Finite Group Databasebeta

← C22×#364592 #72316991

Subgroups — C22×#364592 #72316991

Order 2048.

At least 6015 conjugacy classes of subgroups; only the 14392 normal subgroups are shown.

The subgroup lattice has 939 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11100C211yesmaximal, characteristic, complemented
2C22×#10937C211yesmaximal, characteristic, complemented
3C22×#10948C211yesmaximal, characteristic, complemented
4C22×#11129C211yesmaximal, characteristic, complemented
5C22×#10776C211yesmaximal, characteristic, complemented
6C22×#10785C211yesmaximal, characteristic, complemented
7C22×#11030C211yesmaximal, characteristic, complemented
8C22×#20959C211yesmaximal, characteristic, complemented
9C22×#20945C211yesmaximal, characteristic, complemented
10C22×#60168C211yesmaximal, characteristic, complemented
11C22×#10994C211yesmaximal, characteristic, complemented
12C22×#20598C211yesmaximal, characteristic, complemented
13C22×#34171C211yesmaximal, characteristic, complemented
14C23×#1904C211yesmaximal, characteristic, complemented
15C2×#364592C2148yesmaximal, direct product factor
16C23×#3003C211yesmaximal, characteristic
17C26×D4C2211yescharacteristic
18C24×AGL(1,ℤ/8)C2211yescharacteristic
19C24×AGL(1,ℤ/8)C2211yescharacteristic
20C23×#525C2211yescharacteristic
21C22×#3428C2211yescharacteristic, complemented
22C23×#518C2211yescharacteristic
23C23×#518C2211yescharacteristic
24C22×#3003C4132yescomplemented
25C22×#3003C22124yes—
26C2×#60168C22124yescomplemented
27C22×#2911C2211yescharacteristic, complemented
28C23×#407C2211yescharacteristic
29C23×#407C2211yescharacteristic
30C23×#410C2211yescharacteristic, complemented
31C22×#2896C2211yescharacteristic, complemented
32C23×#421C2211yescharacteristic, complemented
33C23×#418C2211yescharacteristic
34C23×#418C2211yescharacteristic
35C23×#418C2211yescharacteristic
36C23×#418C2211yescharacteristic
37C23×#418C2211yescharacteristic
38C23×#418C2211yescharacteristic
39C22×#2873C2211yescharacteristic, complemented
40C2×#34171C22124yescomplemented
41C22×#2309C2211yescharacteristic
42C22×#2309C2211yescharacteristic
43C22×#2280C2211yescharacteristic
44C22×#2280C2211yescharacteristic
45C22×#2280C2211yescharacteristic
46C22×#1904C22124yescomplemented
47C2×#20959C22124yescomplemented
48C2×#20945C22124yescomplemented
49C2×#20598C22124yescomplemented
50C23×#344C2211yescharacteristic, complemented
51C23×#344C2211yescharacteristic, complemented
52C22×#1742C2211yescharacteristic, complemented
53C22×#1740C2211yescharacteristic, complemented
54C22×#1740C2211yescharacteristic, complemented
55C22×#1733C2211yescharacteristic, complemented
56C22×#1733C2211yescharacteristic, complemented
57C22×#1733C2211yescharacteristic, complemented
58C23×H(3,ℤ/4)C2211yescharacteristic, complemented
59C23×H(3,ℤ/4)C2211yescharacteristic, complemented
60#364592C221256yesdirect product factor
61C2×#11129C22124yescomplemented
62C2×#11100C22124yescomplemented
63C2×#11030C22124yescomplemented
64C2×#10994C22124yescomplemented
65C2×#10948C22124yescomplemented
66C2×#10937C22124yescomplemented
67C2×#10785C22124yescomplemented
68C2×#10776C22124yescomplemented
69C24×#41C2311yescharacteristic
70C25×D4C2×C4116yescomplemented
71C25×D4C23112yes—
72C25×D4C2311yescharacteristic
73C25×D4C2311yescharacteristic
74C26×C4C2311yescharacteristic
75C23×AGL(1,ℤ/8)C2×C4116yes—
76C23×AGL(1,ℤ/8)C2×C4116yescomplemented
77C23×AGL(1,ℤ/8)D4116yes—
78C23×AGL(1,ℤ/8)D4112yes—
79C23×AGL(1,ℤ/8)C23112yes—
80C23×AGL(1,ℤ/8)C23112yes—
81C24×SD16D412yes—
82C24×D8D412yes—
83C24×M16C2311yescharacteristic
84C24×M16C2311yescharacteristic
85C24×M16C2311yescharacteristic
86C24×M16C2311yescharacteristic
87C22×#525C2×C4116yescomplemented
88C22×#525C23112yes—
