Finite Group Databasebeta

← #72337492

Subgroups — #72337492

Order 2048.

At least 9938 conjugacy classes of subgroups; only the 2584 normal subgroups are shown.

The subgroup lattice has 677 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72337490C212yesmaximal, complemented
2#72337486C211yesmaximal, characteristic, complemented
3C22×#12718C211yesmaximal, characteristic, complemented
4#72337452C218yesmaximal, complemented
5#72315283C211yesmaximal, characteristic, complemented
6C2×#494609C211yesmaximal, characteristic, complemented
7C2×#494605C211yesmaximal, characteristic, complemented
8#72312697C212yesmaximal, complemented
9#72312474C211yesmaximal, characteristic, complemented
10#72312254C212yesmaximal, complemented
11#72312095C218yesmaximal, complemented
12C22×#60388C211yesmaximal, characteristic
13#72249722C212yesmaximal, complemented
14C22×H(7,𝔽2)C2211yescharacteristic
15C22×#3498C2211yescharacteristic
16C2×#60388C4116yescomplemented
17C2×#60388C2214yes—
18C2×#60388C2214yes—
19C22×#3018C2211yescharacteristic
20C22×#3018C2211yescharacteristic
21C22×#3021C2211yescharacteristic
22C22×#3021C2211yescharacteristic
23C2×#60232C2211yescharacteristic, complemented
24C22×#2888C2211yescharacteristic
25#7625999C2211yescharacteristic, complemented
26C22×#2132C2211yescharacteristic, complemented
27C22×#2126C2211yescharacteristic, complemented
28C22×#2122C2212yescomplemented
29#6386061C2214yescomplemented
30#6386055C2214yescomplemented
31#6374164C2212yescomplemented
32C22×#1795C2212yes—
33C2×#20620C2212yescomplemented
34#6370746C2212yescomplemented
35C2×#20612C2212yescomplemented
36#6370734C2212yescomplemented
37#6370719C2212yes—
38#494620C2214yescomplemented
39#494619C2214yescomplemented
40C2×#13054C2214yescomplemented
41C2×#13053C2214yescomplemented
42C2×#13052C2214yescomplemented
43C2×#13051C2214yescomplemented
44#494599C2214yescomplemented
45#494598C2214yescomplemented
46C2×#12718C2214yescomplemented
47C2×#12718C2214yescomplemented
48C2×#12589C2212yescomplemented
49#492906C2212yescomplemented
50C2×#12579C2212yescomplemented
51#492886C2212yescomplemented
52#392141C22116yescomplemented
53#147759C22116yescomplemented
54#147755C22116yescomplemented
55#146591C22116yescomplemented
56C2×H(7,𝔽2)C2×C418yescomplemented
57C2×H(7,𝔽2)C2314yes—
58C22×#585C2311yescharacteristic
59C22×#585C2311yescharacteristic
60C23×H(5,𝔽2)D411yescharacteristic
61C23×H(5,𝔽2)C2311yescharacteristic
62C2×#3498C2×C418yes—
63C2×#3498D418yes—
64C2×#3498D412yes—
65C2×#3498D412yes—
66C2×#3498C2312yes—
67C2×#3498C2312yes—
68C22×#535D411yescharacteristic
