Finite Group Databasebeta

← C4×#91518 #14416875

Subgroups — C4×#91518 #14416875

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#91518C211yesmaximal, characteristic
3C4×#6765C211yesmaximal, characteristic
4C4×#6718C211yesmaximal, characteristic, complemented
5C3×C4×#688C211yesmaximal, characteristic, complemented
6#11749260C211yesmaximal, characteristic, complemented
7#11749234C211yesmaximal, characteristic, complemented
8#11749213C211yesmaximal, characteristic, complemented
9#11747503C211yesmaximal, characteristic
10#11747455C211yesmaximal, characteristic, complemented
11#11747276C211yesmaximal, characteristic, complemented
12#11747222C211yesmaximal, characteristic, complemented
13C4×#6663C211yesmaximal, characteristic, complemented
14C4×#6655C211yesmaximal, characteristic, complemented
15C4×#6650C211yesmaximal, characteristic, complemented
16C4×#4088—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×#6765C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C2×#6718C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C5×D3×C4⋊C4—21no—
24C5×D3×C4⋊C4C2211yescharacteristic
25C5×#887—21no—
26C5×#887C2211yescharacteristic
27C42×C5×D3—21no—
28C42×C5×D3C2211yescharacteristic
29C4×C5×Dic6—21no—
30C4×C5×Dic6C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33#91518C418yesdirect product factor
34#91441—21no—
35C4×#1201—21no—
36Dic3×D20C2211yescharacteristic
37#91393—21no—
38C4×D5×Dic3—21no—
39#91340C2211yescharacteristic
40#91338C2211yescharacteristic
41C2×#6663C2211yescharacteristic
42C2×#6655C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×#6650C2211yescharacteristic
45#91119C2211yescharacteristic
46#91094C2211yescharacteristic
47#91091C2211yescharacteristic
48C4×C3⋊#168C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic
52C3×C4×#168C2211yescharacteristic
53#90988C2211yescharacteristic
54#90986C2211yescharacteristic
55#90975C2211yescharacteristic
56#90973C2211yescharacteristic
57#90972C2211yescharacteristic
58#90964C2211yescharacteristic
59#90953C2211yescharacteristic
60#90953C2211yescharacteristic
61C4×#915—51nomaximal, Hall
62C2×C4×C5×Q8—31no—
63C2×#4088—31no—
64C4×#709—31no—
65#65514—31no—
66#65319—31no—
67#65319—31no—
68C4×#689—31no—
69C4×#689—31no—
70#65315—31no—
71#65315—31no—
72C4×#688—31no—
73C4×#688D311yescharacteristic, complemented
74#65255—31no—
75#65253—31no—
76C4×#681—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C5×D3×Q8—22no—
80C5×D3×Q8C2×C414yescomplemented
81C2×C4×C5×D3—21no—
82C2×C4×C5×D3—21no—
83C2×C4×C5×D3D411yescharacteristic
84C2×C4×C5×D3D411yescharacteristic
85C2×C4×C5×D3C2311yescharacteristic
86C2×C5×Dic6—21no—
87C2×C5×Dic6C2311yescharacteristic
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×#1201—21no—
91C2×D5×Dic3—21no—
92C2×D5×Dic3—21no—
93#6765—22no—
94#6765C2×C414yes—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C42×C5—21no—
98C3×C42×C5C2311yescharacteristic
99#6718C2×C414yescomplemented
100C4⋊Dic15C2311yescharacteristic
101#6712—21no—
102C4×Dic15—21no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×C4⋊Dic3—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C5×Dic3⋊C4—21no—
110C4×C5×Dic3—21no—
111C4×C5×Dic3—21no—
