Finite Group Databasebeta

← C2×#11737221 #14217902

Subgroups — C2×#11737221 #14217902

Order 1792.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6478C211yesmaximal, characteristic
2C2×#90263C211yesmaximal, characteristic, complemented
3C2×#90237C211yesmaximal, characteristic
4C2×C7×#440C211yesmaximal, characteristic, complemented
5C2×SD16×Dic7C211yesmaximal, characteristic, complemented
6C2×C4×#1144C211yesmaximal, characteristic, complemented
7C2×C4×#1142C211yesmaximal, characteristic, complemented
8#11737221C2116yesmaximal, direct product factor
9C2×#89653C211yesmaximal, characteristic, complemented
10C2×#89645C211yesmaximal, characteristic, complemented
11C2×D7×#103C211yesmaximal, characteristic, complemented
12C2×#89561C211yesmaximal, characteristic, complemented
13C2×#89544C211yesmaximal, characteristic
14C2×#89529C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89480C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C2×C4×C22⋊D7—21no—
27C22×Dic7⋊C4—21no—
28C2×#6478C4116yescomplemented
29C2×#6478C2218yes—
30C22×Dic28C2211yescharacteristic
31C22×#1131C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90263—24no—
34#90263C2218yescomplemented
35#90237—24no—
36#90237C2218yes—
37C2×#6455—21no—
38C2×#6455C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6450—21no—
41C2×#6450C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×(C22⋊D7)⋊C4—21no—
44C2×#6440—21no—
45C2×#6435—21no—
46C2×#6435C2211yescharacteristic
47C2×C4×Dic14—21no—
48C2×C4×Dic14C2211yescharacteristic
49C2×C4×Dic14C2211yescharacteristic
50C7×#440C2218yescomplemented
51C2×C7×#107C2211yescharacteristic
52C2×C7×#103C2211yescharacteristic
53C2×C7×#102C2211yescharacteristic
54C2×C7×#97C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57SD16×Dic7C2218yescomplemented
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6390C2211yescharacteristic
61C2×#6389C2211yescharacteristic
62C2×C8×Dic7C2211yescharacteristic
63C4×#1144C2218yescomplemented
64C4×#1142C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×C4×C7⋊C8C2211yescharacteristic
70#89653C2218yescomplemented
71#89645C2218yescomplemented
72D7×#103C2218yescomplemented
73#89561C2218yescomplemented
74#89544C2218yes—
75#89529C2218yescomplemented
76#89488C2218yescomplemented
77#89480C2218yescomplemented
78C2×#2947—71nomaximal, Sylow
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C2×Q8×D7—22no—
86C2×Q8×D7—24no—
87C2×Q8×D7C2×C418yescomplemented
88C2×Q8×D7C2314yes—
89C2×#1159—22no—
90C2×#1159—24no—
91C2×#1159C2×C418yes—
92C2×#1159C2314yes—
93C22×C4×D7—21no—
94C22×C4×D7—21no—
95C22×C4×D7C2311yescharacteristic
96C22×Dic14—21no—
97C22×Dic14C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C2×C7×SD16C2×C418yescomplemented
100C2×C7×SD16C2314yes—
101C22×C7×C8C2311yescharacteristic
102C22×C7×C8C2311yescharacteristic
103C4×C7×Q8—22no—
104C4×C7×Q8C2314yes—
105C4×C7×D4—22no—
106C4×C7×D4C2314yes—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C42×C7—21no—
112C2×C42×C7C2311yescharacteristic
113C2×C22⋊Dic7—21no—
114Q8×Dic7—22no—
115Q8×Dic7C2314yes—
116C2×#1144C2×C418yescomplemented
117C2×#1144C2314yes—
118D4×Dic7—22no—
119D4×Dic7C2314yes—
120C2×#1142C2×C418yescomplemented
121C2×#1142C2314yes—
122C4×C22⋊D7—28no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4D411yescharacteristic