89C2×#3428C23112yescomplemented
90C22×#518D4112yescomplemented
91C22×#518C23112yes—
92C22×#518C23112yes—
93C23×C4×D4D414yescomplemented
94C23×#117C2311yescharacteristic
95C23×#117C2311yescharacteristic
96C23×#117C2311yescharacteristic
97C23×#117C2311yescharacteristic
98C23×#117C2311yescharacteristic
99C23×#117C2311yescharacteristic
100C23×#117C2311yescharacteristic
101C2×#3003C2×C41384yescomplemented
102C2×#3003C23164yes—
103#60168C23164yescomplemented
104C2×#2911C23112yescomplemented
105C22×#421C23112yescomplemented
106C2×#2896C23112yescomplemented
107C22×#418C2×C4116yescomplemented
108C22×#418C2×C4116yescomplemented
109C22×#418D4112yescomplemented
110C22×#418C23112yes—
111C22×#418C23112yes—
112C22×#418C23112yes—
113C22×#418C23112yes—
114C22×#418C23112yes—
115C22×#418C23112yes—
116C23×#102D414yescomplemented
117C22×#410C23112yescomplemented
118C22×#407C2×C4116yescomplemented
119C22×#407C23112yes—
120C22×#407C23112yes—
121C2×#2873C23112yescomplemented
122#34171C23164yescomplemented
123C2×#2309D4112yescomplemented
124C2×#2309C23112yes—
125C2×#2309C23112yes—
126C22×#390D414yescomplemented
127C2×#2280D4112yes—
128C2×#2280C23112yes—
129C2×#2280C23112yes—
130C2×#2280C23112yes—
131C22×#381D412yes—
132C22×#379D412yes—
133C2×#1904C23164yescomplemented
134#20959C23164yescomplemented
135#20945C23164yescomplemented
136#20598C23164yescomplemented
137C22×#344C23112yescomplemented
138C22×#344C23112yescomplemented
139C2×#1742C23112yescomplemented
140C2×#1740C23112yescomplemented
141C2×#1740C23112yescomplemented
142C2×#1733C23112yescomplemented
143C2×#1733C23112yescomplemented
144C2×#1733C23112yescomplemented
145C22×H(3,ℤ/4)C23112yescomplemented
146C22×H(3,ℤ/4)C23112yescomplemented
147#11129C23164yescomplemented
148#11100C23164yescomplemented
149#11030C23164yescomplemented
150#10994C23164yescomplemented
151#10948C23164yescomplemented
152#10937C23164yescomplemented
153#10785C23164yescomplemented
154#10776C23164yescomplemented
155C27C2×D411yescharacteristic
156C23×#41C22×C418yes—
157C23×#41C2×D418yes—
158C23×#41C2×D416yes—
159C23×#41C2416yes—
160C24×Q8C2×D411yescharacteristic
161C24×D4C22×C418yes—
162C24×D4C22×C418yes—
163C24×D4C22×C4196yescomplemented
164C24×D4C2×D411yescharacteristic
165C24×D4C2×D412yes—
166C24×D4C2×D416yes—
167C24×D4C2×D412yes—
168C24×D4C2×D416yes—
169C24×D4C2×D418yes—
170C24×D4C2×D412yes—
171C24×D4C2×D416yes—
172C24×D4C2×D412yes—
173C24×D4C2×D416yes—
174C24×D4#4118yes—
175C24×D4#4118yes—
176C24×D4#4118yes—
177C24×D4C2416yes—
178C24×D4C24116yes—
179C24×D4C2416yes—
180C25×C4C22×C418yes—
181C25×C4C2×D411yescharacteristic
182C25×C4C2×D416yes—
183C25×C4#4118yes—
184C25×C4C2416yes—
185C25×C4C2411yescharacteristic
186C22×AGL(1,ℤ/8)C22⋊C41192yescomplemented
187C22×AGL(1,ℤ/8)C22×C4196yes—
188C22×AGL(1,ℤ/8)C22×C4196yescomplemented
189C22×AGL(1,ℤ/8)C2×D4196yes—
190C22×AGL(1,ℤ/8)C2×D4148yes—
191C22×AGL(1,ℤ/8)C24116yes—
192C22×AGL(1,ℤ/8)C24116yes—
193C23×SD16C22⋊C4132yescomplemented
194C23×SD16C2×D4124yes—
195C23×D8C22⋊C4132yescomplemented
196C23×D8C2×D4124yes—
197C23×M16C22×C418yes—
198C23×M16C22×C418yes—
199C23×M16C2×D418yes—
200C23×M16C2×D416yes—
201C23×M16C2×D416yes—
202C23×M16C2416yes—
203C23×M16C2416yes—
204C23×M16C2416yes—
205C23×M16C2416yes—
206C24×C8C2×D412yes—
207C24×C8C2×D412yes—
208C2×#525C22×C4196yescomplemented
209C2×#525C24116yes—
210#3428C24116yescomplemented
211C2×#518C2×D4148yescomplemented
212C2×#518C24116yes—
213C2×#518C24116yes—
214C22×C4×D4C2×D4148yescomplemented
215C22×#117C22×C418yes—
216C22×#117C2×D416yes—
217C22×#117C2×D416yes—
218C22×#117C2×D416yes—
219C22×#117C2×D416yes—
220C22×#117C2×D416yes—
221C22×#117C2×D416yes—
222C22×#117C2×D416yes—
223C22×#117C2416yes—
224C22×#117C2416yes—
225C22×#117C2416yes—
226C22×#117C2416yes—
