Finite Group Databasebeta

← C2×#11737311 #14217890

Subgroups — C2×#11737311 #14217890

Order 1792.

2946 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6474C211yesmaximal, characteristic
2C2×#90236C211yesmaximal, characteristic, complemented
3C2×#90237C211yesmaximal, characteristic, complemented
4C2×C7×#442C211yesmaximal, characteristic, complemented
5C2×D8×Dic7C211yesmaximal, characteristic, complemented
6C2×C4×#1142C211yesmaximal, characteristic, complemented
7C2×C4×#1141C211yesmaximal, characteristic, complemented
8#11737311C2116yesmaximal, direct product factor
9C2×#89633C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89544C211yesmaximal, characteristic, complemented
12C2×D7×#102C211yesmaximal, characteristic, complemented
13C2×#89557C211yesmaximal, characteristic, complemented
14C2×#89529C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89480C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C22×D4×D7C2211yescharacteristic
19C22×C7×D8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic, complemented
22C2×D4×Dic7C2211yescharacteristic
23C2×D4×Dic7C2211yescharacteristic, complemented
24C22×#1142C2211yescharacteristic
25C22×#1141C2211yescharacteristic
26C2×C4×C22⋊D7—21no—
27C2×C4×C22⋊D7—21no—
28C22×(C2×D7)⋊C4—21no—
29C22×Dic7⋊C4—21no—
30C2×#6474C4116yescomplemented
31C2×#6474C2218yes—
32C22×#1132C2211yescharacteristic
33C22×#1131C2211yescharacteristic
34C22×C8×D7C2211yescharacteristic
35#90237—24no—
36#90237C2218yescomplemented
37#90236—24no—
38#90236C2218yescomplemented
39C2×#6456C2211yescharacteristic
40C2×#6455C2211yescharacteristic
41C2×D7×C4⋊C4C2211yescharacteristic
42C2×#6450C2211yescharacteristic, complemented
43C2×(C22⋊D7)⋊C4—21no—
44C2×(C22⋊D7)⋊C4—21no—
45C2×D7×C22⋊C4—21no—
46C2×#6440—21no—
47C2×C4×D28C2211yescharacteristic
48C2×#6435C2211yescharacteristic
49C2×C4×Dic14C2211yescharacteristic, complemented
50C7×#442C2218yescomplemented
51C2×C7×#106C2211yescharacteristic, complemented
52C2×C7×#102C2211yescharacteristic
53C2×C7×#102C2211yescharacteristic, complemented
54C2×C7×#97C2211yescharacteristic, complemented
55C2×#6406C2211yescharacteristic
56C2×#6406C2211yescharacteristic, complemented
57D8×Dic7C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×#6392C2211yescharacteristic, complemented
60C2×#6390C2211yescharacteristic, complemented
61C2×#6389C2211yescharacteristic, complemented
62C2×C8×Dic7C2211yescharacteristic, complemented
63C4×#1142C2218yescomplemented
64C4×#1141C2218yescomplemented
65C2×#6384C2211yescharacteristic, complemented
66C2×#6383C2211yescharacteristic
67C2×#6382C2211yescharacteristic, complemented
68C2×#6381C2211yescharacteristic, complemented
69C2×C4×C7⋊C8C2211yescharacteristic, complemented
70#89633C2218yescomplemented
71#89624C2218yescomplemented
72#89557C2218yescomplemented
73#89544C2218yescomplemented
74D7×#102C2218yescomplemented
