Finite Group Databasebeta

← C2×#72222519 #72255409

Subgroups — C2×#72222519 #72255409

Order 3072.

1298 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10682657C211yesmaximal, characteristic, complemented
2C2×#10682655C211yesmaximal, characteristic, complemented
3C2×#10715812C211yesmaximal, characteristic
4C2×#10682858C211yesmaximal, characteristic, complemented
5C2×C3×#12068C211yesmaximal, characteristic, complemented
6C2×#10682523C211yesmaximal, characteristic, complemented
7C2×#10707073C211yesmaximal, characteristic, complemented
8#72222519C218yesmaximal, direct product factor
9C2×AGL(1,ℤ/32)—31nomaximal, Sylow
10C2×#71509C411yescharacteristic
11C2×#69078C2211yescharacteristic
12C2×#68077—21no—
13#10715812C414yes—
14#10715812C2214yes—
15C2×#67582C411yescharacteristic
16C2×#67583C411yescharacteristic
17C2×#67828C411yescharacteristic
18C2×#67519C2211yescharacteristic
19C2×#67519C2211yescharacteristic
20#10707073—22no—
21#10707073C2214yescomplemented
22C2×#67513C2211yescharacteristic
23C2×#67516—21no—
24#10682858C2214yescomplemented
25#10682657C2214yescomplemented
26#10682655C2214yescomplemented
27#10682523C2214yescomplemented
28C2×C3×#2179C2211yescharacteristic
29C2×C3×#2171—21no—
30C3×#12068—22no—
31C3×#12068C2214yescomplemented
32C2×C3×#1369C2211yescharacteristic
33C2×C3×#1336—21no—
34C2×C3×#1313C2211yescharacteristic
35C2×#13658—31no—
36C2×#12068D311yescharacteristic, complemented
37C2×#12067—31no—
38AGL(1,ℤ/32)—38no—
39C2×#7457—31no—
40C2×#7390—31no—
41C2×#7389—31no—
42C2×#7333—31no—
43C2×C3×#508C2×C411yescharacteristic
44C2×C3×#504—41no—
45C2×C3×#443—21no—
46C22×D48C2×C411yescharacteristic
47C2×C4×D24—21no—
48C2×C8×D12—41no—
49C3×#2179—21no—
50C3×#2179—21no—
51C3×#2179C2×C412yes—
52C3×#2179C2312yes—
53C3×#2171—24no—
54C3×#2171—42no—
55C2×C3×#368C2×C411yescharacteristic
56C2×C3×#364—21no—
57C2×C3×#359—21no—
58C2×C3×#350—41no—
59C2×C3×#346D411yescharacteristic
60C2×C3×#346C2311yescharacteristic
61C2×C3×#322D411yescharacteristic
62#71509C814yescomplemented
63#71509C2×C414yes—
64C2×#4521C812yescomplemented
65C2×#4519C812yescomplemented
66C2×#4509—21no—
67C2×#4505C2×C411yescharacteristic
68C2×#4499—21no—
69C2×#4499C2×C411yescharacteristic
70C2×#4499C2×C411yescharacteristic
71C2×#4459—41no—
72C2×#4457—21no—
73#69078—21no—
74#69078—21no—
75#69078C2×C412yes—
76#69078C2312yes—
77#68077—24no—
78#68077—42no—
79C3×#1369—21no—
80C3×#1369C2312yes—
81C3×#1336—24no—
82C3×#1313D412yes—
83C3×#1313C2312yes—
84#67828C2×C414yes—
85#67583C2×C414yes—
86#67582C2×C414yes—
87#67519—21no—
88#67519C2×C412yes—
89#67519C2312yes—
90#67519C2312yes—
91#67516—24no—
92#67513—21no—
93#67513C2312yes—
94C2×#2263—31no—
95C2×#2179C2×D311yescharacteristic
96C2×#2177—31no—
97C2×#2171—21no—
98C2×#1580—61no—
99#13658—34no—
100#13658—34no—
101C2×#1426—31no—
102C2×#1419—31no—
103C2×#1418—31no—
104C2×#1398—31no—
105C2×#1398—31no—
106#12068—22no—
107#12068C2×D314yescomplemented
108#12067—34no—
109#12067—62no—
110C2×#1369C2×D311yescharacteristic