227C22×#117C2416yes—
228C22×#117C2416yes—
229C22×#117C2416yes—
230C23×C4⋊C4C2×D412yes—
231C23×C4⋊C4C2×D412yes—
232C23×C4⋊C4C2×D412yes—
233C23×C22⋊C4C2×D412yes—
234C23×C22⋊C4C2×D412yes—
235C23×C42C2×D412yes—
236C23×C42C2×D412yes—
237#3003C22×C41512yescomplemented
238#2911C24116yescomplemented
239C2×#421C24116yescomplemented
240#2896C24116yescomplemented
241C2×#418C22×C4196yescomplemented
242C2×#418C22×C4196yescomplemented
243C2×#418C2×D4148yescomplemented
244C2×#418C24116yes—
245C2×#418C24116yes—
246C2×#418C24116yes—
247C2×#418C24116yes—
248C2×#418C24116yes—
249C2×#418C24116yes—
250C22×#102C2×D4148yescomplemented
251C2×#410C24116yescomplemented
252C2×#407C22×C4196yescomplemented
253C2×#407C24116yes—
254C2×#407C24116yes—
255#2873C24116yescomplemented
256#2309C2×D4148yescomplemented
257#2309C24116yes—
258#2309C24116yes—
259C2×#390C2×D4148yescomplemented
260#2280C2×D4148yes—
261#2280C24116yes—
262#2280C24116yes—
263#2280C24116yes—
264C2×#381C2×D4124yes—
265C2×#379C2×D4124yes—
266C2×#344C24116yescomplemented
267C2×#344C24116yescomplemented
268#1742C24116yescomplemented
269#1740C24116yescomplemented
270#1740C24116yescomplemented
271#1733C24116yescomplemented
272#1733C24116yescomplemented
273#1733C24116yescomplemented
274C2×H(3,ℤ/4)C24116yescomplemented
275C2×H(3,ℤ/4)C24116yescomplemented
276C26C4×D418yes—
277C26C22×D416yes—
278C26C22×D411yescharacteristic
279C22×#41C2×C22⋊C4148yescomplemented
280C22×#41C23×C4124yes—
281C22×#41C22×D4124yes—
282C22×#41C22×D4112yes—
283C22×#41C2514yes—
284C23×Q8C2×C22⋊C418yescomplemented
285C23×Q8C22×D416yes—
286C23×D4C2×C22⋊C4116yes—
287C23×D4C2×C22⋊C4148yes—
288C23×D4C2×C22⋊C418yescomplemented
289C23×D4C4×D4116yes—
290C23×D4C4×D4148yes—
291C23×D4C4×D4116yes—
292C23×D4C4×D4148yes—
293C23×D4C4×D4116yes—
294C23×D4C4×D4148yes—
295C23×D4#12014yes—
296C23×D4#120112yes—
297C23×D4#120112yes—
298C23×D4#120112yes—
299C23×D4#120124yes—
300C23×D4#121116yes—
301C23×D4#121148yes—
302C23×D4#121116yes—
303C23×D4#121148yes—
304C23×D4#123116yes—
305C23×D4#123148yes—
306C23×D4C23×C4124yes—
307C23×D4C23×C4124yes—
308C23×D4C23×C4164yescomplemented
309C23×D4C22×D416yes—
310C23×D4C22×D4112yes—
311C23×D4C22×D4112yes—
312C23×D4C22×D4112yes—
313C23×D4C22×D4112yes—
314C23×D4C22×D4124yes—
315C23×D4C22×D4112yes—
316C23×D4C22×D4112yes—
317C23×D4C22×D4112yes—
318C23×D4C22×D4112yes—
319C23×D4C2×#41124yes—
320C23×D4C2×#41124yes—
321C23×D4C2×#41124yes—
322C23×D4C2514yes—
323C23×D4C2514yes—
324C24×C4C4×D418yes—
325C24×C4C4×D4148yes—
326C24×C4#12014yes—
327C24×C4C23×C4124yes—
328C24×C4C23×C414yes—
329C24×C4C22×D416yes—
330C24×C4C22×D4112yes—
331C24×C4C22×D411yescharacteristic
332C24×C4C22×D413yes—
333C24×C4C22×D414yes—
334C24×C4C22×D411yescharacteristic
335C24×C4C22×D413yes—
336C24×C4C22×D411yescharacteristic
337C24×C4C22×D413yes—
338C24×C4C22×D413yes—
339C24×C4C22×D411yescharacteristic
340C24×C4C22×D413yes—
341C24×C4C2×#41124yes—
342C24×C4C2×#4114yes—
343C24×C4C2×#4114yes—
344C24×C4C2×#4114yes—
345C24×C4C2×#4114yes—
346C24×C4H(5,𝔽2)11yescharacteristic
347C24×C4H(5,𝔽2)11yescharacteristic
348C24×C4H(5,𝔽2)13yes—
349C24×C4H(5,𝔽2)13yes—
350C24×C4H(5,𝔽2)14yes—
351C24×C4H(5,𝔽2)14yes—
352C24×C4C2514yes—
353C24×C4C2513yes—
354C2×AGL(1,ℤ/8)C2×C22⋊C41384yescomplemented
355C2×AGL(1,ℤ/8)C23×C4164yes—
356C2×AGL(1,ℤ/8)C23×C4164yescomplemented
357C2×AGL(1,ℤ/8)C22×D4164yes—
358C22×SD16C2×C22⋊C41192yescomplemented
359C22×SD16C22×D4132yes—
360C22×D8C2×C22⋊C41192yescomplemented
361C22×D8C22×D4132yes—
362C22×M16C2×C22⋊C4148yescomplemented
363C22×M16C23×C4124yes—
364C22×M16C23×C4124yes—
365C22×M16C22×D4124yes—
366C22×M16C22×D4112yes—
367C22×M16C22×D4112yes—
368C22×M16C2514yes—
369C22×M16C2514yes—
370C22×M16C2514yes—
371C22×M16C2514yes—