112C4×C5×Dic3—21no—
113C4×C5×Dic3D411yescharacteristic
114C4×C5×Dic3D411yescharacteristic
115C4×C5×Dic3C2311yescharacteristic
116C3×#688C2×C414yescomplemented
117C3×#685—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121#6669—21no—
122(C2×D3)⋊Dic5—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126#6663C2×C414yescomplemented
127#6655C2×C414yescomplemented
128#6650—22no—
129#6650C2×C414yescomplemented
130C2×#915—51no—
131C4×D3×Q8D511yescharacteristic, complemented
132C4×#237—51no—
133C3×C4×SD16—51no—
134#5164—51no—
135C4×#216—51no—
136C4×#214—51no—
137#4861—51no—
138#4853—51no—
139#4802—51no—
140#4789—51no—
141#4771—51no—
142#4757—51no—
143C4×Dic12—51no—
144C4×ΓL(1,𝔽25)—51no—
145C22×C5×Q8—31no—
146C2×#709—31no—
147C4×C5×Q8—31no—
148C4×C5×Q8—31no—
149C4×C5×Q8—31no—
150C4×C5×Q8—61no—
151C4×C5×Q8—61no—
152C4×C5×Q8C2×D311yescharacteristic
153C2×C5×C4⋊C4—31no—
154C2×C5×C4⋊C4—61no—
155C2×C42×C5—31no—
156C2×C42×C5—61no—
157C2×#689—31no—
158C2×#689—31no—
159#4088—38no—
160C2×#688—31no—
161C2×#688C2×D311yescharacteristic
162C4×C22⋊D5—61no—
163C4×C22⋊D5—61no—
164#4072—31no—
165C2×#681—31no—
166C2×#681—31no—
167C4×D20—31no—
168C4×D20C2×D311yescharacteristic
169#4018—61no—
170C42×D5—61no—
171C4×Dic10—31no—
172C4×Dic10—31no—
173#3967—31no—
174#3967—31no—
175#3967—31no—
176#3967C2×D311yescharacteristic
177#3942—31no—
178#3942—31no—
179#3941—31no—
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3940C2×D311yescharacteristic
183#3939—31no—
184#3939—31no—
185#3935—31no—
186#3935—31no—
187C4×#168—31no—
188C4×#168C2×D311yescharacteristic
189C4×#137—151noSylow
190C22×C5×D3C2×D411yescharacteristic
191C22×C3×D5—21no—
192C3×C5×Q8—21no—
193C3×C5×Q8C22×C412yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200C2×Dic15—21no—
201Dic30—21no—
202Dic30C22×C412yes—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C2×C5×Dic3C2×D411yescharacteristic
208C4×C5×D3—24no—
209C4×C5×D3—22no—
210C4×C5×D3—41no—
211C4×C5×D3—42no—
212C4×C5×D3C22×C412yes—
213C4×C5×D3#4112yes—
214C5×Dic6—21no—
215C5×Dic6—24no—
216C5×Dic6C22×C412yes—
217C2×C3×Dic5—21no—
218C3×D20—21no—
219C3×D20C22×C412yes—
220C3×C4×D5—42no—
221#1201—24no—
222D5×Dic3—24no—
223D5×Dic3—42no—
224C3⋊#168—21no—
225C3⋊#168C22×C412yes—
226C3×#168—21no—
227C3×#168C22×C412yes—
228C2×D3×Q8C2×D511yescharacteristic
229C2×#237—51no—
230C2×C3×SD16—51no—
231C3×C4×Q8C2×D511yescharacteristic
232C3×C4×D4—51no—
233Q8×Dic3C2×D511yescharacteristic
234C2×#216—51no—
235D4×Dic3—51no—
236C2×#214—51no—
237C4×#67—101no—
238C2×C4×Dic3—101no—
239#915—58no—
240C2×Dic12—51no—
241C2×ΓL(1,𝔽25)—51no—
242C2×ΓL(1,𝔽25)—51no—
243#892—51no—
244D3×C4⋊C4—21no—
245D3×C4⋊C4C2×D511yescharacteristic
246#887—21no—
247#887—51no—
248#887C2×D511yescharacteristic
249#67⋊C4—101no—
250#877—101no—
251C42×D3—21no—
252C42×D3C2×D511yescharacteristic
253C4×Dic6—21no—
254C4×Dic6—51no—
255C4×Dic6C2×D511yescharacteristic
256C3×#106—51no—
257C3×#103—51no—
258C3×#102—51no—
259C3×C4×C8—51no—
260#835—51no—
261#832—51no—
262#818—51no—
263#816—51no—
264#816—51no—
265#815—51no—
266#815—51no—
267#810—51no—
268#810—51no—
269#808—51no—
270#807—51no—
271C4×C3⋊C8—51no—
272C2×C5×Q8—34no—
273C2×C5×Q8—31no—
274C2×C5×Q8—61no—