111C2×#1368—31no—
112C2×#1336—21no—
113C2×#1333—61no—
114C2×#1313C2×D311yescharacteristic
115#7457—34no—
116#7390—34no—
117#7389—34no—
118#7333—34no—
119C2×C3×#135—21no—
120C2×C3×#131—41no—
121C22×D24—21no—
122C22×D3×C8—81no—
123C2×C4×D12—41no—
124C3×#508—21no—
125C3×#508—21no—
126C3×#508C2×C812yescomplemented
127C3×#508C22×C412yes—
128C2×C3×Q32C2×C811yescharacteristic, complemented
129C2×C3×SD32—21no—
130C2×C3×D16C2×C811yescharacteristic, complemented
131C3×#504—44no—
132C3×#504—82no—
133C2×C3×M32—41no—
134C2×C3×M32—81no—
135C22×C3×C16—21no—
136C22×C3×C16—81no—
137C22×C3×C16C22×C411yescharacteristic
138C22×C3×C16#4111yescharacteristic
139C3×#443—22no—
140C3×#443—22no—
141C3×#443—41no—
142C3×#443—41no—
143C2×C3×#108—21no—
144C2×C3×#104—41no—
145C2×C3×C4×C8—21no—
146C2×C3×C4×C8C2×D411yescharacteristic
147C2×#821—41no—
148C2×(C2×D3)⋊C8—81no—
149C2×#818—21no—
150C2×C4⋊(C3⋊C8)—41no—
151C2×D48—21no—
152C2×D48—21no—
153C2×D48—21no—
154C2×D48C2×C812yes—
155C2×D48C2×C812yes—
156C2×D48C22×C412yes—
157C4×D24—22no—
158C4×D24—22no—
159C4×D24—41no—
160C4×D24—41no—
161C8×D12—44no—
162C8×D12—82no—
163C3×#368—21no—
164C3×#368C22×C412yes—
165C3×#364—22no—
166C3×#364—41no—
167C3×#359—22no—
168C3×#359—22no—
169C3×#350—44no—
170C3×#346—21no—
171C3×#346C22×C411yescharacteristic
172C3×#346C2×D412yes—
173C3×#346C2×D411yescharacteristic
174C3×#346#4111yescharacteristic
175C3×#346C2411yescharacteristic
176C3×#322—21no—
177C3×#322C2×D412yes—
178#4521C2×C818yescomplemented
179#4519C2×C818yescomplemented
180#4509—22no—
181#4509—22no—
182#4505—21no—
183#4505C22×C412yes—
184#4499—21no—
185#4499—22no—
186#4499—41no—
187#4499C2×C812yescomplemented
188#4499C22×C412yes—
189#4499C22×C412yes—
190C2×C3⋊C32—21no—
191C2×C3⋊C32—41no—
192C2×C3⋊C32C2×C812yescomplemented
193#4459—44no—
194#4457—22no—
195#4457—41no—
196C2×#508C4×D311yescharacteristic
197C22×D16—31no—
198C2×#504—41no—
199C2×#443—21no—
200C2×C4×D8—61no—
201C2×C8×D4—121no—
202#2263—34no—
203#2263—34no—
204C2×SD64—32no—
205C2×D32—32no—
206C2×M64—31no—
207C2×M64—31no—
208C2×M64—61no—
209#2179—21no—
210#2179—21no—
211#2179C4×D312yes—
212#2179C22×D312yes—
213#2177—32no—
214#2177—32no—
215#2177—61no—
216#2177—61no—
217#2171—24no—
218#2171—42no—
219C2×#368C4×D311yescharacteristic
220C2×#367—31no—
221C2×#364—21no—
222C2×#359—21no—
223C2×#357—61no—
224C2×#350—41no—
225C2×#346#6711yescharacteristic
226C2×#346C22×D311yescharacteristic
227#1580—64no—
228#1580—122no—
229C2×#334—61no—
230C2×D4⋊C8—121no—
231C2×#322#6711yescharacteristic
232#1426—34no—
233#1419—34no—
234#1418—34no—
235#1398—32no—
236#1398—32no—
237#1398—32no—
238#1398—61no—
239#1369—21no—
240#1369C22×D312yes—
241#1368—32no—
242#1368—61no—
243#1336—24no—
244#1333—64no—
245#1313#6712yes—
246#1313C22×D312yes—
247C2×C3×#41—41no—
248C22×D12—41no—
249C22×C4×D3—81no—
250C3×#135—22no—
251C3×#135—22no—
252C3×#135—41no—
253C3×#135—41no—
254C2×C3×Q16—21no—
255C2×C3×SD16—41no—
256C2×C3×D8—21no—
257C3×#131—42no—