75#89529C2218yescomplemented
76#89482C2218yescomplemented
77#89480C2218yescomplemented
78C2×#2946—71nomaximal, Sylow
79C24×D7—21no—
80C22×C7×D4C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C23×Dic7—21no—
87C23×Dic7—21no—
88C23×Dic7—21no—
89C2×#1159—22no—
90C2×#1159—24no—
91C2×#1159C2×C418yescomplemented
92C2×#1159C2314yes—
93C2×D4×D7—22no—
94C2×D4×D7—24no—
95C2×D4×D7C2×C418yescomplemented
96C2×D4×D7C2314yes—
97C22×D28C2311yescharacteristic
98C22×C4×D7—21no—
99C22×C4×D7—21no—
100C22×C4×D7—21no—
101C22×C4×D7C2311yescharacteristic
102C22×Dic14C2311yescharacteristic
103C2×C7×D8C2×C418yescomplemented
104C2×C7×D8C2314yes—
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2311yescharacteristic
107C4×C7×D4—22no—
108C4×C7×D4—22no—
109C4×C7×D4C2314yes—
110C4×C7×D4C2314yescomplemented
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C42×C7C2311yescharacteristic
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118D4×Dic7—22no—
119D4×Dic7—22no—
120D4×Dic7C2314yes—
121D4×Dic7C2314yescomplemented
122C2×#1142C2×C418yescomplemented
123C2×#1142C2314yes—
124C2×#1141C2×C418yescomplemented
125C2×#1141C2314yes—
126C4×C22⋊D7—28no—
127C4×C22⋊D7—28no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—28no—
132C2×(C2×D7)⋊C4D411yescharacteristic
133C2×(C2×D7)⋊C4D411yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—28no—
140C2×Dic7⋊C4D411yescharacteristic
141C2×Dic7⋊C4D411yescharacteristic
142C2×C4×Dic7—21no—
143C2×C4×Dic7—21no—
144C2×C4×Dic7—21no—
145C2×C4×Dic7C2311yescharacteristic
146C22×C7⋊C8C2311yescharacteristic
147C22×C7⋊C8C2311yescharacteristic
148#6474C2×C4164yescomplemented
149C2×#1132C2×C418yescomplemented
150C2×#1132C2314yes—
151C2×#1131C2×C418yescomplemented
152C2×#1131C2314yes—
153C2×C8×D7—24no—
154C2×C8×D7C2314yes—
155#6456—22no—
156#6456C2314yes—
157#6455—22no—
158#6455C2314yes—
159D7×C4⋊C4—22no—
160D7×C4⋊C4C2314yes—
161#6450—22no—
162#6450C2314yescomplemented
163(C22⋊D7)⋊C4—28no—
164(C22⋊D7)⋊C4—28no—
165D7×C22⋊C4—28no—
166#6440—28no—
167C4×D28—22no—
168C4×D28C2314yes—
169#6435D414yes—
170#6435C2314yes—
171C4×Dic14—22no—
172C4×Dic14C2314yescomplemented
173C7×#106C2314yescomplemented
174C7×#102C2314yes—
175C7×#102C2314yescomplemented
176C7×#97C2314yescomplemented
177#6406C2314yes—
178#6406C2314yescomplemented
179#6395C2314yes—
180#6392C2314yescomplemented
181#6390C2314yescomplemented
182#6389C2314yescomplemented
183C8×Dic7C2314yescomplemented
184#6384C2314yescomplemented
185#6383C2314yes—
186#6382C2314yescomplemented
187#6381C2314yescomplemented
188C4×C7⋊C8C2314yescomplemented
189C22×AGL(1,ℤ/8)—71no—
190C2×#520—71no—
191C2×#518—71no—
192#2946—716no—
193C2×#442—71no—
194C2×#442D711yescharacteristic, complemented
195C2×#440—71no—
196C2×#440—71no—
197C2×C4×SD16—71no—
198C2×C4×SD16—71no—
199C2×C4×D8—71no—
200C2×C4×D8—71no—
201C2×#428—71no—
202C2×#416—71no—
203C22×#102—71no—
204C2×#405—71no—