69C22×#535C2311yescharacteristic
70C22×#532C2311yescharacteristic
71C23×#127D411yescharacteristic
72C22×C4×#41D411yescharacteristic
73#60388C2×C4132yescomplemented
74#60388C2×C4132yescomplemented
75C2×#3021C2×C418yescomplemented
76C2×#3021C2×C418yescomplemented
77C2×#3021C2314yes—
78C2×#3021C2314yes—
79C2×#3018C2×C418yes—
80C2×#3018C2×C418yes—
81C2×#3018D418yes—
82C2×#3018D412yes—
83C2×#3018D412yes—
84C2×#3018D418yes—
85C2×#3018D412yes—
86C2×#3018D412yes—
87C2×#3018C2312yes—
88C2×#3018C2312yes—
89C2×#3018C2312yes—
90C2×#3018C2312yes—
91C22×#456D412yes—
92C22×#454D412yes—
93C22×#455D412yes—
94C22×#453D412yes—
95C2×#2980C2312yescomplemented
96C2×#2979C2312yescomplemented
97C2×#2896D412yes—
98C2×#2896D412yes—
99C22×#418D412yes—
100C22×#418D412yes—
101C2×#2888C2×C418yescomplemented
102C2×#2888C2314yes—
103C22×#413C2312yes—
104C22×#413C2311yescharacteristic
105C22×#413C2311yescharacteristic
106C22×#410C2312yes—
107C2×#2879C2312yes—
108#34369C2312yescomplemented
109#34368C2312yescomplemented
110#34044C2312yes—
111C2×#2132C2312yescomplemented
112C2×#2132C2312yescomplemented
113C2×#2126C2312yescomplemented
114C2×#2126C2312yescomplemented
115C2×#2122C2318yescomplemented
116#21770C2318yescomplemented
117C2×#1795C2318yes—
118C2×#1794C2318yescomplemented
119#20618C2318yescomplemented
120C2×#1791C2318yescomplemented
121#20610C2318yescomplemented
122#20602D418yes—
123#20602C2318yes—
124C2×#1395C2318yescomplemented
125#12587C2318yescomplemented
126C2×#1392C2318yescomplemented
127#12575C2318yescomplemented
128H(7,𝔽2)C22×C4116yes—
129C2×#585C22×C414yes—
130C2×#585C22×C414yes—
131C2×#585C2×D414yes—
132C2×#585C2×D412yes—
133C2×#585C2×D414yes—
134C2×#585C2×D412yes—
135C2×#585C2412yes—
136C2×#585C2412yes—
137C22×2−1+4C2×D412yes—
138C22×H(5,𝔽2)C22⋊C418yescomplemented
139C22×H(5,𝔽2)C22×C414yes—
140C22×H(5,𝔽2)C2×D414yes—
141C22×H(5,𝔽2)C2×D412yes—
142C22×H(5,𝔽2)C2×D414yes—
143C22×H(5,𝔽2)C2×D412yes—
144C22×H(5,𝔽2)C2×D412yes—
145C22×H(5,𝔽2)C2×D412yes—
146C22×H(5,𝔽2)#4118yes—
147C22×H(5,𝔽2)C2412yes—
148C23×#41C2×D411yescharacteristic
149C23×#41C2×D412yes—
150C23×#41C2×D411yescharacteristic
151C23×#41C2411yescharacteristic
152C24×D4C2×D412yes—
153C24×D4C2×D411yescharacteristic
154C24×D4C2×D411yescharacteristic
155C23×M16C2×D412yes—
156C23×M16C2×D412yes—
157#3498C22⋊C4116yescomplemented
158#3498C22⋊C4116yescomplemented
159#3498C22×C418yes—
160#3498C22×C418yes—
161#3498C2×D418yes—
162#3498C2×D418yes—
163C2×#535C22⋊C418yescomplemented
164C2×#535C22×C414yes—
165C2×#535C2×D414yes—
166C2×#535C2×D412yes—
167C2×#535C2×D412yes—