258C3×#131—42no—
259C3×#131—81no—
260C3×#131—81no—
261C2×C3×M16—41no—
262C2×C3×M16—81no—
263C22×C3×C8—41no—
264C22×C3×C8—81no—
265C22×C3×C8C4×D411yescharacteristic
266C22×C3×C8AGL(1,ℤ/8)11yescharacteristic
267C2×C3×C42AGL(1,ℤ/8)11yescharacteristic
268C2×(C2×D3)⋊C4—81no—
269C2×C4⋊Dic3—41no—
270C22×C3⋊C8—81no—
271C2×D24—22no—
272C2×D24—22no—
273C2×D24—22no—
274C2×D24—41no—
275C2×D24—41no—
276C2×D24—41no—
277C2×D3×C8—84no—
278C2×D3×C8—164no—
279C4×D12—42no—
280C4×D12—42no—
281C4×D12—81no—
282C4×D12—81no—
283C3×Q32—21no—
284C3×Q32C22×C812yescomplemented
285C3×SD32—22no—
286C3×SD32—22no—
287C3×D16—21no—
288C3×D16C22×C812yescomplemented
289C3×M32—42no—
290C3×M32—84no—
291C3×M32—81no—
292C2×C3×C16—21no—
293C2×C3×C16—21no—
294C2×C3×C16—22no—
295C2×C3×C16—41no—
296C2×C3×C16—41no—
297C2×C3×C16—84no—
298C2×C3×C16—81no—
299C2×C3×C16C4×D411yescharacteristic
300C2×C3×C16C4×D411yescharacteristic
301C2×C3×C16C22×C811yescharacteristic
302C2×C3×C16C22×C811yescharacteristic
303C2×C3×C16#13111yescharacteristic
304C2×C3×C16#13111yescharacteristic
305C2×C3×C16C23×C411yescharacteristic
306C2×C3×C16C2×#4111yescharacteristic
307C3×#108—22no—
308C3×#108—41no—
309C3×#104—42no—
310C3×#104—42no—
311C3×C4×C8—22no—
312C3×C4×C8—41no—
313C3×C4×C8C4×D411yescharacteristic
314C3×C4×C8AGL(1,ℤ/8)11yescharacteristic
315C3×C4×C8AGL(1,ℤ/8)11yescharacteristic
316C3×C4×C8C22×D411yescharacteristic
317#821—42no—
318#821—42no—
319(C2×D3)⋊C8—84no—
320#818—22no—
321#818—41no—
322C4⋊(C3⋊C8)—42no—
323C4⋊(C3⋊C8)—81no—
324D48—22no—
325D48—22no—
326D48—22no—
327D48C22×C814yes—
328C3⋊C32—22no—
329C3⋊C32—42no—
330C3⋊C32C22×C814yescomplemented
331C2×#135—21no—
332C22×D8—61no—
333C2×#131—41no—
334C23×C8—241no—
335C2×C4×D4—121no—
336#508—21no—
337#508—21no—
338#508D3×C812yescomplemented
339#508C2×C4×D312yes—
340C2×Q32D3×C811yescharacteristic, complemented
341C2×SD32—21no—
342C2×D16—32no—
343C2×D16—32no—
344C2×D16—32no—
345C2×D16—61no—
346C2×D16—61no—
347C2×D16—61no—
348C2×D16D3×C811yescharacteristic, complemented
349#504—44no—
350#504—82no—
351C2×M32—41no—
352C2×M32—81no—
353C22×C16—21no—
354C22×C16—81no—
355C22×C16C2×C4×D311yescharacteristic
356C22×C16#23511yescharacteristic
357#443—22no—
358#443—22no—
359#443—41no—
360#443—41no—
361C4×D8—62no—
362C4×D8—62no—
363C4×D8—121no—
364C4×D8—121no—
365C8×D4—124no—
366C8×D4—242no—
367C2×#108—21no—
368C2×#107—61no—
369C2×C4⋊C8—121no—
370C2×#104—41no—
371C2×#102—121no—
372C2×C22⋊C8—241no—
373C2×C4×C8—21no—
374C2×C4×C8C2×#6711yescharacteristic
375SD64—38no—
376D32—38no—
377M64—32no—
378M64—32no—
379M64—32no—
380M64—61no—
381M64—62no—
382M64—121no—
383C2×C32—32no—
384C2×C32—61no—
385C2×C32—121no—
386#368—21no—
387#368C2×C4×D312yes—
388#367—32no—
389#367—61no—
390#364—22no—
391#364—41no—
392#359—22no—
393#359—22no—
394#357—62no—
395#357—62no—
396#350—44no—
397#346—21no—
398#346C2×C4×D311yescharacteristic
399#346#23511yescharacteristic
400#346C2×#6712yes—
401#346C2×#6711yescharacteristic
402#346C23×D311yescharacteristic