205C24×C7—21no—
206C24×C7—21no—
207C23×D7—21no—
208C23×D7—28no—
209C23×D7—24no—
210C23×D7—82no—
211C23×D7—82no—
212C23×D7C2×D411yescharacteristic
213C2×C7×D4—21no—
214C2×C7×D4—21no—
215C2×C7×D4—22no—
216C2×C7×D4—22no—
217C2×C7×D4C22×C414yes—
218C2×C7×D4C22×C414yes—
219C2×C7×D4C2412yes—
220C2×C7×D4C2412yes—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—24no—
224C22×C4×C7—24no—
225C22×C4×C7—82no—
226C22×C4×C7—82no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2411yescharacteristic
230C2×C22⋊D7—28no—
231C2×C22⋊D7—24no—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—24no—
234C22×Dic7—21no—
235C22×Dic7—28no—
236C22×Dic7—24no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—24no—
240C22×Dic7—24no—
241C22×Dic7—82no—
242C22×Dic7—82no—
243C22×Dic7C2×D411yescharacteristic
244C22×Dic7C2×D411yescharacteristic
245C22×Dic7C2×D411yescharacteristic
246#1159—216no—
247#1159—28no—
248#1159C22×C4116yescomplemented
249D4×D7—216no—
250D4×D7—28no—
251D4×D7C22×C4116yescomplemented
252C2×D28—21no—
253C2×D28—22no—
254C2×D28C22×C414yes—
255C2×D28C2412yes—
256C2×C4×D7—24no—
257C2×C4×D7—24no—
258C2×C4×D7—24no—
259C2×C4×D7—82no—
260C2×C4×D7—82no—
261C2×C4×D7—82no—
262C2×C4×D7C22×C414yes—
263C2×C4×D7C2×D412yes—
264C2×C4×D7#4114yes—
265C2×C4×D7C2412yes—
266C2×Dic14—21no—
267C2×Dic14—22no—
268C2×Dic14C22×C414yes—
269C2×Dic14C2412yes—
270C7×D8C22×C4116yescomplemented
271C2×C7×C8—22no—
272C2×C7×C8C22×C414yes—
273C2×C7×C8C2412yes—
274C2×C7×C8C2412yes—
275C7×C4⋊C4—21no—
276C7×C4⋊C4—21no—
277C7×C4⋊C4C2412yes—
278C7×C4⋊C4C2412yes—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—24no—
281C42×C7C2×D412yes—
282C42×C7C2412yes—
283C22⋊Dic7—24no—
284C22⋊Dic7—24no—
285#1142C22×C4116yescomplemented
286#1141C22×C4116yescomplemented
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4—24no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4C2×D414yes—
291(C2×D7)⋊C4C2×D414yes—
292C4⋊Dic7—21no—
293C4⋊Dic7—21no—
294C4⋊Dic7C2412yes—
295C4⋊Dic7C2412yes—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298Dic7⋊C4—24no—
299Dic7⋊C4C2×D414yes—
300Dic7⋊C4C2×D414yes—
301C4×Dic7—24no—
302C4×Dic7—24no—
303C4×Dic7—24no—
304C4×Dic7C2×D412yes—
305C4×Dic7C2412yes—
306C2×C7⋊C8—22no—
307C2×C7⋊C8C22×C414yes—
308C2×C7⋊C8C2412yes—
309C2×C7⋊C8C2412yes—
310#1132C22×C4116yescomplemented
311#1131C22×C4116yescomplemented
312C8×D7—28no—
313C22×#41—71no—
314C23×D4—71no—
315C2×AGL(1,ℤ/8)—716no—
316C2×AGL(1,ℤ/8)—78no—
317C22×SD16—71no—
318C22×SD16—71no—
319C22×D8—71no—
320C22×D8C2×D711yescharacteristic
321C22×M16—71no—
322C23×C8—71no—
323#520—78no—
324#520—144no—
325#518—78no—
326#518—144no—
327C2×C4×Q8—71no—
328C2×C4×Q8—71no—
329C2×C4×D4—71no—
330C2×C4×D4—71no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×C4×D4—141no—
335C2×C4×D4—141no—
336C2×C4×D4—141no—
337C2×C4×D4C2×D711yescharacteristic
338C2×C4×D4C2×D711yescharacteristic, complemented