275C2×C5×Q8—62no—
276C2×C5×Q8C22×D311yescharacteristic
277C22×C4×C5—31no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5—61no—
281C22×C4×C5—61no—
282C2×C22⋊D5—61no—
283#709—34no—
284#709—62no—
285C2×D20C22×D311yescharacteristic
286C2×C4×D5—21no—
287C2×C4×D5—61no—
288C2×C4×D5—61no—
289C2×Dic10—31no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—31no—
292C5×C4⋊C4—61no—
293C5×C4⋊C4—61no—
294C5×C4⋊C4—61no—
295C5×C4⋊C4—61no—
296C5×C4⋊C4C22×D311yescharacteristic
297C42×C5—21no—
298C42×C5—31no—
299C42×C5—31no—
300C42×C5—31no—
301C42×C5—61no—
302C42×C5—61no—
303C42×C5—61no—
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—61no—
306#689—34no—
307#689—34no—
308#688—34no—
309#688C4×D314yescomplemented
310#685—21no—
311#685—61no—
312C4⋊Dic5—31no—
313C4⋊Dic5C22×D311yescharacteristic
314#683—61no—
315#683—61no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319#681—34no—
320#681—62no—
321C2×#168—31no—
322C2×#168—31no—
323C2×#168C22×D311yescharacteristic
324C2×#168C22×D311yescharacteristic
325C2×#137—151no—
326C4×#41—151no—
327C2×C4×Q8—31no—
328#441—151no—
329#441—151no—
330#440—151no—
331#440—151no—
332C4×Q16—151no—
333C4×Q16—151no—
334C4×SD16—51no—
335C4×SD16—151no—
336#428—151no—
337#419—151no—
338#417—151no—
339C4×M16—151no—
340C22×C3×C5C22×D411yescharacteristic
341C2×C5×D3—21no—
342C2×C5×D3—21no—
343C2×C5×D3C4×D412yes—
344C2×C3×D5—22no—
345C2×C3×D5—41no—
346C2×C3×D5—41no—
347C3×C4×C5—22no—
348C3×C4×C5—21no—
349C3×C4×C5—41no—
350C3×C4×C5#13712yescomplemented
351C3×C4×C5C23×C411yescharacteristic
352C3×C4×C5C2×#4111yescharacteristic
353Dic15—22no—
354Dic15—41no—
355C3×Dic5—41no—
356C5×Dic3—22no—
357C5×Dic3—21no—
358C5×Dic3—21no—
359C5×Dic3—41no—
360C5×Dic3C4×D412yes—
361C2×C3×Q8C22×D511yescharacteristic
362C2×C3×D4—51no—
363C22×C3×C4—101no—
364C2×#67—101no—
365C22×Dic3—101no—
366C22×Dic3—101no—
367D3×Q8—22no—
368D3×Q8C4×D514yescomplemented
369#237—54no—
370#237—102no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3C22⋊D511yescharacteristic
374C2×C4×D3C22⋊D511yescharacteristic
375C2×C4×D3C22×D511yescharacteristic
376C2×Dic6—21no—
377C2×Dic6—51no—
378C2×Dic6C22×D511yescharacteristic
379C3×SD16—54no—
380C2×C3×C8—51no—
381C2×C3×C8—51no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4C22×D511yescharacteristic
385C3×C22⋊C4—101no—
386C3×C42—21no—
387C3×C42C22×D511yescharacteristic
388#217—101no—
389#216—54no—
390#214—54no—
391(C2×D3)⋊C4—101no—
392C4⋊Dic3—21no—
393C4⋊Dic3—51no—
394C4⋊Dic3C22×D511yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—101no—
399Dic3⋊C4—101no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—101no—
404C4×Dic3—101no—
405C4×Dic3—101no—
406C4×Dic3C22⋊D511yescharacteristic
407C4×Dic3C22⋊D511yescharacteristic
408C4×Dic3C22×D511yescharacteristic
409C2×C3⋊C8—51no—
410C2×C3⋊C8—51no—
411Dic12—54no—
412ΓL(1,𝔽25)—54no—
413ΓL(1,𝔽25)—102no—
414C23×C5—31no—
415C22×D5—21no—
416C5×Q8—21no—
417C5×Q8—32no—
418C5×Q8—64no—
419C5×Q8—61no—
420C5×Q8C2×C4×D312yes—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—31no—
424C2×C4×C5—32no—
425C2×C4×C5—32no—
426C2×C4×C5—31no—
427C2×C4×C5—31no—
428C2×C4×C5—64no—
429C2×C4×C5—61no—
430C2×C4×C5—62no—
431C2×C4×C5—61no—
432C2×C4×C5—121no—