372C23×C8C2×C22⋊C4116yescomplemented
373C23×C8C22×D4112yes—
374C23×C8C22×D4112yes—
375#525C23×C4164yescomplemented
376C2×C4×D4C22×D4164yescomplemented
377C2×#117#120124yes—
378C2×#117C23×C4124yes—
379C2×#117C22×D4112yes—
380C2×#117C22×D4112yes—
381C2×#117C22×D4112yes—
382C2×#117C22×D4112yes—
383C2×#117C22×D4112yes—
384C2×#117C22×D4112yes—
385C2×#117C22×D4112yes—
386C2×#117C2514yes—
387C2×#117C2514yes—
388C2×#117C2514yes—
389C2×#117C2514yes—
390C2×#117C2514yes—
391C2×#117C2514yes—
392C2×#117C2514yes—
393C22×C4⋊C4#120112yes—
394C22×C4⋊C4C22×D4112yes—
395C22×C4⋊C4C22×D4112yes—
396C22×C4⋊C4C22×D4112yes—
397C22×C22⋊C4#120112yes—
398C22×C22⋊C4C22×D4112yes—
399C22×C22⋊C4C22×D4112yes—
400C22×C42#120112yes—
401C22×C42C22×D4112yes—
402C22×C42C22×D4112yes—
403#418C23×C4164yescomplemented
404#418C23×C4164yescomplemented
405C2×#102C22×D4164yescomplemented
406#407C23×C4164yescomplemented
407#390C22×D4164yescomplemented
408#381C22×D4132yes—
409#379C22×D4132yes—
410C25C2×C4×D4124yes—
411C25C2×C4×D414yes—
412C25C2×#12011yescharacteristic
413C25C2×#12013yes—
414C25#52514yes—
415C25D4211yescharacteristic
416C25D4211yescharacteristic
417C25D4213yes—
418C25D4214yes—
419C25D4213yes—
420C25#54614yes—
421C25C23×D414yes—
422C25C23×D413yes—
423C2×#41C22×C22⋊C4148yescomplemented
424C2×#41C24×C418yes—
425C2×#41C23×D418yes—
426C22×Q8C22×C22⋊C4124yescomplemented
427C22×Q8C23×D414yes—
428C22×D4#386132yes—
429C22×D4#386196yes—
430C22×D4#386196yes—
431C22×D4#386196yes—
432C22×D4#3861192yes—
433C22×D4C22×C22⋊C4148yes—
434C22×D4C22×C22⋊C4148yes—
435C22×D4C22×C22⋊C4124yescomplemented
436C22×D4C2×C4×D4148yes—
437C22×D4C2×C4×D4148yes—
438C22×D4C2×C4×D4148yes—
439C22×D4C2×C4×D4148yes—
440C22×D4C2×C4×D4148yes—
441C22×D4C2×C4×D4148yes—
442C22×D4C2×#120124yes—
443C22×D4C2×#120124yes—
444C22×D4C2×#120124yes—
445C22×D4C2×#120124yes—
446C22×D4C2×#121148yes—
447C22×D4C2×#121148yes—
448C22×D4C2×#121148yes—
449C22×D4C2×#121148yes—
450C22×D4C2×#123148yes—
451C22×D4C2×#123148yes—
452C22×D4C24×C418yes—
453C22×D4C24×C418yes—
454C22×D4C23×D414yes—
455C22×D4C23×D418yes—
456C22×D4C23×D418yes—
457C22×D4C23×D418yes—
458C22×D4C23×D418yes—
459C22×D4C23×D418yes—
460C22×D4C22×#4118yes—
461C22×D4C22×#4118yes—
462C22×D4C22×#4118yes—
463C23×C4C22×C22⋊C414yes—
464C23×C4C22×C22⋊C4112yes—
465C23×C4C2×C4×D4124yes—
466C23×C4C2×C4×D4148yes—
467C23×C4C2×C4×D414yes—
468C23×C4C2×C4×D4112yes—
469C23×C4C2×C4×D414yes—
470C23×C4C2×C4×D4112yes—
471C23×C4C2×C4×D4112yes—
472C23×C4C2×C4×D414yes—
473C23×C4C2×C4×D4112yes—
474C23×C4#51814yes—
475C23×C4#518112yes—
476C23×C4#518112yes—
477C23×C4#51814yes—
478C23×C4C2×#120124yes—
479C23×C4C2×#12013yes—
480C23×C4C2×#12013yes—
481C23×C4C2×#12016yes—
482C23×C4C2×#12013yes—
483C23×C4C2×#12013yes—
484C23×C4C2×#12013yes—
485C23×C4C2×#12016yes—
486C23×C4C2×#12011yescharacteristic
487C23×C4C2×#12114yes—
488C23×C4C2×#121112yes—
489C23×C4C2×#12114yes—
490C23×C4C2×#121112yes—
491C23×C4C2×#12314yes—
492C23×C4C2×#123112yes—
493C23×C4#52514yes—
494C23×C4#525112yes—
495C23×C4#52514yes—
496C23×C4#525112yes—
497C23×C4#525112yes—
498C23×C4#53413yes—
499C23×C4#53413yes—
500C23×C4#53416yes—
501C23×C4#53413yes—
502C23×C4#53411yescharacteristic
503C23×C4#53514yes—
504C23×C4#535112yes—
505C23×C4#538112yes—
506C23×C4#53814yes—
507C23×C4#53814yes—
508C23×C4#538112yes—
509C23×C4D4213yes—
510C23×C4D4216yes—
511C23×C4D4213yes—
512C23×C4D4213yes—
513C23×C4D4213yes—
514C23×C4D4216yes—
515C23×C4D4213yes—
516C23×C4D4211yescharacteristic
517C23×C4D42112yes—
518C23×C4D4214yes—
519C23×C4D42112yes—
520C23×C4D4213yes—
521C23×C4D4216yes—
522C23×C4D4213yes—
523C23×C4D4213yes—
524C23×C4D4213yes—
525C23×C4D4213yes—
526C23×C4D4216yes—
527C23×C4D4211yescharacteristic
528C23×C4#54614yes—
529C23×C4#546112yes—