403#334—62no—
404#334—121no—
405D4⋊C8—124no—
406#322—21no—
407#322C2×#6712yes—
408C23×D3—81no—
409C3×#41—42no—
410C3×#41—42no—
411C3×#41—81no—
412C3×#41—81no—
413C2×C3×Q8—41no—
414C2×C3×D4—41no—
415C2×C3×D4—81no—
416C22×C3×C4—21no—
417C22×C3×C4—81no—
418C22×C3×C4#44211yescharacteristic
419C22×Dic3—81no—
420C2×D12—42no—
421C2×D12—42no—
422C2×D12—42no—
423C2×D12—81no—
424C2×D12—81no—
425C2×D12—81no—
426C2×C4×D3—82no—
427C2×C4×D3—82no—
428C2×C4×D3—162no—
429C2×C4×D3—162no—
430C3×Q16—22no—
431C3×Q16—41no—
432C3×SD16—42no—
433C3×SD16—42no—
434C3×D8—22no—
435C3×D8—41no—
436C3×M16—42no—
437C3×M16—82no—
438C3×M16—82no—
439C3×M16—81no—
440C2×C3×C8—21no—
441C2×C3×C8—21no—
442C2×C3×C8—42no—
443C2×C3×C8—82no—
444C2×C3×C8—82no—
445C2×C3×C8—82no—
446C2×C3×C8—81no—
447C2×C3×C8C8×D411yescharacteristic
448C2×C3×C8C8×D411yescharacteristic
449C2×C3×C8#44211yescharacteristic
450C2×C3×C8#44211yescharacteristic
451C2×C3×C8#44411yescharacteristic
452C2×C3×C8#44411yescharacteristic
453C2×C3×C8C2×C4×D411yescharacteristic
454C2×C3×C8C2×AGL(1,ℤ/8)11yescharacteristic
455C3×C42—21no—
456C3×C42#44211yescharacteristic
457C3×C42C2×AGL(1,ℤ/8)11yescharacteristic
458(C2×D3)⋊C4—82no—
459(C2×D3)⋊C4—82no—
460C4⋊Dic3—42no—
461C4⋊Dic3—81no—
462C2×C3⋊C8—82no—
463C2×C3⋊C8—162no—
464D24—24no—
465D24—42no—
466D24—42no—
467D24—42no—
468D3×C8—168no—
469C3×C16—21no—
470C3×C16—21no—
471C3×C16—42no—
472C3×C16—82no—
473C3×C16C8×D411yescharacteristic
474C3×C16C8×D411yescharacteristic
475C3×C16C23×C811yescharacteristic
476C3×C16C2×#13111yescharacteristic
477C2×#41—41no—
478C22×D4—121no—
479C23×C4—241no—
480#135—22no—
481#135—22no—
482#135—41no—
483#135—41no—
484C2×Q16—21no—
485C2×SD16—41no—
486C2×D8—21no—
487C2×D8—62no—
488C2×D8—62no—
489C2×D8—62no—
490C2×D8—121no—
491C2×D8—121no—
492C2×D8—121no—
493#131—42no—
494#131—42no—
495#131—81no—
496#131—81no—
497C2×M16—41no—
498C2×M16—81no—
499C22×C8—41no—
500C22×C8—81no—
501C22×C8—244no—
502C22×C8—241no—
503C22×C8—484no—
504C22×C8C4×#6711yescharacteristic
505C22×C8#93211yescharacteristic
506C4×D4—122no—
507C4×D4—122no—
508C4×D4—241no—
509C4×D4—241no—
510C2×C4⋊C4—121no—
511C2×C22⋊C4—241no—
512C2×C42#94911yescharacteristic
513Q32—21no—
514Q32C2×D3×C812yescomplemented
515SD32—22no—
516SD32—22no—
517D16—21no—
518D16—34no—
519D16—62no—
520D16—62no—
521D16—62no—
522D16C2×D3×C812yescomplemented
523M32—42no—
524M32—84no—
525M32—81no—
526C2×C16—21no—
527C2×C16—21no—
528C2×C16—22no—
529C2×C16—41no—
530C2×C16—41no—
531C2×C16—84no—
532C2×C16—81no—
533C2×C16C2×D3×C811yescharacteristic
534C2×C16C2×D3×C811yescharacteristic
535C2×C16#90111yescharacteristic
536C2×C16#90111yescharacteristic
537C2×C16C4×#6711yescharacteristic
538C2×C16C4×#6711yescharacteristic
539C2×C16C22×C4×D311yescharacteristic
540C2×C16C2×#23511yescharacteristic
541#108—22no—
542#108—41no—
543#107—62no—
544#107—121no—
545C4⋊C8—122no—
546C4⋊C8—241no—
547#104—42no—
548#104—42no—
549#102—122no—
550#102—122no—
551C22⋊C8—244no—
552C4×C8—22no—
553C4×C8—41no—
