Finite Group Databasebeta

← C2×#19147076 #25975172

Subgroups — C2×#19147076 #25975172

Order 11008.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583604C211yesmaximal, characteristic, complemented
2C2×#14583597C211yesmaximal, characteristic
3#19147076C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583234C211yesmaximal, characteristic, complemented
6C2×#14583217C211yesmaximal, characteristic, complemented
7C2×#14583242C211yesmaximal, characteristic, complemented
8C2×#14583214C211yesmaximal, characteristic, complemented
9C2×#14583205C211yesmaximal, characteristic, complemented
10C2×#14583178C211yesmaximal, characteristic, complemented
11C2×#14583146C211yesmaximal, characteristic, complemented
12C2×#14583128C211yesmaximal, characteristic, complemented
13C2×#14582998C211yesmaximal, characteristic, complemented
14C2×#14582970C211yesmaximal, characteristic, complemented
15C2×#14582940C211yesmaximal, characteristic, complemented
16C22×#107×C43C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583604—24no—
20#14583604C2218yescomplemented
21#14583597—24no—
22#14583597C2218yes—
23C2×#13063324C2211yescharacteristic
24C2×#13063320—21no—
25C2×#13063316C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063310—21no—
28C2×#13063305C2211yescharacteristic
29C2×#13063304—21no—
30C2×#13063304C2211yescharacteristic
31C2×#13063303—21no—
32C2×#13063300C2211yescharacteristic
33C2×#13063299—21no—
34C2×#13063299C2211yescharacteristic
35C2×#13063290C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583307C2218yescomplemented
43#14583242C2218yescomplemented
44#14583234C2218yescomplemented
45#14583217C2218yescomplemented
46#14583214C2218yescomplemented
47#14583205C2218yescomplemented
48#14583178C2218yescomplemented
49#14583146C2218yescomplemented
50#14583128C2218yescomplemented
51#14582998C2218yescomplemented
52#14582970C2218yescomplemented
53#14582940C2218yescomplemented
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×#107×C43C2211yescharacteristic
75C2×#107×C43C2211yescharacteristic
76C2×#107×C43C2218yescomplemented
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43D411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621873—24no—
87C2×#10621873C2314yes—
88C2×#10621872—24no—
89C2×#10621872C2314yes—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063324—22no—
93#13063324C2314yes—
94#13063320—28no—
95#13063316—22no—
96#13063316C2314yes—
97#13063315—28no—
98#13063310—28no—
99#13063305—22no—
100#13063305C2314yes—
101#13063304—22no—
102#13063304—28no—
103#13063304C2314yes—
104#13063303—28no—
105#13063300—22no—
106#13063300C2314yes—
107#13063299—22no—
108#13063299—28no—
109#13063299C2314yes—
110#13063290—22no—
111#13063290C2314yes—
112#13063287—22no—
113#13063287C2314yes—
114C4×C22⋊D43—28no—
115C4×C22⋊D43—28no—
116C4×C22⋊D43D414yes—
117C4×C22⋊D43C2314yes—
118#13063283—22no—
119#13063283C2314yes—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4D411yescharacteristic
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2314yes—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43D411yescharacteristic
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43C2311yescharacteristic
143#13063258C2314yes—
144#13063258C2314yes—
145#13063257C2314yes—
146#13063256C2314yes—
147#13063256C2314yes—
148Dic43⋊C8C2314yes—
149#13063250C2314yes—
150#13063248C2314yes—
151#13063248C2314yes—
152#13063247C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156(C2×D43)⋊C8C2314yes—
157#13063235C2314yes—
158C23×C4×C43—21no—
159C23×C4×C43—21no—
160C23×C4×C43C2311yescharacteristic
161C22×C8×C43—24no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2314yes—
164C22×C8×C43C2311yescharacteristic
165C2×C4⋊C4×C43—22no—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2314yes—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2314yes—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175#107×C43C2314yes—
176#107×C43C2314yes—
177#107×C43C2314yes—
178#107×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—24no—
189C22×C4×C43—24no—
190C22×C4×C43—82no—
191C22×C4×C43—82no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—44no—
199C2×C22⋊D43C2×D414yes—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C2×D172—21no—
207C2×D172—24no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—82no—
211C2×D172C2412yes—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—82no—
217C2×C4×D43—82no—
218C2×C4×D43C2×D412yes—
