Finite Group Databasebeta

← C2×#11737219 #14217873

Subgroups — C2×#11737219 #14217873

Order 1792.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6478C211yesmaximal, characteristic
2C2×C4×Q8×D7C211yesmaximal, characteristic, complemented
3C2×C4×#1159C211yesmaximal, characteristic
4C2×C7×#440C211yesmaximal, characteristic, complemented
5C2×SD16×Dic7C211yesmaximal, characteristic, complemented
6C2×#89802C211yesmaximal, characteristic, complemented
7C2×#89790C211yesmaximal, characteristic, complemented
8#11737219C2116yesmaximal, direct product factor
9C2×#89653C211yesmaximal, characteristic, complemented
10C2×#89645C211yesmaximal, characteristic, complemented
11C2×#89574C211yesmaximal, characteristic, complemented
12C2×#89562C211yesmaximal, characteristic, complemented
13C2×#89543C211yesmaximal, characteristic
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89479C211yesmaximal, 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×C4×Dic7—21no—
28C2×#6478C4116yescomplemented
29C2×#6478C2218yes—
30C22×Dic28C2211yescharacteristic
31C22×#1131C2211yescharacteristic
32C22×#1131C2211yescharacteristic
33C4×Q8×D7—24no—
34C4×Q8×D7C2218yescomplemented
35C4×#1159—24no—
36C4×#1159C2218yes—
37C2×#6455C2211yescharacteristic
38C2×D7×C4⋊C4—21no—
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6450—21no—
41C2×#6450C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×(C22⋊D7)⋊C4—21no—
44C2×#6440—21no—
45C2×C42×D7—21no—
46C2×C42×D7C2211yescharacteristic
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×C8×Dic7C2211yescharacteristic
62C2×C8×Dic7C2211yescharacteristic
63#89802C2218yescomplemented
64#89790C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6377C2211yescharacteristic
70#89653C2218yescomplemented
71#89645C2218yescomplemented
72#89574C2218yescomplemented
73#89562C2218yescomplemented
74#89543C2218yes—
75#89530C2218yescomplemented
76#89488C2218yescomplemented
77#89479C2218yescomplemented
78C2×C4×#137—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×D7D411yescharacteristic
96C22×C4×D7D411yescharacteristic
97C22×C4×D7C2311yescharacteristic
98C22×Dic14—21no—
99C22×Dic14C2311yescharacteristic
100C22×Dic14C2311yescharacteristic
101C2×C7×SD16C2×C418yescomplemented
102C2×C7×SD16C2314yes—
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C4×C7×Q8—22no—
106C4×C7×Q8C2314yes—
107C4×C7×D4—22no—
108C4×C7×D4C2314yes—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C42×C7—21no—
114C2×C42×C7C2311yescharacteristic
115C2×C22⋊Dic7—21no—
116Q8×Dic7—22no—
117Q8×Dic7C2314yes—
118C2×#1144C2×C418yescomplemented
119C2×#1144C2314yes—
120D4×Dic7—22no—
121D4×Dic7C2314yes—
122C2×#1142C2×C418yescomplemented
123C2×#1142C2314yes—
124C4×C22⋊D7—28no—
125C2×(C2×D7)⋊C4—21no—
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×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7—28no—
141C2×C4×Dic7D411yescharacteristic
142C2×C4×Dic7D411yescharacteristic
