Finite Group Databasebeta

← C2×#11737095 #14217954

Subgroups — C2×#11737095 #14217954

Order 1792.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6479C211yesmaximal, characteristic
2C2×#90265C211yesmaximal, characteristic, complemented
3C2×#90237C211yesmaximal, characteristic, complemented
4C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
5C2×SD16×Dic7C211yesmaximal, characteristic, complemented
6C2×#89802C211yesmaximal, characteristic, complemented
7C2×#89786C211yesmaximal, characteristic, complemented
8#11737095C2116yesmaximal, direct product factor
9C2×D7×#106C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89575C211yesmaximal, characteristic, complemented
12C2×#89561C211yesmaximal, characteristic, complemented
13C2×#89543C211yesmaximal, characteristic, complemented
14C2×#89557C211yesmaximal, characteristic, complemented
15C2×C4×#1132C211yesmaximal, characteristic, complemented
16C2×#89461C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C2×D4×Dic7C2211yescharacteristic
25C22×#1141C2211yescharacteristic
26C2×C4×C22⋊D7—21no—
27C22×Dic7⋊C4—21no—
28C2×#6479C4116yescomplemented
29C2×#6479C2218yes—
30C22×#1132C2211yescharacteristic
31C22×#1131C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90265—24no—
34#90265C2218yescomplemented
35#90237—24no—
36#90237C2218yescomplemented
37C2×#6456—21no—
38C2×#6456C2211yescharacteristic
39C2×D7×C4⋊C4—21no—
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×D7×C4⋊C4C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×(C22⋊D7)⋊C4—21no—
44C2×#6440—21no—
45C2×C4×D28—21no—
46C2×C4×D28C2211yescharacteristic
47C2×#6435—21no—
48C2×#6435C2211yescharacteristic
49C2×C4×Dic14C2211yescharacteristic
50C4×C7×SD16C2218yescomplemented
51C2×C7×#106C2211yescharacteristic
52C2×C7×#103C2211yescharacteristic
53C2×C7×#102C2211yescharacteristic
54C2×C4×C7×C8C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57SD16×Dic7C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6390C2211yescharacteristic
61C2×#6389C2211yescharacteristic
62C2×C8×Dic7C2211yescharacteristic
63#89802C2218yescomplemented
64#89786C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6377C2211yescharacteristic
70D7×#106C2218yescomplemented
71#89624C2218yescomplemented
72#89575C2218yescomplemented
73#89561C2218yescomplemented
74#89557C2218yescomplemented
75#89543C2218yescomplemented
76C4×#1132C2218yescomplemented
77#89461C2218yescomplemented
78C2×#2952—71nomaximal, Sylow
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C2×#1161—22no—
86C2×#1161—24no—
87C2×#1161C2×C418yescomplemented
88C2×#1161C2314yes—
89C2×#1159—22no—
90C2×#1159—24no—
91C2×#1159C2×C418yescomplemented
92C2×#1159C2314yes—
93C22×D28—21no—
94C22×D28C2311yescharacteristic
95C22×C4×D7—21no—
96C22×C4×D7—21no—
97C22×C4×D7—21no—
98C22×C4×D7—21no—
99C22×C4×D7—21no—
100C22×C4×D7C2311yescharacteristic
101C22×Dic14C2311yescharacteristic