339C2×#117—71no—
340C2×#117—71no—
341C2×#117—141no—
342C22×C4⋊C4—71no—
343C22×C4⋊C4—141no—
344C22×C22⋊C4—141no—
345C22×C22⋊C4—141no—
346#442—78no—
347#442C2×D718yescomplemented
348#440—78no—
349#440—78no—
350C4×SD16—78no—
351C4×SD16—78no—
352C4×D8—78no—
353C4×D8—78no—
354#428—78no—
355C2×#107—71no—
356C2×#107—71no—
357C2×#106—71no—
358C2×#106C2×D711yescharacteristic, complemented
359#416—78no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×#102—71no—
366C2×#102—78no—
367C2×#102C2×D711yescharacteristic
368C2×#102C2×D711yescharacteristic, complemented
369#405—78no—
370C2×#97—71no—
371C2×#97C2×D711yescharacteristic, complemented
372C2×C4×C8—71no—
373C2×C4×C8—71no—
374C23×C7—24no—
375C23×C7—24no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—42no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7—42no—
382C23×C7C22×D411yescharacteristic
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—24no—
386C22×D7—22no—
387C22×D7—216no—
388C22×D7—42no—
389C22×D7—42no—
390C22×D7—816no—
391C22×D7—84no—
392C22×D7—84no—
393C22×D7C4×D414yes—
394C22×D7C22×D412yes—
395C7×D4—24no—
396C7×D4—24no—
397C7×D4—22no—
398C7×D4—22no—
399C7×D4C23×C414yes—
400C7×D4C23×C414yes—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—84no—
408C2×C4×C7—84no—
409C2×C4×C7C23×C412yes—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D411yescharacteristic
413C2×C4×C7C2×#4112yes—
414C2×C4×C7C2511yescharacteristic
415C22⋊D7—216no—
416C22⋊D7—216no—
417C2×Dic7—24no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—216no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—42no—
425C2×Dic7—42no—
426C2×Dic7—84no—
427C2×Dic7—84no—
428C2×Dic7C4×D414yes—
429C2×Dic7C22×D412yes—
430C2×Dic7C22×D412yes—
431C2×Dic7C22×D412yes—
432D28—24no—
433D28—22no—
434D28C23×C414yes—
435C4×D7—84no—
436C4×D7—84no—
437C4×D7—84no—
438C4×D7C4×D418yes—
439C4×D7C23×C414yes—
440C4×D7C2×#4114yes—
441Dic14—24no—
442Dic14—22no—
443Dic14C23×C414yes—
444C7×C8—22no—
445C7×C8C23×C414yes—
446C7⋊C8—22no—
447C7⋊C8C23×C414yes—
448C25—141no—
449C2×#41—78no—
450C2×#41—74no—
451C2×#41—142no—
452C2×#41—144no—
453C22×Q8—71no—
454C22×D4—78no—
455C22×D4—74no—
456C22×D4—71no—
457C22×D4—142no—
458C22×D4—144no—
459C22×D4—141no—
460C22×D4—141no—
461C22×D4C22×D711yescharacteristic
462C22×D4C22×D711yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—71no—
466C23×C4—141no—
467C23×C4—141no—
468C23×C4—141no—
469C23×C4—141no—
470C23×C4—141no—
471C23×C4—141no—
472AGL(1,ℤ/8)—764no—
473C2×SD16—78no—
474C2×SD16—74no—
475C2×SD16—78no—
476C2×SD16—74no—
477C2×D8—78no—
478C2×D8—74no—
479C2×D8C4×D718yescomplemented
480C2×D8C22×D714yes—
481C2×M16—78no—
482C2×M16—74no—
483C22×C8—71no—
484C22×C8—71no—
485C22×C8—74no—
486C22×C8—144no—
487C22×C8C22×D711yescharacteristic
488C22×C8C22×D711yescharacteristic
489C4×Q8—74no—
490C4×Q8—74no—
491C4×Q8—142no—