143C2×C4×Dic7C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6478C2×C4164yescomplemented
147C2×Dic28C2×C418yescomplemented
148C2×Dic28C2314yes—
149C2×#1131—24no—
150C2×#1131C2×C418yescomplemented
151C2×#1131C2314yes—
152C2×#1131C2314yes—
153#6455—22no—
154#6455C2314yes—
155D7×C4⋊C4—28no—
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—
165C42×D7—28no—
166C42×D7D414yes—
167C42×D7C2314yes—
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—
182C8×Dic7C2314yes—
183C8×Dic7C2314yes—
184#6384C2314yes—
185#6384C2314yes—
186#6382C2314yes—
187#6381C2314yes—
188#6377C2314yes—
189C22×#137—71no—
190C2×C4×#41—71no—
191C22×C4×Q8—71no—
192C4×#137—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×#417—71no—
203C2×#419—71no—
204C2×C4×M16—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—44no—
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—44no—
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—24no—
246C2×C4×D7—42no—
247C2×C4×D7—44no—
248C2×C4×D7C22×C414yes—
249C2×C4×D7C2×D414yes—
250C2×C4×D7C2×D414yes—
251C2×C4×D7C2×D412yes—
252C2×C4×D7#4114yes—
253C2×C4×D7C2412yes—
254C2×Dic14—21no—
255C2×Dic14—21no—
256C2×Dic14—22no—
257C2×Dic14—22no—
258C2×Dic14—28no—
259C2×Dic14—24no—
260C2×Dic14C22×C414yes—
261C2×Dic14C22×C414yes—
262C2×Dic14C2412yes—
263C2×Dic14C2412yes—
264C7×SD16C22×C4116yescomplemented
265C2×C7×C8—22no—
266C2×C7×C8C22×C414yes—
267C2×C7×C8C2412yes—
268C2×C7×C8C2412yes—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4C2412yes—
273C7×C4⋊C4C2412yes—
274C7×C22⋊C4—24no—
275C42×C7—24no—
276C42×C7C2×D412yes—
277C42×C7C2412yes—
278C22⋊Dic7—24no—
279#1144C22×C4116yescomplemented
280#1142C22×C4116yescomplemented
281(C2×D7)⋊C4—24no—
282C4⋊Dic7—21no—
283C4⋊Dic7—21no—
284C4⋊Dic7—24no—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C4×Dic7—24no—
298C4×Dic7C2×D414yes—
299C4×Dic7C2×D412yes—
300C4×Dic7C2×D414yes—
301C4×Dic7C2412yes—
302C2×C7⋊C8—22no—
303C2×C7⋊C8C22×C414yes—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306Dic28C22×C4116yescomplemented
307#1131—28no—
308#1131C22×C4116yescomplemented
309C22×#41—71no—
310C23×Q8—71no—
311C2×#137—716no—
312C2×#137—78no—
313C22×Q16—71no—
314C22×Q16—71no—
315C22×SD16—71no—
316C22×SD16C2×D711yescharacteristic
317C22×M16—71no—
318C22×M16—71no—
319C4×#41—78no—
320C4×#41—144no—
321C2×C4×Q8—71no—
322C2×C4×Q8—78no—
323C2×C4×Q8—71no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8—71no—
327C2×C4×Q8—141no—
328C2×C4×Q8—141no—
329C2×C4×Q8—144no—
330C2×C4×Q8C2×D711yescharacteristic
331C2×C4×D4—71no—
332C2×C4×D4—141no—
333C2×C4×D4—141no—
334C2×C4×D4C2×D711yescharacteristic
335C2×#117—71no—
336C2×#117—141no—
337C22×C4⋊C4—71no—
338C22×C4⋊C4—141no—
339C22×C42—71no—
340C22×C42—141no—
341C22×C42—141no—
342#441—78no—
343#441—78no—
344#440—78no—
345#440C2×D718yescomplemented
346C4×Q16—78no—
347C4×Q16—78no—
348C4×SD16—78no—
349C4×SD16—78no—
350#428—78no—
351C2×#107—71no—
352C2×#107C2×D711yescharacteristic
353C2×#106—71no—
354C2×#106—71no—
355#419—78no—