102C2×C7×SD16C2×C418yescomplemented
103C2×C7×SD16C2314yes—
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2311yescharacteristic
106C4×C7×Q8—22no—
107C4×C7×Q8C2314yes—
108C4×C7×D4—22no—
109C4×C7×D4C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C22⋊C4—21no—
114C2×C42×C7—21no—
115C2×C42×C7C2311yescharacteristic
116C2×C22⋊Dic7—21no—
117Q8×Dic7—22no—
118Q8×Dic7C2314yes—
119C2×#1144C2×C418yescomplemented
120C2×#1144C2314yes—
121D4×Dic7—22no—
122D4×Dic7C2314yes—
123C2×#1141C2×C418yescomplemented
124C2×#1141C2314yes—
125C4×C22⋊D7—28no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4D411yescharacteristic
129C2×(C2×D7)⋊C4D411yescharacteristic
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—28no—
138C2×Dic7⋊C4D411yescharacteristic
139C2×Dic7⋊C4D411yescharacteristic
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6479C2×C4164yescomplemented
147C2×#1132C2×C418yescomplemented
148C2×#1132C2314yes—
149C2×#1131—24no—
150C2×#1131C2314yes—
151C2×C8×D7C2×C418yescomplemented
152C2×C8×D7C2314yes—
153#6456—28no—
154#6456—22no—
155#6456C2314yes—
156D7×C4⋊C4—22no—
157D7×C4⋊C4—22no—
158D7×C4⋊C4—28no—
159D7×C4⋊C4C2314yes—
160D7×C4⋊C4C2314yes—
161#6450—22no—
162#6450C2314yes—
163(C22⋊D7)⋊C4—28no—
164#6440—28no—
165C4×D28—22no—
166C4×D28—28no—
167C4×D28C2314yes—
168#6435—28no—
169#6435D414yes—
170#6435C2314yes—
171C4×Dic14—22no—
172C4×Dic14C2314yes—
173C7×#106C2314yes—
174C7×#103C2314yes—
175C7×#102C2314yes—
176C4×C7×C8C2314yes—
177#6409C2314yes—
178#6406C2314yes—
179#6395C2314yes—
180#6391C2314yes—
181#6390C2314yes—
182#6389C2314yes—
183C8×Dic7C2314yes—
184#6384C2314yes—
185#6383C2314yes—
186#6382C2314yes—
187#6382C2314yes—
188#6377C2314yes—
189C22×#135—71no—
190C2×#520—71no—
191C2×#520—71no—
192#2952—716no—
193C2×#442—71no—
194C2×#442—71no—
195C2×#441—71no—
196C2×#441—71no—
197C2×C4×SD16—71no—
198C2×C4×SD16—71no—
199C2×C4×SD16—71no—
200C2×C4×SD16D711yescharacteristic, complemented
201C22×#106—71no—
202C2×#417—71no—
203C2×#417—71no—
204C2×#405—71no—
205C24×C7—21no—
206C23×D7—21no—
207C23×D7C2×D411yescharacteristic
208C2×C7×Q8—21no—
209C2×C7×Q8—22no—
210C2×C7×Q8C22×C414yes—
211C2×C7×Q8C2412yes—
212C2×C7×D4—21no—
213C2×C7×D4—22no—
214C2×C7×D4C22×C414yes—
215C2×C7×D4C2412yes—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—24no—
220C22×C4×C7—82no—
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2411yescharacteristic
224C2×C22⋊D7—28no—
225C2×C22⋊D7—24no—
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
236#1161—216no—
237#1161—28no—
238#1161C22×C4116yescomplemented
239#1159—216no—
240#1159—28no—
241#1159C22×C4116yescomplemented
242C2×D28—28no—
243C2×D28—24no—
244C2×D28—21no—
245C2×D28—22no—
246C2×D28C22×C414yes—
247C2×D28C2412yes—
248C2×C4×D7—28no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—24no—
252C2×C4×D7—24no—
253C2×C4×D7—24no—
254C2×C4×D7—82no—
255C2×C4×D7—82no—
256C2×C4×D7—82no—
257C2×C4×D7—82no—
258C2×C4×D7C22×C414yes—
