Finite Group Databasebeta

← #10829213

Subgroups — #10829213

Order 768.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5581C211yesmaximal, characteristic
2C2×C3×C4×Q16C211yesmaximal, characteristic, complemented
3#82499C211yesmaximal, characteristic
4C2×#5022C211yesmaximal, characteristic, complemented
5#72071C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7#71627C211yesmaximal, characteristic, complemented
8#70633C211yesmaximal, characteristic, complemented
9#70632C211yesmaximal, characteristic, complemented
10#70275C211yesmaximal, characteristic, complemented
11#70274C211yesmaximal, characteristic, complemented
12#70269C211yesmaximal, characteristic, complemented
13#70268C211yesmaximal, characteristic, complemented
14#69787C211yesmaximal, characteristic
15#69778C211yesmaximal, characteristic, complemented
16#24127—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24#5581—24no—
25#5581—24no—
26C2×#894—21no—
27C2×#892C2211yescharacteristic
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#889—21no—
30C2×#876—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#872—21no—
33C2×#870C2211yescharacteristic
34C3×C4×Q16—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×C4×C8C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47#5022—24no—
48#4991—21no—
49#4987C2211yescharacteristic
50#4987C2211yescharacteristic
51#4981—21no—
52C2×#808C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4940—21no—
55#4940—21no—
56#4936C2211yescharacteristic
57C2×C4⋊(C3⋊C8)C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#552—31no—
65C2×#479—31no—
66C2×C4×Q16D311yescharacteristic, complemented
67#2536—31no—
68#2036—31no—
69#2035—31no—
70#2001—31no—
71#2001—31no—
72#1991—31no—
73#1954—31no—
74#1873—31no—
75#1872—31no—
76#1854—31no—
77#1852—31no—
78#1805—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×D12D411yescharacteristic
82C22×C4×D3—21no—
83C22×C4×D3C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—22no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4×Q8—22no—
91C3×C4×Q8—22no—
92C3×C4×Q8—22no—
93C3×C4×Q8D414yes—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C42—21no—
99C2×C3×C42—21no—
100C2×C3×C42C2311yescharacteristic
101#946—22no—
102#946—22no—
103#946—22no—
104#946—22no—
105#946—22no—
106#946—22no—
107#946—41no—
108#946—41no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4D411yescharacteristic
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3D411yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—21no—
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#894—28no—
134#892—22no—
135#892—22no—
136D3×C4⋊C4—22no—
137D3×C4⋊C4—22no—
138#889—28no—
139#876—28no—
140C4×D12—22no—
141C4×D12—22no—
142#872—28no—
143#870—22no—
144#870D414yes—
145C3×#107—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×C4×C8—22no—
149#835—22no—
150#835—22no—
151#835—41no—
152#835—41no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—41no—
160(C2×D3)⋊C8—41no—
161#808—22no—
162#807—22no—
163C4⋊(C3⋊C8)—22no—
164C22×Q16C2×D311yescharacteristic
165#552—64no—
166#552—64no—
167C2×#126—61no—
168C2×#125—31no—
169C2×#125—61no—
170C2×#123—61no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×C4×Q8C2×D311yescharacteristic
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×#117—31no—
179C2×#117—61no—
180C22×C4⋊C4—31no—
181#479—64no—
182C4×Q16—24no—
183C2×#107—31no—
184C2×#107C2×D311yescharacteristic
185C2×#106—31no—
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103C2×D311yescharacteristic
192C2×#103C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C4×C8C2×D311yescharacteristic
198#398—61no—
199#394—61no—
200#388—61no—
201#388—61no—
202#382—31no—
203#380—31no—
204#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211C23×D3C2×D411yescharacteristic