433C2×C4×C5—122no—
434C2×C4×C5D3×D411yescharacteristic
435C2×C4×C5D3×D411yescharacteristic
436C2×C4×C5C23×D311yescharacteristic
437C22⋊D5—64no—
438C2×Dic5—21no—
439C2×Dic5—61no—
440C2×Dic5—61no—
441D20—21no—
442D20C2×C4×D312yes—
443C4×D5—42no—
444C4×D5—64no—
445C4×D5—122no—
446Dic10—32no—
447Dic10—61no—
448#168—21no—
449#168—32no—
450#168—61no—
451#168C2×C4×D312yes—
452C2×#41—151no—
453C22×Q8—31no—
454#137—158no—
455C2×Q16—151no—
456C2×Q16—151no—
457C2×SD16—51no—
458C2×SD16—151no—
459C2×M16—151no—
460C2×M16—151no—
461C4×Q8—31no—
462C4×Q8—31no—
463C4×Q8—31no—
464C4×Q8—61no—
465C4×Q8—61no—
466C4×Q8—151no—
467C4×Q8—151no—
468C4×Q8D3×D511yescharacteristic
469C4×D4—51no—
470C4×D4—151no—
471C4×D4—301no—
472C4×D4—301no—
473#117—151no—
474#117—301no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—61no—
477C2×C42—31no—
478C2×C42—61no—
479C2×C42—301no—
480#107—151no—
481#107—151no—
482#106—51no—
483#106—151no—
484#103—51no—
485#103—151no—
486#103—151no—
487#103—151no—
488#103—151no—
489#103—151no—
490#102—51no—
491#102—151no—
492#97—151no—
493#97—151no—
494C4×C8—51no—
495C4×C8—151no—
496C2×C3×C5C2×C4×D411yescharacteristic
497C2×C3×C5C2×#13711yescharacteristic
498C2×C3×C5#57511yescharacteristic
499C3×D5—42no—
500C5×D3—22no—
501C23×C3—101no—
502C22×D3C2×C22⋊D511yescharacteristic
503C3×Q8—21no—
504C3×Q8C2×C4×D512yes—
505C3×D4—52no—
506C3×D4—101no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—101no—
510C2×C3×C4—202no—
511C2×C3×C4C2×C22⋊D511yescharacteristic
512C2×C3×C4C2×C22⋊D511yescharacteristic
513C2×C3×C4C23×D511yescharacteristic
514#67—104no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—101no—
518C2×Dic3—104no—
519C2×Dic3—101no—
520C2×Dic3—202no—
521C2×Dic3C2×C22⋊D511yescharacteristic
522C2×Dic3C2×C22⋊D511yescharacteristic
523C2×Dic3C2×C22⋊D511yescharacteristic
524C4×D3—24no—
525C4×D3—22no—
526C4×D3—41no—
527C4×D3—42no—
528C4×D3C2×C4×D512yes—
529C4×D3#70912yes—
530Dic6—21no—
531Dic6—24no—
532Dic6—52no—
533Dic6—101no—
534Dic6C2×C4×D512yes—
535C3×C8—52no—
536C3×C8—101no—
537C3⋊C8—52no—
538C3⋊C8—101no—
539C22×C5—32no—
540C22×C5—61no—
541C22×C5—61no—
542C22×C5C2×D3×D411yescharacteristic
543C2×D5—22no—
544C2×D5—41no—
545C2×D5—41no—
546C4×C5—21no—
547C4×C5—22no—
548C4×C5—32no—
549C4×C5—41no—
550C4×C5—61no—
551C4×C5—61no—
552C4×C5—62no—
553C4×C5—121no—
554C4×C5#91512yescomplemented
555C4×C5C22×C4×D311yescharacteristic
556C4×C5D3×#4111yescharacteristic
557Dic5—41no—
558Dic5—62no—
559Dic5—121no—
560#41—154no—
561#41—302no—
562C2×Q8—34no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—62no—
566C2×Q8—151no—
567C2×Q8C2×D3×D511yescharacteristic
568C2×D4—51no—
569C2×D4—301no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—101no—
576C22×C4—301no—
577C22×C4—301no—
578Q16—154no—
579Q16—154no—
580SD16—54no—
581SD16—154no—
582M16—154no—
583M16—302no—
584C2×C8—51no—
585C2×C8—51no—
586C2×C8—151no—
587C2×C8—151no—
588C4⋊C4—21no—
589C4⋊C4—31no—
590C4⋊C4—51no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—151no—
596C4⋊C4—301no—
597C4⋊C4—301no—
598C4⋊C4C2×D3×D511yescharacteristic
599C22⋊C4—101no—
600C22⋊C4—301no—
601C22⋊C4—301no—
602C42—21no—
603C42—31no—
604C42—31no—
605C42—31no—
