—
964C22C2×#1471611yescharacteristic
965C22C2×#1471611yescharacteristic
966C22C2×#1471611yescharacteristic
967C22C2×#1525712yes—
968C22C2×#1525811yescharacteristic
969C22C2×#1525811yescharacteristic
970C22C2×#1525811yescharacteristic
971C22C2×#1526712yes—
972C22C2×#1594711yescharacteristic
973C22C2×#1624912yes—
974C22C2×#2388214yes—
975C4#15668414yes—
976C4#15668418yes—
977C4#15668414yes—
978C4C2×#1471512yes—
979C4C2×#1471512yes—
980C4C2×#1525712yes—
981C4C2×#1525712yes—
982C4C2×#1526712yes—
983C4C2×#1526712yes—
984C4C2×#1624912yes—
985C4C2×#1624912yes—
986C2C2×#41777412yes—
987C2C2×#39424912yes—
988C2C2×#44949612yes—
989C2#7225120118yesdirect product factor
990C2C2×#15668411yescharacteristic
subgroupG/H
center, socleC24#2403
commutator, Frattini, cosocleC24×C4C25
LCSG ▷ C24×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#123535C2semidirect
2. C2×#123560C2semidirect
3. C22×#11030C2semidirect
4. C22×#11012C2semidirect
5. C2×#123547C2semidirect
6. C22×#23407C2semidirect
7. C2×#6431766C2semidirect
8. C22×#23443C2semidirect
9. C2×#517415C2semidirect
10. C22×#10994C2semidirect
11. #72251201C2direct (N × H)
12. C23×#3003C2semidirect
16. C22×#3449C22semidirect
18. C22×#3003C22semidirect
20. C23×#410C22semidirect
21. C22×#2896C22semidirect
22. C23×#421C22semidirect
31. C2×#23443C22semidirect
32. #6431766C22semidirect
33. C2×#23407C22semidirect
34. C23×#344C22semidirect
35. C22×#1742C22semidirect
36. C22×#1740C22semidirect
37. C22×#1733C22semidirect
38. C23×H(3,ℤ/4)C22semidirect
39. C2×#20335C22semidirect
40. #517415C22semidirect
41. C2×#11030C22semidirect
42. C2×#11012C22semidirect
43. C2×#10994C22semidirect
44. #123560C22semidirect
45. #123547C22semidirect
46. #123535C22semidirect
48. C25×D4D4semidirect
53. C23×AGL(1,ℤ/8)D4semidirect
54. C23×AGL(1,ℤ/8)D4semidirect
57. C24×SD16D4semidirect
58. C24×D8D4semidirect
61. C2×#3449C23semidirect
69. C22×#421C23semidirect
70. C2×#2896C23semidirect
71. C22×#418D4semidirect
72. C22×#418D4semidirect
75. C22×#410C23semidirect
76. C22×#407D4semidirect
78. C2×#2309D4semidirect
79. C2×#2309D4semidirect
84. C22×#390D4semidirect
85. C22×#390D4semidirect
91. C22×#344C23semidirect
92. C2×#1742C23semidirect
93. C2×#1740C23semidirect
94. C2×#1733C23semidirect
95. C22×H(3,ℤ/4)C23semidirect
96. #20335C23semidirect
115. C24×D4C2×D4semidirect
128. C22×AGL(1,ℤ/8)C2×D4semidirect
129. C23×SD16C2×D4semidirect
130. C23×D8C2×D4semidirect
161. C2×#418C2×D4semidirect
162. C2×#418C2×D4semidirect
163. C2×#407C2×D4semidirect
164. C2×#390C2×D4semidirect
165. C2×#390C2×D4semidirect
989. C2#72251201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1235352
C2×#1235602
C22×#110302
C22×#110122
C2×#1235472
C22×#234072
C2×#64317662
C22×#234432
C2×#5174152
C22×#109942
#722512012
C23×#30032