Finite Group Databasebeta

← C2×#19145260 #25966462

Subgroups — C2×#19145260 #25966462

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583518C211yesmaximal, characteristic
2C2×#14583510C211yesmaximal, characteristic, complemented
3#19145260C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583253C211yesmaximal, characteristic, complemented
6C2×#14583249C211yesmaximal, characteristic, complemented
7C2×#14583154C211yesmaximal, characteristic, complemented
8C2×#14583142C211yesmaximal, characteristic
9C2×#14583137C211yesmaximal, characteristic, complemented
10C2×#14583125C211yesmaximal, characteristic
11C2×#14583006C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×Q16×Dic43C211yesmaximal, characteristic, complemented
14C2×SD16×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582856C211yesmaximal, characteristic, complemented
16C2×C43×#497C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583518—24no—
20#14583518C2218yes—
21#14583510—24no—
22#14583510C2218yescomplemented
23C2×#13063325C2211yescharacteristic
24C2×#13063320—21no—
25C2×#13063320—21no—
26C2×#13063318—21no—
27C2×#13063317C2211yescharacteristic
28C2×#13063315—21no—
29C2×#13063315—21no—
30C2×#13063311—21no—
31C2×#13063309—21no—
32C2×#13063302—21no—
33C2×#13063301C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063301C2211yescharacteristic
36C2×#13063296C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×Q8×Dic43C2211yescharacteristic
39C2×Q8×Dic43C2211yescharacteristic
40C2×D4×Dic43C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583253C2218yescomplemented
44#14583249C2218yescomplemented
45#14583154C2218yescomplemented
46#14583142C2218yes—
47#14583137C2218yescomplemented
48#14583125C2218yes—
49#14583006C2218yescomplemented
50#14583000C2218yescomplemented
51Q16×Dic43C2218yescomplemented
52SD16×Dic43C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65#14582856C2218yescomplemented
66C2×#13063235C2211yescharacteristic
67C2×C4×C43⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×C4⋊Q8×C43C2211yescharacteristic
74C2×#124×C43C2211yescharacteristic
75C43×#497C2218yescomplemented
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×C22⋊D43—21no—
79C23×Dic43—21no—
80C22×C4×D43C2311yescharacteristic
81C2×#10621872—24no—
82C2×#10621872C2314yes—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—24no—
86C2×C8×D43C2314yes—
87#13063325—22no—
88#13063325C2314yes—
89#13063320—28no—
90#13063320—28no—
91#13063318—28no—
92#13063317—22no—
93#13063317C2314yes—
94#13063315—28no—
95#13063315—28no—
96#13063311—28no—
97#13063309—28no—
98#13063302—28no—
99#13063301—22no—
100#13063301—22no—
101#13063301—22no—
102#13063301C2314yes—
103#13063301C2314yes—
104#13063301C2314yes—
105#13063296—22no—
106#13063296C2314yes—
107Q8×Dic43—22no—
108Q8×Dic43—22no—
109Q8×Dic43—22no—
110Q8×Dic43C2314yes—
111Q8×Dic43C2314yes—
112Q8×Dic43C2314yes—
113D4×Dic43—22no—
114D4×Dic43C2314yes—
115#13063282D414yes—
116#13063282C2314yes—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C2×Dic43⋊C4D411yescharacteristic
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4D411yescharacteristic
138C2×(C2×D43)⋊C4D411yescharacteristic
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43C2311yescharacteristic
143#13063259C2314yes—
144#13063259C2314yes—
145#13063257C2314yes—
146#13063257C2314yes—
147#13063249C2314yes—
148#13063249C2314yes—
149#13063249C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063246C2314yes—
154#13063246C2314yes—
155#13063235C2314yes—
156C4×C43⋊C8C2314yes—
157C8×Dic43C2314yes—
158C22×Q8×C43C2311yescharacteristic
159C22×Q8×C43C2311yescharacteristic
160C22×Q8×C43C2311yescharacteristic
161C22×D4×C43C2311yescharacteristic
162C2×Q16×C43—24no—
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C2×Q16×C43C2314yes—
166C2×SD16×C43—24no—
167C2×SD16×C43—24no—
168C2×SD16×C43C2314yes—
169C2×SD16×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C4⋊Q8×C43—22no—
173C4⋊Q8×C43C2314yes—
174#124×C43—22no—
175#124×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#97×C43C2314yes—
182C24×C43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43C2412yes—
194C2×Q8×C43C2412yes—