554C4×C8C4×#6711yescharacteristic
555C4×C8#93211yescharacteristic
556C4×C8#94911yescharacteristic
557C4×C8C22×#6711yescharacteristic
558C32—34no—
559C32—62no—
560C32—122no—
561C23×C3—81no—
562C23×C3AGL(1,ℤ/16)11yescharacteristic
563C22×D3—82no—
564C22×D3—82no—
565C22×D3—82no—
566C22×D3—162no—
567C22×D3—162no—
568C3×Q8—42no—
569C3×Q8—81no—
570C3×D4—42no—
571C3×D4—82no—
572C3×D4—82no—
573C3×D4—81no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—42no—
577C2×C3×C4—81no—
578C2×C3×C4—82no—
579C2×C3×C4—82no—
580C2×C3×C4#158011yescharacteristic
581C2×C3×C4#158011yescharacteristic
582C2×C3×C4AGL(1,ℤ/16)11yescharacteristic
583C2×C3×C4AGL(1,ℤ/16)11yescharacteristic
584C2×C3×C4AGL(1,ℤ/16)11yescharacteristic
585C2×C3×C4C2×#44211yescharacteristic
586C2×Dic3—82no—
587C2×Dic3—162no—
588D12—44no—
589D12—82no—
590D12—82no—
591D12—82no—
592C4×D3—162no—
593C4×D3—162no—
594C4×D3—164no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—82no—
598C3×C8—82no—
599C3×C8#158011yescharacteristic
600C3×C8#158011yescharacteristic
601C3×C8C2×C8×D411yescharacteristic
602C3×C8C2×#44411yescharacteristic
603C3⋊C8—162no—
604C24—241no—
605#41—42no—
606#41—42no—
607#41—81no—
608#41—81no—
609C2×Q8—41no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—122no—
613C2×D4—122no—
614C2×D4—122no—
615C2×D4—241no—
616C2×D4—241no—
617C2×D4—241no—
618C22×C4—21no—
619C22×C4—81no—
620C22×C4—242no—
621C22×C4—242no—
622C22×C4—241no—
623C22×C4—482no—
624C22×C4—482no—
625C22×C4#501411yescharacteristic
626Q16—22no—
627Q16—41no—
628SD16—42no—
629SD16—42no—
630D8—22no—
631D8—41no—
632D8—64no—
633D8—122no—
634D8—122no—
635D8—122no—
636M16—42no—
637M16—82no—
638M16—82no—
639M16—81no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—42no—
643C2×C8—82no—
644C2×C8—82no—
645C2×C8—82no—
646C2×C8—81no—
647C2×C8—242no—
648C2×C8—488no—
649C2×C8—482no—
650C2×C8#501411yescharacteristic
651C2×C8#501411yescharacteristic
652C2×C8C8×#6711yescharacteristic
653C2×C8C8×#6711yescharacteristic
654C2×C8#514511yescharacteristic
655C2×C8#514511yescharacteristic
656C2×C8C2×C4×#6711yescharacteristic
657C2×C8C2×#93211yescharacteristic
658C4⋊C4—122no—
659C4⋊C4—241no—
660C22⋊C4—242no—
661C22⋊C4—242no—
662C42—21no—
663C42#501411yescharacteristic
664C42C2×#94911yescharacteristic
665C16—21no—
666C16—21no—
667C16—42no—
668C16—82no—
669C16C8×#6711yescharacteristic
670C16C8×#6711yescharacteristic
671C16C22×D3×C811yescharacteristic
672C16C2×#90111yescharacteristic
673C22×C3—22no—
674C22×C3—82no—
675C22×C3—162no—
676C22×C3#1206711yescharacteristic
677C22×C3#1206711yescharacteristic
678C22×C3C2×AGL(1,ℤ/16)11yescharacteristic
679C2×D3—84no—
680C2×D3—162no—
681C2×D3—162no—
682C2×D3—164no—
683C2×D3—164no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—82no—
687C3×C4#1206711yescharacteristic
688C3×C4#1206711yescharacteristic
689C3×C4C2×#158011yescharacteristic
690C3×C4C2×AGL(1,ℤ/16)11yescharacteristic
691Dic3—162no—
692C23—81no—
693C23—242no—
694C23—242no—
695C23—242no—