168C2×#535C2×D412yes—
169C2×#535C2412yes—
170C2×#532C22×C414yes—
171C2×#532C2×D414yes—
172C2×#532C2×D414yes—
173C2×#532C2×D411yescharacteristic
174C2×#532C2×D411yescharacteristic
175C2×#532C2×D414yes—
176C2×#532C2×D411yescharacteristic
177C2×#532C2×D411yescharacteristic
178C2×#532C2×D411yescharacteristic
179C2×#532C2×D411yescharacteristic
180C2×#532C2411yescharacteristic
181C2×#532C2411yescharacteristic
182C22×C4⋊Q8C2×D411yescharacteristic
183C22×#127C22⋊C418yescomplemented
184C22×#127C2×D412yes—
185C22×#127C2×D412yes—
186C22×#127C2×D411yescharacteristic
187C22×#124C2×D411yescharacteristic
188C22×#124C2×D411yescharacteristic
189C2×C4×#41C22⋊C418yescomplemented
190C2×C4×#41C2×D412yes—
191C2×C4×#41C2×D412yes—
192C22×#117C2×D411yescharacteristic
193C22×#117C2×D412yes—
194C22×#117C2×D412yes—
195C23×C42C2×D411yescharacteristic
196#3021C22×C4116yes—
197#3021C22×C4116yes—
198#3018C22⋊C4116yes—
199#3018C22⋊C4116yes—
200#3018C22⋊C4116yescomplemented
201#3018C22⋊C4116yescomplemented
202#3018C22×C418yes—
203#3018C22×C418yes—
204#3018C22×C418yes—
205#3018C22×C418yes—
206#3018C2×D418yes—
207#3018C2×D418yes—
208#3018C2×D418yes—
209#3018C2×D418yes—
210C2×#456C22⋊C4116yescomplemented
211C2×#456C2×D414yes—
212C2×#456C2×D414yes—
213C2×#454C22⋊C4116yescomplemented
214C2×#454C2×D414yes—
215C2×#454C2×D414yes—
216C2×#455C22⋊C4116yes—
217C2×#455C2×D414yes—
218C2×#455C2×D414yes—
219C2×#453C22⋊C4116yes—
220C2×#453C2×D414yes—
221C2×#453C2×D414yes—
222C2×#417C2×D418yes—
223C2×#418C2×D418yes—
224C2×#416C2×D418yes—
225C22×#102C2×D418yes—
226#2888C22×C4116yes—
227C2×#413C22×C414yes—
228C2×#413C22×C414yes—
229C2×#413C2×D414yes—
230C2×#413C2×D412yes—
231C2×#413C2×D414yes—
232C2×#413C2×D412yes—
233C2×#413C2414yes—
234C2×#413C2412yes—
235C2×#413C2412yes—
236C22×#101C2×D412yes—
237C22×#100C2×D412yes—
238C2×#410C2414yes—
239C2×#408C2×D414yes—
240C2×#408C2414yes—
241#2311C2×D414yes—
242#2311C2414yes—
243#585C2×C22⋊C418yes—
244#585C2×C22⋊C418yes—
245#585C23×C414yes—
246#585C23×C414yes—
247#585C22×D414yes—
248#585C22×D414yes—
249C2×2−1+4C2×C22⋊C418yes—
250C2×2−1+4C22×D414yes—
251C2×H(5,𝔽2)C2×C22⋊C418yes—
252C2×H(5,𝔽2)C2×C22⋊C418yes—
253C2×H(5,𝔽2)C2×C22⋊C418yes—
254C2×H(5,𝔽2)C2×C22⋊C418yes—
255C2×H(5,𝔽2)C4×D4116yes—
256C2×H(5,𝔽2)#121116yes—
257C2×H(5,𝔽2)#12318yes—
258C2×H(5,𝔽2)C23×C414yes—
259C2×H(5,𝔽2)C22×D414yes—
260C2×H(5,𝔽2)C22×D414yes—
261C2×H(5,𝔽2)C2×#4118yes—
262C22×#41C2×C22⋊C414yes—
263C22×#41C2×C22⋊C414yes—
264C22×#41C4×D418yes—
265C22×#41#12012yes—
266C22×#41#12014yes—
267C22×#41#12011yescharacteristic
268C22×#41#12011yescharacteristic