530C23×C4#546112yes—
531C23×C4#54614yes—
532C23×C4#54614yes—
533C23×C4#546112yes—
534C23×C4#546112yes—
535C23×C4#54614yes—
536C23×C4#54614yes—
537C23×C4#546112yes—
538C23×C4#546112yes—
539C23×C4#54614yes—
540C23×C4#546112yes—
541C23×C4#54614yes—
542C23×C4#546112yes—
543C23×C4#55114yes—
544C23×C4#551112yes—
545C23×C4#55114yes—
546C23×C4#551112yes—
547C23×C4C24×C418yes—
548C23×C4C24×C416yes—
549C23×C4C23×D414yes—
550C23×C4C23×D413yes—
551C23×C4C23×D413yes—
552C23×C4C23×D416yes—
553C23×C4C23×D413yes—
554C23×C4C23×D413yes—
555C23×C4C23×D413yes—
556C23×C4C23×D413yes—
557C23×C4C23×D413yes—
558C23×C4C23×D413yes—
559C23×C4C23×D413yes—
560C23×C4C22×#4118yes—
561C23×C4C22×#4116yes—
562C23×C4C22×#4116yes—
563C23×C4C22×#4116yes—
564C23×C4C22×#4116yes—
565C23×C4C2×H(5,𝔽2)13yes—
566C23×C4C2×H(5,𝔽2)13yes—
567C23×C4C2×H(5,𝔽2)13yes—
568C23×C4C2×H(5,𝔽2)13yes—
569C23×C4C2×H(5,𝔽2)16yes—
570C23×C4C2×H(5,𝔽2)16yes—
571C23×C4C2611yescharacteristic
572C2×SD16C22×C22⋊C41128yescomplemented
573C2×D8C22×C22⋊C41128yescomplemented
574C2×M16C22×C22⋊C4148yescomplemented
575C2×M16C24×C418yes—
576C2×M16C24×C418yes—
577C2×M16C23×D418yes—
578C22×C8C22×C22⋊C4148yescomplemented
579C22×C8C23×D418yes—
580C22×C8C23×D418yes—
581#117C24×C418yes—
582C2×C4⋊C4C2×#120124yes—
583C2×C4⋊C4C23×D418yes—
584C2×C4⋊C4C23×D418yes—
585C2×C4⋊C4C23×D418yes—
586C2×C22⋊C4C2×#120124yes—
587C2×C22⋊C4C23×D418yes—
588C2×C22⋊C4C23×D418yes—
589C2×C42C2×#120124yes—
590C2×C42C23×D418yes—
591C2×C42C23×D418yes—
592C24C4×#12014yes—
593C24C4×#120112yes—
594C24D4×C22⋊C414yes—
595C24D4×C22⋊C4112yes—
596C24#235814yes—
597C24#2358112yes—
598C24#240313yes—
599C24#240313yes—
600C24#240313yes—
601C24#240316yes—
602C24#240311yescharacteristic
603C24#240814yes—
604C24#2408112yes—
605C24#241814yes—
606C24#2418112yes—
607C24#242414yes—
608C24#2424112yes—
609C24C22×C4×D418yes—
610C24C22×C4×D416yes—
611C24C22×#12013yes—
612C24C22×#12013yes—
613C24C2×#52516yes—
614C24C2×D4213yes—
615C24C2×D4213yes—
616C24C2×D4213yes—
617C24C2×D4216yes—
618C24C2×D4213yes—
619C24C2×#54616yes—
620C24C24×D411yescharacteristic
621C2×Q8C23×C22⋊C418yescomplemented
622C2×D4C2×#386196yes—
623C2×D4C2×#386196yes—
624C2×D4C2×#386196yes—
625C2×D4C2×#386196yes—
626C2×D4C23×C22⋊C4116yes—
627C2×D4C23×C22⋊C418yescomplemented
628C2×D4C22×C4×D4116yes—
629C2×D4C22×C4×D4116yes—
630C2×D4C22×C4×D4116yes—
631C2×D4C22×#120116yes—
632C2×D4C22×#121116yes—
633C2×D4C22×#121116yes—
634C2×D4C22×#123116yes—
635C22×C4C2×#386112yes—
636C22×C4C2×#38614yes—
637C22×C4C2×#386112yes—
638C22×C4C2×#386112yes—
639C22×C4C2×#386124yes—
640C22×C4C4×#120112yes—
641C22×C4C4×#120112yes—
642C22×C4C4×#120124yes—
643C22×C4#2321112yes—
644C22×C4#232114yes—
645C22×C4#2321112yes—
646C22×C4#2321112yes—
647C22×C4#2321124yes—
648C22×C4D4×C22⋊C4112yes—
649C22×C4D4×C22⋊C414yes—
650C22×C4D4×C22⋊C4112yes—
651C22×C4D4×C22⋊C4112yes—
652C22×C4D4×C22⋊C4124yes—
653C22×C4D4×C22⋊C4112yes—
654C22×C4D4×C22⋊C4112yes—
655C22×C4D4×C22⋊C4124yes—
656C22×C4#2358112yes—
657C22×C4#235814yes—
658C22×C4#2358112yes—
659C22×C4#2358112yes—
660C22×C4#2358124yes—
661C22×C4#2358112yes—
662C22×C4#2358112yes—
663C22×C4#2358124yes—
664C22×C4#240313yes—
665C22×C4#240313yes—
666C22×C4#240316yes—
667C22×C4#240313yes—
668C22×C4#240313yes—
669C22×C4#240316yes—
670C22×C4#240316yes—
671C22×C4#240316yes—
672C22×C4#240316yes—
673C22×C4#240316yes—
674C22×C4#240414yes—
675C22×C4#2404112yes—
676C22×C4#2404112yes—
677C22×C4#2404112yes—
678C22×C4#2404124yes—
679C22×C4#2408112yes—
680C22×C4#2408112yes—
681C22×C4#2408124yes—
682C22×C4#2418112yes—
683C22×C4#241814yes—
684C22×C4#2418112yes—
685C22×C4#2418112yes—
686C22×C4#2418124yes—
687C22×C4#2418112yes—
688C22×C4#2418112yes—
689C22×C4#2418124yes—
690C22×C4#242414yes—
691C22×C4#2424112yes—