219C2×C4×D43C2412yes—
220C2×Dic86—22no—
221C2×Dic86—22no—
222C2×Dic86—21no—
223C2×Dic86—24no—
224C2×Dic86—82no—
225C2×Dic86C2412yes—
226C2×C8×C43—22no—
227C2×C8×C43—28no—
228C2×C8×C43#4114yes—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43C2×D414yes—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4C2×D414yes—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43C2×D412yes—
264C4×Dic43C2412yes—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269#10621873—28no—
270#10621872—28no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43#13714yes—
274C23×C43C22×D412yes—
275C23×C43C22×D411yescharacteristic
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43C22×D412yes—
284C2×C4×C43—22no—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—84no—
297C2×C4×C43—84no—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4112yes—
301C2×C4×C432−1+412yes—
302C2×C4×C43C2511yescharacteristic
303C22⋊D43—28no—
304C22⋊D43—48no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317D172—22no—
318D172—22no—
319D172—42no—
320D172—84no—
321C4×D43—24no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—84no—
325C4×D43—84no—
326Dic86—22no—
327Dic86—22no—
328Dic86—42no—
329Dic86—84no—
330C8×C43—22no—
331C8×C43C2×#4114yes—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C2×#3346—431nomaximal, Sylow
335C22×C43—28no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43#54712yes—
339C22×C43C2×#13714yes—
340C22×C43C2×#13712yes—
341C22×C43#57612yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—44no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—84no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43#54712yes—
357C4×C43C22×#4111yescharacteristic
358C4×C43C2×2−1+411yescharacteristic
359Dic43—22no—
360Dic43—22no—
361Dic43—22no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365C2×#554—431no—
366C2×#553—431no—
367#3346—4316no—
368C2×#501—431no—
369C2×#484—431no—
370C2×#481—431no—
371C2×#485—431no—
372C2×#480—431no—
373C2×#479—431no—
374C2×#474—431no—
375C2×#468—431no—
376C2×#465—431no—
377C2×#440—431no—
378C2×#435—431no—
379C2×#428—431no—
380C22×#107D4311yescharacteristic, complemented
381C2×C43—24no—
382C2×C43#334614yescomplemented
383C2×C43C2×#54711yescharacteristic
384C2×C43C22×#13711yescharacteristic
385C2×C43C2×#57611yescharacteristic
386D43—42no—
387D43—82no—
388C22×SD16—431no—
389C22×M16—431no—
390C23×C8C2×D4311yescharacteristic
391#554—438no—
392#554—864no—
393#553—438no—
394#553—864no—
395C2×C4⋊Q8—431no—
396C2×#126—861no—
397C2×#125—431no—
398C2×#125—861no—
399C2×#123—861no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—431no—
402C2×C22⋊Q8—861no—
403C2×C22⋊Q8—861no—
404C2×#121—431no—
405C2×#121—431no—
406C2×#121—861no—
407C2×C4×Q8—431no—
408C2×C4×D4—431no—
409C2×C4×D4—431no—
410C2×C4×D4—861no—
411C2×C4×D4—861no—
412C2×#117—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4C2×D4311yescharacteristic
415C22×C4⋊C4C2×D4311yescharacteristic
416#501—438no—
417#485—438no—
418#484—438no—
419#481—438no—
420#480—438no—
421#479—438no—
422#474—438no—
423#468—438no—
424#465—438no—
425#440—438no—
426#435—438no—
427#428—438no—
428C2×#107—431no—
429C2×#107—431no—
430C2×#107C2×D4311yescharacteristic
431C2×#107C2×D4311yescharacteristic
432C2×#107C2×D4311yescharacteristic
433C2×#107C2×D4311yescharacteristic
434C2×#107C2×D4318yescomplemented
435C2×#106—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×C4⋊C8—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×#97—431no—
448C43C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—431no—
450C22×Q8—861no—
451C22×D4—431no—
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4C22×D4311yescharacteristic
461C2×SD16—434no—
462C2×SD16—864no—
463C2×M16—434no—
464C2×M16—864no—
465C22×C8—24no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4314yes—
470C22×C8C22×D4311yescharacteristic
471C4⋊Q8—434no—
472C4⋊Q8—862no—
473#126—868no—
474#125—434no—
475#125—862no—
476#125—868no—
477#123—868no—
478C22⋊Q8—434no—
479C22⋊Q8—434no—
480C22⋊Q8—868no—
481C22⋊Q8—868no—
482C22⋊Q8—862no—
483C22⋊Q8—862no—
484#121—434no—
485#121—434no—
486#121—862no—
487#121—868no—
488#121—862no—
489C4×Q8—434no—
490C4×Q8—862no—
491C4×D4—434no—
492C4×D4—434no—
493C4×D4—434no—
494C4×D4—862no—
495C4×D4—868no—
496C4×D4—868no—
497#117—434no—
498#117—862no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—434no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C4⋊C4C22×D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4314yes—