269C22×#41#12014yes—
270C22×#41#12118yes—
271C22×#41#12314yes—
272C22×#41C23×C412yes—
273C22×#41C22×D412yes—
274C22×#41C22×D414yes—
275C22×#41C22×D411yescharacteristic
276C22×#41C22×D411yescharacteristic
277C22×#41C22×D412yes—
278C22×#41C22×D411yescharacteristic
279C22×#41C22×D412yes—
280C22×#41C22×D412yes—
281C22×#41C22×D411yescharacteristic
282C22×#41C22×D412yes—
283C22×#41C22×D411yescharacteristic
284C22×#41C2×#4114yes—
285C22×#41H(5,𝔽2)14yes—
286C22×#41H(5,𝔽2)12yes—
287C22×#41C2511yescharacteristic
288C23×Q8#12011yescharacteristic
289C23×Q8#12011yescharacteristic
290C23×Q8C22×D411yescharacteristic
291C23×D4C2×C22⋊C414yes—
292C23×D4C2×C22⋊C414yes—
293C23×D4C4×D418yes—
294C23×D4#12014yes—
295C23×D4#12011yescharacteristic
296C23×D4#12012yes—
297C23×D4#12012yes—
298C23×D4#12011yescharacteristic
299C23×D4#12118yes—
300C23×D4#12314yes—
301C23×D4C22×D411yescharacteristic
302C23×D4C22×D414yes—
303C23×D4C22×D412yes—
304C23×D4C22×D412yes—
305C23×D4H(5,𝔽2)12yes—
306C24×C4C22×D411yescharacteristic
307C24×C4C22×D412yes—
308C22×M16C22×D414yes—
309C23×C8C22×D414yes—
310#535C2×C22⋊C418yes—
311#535C2×C22⋊C418yes—
312#535C2×C22⋊C418yes—
313#535C23×C414yes—
314#535C22×D414yes—
315#532C2×C22⋊C414yes—
316#532C2×C22⋊C414yes—
317#532C2×C22⋊C414yes—
318#532C2×C22⋊C414yes—
319#532C2×C22⋊C414yes—
320#532C2×C22⋊C414yes—
321#532#12014yes—
322#532#12014yes—
323#532#12014yes—
324#532#12014yes—
325#532#12014yes—
326#532#12014yes—
327#532C23×C412yes—
328#532C23×C412yes—
329#532C22×D412yes—
330#532C22×D412yes—
331#532C22×D412yes—
332#532C22×D412yes—
333#532C22×D412yes—
334#532C22×D412yes—
335C2×C4⋊Q8C2×C22⋊C414yes—
336C2×C4⋊Q8#12011yescharacteristic
337C2×C4⋊Q8#12011yescharacteristic
338C2×C4⋊Q8#12014yes—
339C2×C4⋊Q8C22×D411yescharacteristic
340C2×C4⋊Q8C22×D411yescharacteristic
341C2×#127C2×C22⋊C418yes—
342C2×#127C2×C22⋊C418yes—
343C2×#127C2×C22⋊C414yes—
344C2×#127#12011yescharacteristic
345C2×#127#12011yescharacteristic
346C2×#127#12014yes—
347C2×#127C22×D411yescharacteristic
348C2×#127C22×D411yescharacteristic
349C2×#124C2×C22⋊C414yes—
350C2×#124C2×C22⋊C414yes—
351C2×#124#12011yescharacteristic
352C2×#124#12011yescharacteristic
353C2×#124#12011yescharacteristic
354C2×#124#12011yescharacteristic
355C2×#124#12014yes—
356C2×#124#12014yes—
357C2×#124C22×D411yescharacteristic
358C2×#124C22×D411yescharacteristic
359C2×#124C22×D411yescharacteristic
360C2×#124C22×D411yescharacteristic
361C4×#41C2×C22⋊C418yes—
362C4×#41C2×C22⋊C418yes—
363C2×#117C2×C22⋊C414yes—
364C2×#117C22×D412yes—
365C2×#117C22×D414yes—
366C22×C4⋊C4C22×D414yes—