692C22×C4#2424112yes—
693C22×C4#2424112yes—
694C22×C4#2424124yes—
695C22×C4#2424112yes—
696C22×C4#2424112yes—
697C22×C4#2424124yes—
698C22×C4#2534112yes—
699C22×C4#253414yes—
700C22×C4#2534112yes—
701C22×C4#2534112yes—
702C22×C4#2534124yes—
703C22×C4C23×C22⋊C416yes—
704C22×C4C23×C22⋊C416yes—
705C22×C4C22×C4×D418yes—
706C22×C4C22×C4×D416yes—
707C22×C4C22×C4×D416yes—
708C22×C4C22×C4×D416yes—
709C22×C4C22×C4×D416yes—
710C22×C4C22×C4×D416yes—
711C22×C4C22×C4×D416yes—
712C22×C4C22×C4×D416yes—
713C22×C4C2×#51816yes—
714C22×C4C2×#51816yes—
715C22×C4C2×#51816yes—
716C22×C4C2×#51816yes—
717C22×C4C22×#120116yes—
718C22×C4C22×#12013yes—
719C22×C4C22×#12013yes—
720C22×C4C22×#12013yes—
721C22×C4C22×#12013yes—
722C22×C4C22×#12013yes—
723C22×C4C22×#12013yes—
724C22×C4C22×#12116yes—
725C22×C4C22×#12116yes—
726C22×C4C22×#12116yes—
727C22×C4C22×#12116yes—
728C22×C4C22×#12316yes—
729C22×C4C22×#12316yes—
730C22×C4C2×#52516yes—
731C22×C4C2×#52516yes—
732C22×C4C2×#52516yes—
733C22×C4C2×#52516yes—
734C22×C4C2×#52516yes—
735C22×C4C2×#53413yes—
736C22×C4C2×#53413yes—
737C22×C4C2×#53413yes—
738C22×C4C2×#53413yes—
739C22×C4C2×#53516yes—
740C22×C4C2×#53516yes—
741C22×C4C2×#53816yes—
742C22×C4C2×#53816yes—
743C22×C4C2×#53816yes—
744C22×C4C2×#53816yes—
745C22×C4C2×D4213yes—
746C22×C4C2×D4213yes—
747C22×C4C2×D4213yes—
748C22×C4C2×D4213yes—
749C22×C4C2×D4213yes—
750C22×C4C2×D4213yes—
751C22×C4C2×D4216yes—
752C22×C4C2×D4216yes—
753C22×C4C2×D4216yes—
754C22×C4C2×D4213yes—
755C22×C4C2×D4213yes—
756C22×C4C2×D4213yes—
757C22×C4C2×D4213yes—
758C22×C4C2×D4213yes—
759C22×C4C2×D4213yes—
760C22×C4C2×#54616yes—
761C22×C4C2×#54616yes—
762C22×C4C2×#54616yes—
763C22×C4C2×#54616yes—
764C22×C4C2×#54616yes—
765C22×C4C2×#54616yes—
766C22×C4C2×#54616yes—
767C22×C4C2×#54616yes—
768C22×C4C2×#54616yes—
769C22×C4C2×#54616yes—
770C22×C4C2×#54616yes—
771C22×C4C2×#54616yes—
772C22×C4C2×#54616yes—
773C22×C4C2×#54616yes—
774C22×C4C2×#54616yes—
775C22×C4C2×#55116yes—
776C22×C4C2×#55116yes—
777C22×C4C2×#55116yes—
778C22×C4C2×#55116yes—
779C22×C4C25×C411yescharacteristic
780C22×C4C24×D411yescharacteristic
781C22×C4C24×D411yescharacteristic
782C22×C4C24×D411yescharacteristic
783C22×C4C24×D411yescharacteristic
784C22×C4C24×D411yescharacteristic
785C22×C4C23×#4111yescharacteristic
786C22×C4C23×#4111yescharacteristic
787C22×C4C23×#4111yescharacteristic
788C22×C4C23×#4111yescharacteristic
789C22×C4C22×H(5,𝔽2)11yescharacteristic
790C22×C4C22×H(5,𝔽2)11yescharacteristic
791C22×C4C22×H(5,𝔽2)11yescharacteristic
792C22×C4C22×H(5,𝔽2)11yescharacteristic
793C2×C8C23×C22⋊C4116yescomplemented
794C23#13967112yes—
795C23#13967112yes—
796C23#13967112yes—
797C23#13967124yes—
798C23#1396714yes—
799C23#2388218yes—
800C23C2×C4×#12016yes—
801C23C2×C4×#12016yes—
802C23C2×D4×C22⋊C416yes—
803C23C2×D4×C22⋊C416yes—
804C23C2×#235816yes—
805C23C2×#235816yes—
806C23C2×#240313yes—
807C23C2×#240313yes—
808C23C2×#240313yes—
809C23C2×#240313yes—
810C23C2×#241816yes—
811C23C2×#241816yes—
812C23C2×#242416yes—
813C23C2×#242416yes—
814C23C2×#240816yes—
815C23C2×#240816yes—
816C23C23×C4×D411yescharacteristic
817C23C23×#12011yescharacteristic
818C23C22×#52511yescharacteristic
819C23C22×D4211yescharacteristic
820C23C22×D4211yescharacteristic
821C23C22×D4211yescharacteristic
822C23C22×#54611yescharacteristic
823D4C22×#386132yes—
824C2×C4#13967124yes—
825C2×C4#13967112yes—
826C2×C4#13967112yes—
827C2×C4#13967124yes—
828C2×C4#13967112yes—
829C2×C4#13967112yes—
830C2×C4#13967124yes—
831C2×C4#13967124yes—
832C2×C4#13967124yes—
833C2×C4#13967124yes—
834C2×C4C22×#38616yes—
835C2×C4C22×#38616yes—
836C2×C4C22×#38616yes—
837C2×C4C22×#38616yes—
838C2×C4C2×C4×#12016yes—
839C2×C4C2×C4×#12016yes—
840C2×C4C2×#232116yes—
841C2×C4C2×#232116yes—