125C2×(C2×D7)⋊C4D411yescharacteristic
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—28no—
135C2×Dic7⋊C4D411yescharacteristic
136C2×Dic7⋊C4D411yescharacteristic
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6478C2×C4164yescomplemented
147C2×Dic28C2×C418yescomplemented
148C2×Dic28C2314yes—
149C2×#1131C2×C418yescomplemented
150C2×#1131C2314yes—
151C2×C8×D7—24no—
152C2×C8×D7C2314yes—
153#6455—22no—
154#6455—28no—
155#6455C2314yes—
156D7×C4⋊C4—22no—
157D7×C4⋊C4C2314yes—
158#6450—28no—
159#6450—22no—
160#6450—22no—
161#6450C2314yes—
162#6450C2314yes—
163(C22⋊D7)⋊C4—28no—
164#6440—28no—
165#6435—28no—
166#6435D414yes—
167#6435C2314yes—
168C4×Dic14—22no—
169C4×Dic14—22no—
170C4×Dic14—28no—
171C4×Dic14C2314yes—
172C4×Dic14C2314yes—
173C7×#107C2314yes—
174C7×#103C2314yes—
175C7×#102C2314yes—
176C7×#97C2314yes—
177#6409C2314yes—
178#6406C2314yes—
179#6391C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6389C2314yes—
183C8×Dic7C2314yes—
184#6384C2314yes—
185#6384C2314yes—
186#6382C2314yes—
187#6381C2314yes—
188C4×C7⋊C8C2314yes—
189C22×#137—71no—
190C2×#520—71no—
191C2×#519—71no—
192#2947—716no—
193C2×#441—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×#440D711yescharacteristic, complemented
197C2×C4×Q16—71no—
198C2×C4×Q16—71no—
199C2×C4×SD16—71no—
200C2×C4×SD16—71no—
201C2×#428—71no—
202C2×#416—71no—
203C22×#103—71no—
204C2×#405—71no—
205C24×C7—21no—
206C23×D7C2×D411yescharacteristic
207C2×C7×Q8—21no—
208C2×C7×Q8—22no—
209C2×C7×Q8C22×C414yes—
210C2×C7×Q8C2412yes—
211C2×C7×D4—21no—
212C2×C7×D4—22no—
213C2×C7×D4C22×C414yes—
214C2×C7×D4C2412yes—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—24no—
219C22×C4×C7—82no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2411yescharacteristic
223C2×C22⋊D7—28no—
224C2×C22⋊D7—24no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—28no—
228C22×Dic7—24no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—24no—
232C22×Dic7—82no—
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C22×Dic7C2×D411yescharacteristic
236Q8×D7—216no—
237Q8×D7—28no—
238Q8×D7C22×C4116yescomplemented
239#1159—216no—
240#1159—28no—
241#1159C22×C4116yes—
242C2×C4×D7—28no—
243C2×C4×D7—24no—
244C2×C4×D7—24no—
245C2×C4×D7—82no—
246C2×C4×D7C22×C414yes—
247C2×C4×D7C2×D412yes—
248C2×C4×D7#4114yes—
249C2×C4×D7C2412yes—
250C2×Dic14—21no—
251C2×Dic14—21no—
252C2×Dic14—22no—
253C2×Dic14—22no—
254C2×Dic14—28no—
255C2×Dic14—24no—
256C2×Dic14C22×C414yes—
257C2×Dic14C22×C414yes—
258C2×Dic14C2412yes—
259C2×Dic14C2412yes—
260C7×SD16C22×C4116yescomplemented
261C2×C7×C8—22no—
262C2×C7×C8C22×C414yes—
263C2×C7×C8C2412yes—
264C2×C7×C8C2412yes—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C22⋊C4—24no—
271C42×C7—24no—
272C42×C7C2×D412yes—
273C42×C7C2412yes—
274C22⋊Dic7—24no—
275#1144C22×C4116yescomplemented
276#1142C22×C4116yescomplemented
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4C2×D414yes—
279(C2×D7)⋊C4C2×D414yes—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—24no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4C2×D414yes—
291Dic7⋊C4C2×D414yes—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C4×Dic7—24no—
298C4×Dic7C2×D412yes—
299C4×Dic7C2412yes—
300C2×C7⋊C8—22no—
301C2×C7⋊C8C22×C414yes—
302C2×C7⋊C8C2412yes—