520C2×C4⋊C4C22×D4314yes—
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×C22⋊C4—861no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532#107—434no—
533#107—434no—
534#107C22×D4314yes—
535#107C22×D4314yes—
536#107C22×D4314yes—
537#107C22×D4314yes—
538#106—434no—
539#106—434no—
540#106—434no—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#102—434no—
546#102—434no—
547#102—434no—
548C22⋊C8—434no—
549C22⋊C8—434no—
550#97—434no—
551C24—431no—
552C24—861no—
553C24D4×D4311yescharacteristic
554C2×Q8—432no—
555C2×Q8—864no—
556C2×Q8—861no—
557C2×Q8—862no—
558C2×Q8—862no—
559C2×Q8—3442no—
560C2×D4—434no—
561C2×D4—432no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—864no—
565C2×D4—861no—
566C2×D4—862no—
567C2×D4—862no—
568C2×D4—3442no—
569C2×D4—1724no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—3442no—
593C22×C4—3442no—
594C22×C4D4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4C23×D4312yes—
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599M16—868no—
600C2×C8—22no—
601C2×C8—28no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—862no—
605C2×C8—862no—
606C2×C8#1062189814yes—
607C2×C8C23×D4312yes—
608C2×C8C23×D4312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—434no—
616C4⋊C4—432no—
617C4⋊C4—432no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—864no—
627C4⋊C4C23×D4312yes—
628C4⋊C4C23×D4312yes—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—434no—
632C22⋊C4—434no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—432no—
640C42—432no—
641C42—864no—
642C42—864no—
643C23—22no—
644C23—22no—
645C23—432no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—1722no—
651C23—1722no—
652C23—1722no—
653C23#1306335714yes—
654C23C2×D4×D4312yes—
655C23C2×D4×D4311yescharacteristic
656Q8—862no—
657Q8—862no—
658Q8—3444no—
659Q8—1722no—
660D4—868no—
661D4—862no—
662D4—862no—
663D4—3444no—
664D4—1728no—
665D4—1722no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—864no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—3444no—
693C2×C4—3444no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4C2×D4×D4312yes—
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4C2×#1062189812yes—
700C2×C4#1306337312yes—
701C2×C4C24×D4311yescharacteristic
702C8—22no—
703C8—862no—
704C8—862no—
705C8C2×#1062189814yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—862no—
710C22—862no—
711C22—862no—
712C22—3444no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1724no—
717C22#1458355012yes—
718C22C2×#1306335714yes—
719C22C2×#1306335712yes—
720C22#1458370012yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—862no—
728C4—862no—
729C4—862no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4#1458355012yes—
734C4C22×#1062189811yescharacteristic
735C4C2×#1306337311yescharacteristic
736C2—24no—
737C2—3442no—
738C2—1722no—
739C2#1914707614yesdirect product factor
740C2C2×#1458355011yescharacteristic
741C2C22×#1306335711yescharacteristic
742C2C2×#1458370011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#107×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583597C2
hypercenterC22×#107D43
hypocenterC43C2×#3346
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14583604C2semidirect
3. #19147076C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583234C2semidirect
6. C2×#14583217C2semidirect
7. C2×#14583242C2semidirect
8. C2×#14583214C2semidirect
9. C2×#14583205C2semidirect
10. C2×#14583178C2semidirect
11. C2×#14583146C2semidirect
12. C2×#14583128C2semidirect
13. C2×#14582998C2semidirect
14. C2×#14582970C2semidirect
15. C2×#14582940C2semidirect
16. C22×#107×C43C2semidirect
20. #14583604C22semidirect
42. #14583307C22semidirect
43. #14583242C22semidirect
44. #14583234C22semidirect
45. #14583217C22semidirect
46. #14583214C22semidirect
47. #14583205C22semidirect
48. #14583178C22semidirect
49. #14583146C22semidirect
50. #14583128C22semidirect
51. #14582998C22semidirect
52. #14582970C22semidirect
53. #14582940C22semidirect
76. C2×#107×C43C22semidirect
380. C22×#107D43semidirect
382. C2×C43#3346semidirect
434. C2×#107C2×D43semidirect
448. C43C2×#3346semidirect
739. C2#19147076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145835972
#191470762
C2×#145833072
C2×#145832342
C2×#145832172
C2×#145832422
C2×#145832142
C2×#145832052
C2×#145831782
C2×#145831462
C2×#145831282
C2×#145829982
C2×#145829702
C2×#145829402
C22×#107×C432
C2×#334643