367C22×C42C2×C22⋊C414yes—
368C22×C42#12011yescharacteristic
369C22×C42#12011yescharacteristic
370C22×C42#12014yes—
371C22×C42#12011yescharacteristic
372C22×C42#12011yescharacteristic
373C22×C42C22×D411yescharacteristic
374C22×C42C22×D411yescharacteristic
375#456C2×C22⋊C4116yes—
376#456C2×C22⋊C4116yes—
377#455C2×C22⋊C4116yes—
378#455C2×C22⋊C4116yes—
379#454C2×C22⋊C4116yes—
380#454C2×C22⋊C4116yes—
381#453C2×C22⋊C4116yes—
382#453C2×C22⋊C4116yes—
383#413C2×C22⋊C418yes—
384#413C2×C22⋊C418yes—
385#413C23×C414yes—
386#413C23×C414yes—
387#413C22×D414yes—
388#413C22×D414yes—
389C2×#101C2×C22⋊C418yes—
390C2×#101C22×D414yes—
391C2×#100C2×C22⋊C418yes—
392C2×#100C22×D414yes—
393C25#53411yescharacteristic
394C25D4212yes—
3952−1+4C22×C22⋊C418yes—
396H(5,𝔽2)C22×C22⋊C418yes—
397C2×#41#37914yes—
398C2×#41#37914yes—
399C2×#41#38618yes—
400C2×#41#386116yes—
401C2×#41C22×C22⋊C412yes—
402C2×#41C22×C22⋊C412yes—
403C2×#41C22×C22⋊C414yes—
404C2×#41C22×C22⋊C412yes—
405C2×#41C22×C22⋊C412yes—
406C2×#41C22×C22⋊C412yes—
407C2×#41C2×C4×D418yes—
408C2×#41C2×C4×D414yes—
409C2×#41#51814yes—
410C2×#41C2×#12012yes—
411C2×#41C2×#12012yes—
412C2×#41C2×#12012yes—
413C2×#41C2×#12012yes—
414C2×#41C2×#12012yes—
415C2×#41C2×#12118yes—
416C2×#41C2×#12114yes—
417C2×#41C2×#12314yes—
418C2×#41C2×#12312yes—
419C2×#41#53414yes—
420C2×#41#53412yes—
421C2×#41D4214yes—
422C2×#41D4214yes—
423C2×#41#54614yes—
424C2×#41#54614yes—
425C2×#41#54614yes—
426C2×#41#54614yes—
427C2×#41C24×C411yescharacteristic
428C2×#41C23×D411yescharacteristic
429C2×#41C23×D411yescharacteristic
430C2×#41C23×D411yescharacteristic
431C2×#41C22×#4112yes—
432C2×#41C2×H(5,𝔽2)12yes—
433C22×Q8#37914yes—
434C22×Q8#38614yes—
435C22×Q8B(4,𝔽2)12yes—
436C22×Q8B(4,𝔽2)14yes—
437C22×Q8B(4,𝔽2)12yes—
438C22×Q8C22×C22⋊C412yes—
439C22×Q8C2×#12012yes—
440C22×Q8C2×#12011yescharacteristic
441C22×Q8C2×#12011yescharacteristic
442C22×Q8C2×#12011yescharacteristic
443C22×Q8C2×#12012yes—
444C22×Q8D4212yes—
445C22×Q8#54614yes—
446C22×Q8C23×D411yescharacteristic
447C22×D4#37914yes—
448C22×D4#38618yes—
449C22×D4#386116yes—
450C22×D4#38614yes—
451C22×D4#38618yes—
452C22×D4B(4,𝔽2)12yes—
453C22×D4B(4,𝔽2)14yes—
454C22×D4B(4,𝔽2)12yes—
455C22×D4C22×C22⋊C414yes—
456C22×D4C22×C22⋊C414yes—
457C22×D4C22×C22⋊C412yes—
458C22×D4C2×C4×D418yes—
459C22×D4#51814yes—
460C22×D4C2×#12014yes—
461C22×D4C2×#12012yes—
462C22×D4C2×#12011yescharacteristic
463C22×D4C2×#12011yescharacteristic
464C22×D4C2×#12011yescharacteristic
465C22×D4C2×#12012yes—
466C22×D4C2×#12118yes—
467C22×D4C2×#12314yes—
468C22×D4#53412yes—
469C22×D4#53414yes—