303C2×C7⋊C8C2412yes—
304Dic28C22×C4116yescomplemented
305#1131C22×C4116yescomplemented
306C8×D7—28no—
307C22×#41—71no—
308C23×Q8—71no—
309C2×#137—716no—
310C2×#137—78no—
311C22×Q16—71no—
312C22×Q16—71no—
313C22×SD16—71no—
314C22×SD16C2×D711yescharacteristic
315C22×M16—71no—
316C23×C8—71no—
317#520—78no—
318#520—144no—
319#519—78no—
320#519—144no—
321C2×C4×Q8—71no—
322C2×C4×Q8—71no—
323C2×C4×Q8—71no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8—141no—
327C2×C4×Q8—141no—
328C2×C4×Q8C2×D711yescharacteristic
329C2×C4×D4—71no—
330C2×C4×D4—141no—
331C2×C4×D4—141no—
332C2×C4×D4C2×D711yescharacteristic
333C2×#117—71no—
334C2×#117—71no—
335C2×#117—141no—
336C2×#117—141no—
337C2×#117—141no—
338C22×C4⋊C4—71no—
339C22×C4⋊C4—141no—
340#441—78no—
341#441—78no—
342#440—78no—
343#440C2×D718yescomplemented
344C4×Q16—78no—
345C4×Q16—78no—
346C4×SD16—78no—
347C4×SD16—78no—
348#428—78no—
349C2×#107—71no—
350C2×#107C2×D711yescharacteristic
351C2×#106—71no—
352C2×#106—71no—
353#416—78no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—78no—
360C2×#103C2×D711yescharacteristic
361C2×#102—71no—
362C2×#102C2×D711yescharacteristic
363#405—78no—
364C2×#97—71no—
365C2×#97C2×D711yescharacteristic
366C2×C4×C8—71no—
367C2×C4×C8—71no—
368C23×C7—24no—
369C23×C7—22no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7C22×D411yescharacteristic
373C22×D7—22no—
374C22×D7—22no—
375C22×D7C4×D414yes—
376C22×D7C22×D412yes—
377C7×Q8—24no—
378C7×Q8—22no—
379C7×Q8C23×C414yes—
380C7×D4—24no—
381C7×D4—22no—
382C7×D4C23×C414yes—
383C2×C4×C7—24no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—84no—
392C2×C4×C7C23×C412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D411yescharacteristic
396C2×C4×C7C2×#4112yes—
397C2×C4×C7C2511yescharacteristic
398C22⋊D7—216no—
399C2×Dic7—24no—
400C2×Dic7—24no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—216no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—42no—
409C2×Dic7—42no—
410C2×Dic7—84no—
411C2×Dic7C4×D414yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415C4×D7—216no—
416C4×D7—84no—
417C4×D7C4×D418yes—
418C4×D7C23×C414yes—
419C4×D7C2×#4114yes—
420Dic14—24no—
421Dic14—24no—
422Dic14—22no—
423Dic14—22no—
424Dic14—216no—
425Dic14C23×C414yes—
426Dic14C23×C414yes—
427C7×C8—22no—
428C7×C8C23×C414yes—
429C7⋊C8—22no—
430C7⋊C8C23×C414yes—
431C2×#41—78no—
432C2×#41—74no—
433C2×#41—142no—
434C2×#41—144no—
435C22×Q8—78no—
436C22×Q8—74no—
437C22×Q8—71no—
438C22×Q8—71no—
439C22×Q8—141no—
440C22×Q8—142no—
441C22×Q8—144no—
442C22×Q8C22×D711yescharacteristic
443C22×D4—141no—
444C22×D4C22×D711yescharacteristic
445C23×C4—21no—
446C23×C4—71no—
447C23×C4—141no—
448C23×C4—141no—
449C23×C4—141no—
450C23×C4—141no—
451#137—764no—
452C2×Q16—78no—
453C2×Q16—74no—
454C2×Q16—78no—
455C2×Q16—74no—
456C2×SD16—78no—
457C2×SD16—74no—
458C2×SD16C4×D718yescomplemented
459C2×SD16C22×D714yes—
460C2×M16—78no—
461C2×M16—74no—
462C22×C8—71no—
463C22×C8—71no—
464C22×C8—74no—
465C22×C8—144no—
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D711yescharacteristic
468C4×Q8—22no—
469C4×Q8—74no—
470C4×Q8—74no—
471C4×Q8—74no—
472C4×Q8—74no—
473C4×Q8—74no—
474C4×Q8—148no—
475C4×Q8—142no—
476C4×Q8—142no—
477C4×Q8—142no—
478C4×Q8—148no—
479C4×Q8—142no—
480C4×Q8—142no—
481C4×Q8C22×D714yes—
482C4×D4—22no—