259C2×C4×D7C2×D412yes—
260C2×C4×D7#4114yes—
261C2×C4×D7C2412yes—
262C2×Dic14—21no—
263C2×Dic14—22no—
264C2×Dic14C22×C414yes—
265C2×Dic14C2412yes—
266C7×SD16C22×C4116yescomplemented
267C2×C7×C8—22no—
268C2×C7×C8C22×C414yes—
269C2×C7×C8C2412yes—
270C2×C7×C8C2412yes—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—24no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C22⋊C4—24no—
277C42×C7—24no—
278C42×C7C2×D412yes—
279C42×C7C2412yes—
280C22⋊Dic7—24no—
281#1144C22×C4116yescomplemented
282#1141C22×C4116yescomplemented
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4C2×D414yes—
286(C2×D7)⋊C4C2×D414yes—
287C4⋊Dic7—21no—
288C4⋊Dic7—21no—
289C4⋊Dic7—24no—
290C4⋊Dic7C2412yes—
291C4⋊Dic7C2412yes—
292Dic7⋊C4—24no—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4C2×D414yes—
297Dic7⋊C4C2×D414yes—
298C4×Dic7—24no—
299C4×Dic7—24no—
300C4×Dic7—24no—
301C4×Dic7C2×D412yes—
302C4×Dic7C2412yes—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C22×C414yes—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307#1132C22×C4116yescomplemented
308#1131—28no—
309C8×D7C22×C4116yescomplemented
310C22×#41—71no—
311C22×#41—71no—
312C2×#135—716no—
313C2×#135—78no—
314C22×Q16—71no—
315C22×SD16—71no—
316C22×SD16C2×D711yescharacteristic
317C22×D8—71no—
318C22×M16—71no—
319C23×C8—71no—
320#520—78no—
321#520—78no—
322#520—144no—
323#520—144no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8—71no—
327C2×C4×Q8C2×D711yescharacteristic
328C2×C4×D4—71no—
329C2×C4×D4—71no—
330C2×C4×D4—71no—
331C2×C4×D4—141no—
332C2×C4×D4—141no—
333C2×C4×D4—141no—
334C2×C4×D4—141no—
335C2×C4×D4C2×D711yescharacteristic
336C2×#117—71no—
337C2×#117—141no—
338C2×#117—141no—
339C22×C4⋊C4—71no—
340C22×C4⋊C4—71no—
341C22×C4⋊C4—141no—
342C22×C4⋊C4—141no—
343#442—78no—
344#442—78no—
345#441—78no—
346#441—78no—
347C4×SD16—78no—
348C4×SD16—78no—
349C4×SD16—78no—
350C4×SD16C2×D718yescomplemented
351C2×#106—71no—
352C2×#106—71no—
353C2×#106—71no—
354C2×#106—78no—
355C2×#106C2×D711yescharacteristic
356#417—78no—
357#417—78no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103C2×D711yescharacteristic
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×#102C2×D711yescharacteristic
366#405—78no—
367C2×#97—71no—
368C2×#97—71no—
369C2×C4×C8—71no—
370C2×C4×C8C2×D711yescharacteristic
371C23×C7—24no—
372C23×C7—22no—
373C23×C7—42no—
374C23×C7—42no—
375C23×C7C22×D411yescharacteristic
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—24no—
379C22×D7—22no—
380C22×D7—42no—
381C22×D7—42no—
382C22×D7C4×D414yes—
383C22×D7C22×D412yes—
384C7×Q8—24no—
385C7×Q8—22no—
386C7×Q8C23×C414yes—
387C7×D4—24no—
388C7×D4—22no—
389C7×D4C23×C414yes—
390C2×C4×C7—24no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—84no—
399C2×C4×C7C23×C412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D411yescharacteristic
403C2×C4×C7C2×#4112yes—
404C2×C4×C7C2511yescharacteristic