470C22×D4D4212yes—
471C22×D4D4212yes—
472C22×D4D4212yes—
473C22×D4#54614yes—
474C22×D4#54614yes—
475C22×D4#54614yes—
476C22×D4C23×D411yescharacteristic
477C22×D4C2×H(5,𝔽2)12yes—
478C23×C4C22×C22⋊C412yes—
479C23×C4C2×C4×D414yes—
480C23×C4C2×#12012yes—
481C23×C4C2×#12011yescharacteristic
482C23×C4C2×#12012yes—
483C23×C4C2×#12011yescharacteristic
484C23×C4C2×#12011yescharacteristic
485C23×C4C2×#12011yescharacteristic
486C23×C4C2×#12114yes—
487C23×C4C2×#12312yes—
488C23×C4#53411yescharacteristic
489C23×C4#53412yes—
490C23×C4D4212yes—
491C23×C4D4214yes—
492C23×C4D4212yes—
493C23×C4D4212yes—
494C23×C4D4214yes—
495C23×C4C23×D411yescharacteristic
496C23×C4C23×D412yes—
497C4⋊Q8#37914yes—
498C4⋊Q8#37914yes—
499C4⋊Q8C22×C22⋊C412yes—
500C4⋊Q8C22×C22⋊C412yes—
501C4⋊Q8C2×#12012yes—
502C4⋊Q8C2×#12012yes—
503#127#37914yes—
504#127#37914yes—
505#127C22×C22⋊C412yes—
506#127C22×C22⋊C412yes—
507#127C2×#12012yes—
508#127C2×#12012yes—
509#124#37914yes—
510#124#37914yes—
511#124#37914yes—
512#124#37914yes—
513#124C22×C22⋊C412yes—
514#124C22×C22⋊C412yes—
515#124C22×C22⋊C412yes—
516#124C22×C22⋊C412yes—
517#124C2×#12012yes—
518#124C2×#12012yes—
519#124C2×#12012yes—
520#124C2×#12012yes—
521#117C22×C22⋊C414yes—
522C2×C42#37914yes—
523C2×C42#37914yes—
524C2×C42#37914yes—
525C2×C42#37914yes—
526C2×C42C22×C22⋊C412yes—
527C2×C42C22×C22⋊C412yes—
528C2×C42C2×#12011yescharacteristic
529C2×C42C2×#12011yescharacteristic
530C2×C42C2×#12012yes—
531C2×C42C2×#12012yes—
532C2×C42C2×#12011yescharacteristic
533C2×C42C2×#12011yescharacteristic
534#101C22×C22⋊C418yes—
535#100C22×C22⋊C418yes—
536C24#230812yes—
537C24D4×C22⋊C414yes—
538C24#240312yes—
539C24#240311yescharacteristic
540C24#240311yescharacteristic
541C24#240512yes—
542C24#241014yes—
543C24C2×#53411yescharacteristic
544C24C2×D4212yes—
545C2×Q8#188918yes—
546C2×Q8#188918yes—
547C2×Q8C2×#37912yes—
548C2×Q8C2×#37912yes—
549C2×Q8C2×#37912yes—
550C2×Q8C2×#38614yes—
551C2×Q8D4×C22⋊C414yes—
552C2×Q8#240512yes—
553C2×Q8#241014yes—
554C2×Q8C2×B(4,𝔽2)14yes—
555C2×Q8C2×B(4,𝔽2)14yes—
556C2×Q8C23×C22⋊C411yescharacteristic
557C2×Q8C22×#12011yescharacteristic
558C2×Q8C2×#54612yes—
559C2×D4#188918yes—
560C2×D4#188918yes—
561C2×D4C2×#37912yes—
562C2×D4C2×#37912yes—
563C2×D4C2×#37912yes—
564C2×D4C2×#38618yes—
565C2×D4C2×#38614yes—
566C2×D4#230814yes—
567C2×D4D4×C22⋊C414yes—
568C2×D4D4×C22⋊C414yes—
569C2×D4D4×C22⋊C414yes—
570C2×D4#240514yes—
571C2×D4#240512yes—
572C2×D4#241014yes—
573C2×D4#241014yes—
574C2×D4#241014yes—
575C2×D4C2×B(4,𝔽2)14yes—
576C2×D4C2×B(4,𝔽2)14yes—
577C2×D4C23×C22⋊C411yescharacteristic