195C2×Q8×C43C2412yes—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43C2412yes—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—82no—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—82no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43C2×D412yes—
220C2×C4×D43C2412yes—
221C2×Dic86—24no—
222C2×Dic86—82no—
223Q16×C43—28no—
224Q16×C43—28no—
225SD16×C43—28no—
226SD16×C43—28no—
227C2×C8×C43#4114yes—
228C2×C8×C43#4114yes—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C42×C43C2×D412yes—
236C42×C43C2412yes—
237C22⋊Dic43—24no—
238C22⋊Dic43—24no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4C2×D414yes—
243(C2×D43)⋊C4C2×D414yes—
244C4⋊Dic43—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43C2412yes—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4C2×D414yes—
262Dic43⋊C4C2×D414yes—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43C2×D412yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272#10621872—28no—
273C8×D43—28no—
274C23×C43—22no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43C22×D412yes—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—42no—
290Q8×C43—42no—
291Q8×C43—42no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—42no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4112yes—
307C2×C4×C43C2×#4112yes—
308C2×C4×C43C2511yescharacteristic
309C22⋊D43—84no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—84no—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C2×Dic43C22×D412yes—
325C4×D43—24no—
326C4×D43—22no—
327C4×D43—22no—
328Dic86—84no—
329C8×C43C2×#4114yes—
330C8×C43C2×#4114yes—
331C43⋊C8—22no—
332C43⋊C8—22no—
333C2×#3178—431nomaximal, Sylow
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—84no—
338C22×C43#53212yes—
339C22×C43#57712yes—
340C22×C43#57812yes—
341C22×C43C23×D411yescharacteristic
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—44no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43#53212yes—
352C4×C43C22×#4111yescharacteristic
353C4×C43C22×#4111yescharacteristic
354Dic43—22no—
355Dic43—22no—
356Dic43—22no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542—431no—
362C2×#541—431no—
363#3178—4316no—
364C2×#501—431no—
365C2×#497D4311yescharacteristic, complemented
366C2×#488—431no—
367C2×#487—431no—
368C2×#470—431no—
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#441—431no—
373C2×#440—431no—
374C2×C4×Q16—431no—
375C2×C4×SD16—431no—
376C2×#405—431no—
377C2×C43—82no—
378C2×C43#317814yescomplemented
379C2×C43C2×#53211yescharacteristic
380C2×C43C2×#57711yescharacteristic
381C2×C43C2×#57811yescharacteristic
382D43—42no—
383C22×Q16C2×D4311yescharacteristic
384C22×Q16C2×D4311yescharacteristic
385C22×SD16C2×D4311yescharacteristic
386C22×SD16C2×D4311yescharacteristic
387C22×M16—431no—
388C23×C8—431no—
389#542—438no—
390#542—864no—
391#541—438no—
392#541—864no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8C2×D4311yescharacteristic
395C2×#126—861no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×#124—861no—
402C2×#124C2×D4311yescharacteristic
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×D4—431no—
413C2×#117—431no—
414#501—438no—
415#497C2×D4318yescomplemented
416#488—438no—
417#487—438no—
418#470—438no—
419#468—438no—
420#467—438no—
421#465—438no—
422#441—438no—
423#440—438no—
424C4×Q16—438no—
425C4×SD16—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×#106—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#102—431no—
437C2×#102—431no—
438#405—438no—
439C2×#97—431no—
440C2×#97C2×D4311yescharacteristic
441C2×C4×C8—431no—
442C2×C4×C8—431no—
443C43C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—861no—
445C22×Q8C22×D4311yescharacteristic
446C22×Q8C22×D4311yescharacteristic
447C22×Q8C22×D4311yescharacteristic
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—431no—
451C23×C4—861no—
452C2×Q16—24no—
453C2×Q16—24no—
454C2×Q16C22×D4314yes—
455C2×Q16C22×D4314yes—
456C2×SD16—24no—
457C2×SD16—24no—
458C2×SD16C22×D4314yes—
459C2×SD16C22×D4314yes—
460C2×M16—434no—
461C2×M16—864no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—434no—
465C22×C8—864no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C4⋊Q8—22no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8C22×D4314yes—
472#126—868no—
473#126—868no—
474#126—868no—
475#125—434no—
476#125—868no—
477#125—868no—
478#125—862no—