492C4×Q8—142no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—74no—
496C4×D4—74no—
497C4×D4—74no—
498C4×D4—74no—
499C4×D4—142no—
500C4×D4—142no—
501C4×D4—142no—
502C4×D4—148no—
503C4×D4—148no—
504C4×D4—148no—
505C4×D4—148no—
506C4×D4—142no—
507C4×D4C22×D714yes—
508C4×D4C22×D714yescomplemented
509#117—74no—
510#117—74no—
511#117—74no—
512#117—148no—
513#117—142no—
514C2×C4⋊C4—71no—
515C2×C4⋊C4—71no—
516C2×C4⋊C4—71no—
517C2×C4⋊C4—71no—
518C2×C4⋊C4—74no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—148no—
521C2×C4⋊C4—141no—
522C2×C4⋊C4—141no—
523C2×C4⋊C4—141no—
524C2×C4⋊C4C22×D711yescharacteristic
525C2×C4⋊C4C22×D711yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—71no—
529C2×C22⋊C4—71no—
530C2×C22⋊C4—148no—
531C2×C22⋊C4—148no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4—141no—
536C2×C22⋊C4—141no—
537C2×C42—71no—
538C2×C42—141no—
539C2×C42—141no—
540C2×C42—141no—
541C2×C42C22×D711yescharacteristic
542#107—74no—
543#107—74no—
544#106—74no—
545#106C22×D714yescomplemented
546#103—74no—
547#103—74no—
548#102—74no—
549#102—74no—
550#102—74no—
551#102—74no—
552#102C22×D714yes—
553#102C22×D714yescomplemented
554#97—74no—
555#97C22×D714yescomplemented
556C4×C8—74no—
557C4×C8—74no—
558C22×C7—24no—
559C22×C7—24no—
560C22×C7—48no—
561C22×C7—48no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7C2×C4×D412yes—
567C22×C7#57612yes—
568C22×C7#57712yes—
569C22×C7C23×D411yescharacteristic
570C2×D7—28no—
571C2×D7—22no—
572C2×D7—22no—
573C2×D7—24no—
574C2×D7—48no—
575C2×D7—42no—
576C2×D7—42no—
577C2×D7—816no—
578C2×D7C2×C4×D414yes—
579C4×C7—22no—
580C4×C7—22no—
581C4×C7—42no—
582C4×C7—42no—
583C4×C7C2×C4×D412yes—
584C4×C7C24×C411yescharacteristic
585C4×C7C22×#4111yescharacteristic
586Dic7—24no—
587Dic7—22no—
588Dic7—22no—
589Dic7—42no—
590Dic7—42no—
591Dic7C2×C4×D414yes—
592C24—21no—
593C24—21no—
594C24—71no—
595C24—144no—
596C24—148no—
597C24—141no—
598C24—562no—
599C24—562no—
600#41—716no—
601#41—1416no—
602#41—148no—
603C2×Q8—74no—
604C2×Q8—72no—
605C2×Q8—141no—
606C2×Q8—142no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—716no—
612C2×D4—74no—
613C2×D4—72no—
614C2×D4—1416no—
615C2×D4—148no—
616C2×D4—144no—
617C2×D4—148no—
618C2×D4—144no—
619C2×D4—148no—
620C2×D4—141no—
621C2×D4—142no—
622C2×D4C2×C4×D714yes—
623C2×D4C2×C4×D714yes—
624C2×D4C23×D712yes—
625C2×D4C23×D712yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—71no—
631C22×C4—74no—
632C22×C4—72no—
633C22×C4—74no—
634C22×C4—72no—
635C22×C4—71no—
636C22×C4—71no—
637C22×C4—82no—
638C22×C4—82no—
639C22×C4—144no—
640C22×C4—144no—
641C22×C4—144no—
642C22×C4—148no—
643C22×C4—144no—
644C22×C4—144no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—141no—
648C22×C4—144no—
649C22×C4—562no—
650C22×C4—562no—
651C22×C4—562no—
652C22×C4—562no—
653C22×C4—562no—
654C22×C4D4×D711yescharacteristic
655C22×C4D4×D711yescharacteristic