483C4×D4—74no—
484C4×D4—142no—
485C4×D4—148no—
486C4×D4—148no—
487C4×D4C22×D714yes—
488#117—74no—
489#117—74no—
490#117—74no—
491#117—148no—
492#117—148no—
493#117—148no—
494#117—142no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—74no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—148no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4C22×D711yescharacteristic
510C2×C4⋊C4C22×D711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—71no—
513C2×C22⋊C4—71no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C42—21no—
517C2×C42—71no—
518C2×C42—141no—
519C2×C42—141no—
520C2×C42—141no—
521C2×C42—141no—
522C2×C42—141no—
523C2×C42—141no—
524C2×C42C22×D711yescharacteristic
525#107—74no—
526#107C22×D714yes—
527#106—74no—
528#106—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103—74no—
533#103—74no—
534#103C22×D714yes—
535#102—74no—
536#102C22×D714yes—
537#97—74no—
538#97C22×D714yes—
539C4×C8—74no—
540C4×C8—74no—
541C22×C7—24no—
542C22×C7—48no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7C2×C4×D412yes—
546C22×C7#57712yes—
547C22×C7#57812yes—
548C22×C7C23×D411yescharacteristic
549C2×D7—28no—
550C2×D7—22no—
551C2×D7—22no—
552C2×D7C2×C4×D414yes—
553C4×C7—24no—
554C4×C7—22no—
555C4×C7—22no—
556C4×C7—42no—
557C4×C7—42no—
558C4×C7C2×C4×D412yes—
559C4×C7C24×C411yescharacteristic
560C4×C7C22×#4111yescharacteristic
561Dic7—24no—
562Dic7—24no—
563Dic7—22no—
564Dic7—22no—
565Dic7—42no—
566Dic7—42no—
567Dic7C2×C4×D414yes—
568C24—21no—
569C24—71no—
570#41—716no—
571#41—1416no—
572#41—148no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—716no—
576C2×Q8—74no—
577C2×Q8—74no—
578C2×Q8—72no—
579C2×Q8—72no—
580C2×Q8—144no—
581C2×Q8—148no—
582C2×Q8—1416no—
583C2×Q8—148no—
584C2×Q8—141no—
585C2×Q8—141no—
586C2×Q8—142no—
587C2×Q8—142no—
588C2×Q8C2×C4×D714yes—
589C2×Q8C23×D712yes—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—144no—
593C2×D4—148no—
594C2×D4C2×C4×D714yes—
595C2×D4C23×D712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—71no—
601C22×C4—74no—
602C22×C4—72no—
603C22×C4—74no—
604C22×C4—72no—
605C22×C4—71no—
606C22×C4—71no—
607C22×C4—82no—
608C22×C4—144no—
609C22×C4—148no—
610C22×C4—144no—
611C22×C4—144no—
612C22×C4—148no—
613C22×C4—144no—
614C22×C4—141no—
615C22×C4—141no—
616C22×C4—141no—
617C22×C4—141no—
618C22×C4—562no—
619C22×C4—562no—
620C22×C4D4×D711yescharacteristic
621C22×C4D4×D711yescharacteristic
622C22×C4C23×D711yescharacteristic
623Q16—716no—
624Q16—716no—
625SD16—716no—
626SD16C2×C4×D7116yescomplemented
627M16—716no—
628C2×C8—22no—
629C2×C8—74no—
630C2×C8—72no—
631C2×C8—72no—
632C2×C8—148no—
633C2×C8—142no—
634C2×C8C2×C4×D714yes—
635C2×C8C23×D712yes—
636C2×C8C23×D712yes—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—74no—
641C4⋊C4—74no—
642C4⋊C4—72no—
643C4⋊C4—72no—
644C4⋊C4—144no—
645C4⋊C4—144no—
646C4⋊C4—144no—
647C4⋊C4—144no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—141no—
651C4⋊C4—141no—
652C4⋊C4C23×D712yes—
653C4⋊C4C23×D712yes—
654C22⋊C4—24no—
655C22⋊C4—74no—
656C22⋊C4—74no—
657C22⋊C4—144no—
658C22⋊C4—144no—
659C42—24no—
660C42—72no—
661C42—72no—
662C42—144no—
663C42—144no—
664C42—144no—
665C42—144no—
666C42—144no—
667C42—144no—
668C42D4×D712yes—
669C42C23×D712yes—
670C2×C7—44no—
671C2×C7#294714yescomplemented
672C2×C7C22×C4×D411yescharacteristic