479#124—22no—
480#124—868no—
481#124C22×D4314yes—
482#123—868no—
483C22⋊Q8—434no—
484C22⋊Q8—434no—
485C22⋊Q8—434no—
486C22⋊Q8—868no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490#121—434no—
491#121—862no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—862no—
498C4×D4—434no—
499C4×D4—862no—
500#117—434no—
501#117—434no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—431no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42—861no—
532C2×C42C22×D4311yescharacteristic
533#107—434no—
534#107—434no—
535#106—434no—
536#106—434no—
537#103—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#103—434no—
542#103—434no—
543#102—434no—
544#102—434no—
545#97—434no—
546#97C22×D4314yes—
547C4×C8—434no—
548C4×C8—434no—
549C24—21no—
550C24—431no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—864no—
561C2×Q8—3442no—
562C2×Q8C23×D4312yes—
563C2×Q8C23×D4312yes—
564C2×Q8C23×D4312yes—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—864no—
569C2×D4—3442no—
570C2×D4C23×D4312yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—864no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—3442no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590Q16—28no—
591Q16—28no—
592SD16—28no—
593SD16—28no—
594M16—868no—
595C2×C8—432no—
596C2×C8—432no—
597C2×C8—862no—
598C2×C8—862no—
599C2×C8—868no—
600C2×C8#1062190014yes—
601C2×C8#1062190014yes—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—434no—
607C4⋊C4—434no—
608C4⋊C4—432no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—434no—
628C22⋊C4—434no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C42—432no—
635C42—432no—
636C42—864no—
637C42—864no—
638C42—864no—
639C42D4×D4312yes—
640C42C23×D4312yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—432no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23C2×D4×D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—3444no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—3444no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—432no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—864no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—3444no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4C2×D4×D4312yes—
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4C2×#1062190012yes—
694C2×C4C2×#1062190012yes—
695C2×C4C24×D4311yescharacteristic
696C8—862no—
697C8—862no—
698C8C2×#1062190014yes—
699C8C2×#1062190014yes—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—1724no—
708C22#1458344712yes—
709C22#1458370812yes—
710C22#1458371512yes—
711C22C22×D4×D4311yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—862no—
718C4—862no—
719C4—862no—
720C4—1722no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458344712yes—
725C4C22×#1062190011yescharacteristic
726C4C22×#1062190011yescharacteristic
727C2—82no—
728C2—1722no—
729C2#1914526014yesdirect product factor
730C2C2×#1458344711yescharacteristic
731C2C2×#1458370811yescharacteristic
732C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#497C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#497D43
hypocenterC43C2×#3178
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. C2×#14583510C2semidirect
3. #19145260C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583253C2semidirect
6. C2×#14583249C2semidirect
7. C2×#14583154C2semidirect
9. C2×#14583137C2semidirect
11. C2×#14583006C2semidirect
12. C2×#14583000C2semidirect
13. C2×Q16×Dic43C2semidirect
14. C2×SD16×Dic43C2semidirect
15. C2×#14582856C2semidirect
16. C2×C43×#497C2semidirect
22. #14583510C22semidirect
42. #14583308C22semidirect
43. #14583253C22semidirect
44. #14583249C22semidirect
45. #14583154C22semidirect
47. #14583137C22semidirect
49. #14583006C22semidirect
50. #14583000C22semidirect
51. Q16×Dic43C22semidirect
52. SD16×Dic43C22semidirect
65. #14582856C22semidirect
75. C43×#497C22semidirect
365. C2×#497D43semidirect
378. C2×C43#3178semidirect
415. #497C2×D43semidirect
443. C43C2×#3178semidirect
729. C2#19145260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835182
C2×#145835102
#191452602
C2×#145833082
C2×#145832532
C2×#145832492
C2×#145831542
C2×#145831422
C2×#145831372
C2×#145831252
C2×#145830062
C2×#145830002
C2×Q16×Dic432
C2×SD16×Dic432
C2×#145828562
C2×C43×#4972
C2×#317843