405C22⋊D7—216no—
406C2×Dic7—24no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—216no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—42no—
414C2×Dic7—42no—
415C2×Dic7—84no—
416C2×Dic7C4×D414yes—
417C2×Dic7C22×D412yes—
418C2×Dic7C22×D412yes—
419C2×Dic7C22×D412yes—
420D28—216no—
421D28—24no—
422D28—22no—
423D28C23×C414yes—
424C4×D7—216no—
425C4×D7—84no—
426C4×D7—84no—
427C4×D7—84no—
428C4×D7—84no—
429C4×D7C4×D418yes—
430C4×D7C23×C414yes—
431C4×D7C2×#4114yes—
432Dic14—24no—
433Dic14—22no—
434Dic14C23×C414yes—
435C7×C8—22no—
436C7×C8C23×C414yes—
437C7⋊C8—22no—
438C7⋊C8C23×C414yes—
439C2×#41—78no—
440C2×#41—74no—
441C2×#41—78no—
442C2×#41—74no—
443C2×#41—142no—
444C2×#41—144no—
445C2×#41—142no—
446C2×#41—144no—
447C22×Q8—71no—
448C22×Q8C22×D711yescharacteristic
449C22×D4—71no—
450C22×D4—141no—
451C22×D4—141no—
452C22×D4C22×D711yescharacteristic
453C23×C4—21no—
454C23×C4—71no—
455C23×C4—141no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4—141no—
459C23×C4—141no—
460C23×C4—141no—
461C23×C4—141no—
462#135—764no—
463C2×Q16—78no—
464C2×Q16—74no—
465C2×SD16—78no—
466C2×SD16—74no—
467C2×SD16C4×D718yescomplemented
468C2×SD16C22×D714yes—
469C2×D8—78no—
470C2×D8—74no—
471C2×M16—74no—
472C2×M16—144no—
473C22×C8—71no—
474C22×C8—78no—
475C22×C8—74no—
476C22×C8—71no—
477C22×C8C22×D711yescharacteristic
478C22×C8C22×D711yescharacteristic
479C4×Q8—22no—
480C4×Q8—74no—
481C4×Q8—74no—
482C4×Q8—74no—
483C4×Q8—142no—
484C4×Q8—142no—
485C4×Q8—142no—
486C4×Q8C22×D714yes—
487C4×D4—22no—
488C4×D4—74no—
489C4×D4—74no—
490C4×D4—74no—
491C4×D4—148no—
492C4×D4—142no—
493C4×D4—142no—
494C4×D4—148no—
495C4×D4—148no—
496C4×D4—148no—
497C4×D4—142no—
498C4×D4C22×D714yes—
499#117—74no—
500#117—74no—
501#117—148no—
502#117—148no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—71no—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—71no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—148no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—148no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4—141no—
518C2×C4⋊C4—141no—
519C2×C4⋊C4C22×D711yescharacteristic
520C2×C4⋊C4C22×D711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—71no—
523C2×C22⋊C4—71no—
524C2×C22⋊C4—141no—
525C2×C22⋊C4—141no—
526C2×C22⋊C4—141no—
527C2×C42—21no—
528C2×C42—71no—
529C2×C42—141no—
530C2×C42—141no—
531C2×C42—141no—
532C2×C42C22×D711yescharacteristic
533#106—74no—
534#106—74no—
535#106—74no—
536#106C22×D714yes—
537#103—74no—
538#103—74no—
539#103—74no—
540#103C22×D714yes—
541#102—74no—
542#102—74no—
543#102—74no—
544#102C22×D714yes—
545#97—74no—
546#97—74no—
547C4×C8—74no—
548C4×C8C22×D714yes—
549C22×C7—24no—
550C22×C7—48no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7C2×C4×D412yes—
554C22×C7#57712yes—
555C22×C7#57712yes—
556C22×C7C23×D411yescharacteristic
557C2×D7—28no—
558C2×D7—22no—
559C2×D7—22no—
560C2×D7—24no—