656C22×C4C23×D711yescharacteristic
657SD16—716no—
658SD16—716no—
659D8—716no—
660D8C2×C4×D7116yescomplemented
661M16—716no—
662C2×C8—22no—
663C2×C8—74no—
664C2×C8—72no—
665C2×C8—72no—
666C2×C8—148no—
667C2×C8—142no—
668C2×C8C2×C4×D714yes—
669C2×C8C23×D712yes—
670C2×C8C23×D712yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—74no—
674C4⋊C4—74no—
675C4⋊C4—72no—
676C4⋊C4—72no—
677C4⋊C4—144no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—141no—
681C4⋊C4—141no—
682C4⋊C4C23×D712yes—
683C4⋊C4C23×D712yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—74no—
687C22⋊C4—74no—
688C22⋊C4—144no—
689C22⋊C4—144no—
690C22⋊C4—144no—
691C22⋊C4—144no—
692C22⋊C4—144no—
693C42—72no—
694C42—72no—
695C42—144no—
696C42—144no—
697C42—144no—
698C42D4×D712yes—
699C42C23×D712yes—
700C2×C7—44no—
701C2×C7—44no—
702C2×C7#294614yescomplemented
703C2×C7C22×C4×D411yescharacteristic
704C2×C7C2×#57611yescharacteristic
705C2×C7C2×#57711yescharacteristic
706D7—24no—
707D7—44no—
708C23—24no—
709C23—24no—
710C23—22no—
711C23—22no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—74no—
717C23—72no—
718C23—1416no—
719C23—142no—
720C23—142no—
721C23—144no—
722C23—142no—
723C23—282no—
724C23—282no—
725C23—564no—
726C23—564no—
727C23—5616no—
728C23C2×D4×D711yescharacteristic
729Q8—74no—
730Q8—144no—
731Q8—142no—
732D4—24no—
733D4—24no—
734D4—22no—
735D4—22no—
736D4—74no—
737D4—1416no—
738D4—1416no—
739D4—144no—
740D4—142no—
741D4C22×C4×D714yes—
742D4C22×C4×D714yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—74no—
750C2×C4—72no—
751C2×C4—78no—
752C2×C4—74no—
753C2×C4—74no—
754C2×C4—72no—
755C2×C4—72no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4—1416no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—144no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—282no—
766C2×C4—282no—
767C2×C4—564no—
768C2×C4—564no—
769C2×C4—564no—
770C2×C4—564no—
771C2×C4—564no—
772C2×C4C22×C4×D712yes—
773C2×C4C2×D4×D712yes—
774C2×C4C2×D4×D712yes—
775C2×C4C2×D4×D711yescharacteristic
776C2×C4D7×#4112yes—
777C2×C4C24×D711yescharacteristic
778C8—22no—
779C8—74no—
780C8—142no—
781C8C22×C4×D714yes—
782C7C2×#294611yescharacteristic, complemented, Sylow
783C22—24no—
784C22—24no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—48no—
790C22—48no—
791C22—74no—
792C22—142no—
793C22—142no—
794C22—148no—
795C22—144no—
796C22—282no—
797C22—282no—
798C22—288no—
799C22—5616no—
800C22C4×D4×D712yes—
801C22#9046512yes—
802C22#9046612yes—
803C22C22×D4×D711yescharacteristic
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—74no—
809C4—142no—
810C4—142no—
811C4—144no—
812C4—282no—
813C4—282no—
814C4C4×D4×D712yes—
815C4C23×C4×D711yescharacteristic
816C4C2×D7×#4111yescharacteristic
817C2—44no—
818C2—44no—
819C2—144no—
820C2—284no—
821C2#1173731114yesdirect product factor
822C2C2×C4×D4×D711yescharacteristic
823C2C2×#9046511yescharacteristic