606C42—61no—
607C42—61no—
608C42—61no—
609C42—301no—
610C42—301no—
611C42—301no—
612C42C2×D3×D511yescharacteristic
613C3×C5C4×#13711yescharacteristic, complemented, Hall
614C22×C3—102no—
615C22×C3—201no—
616C22×C3—201no—
617C22×C3C22×C22⋊D511yescharacteristic
618C2×D3—21no—
619C2×D3—21no—
620C2×D3C4×C22⋊D512yes—
621C3×C4—22no—
622C3×C4—21no—
623C3×C4—41no—
624C3×C4—201no—
625C3×C4#408812yescomplemented
626C3×C4C22×C4×D511yescharacteristic
627C3×C4C2×#70911yescharacteristic
628Dic3—22no—
629Dic3—21no—
630Dic3—21no—
631Dic3—41no—
632Dic3—102no—
633Dic3—201no—
634Dic3C4×C22⋊D512yes—
635C2×C5—62no—
636C2×C5C4×D3×D411yescharacteristic
637C2×C5C2×#91511yescharacteristic
638C2×C5#576811yescharacteristic
639D5—42no—
640C23—31no—
641C23—101no—
642Q8—21no—
643Q8—32no—
644Q8—64no—
645Q8—61no—
646Q8—152no—
647Q8—301no—
648Q8C4×D3×D512yes—
649D4—52no—
650D4—101no—
651D4—304no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—64no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—101no—
664C2×C4—121no—
665C2×C4—122no—
666C2×C4—202no—
667C2×C4—304no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—602no—
671C2×C4D3×C22⋊D511yescharacteristic
672C2×C4D3×C22⋊D511yescharacteristic
673C2×C4C22×D3×D511yescharacteristic
674C8—52no—
675C8—101no—
676C8—152no—
677C8—301no—
678C2×C3—202no—
679C2×C3C2×C4×C22⋊D511yescharacteristic
680C2×C3C2×#408811yescharacteristic
681C2×C3#6615611yescharacteristic
682D3—22no—
683C5C4×#91511yescharacteristic, complemented, Sylow
684C22—32no—
685C22—61no—
686C22—61no—
687C22—102no—
688C22—201no—
689C22—201no—
690C22C2×D3×C22⋊D511yescharacteristic
691C4—21no—
692C4—22no—
693C4—32no—
694C4—41no—
695C4—61no—
696C4—61no—
697C4—62no—
698C4—121no—
699C4—201no—
700C4—302no—
701C4—601no—
702C4#9151812yesdirect product factor
703C4C2×C4×D3×D511yescharacteristic
704C4D3×#70911yescharacteristic
705C3C4×#408811yescharacteristic, complemented, Sylow
706C2—62no—
707C2—202no—
708C2C4×D3×C22⋊D511yescharacteristic
709C2C2×#9151811yescharacteristic
710C2#1175532211yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6765C22
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×C5×D3×Q8C2semidirect
4. C4×#6718C2semidirect
5. C3×C4×#688C2semidirect
6. #11749260C2semidirect
7. #11749234C2semidirect
8. #11749213C2semidirect
10. #11747455C2semidirect
11. #11747276C2semidirect
12. #11747222C2semidirect
13. C4×#6663C2semidirect
14. C4×#6655C2semidirect
15. C4×#6650C2semidirect
33. #91518C4direct (N × H)
73. C4×#688D3semidirect
80. C5×D3×Q8C2×C4semidirect
99. #6718C2×C4semidirect
116. C3×#688C2×C4semidirect
126. #6663C2×C4semidirect
127. #6655C2×C4semidirect
129. #6650C2×C4semidirect
131. C4×D3×Q8D5semidirect
309. #688C4×D3semidirect
350. C3×C4×C5#137semidirect
368. D3×Q8C4×D5semidirect
554. C4×C5#915semidirect
613. C3×C5C4×#137semidirect
625. C3×C4#4088semidirect
683. C5C4×#915semidirect
702. C4#91518direct (N × H)
705. C3C4×#4088semidirect

Maximal subgroups

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

subgroupindex
C4×C5×D3×Q82
C2×#915182
C4×#67652
C4×#67182
C3×C4×#6882
#117492602
#117492342
#117492132
#117475032
#117474552
#117472762
#117472222
C4×#66632
C4×#66552
C4×#66502
C4×#40883
C4×#9155