Finite Group Databasebeta

← C2×#11736998 #14230595

Subgroups — C2×#11736998 #14230595

Order 1792.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90241C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic, complemented
3C2×C7×#436C211yesmaximal, characteristic, complemented
4C2×#89907C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic, complemented
6C2×#89905C211yesmaximal, characteristic, complemented
7C2×#89903C211yesmaximal, characteristic, complemented
8#11736998C2116yesmaximal, direct product factor
9C2×#89619C211yesmaximal, characteristic, complemented
10C2×#89616C211yesmaximal, characteristic, complemented
11C2×#89506C211yesmaximal, characteristic, complemented
12C2×#89504C211yesmaximal, characteristic, complemented
13C2×#89495C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×#89469C211yesmaximal, characteristic, complemented
16C2×C4×D56C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C23×D28C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic, complemented
21C2×C4×C7×D4C2211yescharacteristic
22C2×#6502—21no—
23C2×#6500—21no—
24C2×#6493C2211yescharacteristic
25C2×#6493C2211yescharacteristic
26C2×#6493C2211yescharacteristic, complemented
27C2×#6489C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic, complemented
29C2×#6487C2211yescharacteristic
30C22×D56C2211yescharacteristic
31C22×D56C2211yescharacteristic
32C22×#1132C2211yescharacteristic, complemented
33#90256—24no—
34#90256C2218yescomplemented
35#90241—24no—
36#90241C2218yescomplemented
37C2×#6461—21no—
38C2×#6457—21no—
39C2×#6447—21no—
40C2×#6446—21no—
41C2×(C22⋊D7)⋊C4—21no—
42C2×D7×C22⋊C4—21no—
43C2×#6438C2211yescharacteristic
44C2×C4×D28C2211yescharacteristic
45C2×C4×D28C2211yescharacteristic, complemented
46C2×#6433C2211yescharacteristic, complemented
47C7×#436C2218yescomplemented
48C2×C7×C4⋊C8C2211yescharacteristic, complemented
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C7×C8C2211yescharacteristic, complemented
52#89907C2218yescomplemented
53#89906C2218yescomplemented
54#89905C2218yescomplemented
55#89903C2218yescomplemented
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6395C2211yescharacteristic
60C2×#6395C2211yescharacteristic
61C2×#6395C2211yescharacteristic
62C2×#6395C2211yescharacteristic, complemented
63C2×#6392C2211yescharacteristic, complemented
64C2×#6392C2211yescharacteristic, complemented
65C2×#6391C2211yescharacteristic, complemented
66C2×#6390C2211yescharacteristic, complemented
67C2×#6390C2211yescharacteristic, complemented
68C2×#6390C2211yescharacteristic, complemented
69#89619C2218yescomplemented
70#89616C2218yescomplemented
71#89508C2218yescomplemented
72#89506C2218yescomplemented
73#89504C2218yescomplemented
74#89495C2218yescomplemented
75#89469C2218yescomplemented
76C4×D56C2218yescomplemented
77C2×#3322—71nomaximal, Sylow
78C24×D7—21no—
79C22×C7×D4D411yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C23×Dic7—21no—
87C2×#1157—22no—
88C2×#1157—24no—
89C2×#1157—42no—
90C2×#1157C2314yes—
91C22×D28—24no—
92C22×D28—21no—
93C22×D28—22no—
94C22×D28—42no—
95C22×D28C2311yescharacteristic
96C22×D28C2311yescharacteristic
97C22×D28C2314yes—
98C22×D28C2311yescharacteristic
99C22×C4×D7—21no—
100C22×C4×D7—21no—
101C22×C4×D7—21no—
102C22×Dic14C2311yescharacteristic
103C2×C7×M16—42no—
104C2×C7×M16—42no—
105C2×C7×M16C2314yes—
106C2×C7×M16C2314yescomplemented
107C22×C7×C8C2311yescharacteristic