212C23×D3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238C2×D12—22no—
239C2×D12—22no—
240C2×D12—41no—
241C2×C4×D3—24no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C3×Q16—28no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8#4112yes—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4C2×D412yes—
269C3×C42—24no—
270C3×C42—42no—
271C3×C42C2×D412yes—
272C3×C42C2×D412yes—
273(C2×D3)⋊C4—24no—
274(C2×D3)⋊C4—24no—
275(C2×D3)⋊C4—24no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—42no—
279(C2×D3)⋊C4—42no—
280(C2×D3)⋊C4—42no—
281(C2×D3)⋊C4—42no—
282C4⋊Dic3—22no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3C2×D412yes—
290C4⋊Dic3C2×D412yes—
291Dic3⋊C4—24no—
292Dic3⋊C4—24no—
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—42no—
297Dic3⋊C4—42no—
298C4×Dic3—24no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C22×Q8C22×D311yescharacteristic
306C22×Q8C22×D311yescharacteristic
307C22×D4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—61no—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×Q16—22no—
314C22×C8—31no—
315C22×C8—31no—
316C22×C8C22×D311yescharacteristic
317C22×C8C22×D311yescharacteristic
318#126—68no—
319#125—34no—
320#125—68no—
321#125—62no—
322#123—68no—
323C22⋊Q8—62no—
324C22⋊Q8—62no—
325C22⋊Q8—62no—
326C22⋊Q8—62no—
327C22⋊Q8—62no—
328C22⋊Q8—62no—
329C22⋊Q8—121no—
330C22⋊Q8—121no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8#6714yes—
335C4×D4—62no—
336C4×D4—62no—
337#117—68no—
338#117—62no—
339#117—62no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—62no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4—61no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4C22×D311yescharacteristic
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C22⋊C4—31no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C22⋊C4—61no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—61no—
370C2×C42C22×D311yescharacteristic
371#107—22no—
372#107—62no—
373#106—62no—
374C4⋊C8—62no—
375#103—22no—
376#103—22no—
377#103—62no—
378#103—62no—
379#103—121no—
380#103—121no—
381C22⋊C8—62no—
382C22⋊C8—62no—
383C22⋊C8—121no—
384C22⋊C8—121no—
385C4×C8—22no—
386#95—61no—
387#95—61no—
388#95—61no—
389#95—61no—
390C23×C3C22×D411yescharacteristic
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3#13512yes—
405C3×Q8—22no—
406C3×Q8—22no—
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—41no—
410C3×Q8—41no—
411C3×Q8—41no—
412C3×Q8—41no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4#12012yes—
430C2×C3×C4#12012yes—
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4C22×D411yescharacteristic
433C2×C3×C4C2×#4111yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435C2×C3×C4H(5,𝔽2)11yescharacteristic
436C2×C3×C42−1+411yescharacteristic
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455D12—44no—
456C4×D3—48no—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C4×D3—41no—
462C4×D3—41no—
463C4×D3—41no—
464C4×D3—41no—
465C3×C8—22no—
466C3×C8—41no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C24—31no—
470C24—31no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8#23512yes—
482C2×Q8C2×#6712yes—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—121no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—64no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—122no—
510C22×C4—122no—
511C22×C4D3×D411yescharacteristic
512C22×C4D3×D411yescharacteristic
513C22×C4C23×D311yescharacteristic
514Q16—28no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8#23512yes—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—32no—
532C4⋊C4—32no—
533C4⋊C4—42no—
534C4⋊C4—64no—
535C4⋊C4—64no—
536C4⋊C4—64no—
537C4⋊C4—62no—
538C4⋊C4—64no—
539C4⋊C4—64no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—122no—
547C4⋊C4—122no—