561C2×D7—48no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7C2×C4×D414yes—
565C4×C7—24no—
566C4×C7—22no—
567C4×C7—22no—
568C4×C7—42no—
569C4×C7—42no—
570C4×C7C2×C4×D412yes—
571C4×C7C24×C411yescharacteristic
572C4×C7C22×#4111yescharacteristic
573Dic7—24no—
574Dic7—22no—
575Dic7—22no—
576Dic7—42no—
577Dic7—42no—
578Dic7C2×C4×D414yes—
579C24—21no—
580C24—71no—
581C24—141no—
582#41—716no—
583#41—716no—
584#41—1416no—
585#41—148no—
586#41—1416no—
587#41—148no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—74no—
591C2×Q8—72no—
592C2×Q8—141no—
593C2×Q8—142no—
594C2×Q8C2×C4×D714yes—
595C2×Q8C23×D712yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—74no—
599C2×D4—72no—
600C2×D4—144no—
601C2×D4—148no—
602C2×D4—144no—
603C2×D4—148no—
604C2×D4—141no—
605C2×D4—142no—
606C2×D4C2×C4×D714yes—
607C2×D4C23×D712yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—71no—
613C22×C4—74no—
614C22×C4—72no—
615C22×C4—74no—
616C22×C4—72no—
617C22×C4—71no—
618C22×C4—71no—
619C22×C4—82no—
620C22×C4—144no—
621C22×C4—148no—
622C22×C4—144no—
623C22×C4—144no—
624C22×C4—144no—
625C22×C4—144no—
626C22×C4—148no—
627C22×C4—144no—
628C22×C4—141no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—144no—
632C22×C4—562no—
633C22×C4—562no—
634C22×C4—562no—
635C22×C4—562no—
636C22×C4—562no—
637C22×C4D4×D711yescharacteristic
638C22×C4D4×D711yescharacteristic
639C22×C4C23×D711yescharacteristic
640Q16—716no—
641SD16—716no—
642SD16C2×C4×D7116yescomplemented
643D8—716no—
644M16—148no—
645C2×C8—22no—
646C2×C8—74no—
647C2×C8—72no—
648C2×C8—716no—
649C2×C8—72no—
650C2×C8—142no—
651C2×C8C2×C4×D714yes—
652C2×C8C23×D712yes—
653C2×C8C23×D712yes—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—74no—
658C4⋊C4—74no—
659C4⋊C4—72no—
660C4⋊C4—72no—
661C4⋊C4—144no—
662C4⋊C4—144no—
663C4⋊C4—144no—
664C4⋊C4—144no—
665C4⋊C4—144no—
666C4⋊C4—141no—
667C4⋊C4—141no—
668C4⋊C4C23×D712yes—
669C4⋊C4C23×D712yes—
670C22⋊C4—24no—
671C22⋊C4—74no—
672C22⋊C4—74no—
673C22⋊C4—144no—
674C22⋊C4—144no—
675C22⋊C4—144no—
676C42—24no—
677C42—72no—
678C42—72no—
679C42—144no—
680C42—144no—
681C42—144no—
682C42D4×D712yes—
683C42C23×D712yes—
684C2×C7—44no—
685C2×C7#295214yescomplemented
686C2×C7C22×C4×D411yescharacteristic
687C2×C7C2×#57711yescharacteristic
688C2×C7C2×#57711yescharacteristic
689D7—24no—
690D7—44no—
691C23—24no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—74no—
696C23—72no—
697C23—142no—
698C23—142no—
699C23—144no—
700C23—142no—
701C23—282no—
702C23—282no—
703C23C2×D4×D711yescharacteristic
704Q8—24no—
705Q8—22no—
706Q8—74no—
707Q8—144no—
708Q8—142no—
709Q8C22×C4×D714yes—
710D4—24no—
711D4—22no—
712D4—74no—
713D4—1416no—
714D4—1416no—
715D4—144no—
716D4—142no—
717D4C22×C4×D714yes—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—74no—
727C2×C4—72no—
728C2×C4—78no—
729C2×C4—74no—
730C2×C4—74no—
731C2×C4—72no—
732C2×C4—72no—
733C2×C4—84no—
734C2×C4—1416no—