108C22×C7×C8C2311yescharacteristic
109C22×C7×C8C2311yescharacteristic
110C22×C7×C8C2311yescharacteristic
111C4×C7×D4D414yes—
112C4×C7×D4C2314yes—
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C22⋊C4D411yescharacteristic
115C2×C7×C22⋊C4D411yescharacteristic
116C2×C42×C7C2311yescharacteristic
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7—21no—
119#6502—28no—
120#6500—28no—
121#6493—22no—
122#6493—22no—
123#6493—22no—
124#6493C2314yes—
125#6493C2314yes—
126#6493C2314yescomplemented
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134#6489—22no—
135#6489C2314yes—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—22no—
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yescomplemented
143#6487—22no—
144#6487C2314yes—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×C4×Dic7—21no—
149C2×D56—24no—
150C2×D56—42no—
151C2×D56C2314yes—
152C2×D56C2314yes—
153C2×#1132—42no—
154C2×#1132C2314yescomplemented
155#6461—28no—
156#6457—28no—
157#6447—28no—
158#6446—28no—
159(C22⋊D7)⋊C4—28no—
160D7×C22⋊C4—28no—
161#6438—22no—
162#6438C2314yes—
163C4×D28—22no—
164C4×D28—22no—
165C4×D28C2314yes—
166C4×D28C2314yescomplemented
167#6433—22no—
168#6433C2314yescomplemented
169C7×C4⋊C8C2314yescomplemented
170C7×C22⋊C8C2314yes—
171C7×C22⋊C8C2314yescomplemented
172C4×C7×C8C2314yescomplemented
173#6395C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177#6395C2314yes—
178#6395C2314yes—
179#6395C2314yescomplemented
180#6392C2314yescomplemented
181#6392C2314yescomplemented
182#6391C2314yescomplemented
183#6390C2314yescomplemented
184#6390C2314yescomplemented
185#6390C2314yescomplemented
186C2×#553—71no—
187C2×#546—71no—
188#3322—716no—
189C2×#488—71no—
190C2×#485—71no—
191C2×#480—71no—
192C2×#478—71no—
193C2×#469—71no—
194C2×#468—71no—
195C2×#463—71no—
196C2×#449—71no—
197C2×#447—71no—
198C2×C4×D8—71no—
199C2×#436D711yescharacteristic, complemented
200C2×#417—71no—
201C2×#418—71no—
202C24×C7C2×D411yescharacteristic
203C24×C7C2×D411yescharacteristic
204C23×D7—21no—
205C23×D7—21no—
206C23×D7—21no—
207C23×D7—24no—
208C23×D7—44no—
209C23×D7—44no—
210C23×D7—82no—
211C2×C7×D4—42no—
212C2×C7×D4C2×D414yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2411yescharacteristic
226C2×C22⋊D7—24no—
227C2×C22⋊D7—24no—
228C2×C22⋊D7—24no—
229C2×C22⋊D7—24no—
230C2×C22⋊D7—44no—
231C2×C22⋊D7—44no—
232C2×C22⋊D7—82no—
233C2×C22⋊D7—82no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—24no—
240C22×Dic7—82no—
241#1157—28no—
242#1157—44no—
243#1157—48no—
244C2×D28—21no—
245C2×D28—22no—
246C2×D28—22no—
247C2×D28—22no—
248C2×D28—22no—
249C2×D28—22no—
250C2×D28—28no—
251C2×D28—21no—
252C2×D28—21no—
253C2×D28—24no—
254C2×D28—44no—
255C2×D28—48no—
256C2×D28—44no—
257C2×D28#4114yes—
258C2×D28C2412yes—
259C2×D28C2412yes—
260C2×D28C2412yes—
261C2×C4×D7—24no—
262C2×C4×D7—24no—
263C2×C4×D7—24no—
264C2×C4×D7—44no—
265C2×C4×D7—82no—
266C2×C4×D7—82no—
267C2×Dic14—22no—
268C2×Dic14—22no—
269C2×Dic14—21no—
270C2×Dic14C2412yes—
271C7×M16—44no—
272C7×M16—44no—
273C2×C7×C8—22no—
274C2×C7×C8—22no—
275C2×C7×C8—22no—
276C2×C7×C8—22no—
277C2×C7×C8C2412yes—
278C2×C7×C8C2412yes—
279C2×C7×C8C2412yes—
280C2×C7×C8C2412yes—
281C7×C4⋊C4C2×D414yes—
282C7×C22⋊C4C2×D414yes—
283C7×C22⋊C4C2×D414yes—
284C42×C7C2×D412yes—
285C42×C7C2412yes—
286C22⋊Dic7—24no—
287C22⋊Dic7—24no—
288(C2×D7)⋊C4—24no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4—24no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—24no—