548C4⋊C4C2×#6712yes—
549C22⋊C4—64no—
550C22⋊C4—64no—
551C22⋊C4—64no—
552C22⋊C4—62no—
553C22⋊C4—62no—
554C22⋊C4—122no—
555C22⋊C4—122no—
556C22⋊C4—122no—
557C22⋊C4—122no—
558C42—24no—
559C42—42no—
560C42—64no—
561C42D3×D412yes—
562C42C2×#6712yes—
563C22×C3C2×#12011yescharacteristic
564C22×C3#54611yescharacteristic
565C22×C3#54711yescharacteristic
566C22×C3C2×#13511yescharacteristic
567C22×C3#57511yescharacteristic
568C22×C3#57811yescharacteristic
569C22×C3#57811yescharacteristic
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—41no—
574C2×D3—41no—
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C2×D3—41no—
582C2×D3—41no—
583C2×D3—41no—
584C3×C4—22no—
585C3×C4—22no—
586C3×C4—42no—
587C3×C4—42no—
588C3×C4—42no—
589C3×C4—81no—
590C3×C4#52511yescharacteristic
591C3×C4#53711yescharacteristic
592C3×C4#54811yescharacteristic
593C3×C4#55011yescharacteristic
594Dic3—41no—
595Dic3—41no—
596Dic3—42no—
597Dic3—42no—
598Dic3—81no—
599Dic3—81no—
600C23—32no—
601C23—61no—
602C23—61no—
603C23—61no—
604C23—61no—
605C23—61no—
606C23—61no—
607C23—61no—
608C23—61no—
609C23—61no—
610C23—61no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23C2×D3×D411yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—41no—
620Q8—41no—
621Q8—41no—
622Q8—41no—
623D4—124no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—61no—
641C2×C4—62no—
642C2×C4—62no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—128no—
649C2×C4—121no—
650C2×C4—121no—
651C2×C4—121no—
652C2×C4—121no—
653C2×C4—121no—
654C2×C4—121no—
655C2×C4—121no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4#93712yes—
668C2×C4#93712yes—
669C2×C4C2×#23511yescharacteristic
670C2×C4C2×#23511yescharacteristic
671C2×C4C2×D3×D411yescharacteristic
672C2×C4#100911yescharacteristic
673C2×C4#101011yescharacteristic
674C2×C4C22×#6711yescharacteristic
675C8—22no—
676C8—41no—
677C8—121no—
678C8—121no—
679C2×C3#240711yescharacteristic
680C2×C3#300211yescharacteristic
681C2×C3#301111yescharacteristic
682C2×C3#330011yescharacteristic
683C2×C3#332711yescharacteristic
684C2×C3#333611yescharacteristic
685C2×C3#335211yescharacteristic
686D3—42no—
687D3—81no—
688C22—62no—
689C22—62no—
690C22—62no—
691C22—121no—
692C22—121no—
693C22—121no—
694C22—121no—
695C22—121no—
696C22—121no—
697C22—121no—
698C22—121no—
699C22—121no—
700C22—121no—
701C22—121no—
702C22#555011yescharacteristic
703C22#555111yescharacteristic
704C22#576611yescharacteristic
705C22#576611yescharacteristic
706C22D3×#13511yescharacteristic
707C22#576811yescharacteristic
708C22C2×#93711yescharacteristic
709C4—22no—
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—122no—
716C4—122no—
717C4—121no—
718C4—121no—
719C4—241no—
720C4—241no—
721C4#555211yescharacteristic
722C4#555311yescharacteristic
723C4#579111yescharacteristic
724C4#583311yescharacteristic
725C3#2412711yescharacteristic, complemented, Sylow
726C2—122no—
727C2—241no—
728C2#7973611yescharacteristic
729C2#7973811yescharacteristic
730C2#7974111yescharacteristic
731C2#7974411yescharacteristic
732C2#8240211yescharacteristic
733C2#8388411yescharacteristic
734C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×Q16C2
socleC23×C3C22×D4
prime radicalC22×D12D4
hypercenterC2×C4×Q16D3
hypocenterC3#24127
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Q16C2semidirect
4. C2×#5022C2semidirect
5. #72071C2semidirect
6. #72071C2semidirect
7. #71627C2semidirect
8. #70633C2semidirect
9. #70632C2semidirect
10. #70275C2semidirect
11. #70274C2semidirect
12. #70269C2semidirect
13. #70268C2semidirect
15. #69778C2semidirect
66. C2×C4×Q16D3semidirect
725. C3#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#55812
C2×C3×C4×Q162
#824992
C2×#50222
#720712
#716272
#706332
#706322
#702752
#702742
#702692
#702682
#697872
#697782
#241273