735C2×C4—1416no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—144no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—564no—
745C2×C4—564no—
746C2×C4—564no—
747C2×C4—564no—
748C2×C4—564no—
749C2×C4C22×C4×D712yes—
750C2×C4C2×D4×D712yes—
751C2×C4C2×D4×D712yes—
752C2×C4C2×D4×D711yescharacteristic
753C2×C4D7×#4112yes—
754C2×C4C24×D711yescharacteristic
755C8—22no—
756C8—74no—
757C8—142no—
758C8C22×C4×D714yes—
759C7C2×#295211yescharacteristic, complemented, Sylow
760C22—24no—
761C22—48no—
762C22—42no—
763C22—42no—
764C22—74no—
765C22—148no—
766C22—142no—
767C22—142no—
768C22—144no—
769C22—288no—
770C22—282no—
771C22—282no—
772C22C4×D4×D712yes—
773C22#9045312yes—
774C22#9046112yes—
775C22C22×D4×D711yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—74no—
782C4—144no—
783C4—142no—
784C4—142no—
785C4—282no—
786C4—282no—
787C4C4×D4×D712yes—
788C4C23×C4×D711yescharacteristic
789C4C2×D7×#4111yescharacteristic
790C2—44no—
791C2—144no—
792C2—284no—
793C2#1173709514yesdirect product factor
794C2C2×C4×D4×D711yescharacteristic
795C2C2×#9045311yescharacteristic
796C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C4×C7×SD16C2
socleC23×C7C22×D4
prime radicalC22×#6479C2
cosocleC2×C4×C7C25
hypercenterC2×C4×SD16D7
hypocenterC7C2×#2952
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#90265C2semidirect
3. C2×#90237C2semidirect
4. C2×C4×C7×SD16C2semidirect
5. C2×SD16×Dic7C2semidirect
6. C2×#89802C2semidirect
7. C2×#89786C2semidirect
8. #11737095C2direct (N × H)
9. C2×D7×#106C2semidirect
10. C2×#89624C2semidirect
11. C2×#89575C2semidirect
12. C2×#89561C2semidirect
13. C2×#89543C2semidirect
14. C2×#89557C2semidirect
15. C2×C4×#1132C2semidirect
16. C2×#89461C2semidirect
28. C2×#6479C4semidirect
34. #90265C22semidirect
36. #90237C22semidirect
50. C4×C7×SD16C22semidirect
57. SD16×Dic7C22semidirect
63. #89802C22semidirect
64. #89786C22semidirect
70. D7×#106C22semidirect
71. #89624C22semidirect
72. #89575C22semidirect
73. #89561C22semidirect
74. #89557C22semidirect
75. #89543C22semidirect
76. C4×#1132C22semidirect
77. #89461C22semidirect
87. C2×#1161C2×C4semidirect
91. C2×#1159C2×C4semidirect
102. C2×C7×SD16C2×C4semidirect
119. C2×#1144C2×C4semidirect
123. C2×#1141C2×C4semidirect
146. #6479C2×C4semidirect
147. C2×#1132C2×C4semidirect
151. C2×C8×D7C2×C4semidirect
200. C2×C4×SD16D7semidirect
238. #1161C22×C4semidirect
241. #1159C22×C4semidirect
266. C7×SD16C22×C4semidirect
281. #1144C22×C4semidirect
282. #1141C22×C4semidirect
307. #1132C22×C4semidirect
309. C8×D7C22×C4semidirect
350. C4×SD16C2×D7semidirect
467. C2×SD16C4×D7semidirect
642. SD16C2×C4×D7semidirect
685. C2×C7#2952semidirect
759. C7C2×#2952semidirect
793. C2#11737095direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64792
C2×#902652
C2×#902372
C2×C4×C7×SD162
C2×SD16×Dic72
C2×#898022
C2×#897862
#117370952
C2×D7×#1062
C2×#896242
C2×#895752
C2×#895612
C2×#895432
C2×#895572
C2×C4×#11322
C2×#894612
C2×#29527