696C23—482no—
697C23—482no—
698C23#7092911yescharacteristic
699Q8—42no—
700Q8—81no—
701D4—42no—
702D4—82no—
703D4—82no—
704D4—81no—
705D4—124no—
706D4—242no—
707D4—242no—
708D4—242no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—242no—
716C2×C4—482no—
717C2×C4—482no—
718C2×C4—484no—
719C2×C4—482no—
720C2×C4#7084011yescharacteristic
721C2×C4#7084011yescharacteristic
722C2×C4#7091811yescharacteristic
723C2×C4#7091811yescharacteristic
724C2×C4#7092911yescharacteristic
725C2×C4C2×#501411yescharacteristic
726C8—21no—
727C8—21no—
728C8—82no—
729C8—82no—
730C8—482no—
731C8#7084011yescharacteristic
732C8#7084011yescharacteristic
733C8C2×C8×#6711yescharacteristic
734C8C2×#514511yescharacteristic
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—162no—
738C2×C3AGL(1,ℤ/32)12yescomplemented
739C2×C3C2×#1206711yescharacteristic
740D3—164no—
741C22—22no—
742C22—82no—
743C22—162no—
744C22—244no—
745C22—482no—
746C22—482no—
747C22—484no—
748C22—484no—
749C22#1070707011yescharacteristic
750C22#1070707011yescharacteristic
751C22C2×#7092911yescharacteristic
752C4—41no—
753C4—41no—
754C4—82no—
755C4—482no—
756C4#1070707011yescharacteristic
757C4#1070707011yescharacteristic
758C4C2×#7084011yescharacteristic
759C4C2×#7091811yescharacteristic
760C3C2×AGL(1,ℤ/32)11yescharacteristic, complemented, Sylow
761C2—21no—
762C2—21no—
763C2—162no—
764C2—484no—
765C2#7222251912yesdirect product factor
766C2C2×#1070707011yescharacteristic
subgroupG/H
centerC22#10707070
commutatorC3×C16C23×C8
Frattini#346C23×D3
FittingC2×C3×#12068C2
socleC22×C3#12067
prime radicalC2×#71509C4
cosocleC3×#346C24
hypercenterC2×#12068D3
hypocenterC3C2×AGL(1,ℤ/32)
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#1313 ◁ C2×#12068

Complements

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

NH ≅ G/Ntype
1. C2×#10682657C2semidirect
2. C2×#10682655C2semidirect
4. C2×#10682858C2semidirect
5. C2×C3×#12068C2semidirect
6. C2×#10682523C2semidirect
7. C2×#10707073C2semidirect
8. #72222519C2direct (N × H)
21. #10707073C22semidirect
24. #10682858C22semidirect
25. #10682657C22semidirect
26. #10682655C22semidirect
27. #10682523C22semidirect
31. C3×#12068C22semidirect
36. C2×#12068D3semidirect
62. #71509C8semidirect
64. C2×#4521C8semidirect
65. C2×#4519C8semidirect
107. #12068C2×D3semidirect
126. C3×#508C2×C8semidirect
128. C2×C3×Q32C2×C8semidirect
130. C2×C3×D16C2×C8semidirect
178. #4521C2×C8semidirect
179. #4519C2×C8semidirect
187. #4499C2×C8semidirect
192. C2×C3⋊C32C2×C8semidirect
284. C3×Q32C22×C8semidirect
288. C3×D16C22×C8semidirect
330. C3⋊C32C22×C8semidirect
338. #508D3×C8semidirect
340. C2×Q32D3×C8semidirect
348. C2×D16D3×C8semidirect
514. Q32C2×D3×C8semidirect
522. D16C2×D3×C8semidirect
738. C2×C3AGL(1,ℤ/32)semidirect
760. C3C2×AGL(1,ℤ/32)semidirect
765. C2#72222519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106826572
C2×#106826552
C2×#107158122
C2×#106828582
C2×C3×#120682
C2×#106825232
C2×#107070732
#722225192
C2×AGL(1,ℤ/32)3