842C2×C4C2×#232116yes—
843C2×C4C2×#232116yes—
844C2×C4C2×D4×C22⋊C416yes—
845C2×C4C2×D4×C22⋊C416yes—
846C2×C4C2×D4×C22⋊C416yes—
847C2×C4C2×D4×C22⋊C416yes—
848C2×C4C2×D4×C22⋊C416yes—
849C2×C4C2×D4×C22⋊C416yes—
850C2×C4C2×#235816yes—
851C2×C4C2×#235816yes—
852C2×C4C2×#235816yes—
853C2×C4C2×#235816yes—
854C2×C4C2×#235816yes—
855C2×C4C2×#235816yes—
856C2×C4C2×#240313yes—
857C2×C4C2×#240313yes—
858C2×C4C2×#240313yes—
859C2×C4C2×#240313yes—
860C2×C4C2×#241816yes—
861C2×C4C2×#241816yes—
862C2×C4C2×#241816yes—
863C2×C4C2×#241816yes—
864C2×C4C2×#241816yes—
865C2×C4C2×#241816yes—
866C2×C4C2×#242416yes—
867C2×C4C2×#242416yes—
868C2×C4C2×#242416yes—
869C2×C4C2×#242416yes—
870C2×C4C2×#242416yes—
871C2×C4C2×#242416yes—
872C2×C4C2×#240816yes—
873C2×C4C2×#240816yes—
874C2×C4C2×#240416yes—
875C2×C4C2×#240416yes—
876C2×C4C2×#240416yes—
877C2×C4C2×#240416yes—
878C2×C4C2×#253416yes—
879C2×C4C2×#253416yes—
880C2×C4C2×#253416yes—
881C2×C4C2×#253416yes—
882C2×C4C24×C22⋊C411yescharacteristic
883C2×C4C23×C4×D411yescharacteristic
884C2×C4C23×C4×D411yescharacteristic
885C2×C4C23×C4×D411yescharacteristic
886C2×C4C22×#51811yescharacteristic
887C2×C4C22×#51811yescharacteristic
888C2×C4C23×#12011yescharacteristic
889C2×C4C23×#12111yescharacteristic
890C2×C4C23×#12111yescharacteristic
891C2×C4C23×#12311yescharacteristic
892C2×C4C22×#52511yescharacteristic
893C2×C4C22×#52511yescharacteristic
894C2×C4C22×#53411yescharacteristic
895C2×C4C22×#53811yescharacteristic
896C2×C4C22×#53811yescharacteristic
897C2×C4C22×#53511yescharacteristic
898C2×C4C22×D4211yescharacteristic
899C2×C4C22×D4211yescharacteristic
900C2×C4C22×D4211yescharacteristic
901C2×C4C22×#54611yescharacteristic
902C2×C4C22×#54611yescharacteristic
903C2×C4C22×#54611yescharacteristic
904C2×C4C22×#54611yescharacteristic
905C2×C4C22×#54611yescharacteristic
906C2×C4C22×#54611yescharacteristic
907C2×C4C22×#54611yescharacteristic
908C2×C4C22×#55111yescharacteristic
909C2×C4C22×#55111yescharacteristic
910C22#364592116yesdirect product factor
911C22C2×#1396716yes—
912C22C2×#1396716yes—
913C22C2×#1396716yes—
914C22C2×#1396716yes—
915C22C2×#23882112yes—
916C22C22×C4×#12011yescharacteristic
917C22C22×D4×C22⋊C411yescharacteristic
918C22C22×#235811yescharacteristic
919C22C22×#240311yescharacteristic
920C22C22×#241811yescharacteristic
921C22C22×#242411yescharacteristic
922C22C22×#240811yescharacteristic
923C4C2×#1396716yes—
924C4C2×#1396716yes—
925C4C2×#1396716yes—
926C4C2×#1396716yes—
927C4C23×#38611yescharacteristic
928C4C22×#232111yescharacteristic
929C4C22×D4×C22⋊C411yescharacteristic
930C4C22×#235811yescharacteristic
931C4C22×#241811yescharacteristic
932C4C22×#242411yescharacteristic
933C4C22×#240411yescharacteristic
934C4C22×#253411yescharacteristic
935C2C22×#2388212yes—
936C2C2×#364592112yesdirect product factor
937C2C22×#1396711yescharacteristic
subgroupG/H
center, socleC24#2403
commutatorC22×C4C25×C4
Frattini, cosocleC23×C4C26
prime radicalC23×#3003C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#11100C2semidirect
2. C22×#10937C2semidirect
3. C22×#10948C2semidirect
4. C22×#11129C2semidirect
5. C22×#10776C2semidirect
6. C22×#10785C2semidirect
7. C22×#11030C2semidirect
8. C22×#20959C2semidirect
9. C22×#20945C2semidirect
10. C22×#60168C2semidirect
11. C22×#10994C2semidirect
12. C22×#20598C2semidirect
13. C22×#34171C2semidirect
14. C23×#1904C2semidirect
15. C2×#364592C2direct (N × H)
21. C22×#3428C22semidirect
24. C22×#3003C4semidirect
26. C2×#60168C22semidirect
27. C22×#2911C22semidirect
30. C23×#410C22semidirect
31. C22×#2896C22semidirect
32. C23×#421C22semidirect
39. C22×#2873C22semidirect
40. C2×#34171C22semidirect
46. C22×#1904C22semidirect
47. C2×#20959C22semidirect
48. C2×#20945C22semidirect