356#417—78no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#103C2×D711yescharacteristic
363C2×#102—71no—
364C2×#102C2×D711yescharacteristic
365C4×M16—78no—
366C2×#97—71no—
367C2×#97C2×D711yescharacteristic
368C2×C4×C8—71no—
369C2×C4×C8—71no—
370C23×C7—24no—
371C23×C7—22no—
372C23×C7—42no—
373C23×C7—42no—
374C23×C7C22×D411yescharacteristic
375C22×D7—22no—
376C22×D7—22no—
377C22×D7C4×D414yes—
378C22×D7C22×D412yes—
379C7×Q8—24no—
380C7×Q8—22no—
381C7×Q8C23×C414yes—
382C7×D4—24no—
383C7×D4—22no—
384C7×D4C23×C414yes—
385C2×C4×C7—24no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—48no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7C23×C412yes—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D411yescharacteristic
398C2×C4×C7C2×#4112yes—
399C2×C4×C7C2511yescharacteristic
400C22⋊D7—216no—
401C2×Dic7—24no—
402C2×Dic7—24no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—216no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—48no—
412C2×Dic7C4×D414yes—
413C2×Dic7#13714yescomplemented
414C2×Dic7C22×D412yes—
415C2×Dic7C22×D412yes—
416C2×Dic7C22×D412yes—
417C4×D7—216no—
418C4×D7—28no—
419C4×D7—44no—
420C4×D7—48no—
421C4×D7C4×D418yes—
422C4×D7C23×C414yes—
423C4×D7C2×#4114yes—
424Dic14—24no—
425Dic14—24no—
426Dic14—22no—
427Dic14—22no—
428Dic14—216no—
429Dic14C23×C414yes—
430Dic14C23×C414yes—
431C7×C8—22no—
432C7×C8C23×C414yes—
433C7⋊C8—22no—
434C7⋊C8C23×C414yes—
435C2×#41—78no—
436C2×#41—74no—
437C2×#41—142no—
438C2×#41—144no—
439C22×Q8—78no—
440C22×Q8—74no—
441C22×Q8—71no—
442C22×Q8—71no—
443C22×Q8—141no—
444C22×Q8—142no—
445C22×Q8—144no—
446C22×Q8C22×D711yescharacteristic
447C22×D4—141no—
448C22×D4C22×D711yescharacteristic
449C23×C4—21no—
450C23×C4—71no—
451C23×C4—71no—
452C23×C4—71no—
453C23×C4—141no—
454C23×C4—141no—
455C23×C4—141no—
456C23×C4—141no—
457#137—764no—
458C2×Q16—78no—
459C2×Q16—74no—
460C2×Q16—78no—
461C2×Q16—74no—
462C2×SD16—78no—
463C2×SD16—74no—
464C2×SD16C4×D718yescomplemented
465C2×SD16C22×D714yes—
466C2×M16—78no—
467C2×M16—74no—
468C2×M16—74no—
469C2×M16—144no—
470C22×C8—71no—
471C22×C8—71no—
472C22×C8C22×D711yescharacteristic
473C22×C8C22×D711yescharacteristic
474C4×Q8—22no—
475C4×Q8—74no—
476C4×Q8—74no—
477C4×Q8—74no—
478C4×Q8—74no—
479C4×Q8—74no—
480C4×Q8—148no—
481C4×Q8—148no—
482C4×Q8—142no—
483C4×Q8—142no—
484C4×Q8—142no—
485C4×Q8—142no—
486C4×Q8—142no—
487C4×Q8C22×D714yes—
488C4×D4—22no—
489C4×D4—74no—
490C4×D4—142no—
491C4×D4—148no—
492C4×D4—148no—
493C4×D4C22×D714yes—
494#117—74no—
495#117—148no—
496#117—142no—
497C2×C4⋊C4—21no—
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—141no—
513C2×C22⋊C4—141no—
514C2×C42—21no—
515C2×C42—71no—
516C2×C42—71no—
517C2×C42—71no—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—148no—
521C2×C42—148no—
522C2×C42—141no—
523C2×C42—141no—
524C2×C42—141no—
525C2×C42—141no—
526C2×C42—141no—
527C2×C42—141no—
528C2×C42C22×D711yescharacteristic
529#107—74no—
530#107C22×D714yes—
531#106—74no—