824C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#442C2
socleC23×C7C22×D4
prime radicalC22×#6474C2
cosocleC2×C4×C7C25
hypercenterC2×#442D7
hypocenterC7C2×#2946
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#90236C2semidirect
3. C2×#90237C2semidirect
4. C2×C7×#442C2semidirect
5. C2×D8×Dic7C2semidirect
6. C2×C4×#1142C2semidirect
7. C2×C4×#1141C2semidirect
8. #11737311C2direct (N × H)
9. C2×#89633C2semidirect
10. C2×#89624C2semidirect
11. C2×#89544C2semidirect
12. C2×D7×#102C2semidirect
13. C2×#89557C2semidirect
14. C2×#89529C2semidirect
15. C2×#89482C2semidirect
16. C2×#89480C2semidirect
21. C2×C4×C7×D4C22semidirect
23. C2×D4×Dic7C22semidirect
30. C2×#6474C4semidirect
36. #90237C22semidirect
38. #90236C22semidirect
42. C2×#6450C22semidirect
49. C2×C4×Dic14C22semidirect
50. C7×#442C22semidirect
51. C2×C7×#106C22semidirect
53. C2×C7×#102C22semidirect
54. C2×C7×#97C22semidirect
56. C2×#6406C22semidirect
57. D8×Dic7C22semidirect
59. C2×#6392C22semidirect
60. C2×#6390C22semidirect
61. C2×#6389C22semidirect
62. C2×C8×Dic7C22semidirect
63. C4×#1142C22semidirect
64. C4×#1141C22semidirect
65. C2×#6384C22semidirect
67. C2×#6382C22semidirect
68. C2×#6381C22semidirect
69. C2×C4×C7⋊C8C22semidirect
70. #89633C22semidirect
71. #89624C22semidirect
72. #89557C22semidirect
73. #89544C22semidirect
74. D7×#102C22semidirect
75. #89529C22semidirect
76. #89482C22semidirect
77. #89480C22semidirect
91. C2×#1159C2×C4semidirect
95. C2×D4×D7C2×C4semidirect
103. C2×C7×D8C2×C4semidirect
110. C4×C7×D4C23semidirect
121. D4×Dic7C23semidirect
122. C2×#1142C2×C4semidirect
124. C2×#1141C2×C4semidirect
148. #6474C2×C4semidirect
149. C2×#1132C2×C4semidirect
151. C2×#1131C2×C4semidirect
162. #6450C23semidirect
172. C4×Dic14C23semidirect
173. C7×#106C23semidirect
175. C7×#102C23semidirect
176. C7×#97C23semidirect
178. #6406C23semidirect
180. #6392C23semidirect
181. #6390C23semidirect
182. #6389C23semidirect
183. C8×Dic7C23semidirect
184. #6384C23semidirect
186. #6382C23semidirect
187. #6381C23semidirect
188. C4×C7⋊C8C23semidirect
194. C2×#442D7semidirect
248. #1159C22×C4semidirect
251. D4×D7C22×C4semidirect
270. C7×D8C22×C4semidirect
285. #1142C22×C4semidirect
286. #1141C22×C4semidirect
310. #1132C22×C4semidirect
311. #1131C22×C4semidirect
338. C2×C4×D4C2×D7semidirect
347. #442C2×D7semidirect
358. C2×#106C2×D7semidirect
368. C2×#102C2×D7semidirect
371. C2×#97C2×D7semidirect
479. C2×D8C4×D7semidirect
508. C4×D4C22×D7semidirect
545. #106C22×D7semidirect
553. #102C22×D7semidirect
555. #97C22×D7semidirect
660. D8C2×C4×D7semidirect
702. C2×C7#2946semidirect
782. C7C2×#2946semidirect
821. C2#11737311direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64742
C2×#902362
C2×#902372
C2×C7×#4422
C2×D8×Dic72
C2×C4×#11422
C2×C4×#11412
#117373112
C2×#896332
C2×#896242
C2×#895442
C2×D7×#1022
C2×#895572
C2×#895292
C2×#894822
C2×#894802
C2×#29467