49. C2×#20598C22semidirect
50. C23×#344C22semidirect
51. C23×#344C22semidirect
52. C22×#1742C22semidirect
53. C22×#1740C22semidirect
54. C22×#1740C22semidirect
55. C22×#1733C22semidirect
56. C22×#1733C22semidirect
57. C22×#1733C22semidirect
58. C23×H(3,ℤ/4)C22semidirect
59. C23×H(3,ℤ/4)C22semidirect
60. #364592C22direct (N × H)
61. C2×#11129C22semidirect
62. C2×#11100C22semidirect
63. C2×#11030C22semidirect
64. C2×#10994C22semidirect
65. C2×#10948C22semidirect
66. C2×#10937C22semidirect
67. C2×#10785C22semidirect
68. C2×#10776C22semidirect
70. C25×D4C2×C4semidirect
76. C23×AGL(1,ℤ/8)C2×C4semidirect
87. C22×#525C2×C4semidirect
89. C2×#3428C23semidirect
90. C22×#518D4semidirect
93. C23×C4×D4D4semidirect
101. C2×#3003C2×C4semidirect
103. #60168C23semidirect
104. C2×#2911C23semidirect
105. C22×#421C23semidirect
106. C2×#2896C23semidirect
107. C22×#418C2×C4semidirect
108. C22×#418C2×C4semidirect
109. C22×#418D4semidirect
116. C23×#102D4semidirect
117. C22×#410C23semidirect
118. C22×#407C2×C4semidirect
121. C2×#2873C23semidirect
122. #34171C23semidirect
123. C2×#2309D4semidirect
126. C22×#390D4semidirect
133. C2×#1904C23semidirect
134. #20959C23semidirect
135. #20945C23semidirect
136. #20598C23semidirect
137. C22×#344C23semidirect
138. C22×#344C23semidirect
139. C2×#1742C23semidirect
140. C2×#1740C23semidirect
141. C2×#1740C23semidirect
142. C2×#1733C23semidirect
143. C2×#1733C23semidirect
144. C2×#1733C23semidirect
145. C22×H(3,ℤ/4)C23semidirect
146. C22×H(3,ℤ/4)C23semidirect
147. #11129C23semidirect
148. #11100C23semidirect
149. #11030C23semidirect
150. #10994C23semidirect
151. #10948C23semidirect
152. #10937C23semidirect
153. #10785C23semidirect
154. #10776C23semidirect
163. C24×D4C22×C4semidirect
186. C22×AGL(1,ℤ/8)C22⋊C4semidirect
188. C22×AGL(1,ℤ/8)C22×C4semidirect
193. C23×SD16C22⋊C4semidirect
195. C23×D8C22⋊C4semidirect
208. C2×#525C22×C4semidirect
210. #3428C24semidirect
211. C2×#518C2×D4semidirect
214. C22×C4×D4C2×D4semidirect
237. #3003C22×C4semidirect
238. #2911C24semidirect
239. C2×#421C24semidirect
240. #2896C24semidirect
241. C2×#418C22×C4semidirect
242. C2×#418C22×C4semidirect
243. C2×#418C2×D4semidirect
250. C22×#102C2×D4semidirect
251. C2×#410C24semidirect
252. C2×#407C22×C4semidirect
255. #2873C24semidirect
256. #2309C2×D4semidirect
259. C2×#390C2×D4semidirect
266. C2×#344C24semidirect
267. C2×#344C24semidirect
268. #1742C24semidirect
269. #1740C24semidirect
270. #1740C24semidirect
271. #1733C24semidirect
272. #1733C24semidirect
273. #1733C24semidirect
274. C2×H(3,ℤ/4)C24semidirect
275. C2×H(3,ℤ/4)C24semidirect
279. C22×#41C2×C22⋊C4semidirect
284. C23×Q8C2×C22⋊C4semidirect
288. C23×D4C2×C22⋊C4semidirect
308. C23×D4C23×C4semidirect
354. C2×AGL(1,ℤ/8)C2×C22⋊C4semidirect
356. C2×AGL(1,ℤ/8)C23×C4semidirect
358. C22×SD16C2×C22⋊C4semidirect
360. C22×D8C2×C22⋊C4semidirect
362. C22×M16C2×C22⋊C4semidirect
372. C23×C8C2×C22⋊C4semidirect
375. #525C23×C4semidirect
376. C2×C4×D4C22×D4semidirect
403. #418C23×C4semidirect
404. #418C23×C4semidirect
405. C2×#102C22×D4semidirect
406. #407C23×C4semidirect
407. #390C22×D4semidirect
423. C2×#41C22×C22⋊C4semidirect
426. C22×Q8C22×C22⋊C4semidirect
435. C22×D4C22×C22⋊C4semidirect
572. C2×SD16C22×C22⋊C4semidirect
573. C2×D8C22×C22⋊C4semidirect
574. C2×M16C22×C22⋊C4semidirect
578. C22×C8C22×C22⋊C4semidirect
621. C2×Q8C23×C22⋊C4semidirect
627. C2×D4C23×C22⋊C4semidirect
793. C2×C8C23×C22⋊C4semidirect
910. C22#364592direct (N × H)
936. C2C2×#364592direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#111002
C22×#109372
C22×#109482
C22×#111292
C22×#107762
C22×#107852
C22×#110302
C22×#209592
C22×#209452
C22×#601682
C22×#109942
C22×#205982
C22×#341712
C23×#19042
C2×#3645922
C23×#30032