673C2×C7C2×#57711yescharacteristic
674C2×C7C2×#57811yescharacteristic
675D7—24no—
676C23—24no—
677C23—22no—
678C23—42no—
679C23—42no—
680C23—74no—
681C23—72no—
682C23—142no—
683C23—142no—
684C23C2×D4×D711yescharacteristic
685Q8—24no—
686Q8—22no—
687Q8—74no—
688Q8—74no—
689Q8—1416no—
690Q8—144no—
691Q8—144no—
692Q8—142no—
693Q8—142no—
694Q8C22×C4×D714yes—
695D4—24no—
696D4—22no—
697D4—1416no—
698D4C22×C4×D714yes—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—74no—
708C2×C4—72no—
709C2×C4—78no—
710C2×C4—74no—
711C2×C4—74no—
712C2×C4—72no—
713C2×C4—72no—
714C2×C4—84no—
715C2×C4—1416no—
716C2×C4—1416no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—144no—
720C2×C4—144no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—564no—
728C2×C4—564no—
729C2×C4C22×C4×D712yes—
730C2×C4C2×D4×D712yes—
731C2×C4C2×D4×D712yes—
732C2×C4C2×D4×D711yescharacteristic
733C2×C4D7×#4112yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—74no—
737C8—142no—
738C8C22×C4×D714yes—
739C7C2×#294711yescharacteristic, complemented, Sylow
740C22—24no—
741C22—42no—
742C22—42no—
743C22—48no—
744C22—74no—
745C22—142no—
746C22—142no—
747C22—148no—
748C22C4×D4×D712yes—
749C22#9046612yes—
750C22#9047012yes—
751C22C22×D4×D711yescharacteristic
752C4—22no—
753C4—22no—
754C4—24no—
755C4—42no—
756C4—42no—
757C4—74no—
758C4—142no—
759C4—142no—
760C4—144no—
761C4—144no—
762C4—282no—
763C4—282no—
764C4C4×D4×D712yes—
765C4C23×C4×D711yescharacteristic
766C4C2×D7×#4111yescharacteristic
767C2—44no—
768C2—144no—
769C2#1173722114yesdirect product factor
770C2C2×C4×D4×D711yescharacteristic
771C2C2×#9046611yescharacteristic
772C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC22×#1159C22
cosocleC2×C4×C7C25
hypercenterC2×#440D7
hypocenterC7C2×#2947
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#90263C2semidirect
4. C2×C7×#440C2semidirect
5. C2×SD16×Dic7C2semidirect
6. C2×C4×#1144C2semidirect
7. C2×C4×#1142C2semidirect
8. #11737221C2direct (N × H)
9. C2×#89653C2semidirect
10. C2×#89645C2semidirect
11. C2×D7×#103C2semidirect
12. C2×#89561C2semidirect
14. C2×#89529C2semidirect
15. C2×#89488C2semidirect
16. C2×#89480C2semidirect
28. C2×#6478C4semidirect
34. #90263C22semidirect
50. C7×#440C22semidirect
57. SD16×Dic7C22semidirect
63. C4×#1144C22semidirect
64. C4×#1142C22semidirect
70. #89653C22semidirect
71. #89645C22semidirect
72. D7×#103C22semidirect
73. #89561C22semidirect
75. #89529C22semidirect
76. #89488C22semidirect
77. #89480C22semidirect
87. C2×Q8×D7C2×C4semidirect
99. C2×C7×SD16C2×C4semidirect
116. C2×#1144C2×C4semidirect
120. C2×#1142C2×C4semidirect
146. #6478C2×C4semidirect
147. C2×Dic28C2×C4semidirect
149. C2×#1131C2×C4semidirect
196. C2×#440D7semidirect
238. Q8×D7C22×C4semidirect
260. C7×SD16C22×C4semidirect
275. #1144C22×C4semidirect
276. #1142C22×C4semidirect
304. Dic28C22×C4semidirect
305. #1131C22×C4semidirect
343. #440C2×D7semidirect
458. C2×SD16C4×D7semidirect
626. SD16C2×C4×D7semidirect
671. C2×C7#2947semidirect
739. C7C2×#2947semidirect
769. C2#11737221direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64782
C2×#902632
C2×#902372
C2×C7×#4402
C2×SD16×Dic72
C2×C4×#11442
C2×C4×#11422
#117372212
C2×#896532
C2×#896452
C2×D7×#1032
C2×#895612
C2×#895442
C2×#895292
C2×#894882
C2×#894802
C2×#29477