578C2×D4C2×#51812yes—
579C2×D4C22×#12011yescharacteristic
580C2×D4C2×#53412yes—
581C2×D4C2×#54612yes—
582C2×D4C2×#54612yes—
583C2×D4C2×#54612yes—
584C22×C4C2×#37912yes—
585C22×C4C2×#37912yes—
586C22×C4C2×#38612yes—
587C22×C4C2×#38614yes—
588C22×C4C2×#38612yes—
589C22×C4#230812yes—
590C22×C4D4×C22⋊C414yes—
591C22×C4D4×C22⋊C414yes—
592C22×C4D4×C22⋊C414yes—
593C22×C4#240311yescharacteristic
594C22×C4#240312yes—
595C22×C4#240312yes—
596C22×C4#240314yes—
597C22×C4#240311yescharacteristic
598C22×C4#240312yes—
599C22×C4#240512yes—
600C22×C4#240512yes—
601C22×C4#240512yes—
602C22×C4#241014yes—
603C22×C4#241014yes—
604C22×C4#241014yes—
605C22×C4C2×B(4,𝔽2)11yescharacteristic
606C22×C4C2×B(4,𝔽2)11yescharacteristic
607C22×C4C2×B(4,𝔽2)12yes—
608C22×C4C2×B(4,𝔽2)11yescharacteristic
609C22×C4C2×B(4,𝔽2)12yes—
610C22×C4C2×B(4,𝔽2)11yescharacteristic
611C22×C4C23×C22⋊C411yescharacteristic
612C22×C4C22×C4×D412yes—
613C22×C4C22×#12011yescharacteristic
614C22×C4C22×#12011yescharacteristic
615C22×C4C22×#12011yescharacteristic
616C22×C4C22×#12112yes—
617C22×C4C22×#12311yescharacteristic
618C22×C4C2×#53411yescharacteristic
619C22×C4C2×D4212yes—
620C22×C4C2×D4212yes—
621C22×C4C2×D4212yes—
622C42C2×#37912yes—
623C42C2×#37912yes—
624C42C2×#37912yes—
625C42C2×#37912yes—
626C23#1386714yes—
627C23#1386712yes—
628C23#1386712yes—
629C23#2390011yescharacteristic
630C23#2390011yescharacteristic
631C23#2390012yes—
632C23C2×#230811yescharacteristic
633C23C2×D4×C22⋊C412yes—
634C23C2×#240311yescharacteristic
635C23C2×#241012yes—
636C23C2×#240511yescharacteristic
637Q8C2×#188918yes—
638D4C2×#188918yes—
639C2×C4#1386712yes—
640C2×C4#1386714yes—
641C2×C4#1386712yes—
642C2×C4C2×#188912yes—
643C2×C4C2×#188912yes—
644C2×C4C2×#188912yes—
645C2×C4C2×#188912yes—
646C2×C4#2390012yes—
647C2×C4#2390011yescharacteristic
648C2×C4#2390011yescharacteristic
649C2×C4#2390012yes—
650C2×C4#2390012yes—
651C2×C4#2390012yes—
652C2×C4#2390012yes—
653C2×C4C22×#37911yescharacteristic
654C2×C4C22×#38611yescharacteristic
655C2×C4C2×D4×C22⋊C412yes—
656C2×C4C2×#240311yescharacteristic
657C2×C4C2×#241012yes—
658C2×C4C2×#240511yescharacteristic
659C2×C4C22×B(4,𝔽2)11yescharacteristic
660C2×C4C22×B(4,𝔽2)11yescharacteristic
661C2×C4C22×B(4,𝔽2)11yescharacteristic
662C2×C4C22×B(4,𝔽2)11yescharacteristic
663C22#35950112yes—
664C22#35950112yes—
665C22C2×#1386711yescharacteristic
666C22C2×#2390011yescharacteristic
667C22C2×#2390011yescharacteristic
668C4#35950112yes—
669C4#35950112yes—
670C4C22×#188911yescharacteristic
671C4C22×#188911yescharacteristic
672C4C2×#2390011yescharacteristic