532#106—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103—74no—
538#103C22×D714yes—
539#102—74no—
540#102C22×D714yes—
541#97—74no—
542#97C22×D714yes—
543C4×C8—74no—
544C4×C8—74no—
545C22×C7—24no—
546C22×C7—48no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7C2×C4×D412yes—
550C22×C7C2×#13712yes—
551C22×C7#57512yes—
552C22×C7C23×D411yescharacteristic
553C2×D7—28no—
554C2×D7—22no—
555C2×D7—22no—
556C2×D7C2×C4×D414yes—
557C4×C7—24no—
558C4×C7—22no—
559C4×C7—22no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7C2×C4×D412yes—
563C4×C7C24×C411yescharacteristic
564C4×C7C22×#4111yescharacteristic
565Dic7—24no—
566Dic7—24no—
567Dic7—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7C2×C4×D414yes—
571Dic7C2×#13714yescomplemented
572C24—21no—
573C24—71no—
574#41—716no—
575#41—1416no—
576#41—148no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—716no—
580C2×Q8—74no—
581C2×Q8—74no—
582C2×Q8—72no—
583C2×Q8—72no—
584C2×Q8—144no—
585C2×Q8—148no—
586C2×Q8—1416no—
587C2×Q8—148no—
588C2×Q8—141no—
589C2×Q8—141no—
590C2×Q8—142no—
591C2×Q8—142no—
592C2×Q8C2×C4×D714yes—
593C2×Q8C23×D712yes—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—144no—
597C2×D4—148no—
598C2×D4C2×C4×D714yes—
599C2×D4C23×D712yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—44no—
605C22×C4—71no—
606C22×C4—71no—
607C22×C4—74no—
608C22×C4—72no—
609C22×C4—74no—
610C22×C4—72no—
611C22×C4—71no—
612C22×C4—74no—
613C22×C4—74no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—148no—
617C22×C4—144no—
618C22×C4—144no—
619C22×C4—148no—
620C22×C4—144no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—282no—
626C22×C4—284no—
627C22×C4—284no—
628C22×C4D4×D711yescharacteristic
629C22×C4D4×D711yescharacteristic
630C22×C4C23×D711yescharacteristic
631Q16—716no—
632Q16—716no—
633SD16—716no—
634SD16C2×C4×D7116yescomplemented
635M16—716no—
636M16—148no—
637C2×C8—22no—
638C2×C8—74no—
639C2×C8—72no—
640C2×C8—72no—
641C2×C8—142no—
642C2×C8C2×C4×D714yes—
643C2×C8C23×D712yes—
644C2×C8C23×D712yes—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—72no—
649C4⋊C4—72no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—144no—
653C4⋊C4—144no—
654C4⋊C4—144no—
655C4⋊C4—144no—
656C4⋊C4—141no—
657C4⋊C4—141no—
658C4⋊C4C23×D712yes—
659C4⋊C4C23×D712yes—
660C22⋊C4—24no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C42—24no—
664C42—74no—
665C42—74no—
666C42—72no—
667C42—72no—
668C42—144no—
669C42—144no—
670C42—144no—
671C42—144no—
672C42—144no—
673C42—144no—
674C42D4×D712yes—
675C42C23×D712yes—
676C2×C7—44no—
677C2×C7C4×#13714yescomplemented
678C2×C7C22×C4×D411yescharacteristic
679C2×C7C22×#13711yescharacteristic
680C2×C7C2×#57511yescharacteristic
681D7—24no—
682C23—24no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—74no—
687C23—72no—
688C23—142no—
689C23—142no—
690C23C2×D4×D711yescharacteristic
691Q8—24no—
692Q8—22no—
693Q8—74no—
694Q8—74no—
695Q8—1416no—
696Q8—144no—
697Q8—144no—
698Q8—142no—
699Q8—142no—
700Q8C22×C4×D714yes—
701D4—24no—
702D4—22no—
703D4—1416no—
704D4C22×C4×D714yes—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—74no—
715C2×C4—74no—
716C2×C4—72no—
717C2×C4—72no—
718C2×C4—78no—
719C2×C4—74no—
720C2×C4—74no—
721C2×C4—72no—
722C2×C4—148no—
723C2×C4—1416no—
724C2×C4—1416no—
725C2×C4—142no—
726C2×C4—144no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—284no—
733C2×C4—288no—
734C2×C4—288no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4C22×C4×D712yes—
738C2×C4C2×D4×D712yes—
739C2×C4C2×D4×D712yes—
740C2×C4C2×D4×D711yescharacteristic
741C2×C4D7×#4112yes—
742C2×C4C24×D711yescharacteristic
743C8—22no—
744C8—74no—
745C8—142no—
746C8C22×C4×D714yes—
747C7C2×C4×#13711yescharacteristic, complemented, Sylow
748C22—24no—
749C22—42no—
750C22—42no—
751C22—48no—
752C22—74no—
753C22—142no—
754C22—142no—
755C22—148no—
756C22C4×D4×D712yes—
757C22#9046412yes—
758C22D7×#13712yes—
759C22C22×D4×D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—24no—
763C4—42no—
764C4—42no—
765C4—74no—
766C4—74no—
767C4—142no—
768C4—144no—
769C4—144no—
770C4—282no—
771C4—282no—
772C4C4×D4×D712yes—
773C4C23×C4×D711yescharacteristic
774C4C2×D7×#4111yescharacteristic
775C2—44no—
776C2—144no—
777C2#1173721914yesdirect product factor
778C2C2×C4×D4×D711yescharacteristic
779C2C2×#9046411yescharacteristic
780C2C2×D7×#13711yescharacteristic
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×C4×#137
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×C4×Q8×D7C2semidirect
4. C2×C7×#440C2semidirect
5. C2×SD16×Dic7C2semidirect
6. C2×#89802C2semidirect
7. C2×#89790C2semidirect
8. #11737219C2direct (N × H)
9. C2×#89653C2semidirect
10. C2×#89645C2semidirect
11. C2×#89574C2semidirect
12. C2×#89562C2semidirect
14. C2×#89530C2semidirect
15. C2×#89488C2semidirect
16. C2×#89479C2semidirect
28. C2×#6478C4semidirect
34. C4×Q8×D7C22semidirect
50. C7×#440C22semidirect
57. SD16×Dic7C22semidirect
63. #89802C22semidirect
64. #89790C22semidirect
70. #89653C22semidirect
71. #89645C22semidirect
72. #89574C22semidirect
73. #89562C22semidirect
75. #89530C22semidirect
76. #89488C22semidirect
77. #89479C22semidirect
87. C2×Q8×D7C2×C4semidirect
101. C2×C7×SD16C2×C4semidirect
118. C2×#1144C2×C4semidirect
122. C2×#1142C2×C4semidirect
146. #6478C2×C4semidirect
147. C2×Dic28C2×C4semidirect
150. C2×#1131C2×C4semidirect
196. C2×#440D7semidirect
238. Q8×D7C22×C4semidirect
264. C7×SD16C22×C4semidirect
279. #1144C22×C4semidirect
280. #1142C22×C4semidirect
306. Dic28C22×C4semidirect
308. #1131C22×C4semidirect
345. #440C2×D7semidirect
413. C2×Dic7#137semidirect
464. C2×SD16C4×D7semidirect
571. Dic7C2×#137semidirect
634. SD16C2×C4×D7semidirect
677. C2×C7C4×#137semidirect
747. C7C2×C4×#137semidirect
777. C2#11737219direct (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×C4×Q8×D72
C2×C4×#11592
C2×C7×#4402
C2×SD16×Dic72
C2×#898022
C2×#897902
#117372192
C2×#896532
C2×#896452
C2×#895742
C2×#895622
C2×#895432
C2×#895302
C2×#894882
C2×#894792
C2×C4×#1377