673C4C2×#2390011yescharacteristic
674C2#7223753212yes—
675C2C2×#35950111yescharacteristic
subgroupG/H
center, socleC22C2×#23900
commutatorC2×#41C24×C4
Frattini, cosocleC22×#41C25
prime radicalC22×#60388C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×H(5,𝔽2) ◁ G
LECSG ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72337490C2semidirect
2. #72337486C2semidirect
3. C22×#12718C2semidirect
4. #72337452C2semidirect
5. #72315283C2semidirect
6. C2×#494609C2semidirect
7. C2×#494605C2semidirect
8. #72312697C2semidirect
9. #72312474C2semidirect
10. #72312254C2semidirect
11. #72312095C2semidirect
13. #72249722C2semidirect
16. C2×#60388C4semidirect
23. C2×#60232C22semidirect
25. #7625999C22semidirect
26. C22×#2132C22semidirect
27. C22×#2126C22semidirect
28. C22×#2122C22semidirect
29. #6386061C22semidirect
30. #6386055C22semidirect
31. #6374164C22semidirect
33. C2×#20620C22semidirect
34. #6370746C22semidirect
35. C2×#20612C22semidirect
36. #6370734C22semidirect
38. #494620C22semidirect
39. #494619C22semidirect
40. C2×#13054C22semidirect
41. C2×#13053C22semidirect
42. C2×#13052C22semidirect
43. C2×#13051C22semidirect
44. #494599C22semidirect
45. #494598C22semidirect
46. C2×#12718C22semidirect
47. C2×#12718C22semidirect
48. C2×#12589C22semidirect
49. #492906C22semidirect
50. C2×#12579C22semidirect
51. #492886C22semidirect
52. #392141C22semidirect
53. #147759C22semidirect
54. #147755C22semidirect
55. #146591C22semidirect
56. C2×H(7,𝔽2)C2×C4semidirect
73. #60388C2×C4semidirect
74. #60388C2×C4semidirect
75. C2×#3021C2×C4semidirect
76. C2×#3021C2×C4semidirect
95. C2×#2980C23semidirect
96. C2×#2979C23semidirect
101. C2×#2888C2×C4semidirect
108. #34369C23semidirect
109. #34368C23semidirect
111. C2×#2132C23semidirect
112. C2×#2132C23semidirect
113. C2×#2126C23semidirect
114. C2×#2126C23semidirect
115. C2×#2122C23semidirect
116. #21770C23semidirect
118. C2×#1794C23semidirect
119. #20618C23semidirect
120. C2×#1791C23semidirect
121. #20610C23semidirect
124. C2×#1395C23semidirect
125. #12587C23semidirect
126. C2×#1392C23semidirect
127. #12575C23semidirect
138. C22×H(5,𝔽2)C22⋊C4semidirect
157. #3498C22⋊C4semidirect
158. #3498C22⋊C4semidirect
163. C2×#535C22⋊C4semidirect
183. C22×#127C22⋊C4semidirect
189. C2×C4×#41C22⋊C4semidirect
200. #3018C22⋊C4semidirect
201. #3018C22⋊C4semidirect
210. C2×#456C22⋊C4semidirect
213. C2×#454C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
#723374902
#723374862
C22×#127182
#723374522
#723152832
C2×#4946092
C2×#4946052
#723126972
#723124742
#723122542
#723120952
C22×#603882
#722497222