293(C2×D7)⋊C4—24no—
294(C2×D7)⋊C4—24no—
295C4⋊Dic7—21no—
296C4⋊Dic7—21no—
297C4⋊Dic7—21no—
298C4⋊Dic7—21no—
299C4⋊Dic7—24no—
300C4⋊Dic7C2412yes—
301C4⋊Dic7C2412yes—
302C4⋊Dic7C2412yes—
303C4⋊Dic7C2412yes—
304Dic7⋊C4—24no—
305Dic7⋊C4—24no—
306Dic7⋊C4—24no—
307C4×Dic7—24no—
308D56—28no—
309D56—44no—
310#1132—44no—
311C22×#41—71no—
312C23×D4—71no—
313C22×SD16—71no—
314C22×D8—71no—
315C22×D8—71no—
316C22×M16C2×D711yescharacteristic
317C22×M16C2×D711yescharacteristic, complemented
318#553—78no—
319#553—144no—
320#546—78no—
321#546—144no—
322C2×#126—141no—
323C2×#125—71no—
324C2×#124—71no—
325C2×#123—141no—
326C2×#123—141no—
327C2×C22⋊Q8—71no—
328C2×#121—71no—
329C2×#121—71no—
330C2×#121—71no—
331C2×#121—141no—
332C2×#121—141no—
333C2×#120—141no—
334C2×C4×D4—71no—
335C2×C4×D4—71no—
336C2×C4×D4—141no—
337C2×C4×D4C2×D711yescharacteristic
338C2×#117—71no—
339C22×C4⋊C4—71no—
340C22×C22⋊C4—141no—
341#488—78no—
342#485—78no—
343#480—78no—
344#478—78no—
345#469—78no—
346#468—78no—
347#463—78no—
348#449—78no—
349#447—78no—
350C4×D8—78no—
351#436C2×D718yescomplemented
352C2×#107—71no—
353C2×#107—71no—
354C2×#106—71no—
355C2×C4⋊C8C2×D711yescharacteristic, complemented
356#418—78no—
357#417—78no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×#102—71no—
366C2×#102—71no—
367C2×#102—71no—
368C2×C22⋊C8C2×D711yescharacteristic
369C2×C22⋊C8C2×D711yescharacteristic, complemented
370C2×C4×C8C2×D711yescharacteristic, complemented
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7C22×D412yes—
378C23×C7C22×D412yes—
379C23×C7C22×D411yescharacteristic
380C22×D7—24no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—48no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7—48no—
388C22×D7—42no—
389C22×D7—42no—
390C22×D7—42no—
391C22×D7—42no—
392C22×D7—42no—
393C22×D7—42no—
394C22×D7—84no—
395C22×D7—816no—
396C7×D4—44no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—24no—
402C2×C4×C7—24no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7C22×D412yes—
408C2×C4×C7C22×D412yes—
409C2×C4×C7C22×D412yes—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D411yescharacteristic
412C2×C4×C7C2×#4112yes—
413C2×C4×C7H(5,𝔽2)12yes—
414C2×C4×C7C2511yescharacteristic
415C22⋊D7—48no—
416C22⋊D7—48no—
417C22⋊D7—84no—
418C22⋊D7—84no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—42no—
425C2×Dic7—42no—
426C2×Dic7—42no—
427C2×Dic7—42no—
428C2×Dic7—42no—
429C2×Dic7—84no—
430D28—24no—
431D28—22no—
432D28—22no—
433D28—22no—
434D28—22no—
435D28—22no—
436D28—48no—
437D28—42no—
438D28—42no—
439D28C2×#4114yes—
440C4×D7—48no—
441C4×D7—84no—
442C4×D7—84no—
443Dic14—22no—
444Dic14—22no—
445Dic14—42no—
446C7×C8—22no—
447C7×C8—22no—
448C7×C8—22no—
449C7×C8—22no—
450C25—141no—
451C2×#41—74no—
452C2×#41—144no—
453C2×#41—142no—
454C2×#41—282no—
455C22×Q8—71no—
456C22×D4—71no—
457C22×D4—71no—
458C22×D4—71no—
459C22×D4—74no—
460C22×D4—144no—
461C22×D4—141no—
462C22×D4—141no—
463C22×D4—141no—
464C22×D4—141no—
465C22×D4—141no—
466C22×D4—142no—
467C22×D4—282no—
468C22×D4D2811yescharacteristic
469C23×C4—141no—
470C23×C4—141no—
471C23×C4—141no—
472C23×C4—141no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C2×SD16—74no—
476C2×SD16—282no—
477C2×D8—74no—
478C2×D8—74no—
479C2×D8—144no—
480C2×D8—282no—
481C2×M16—42no—
482C2×M16—42no—
483C2×M16C22×D714yes—
484C2×M16C22×D714yescomplemented
485C22×C8C22×D711yescharacteristic
486C22×C8C22×D711yescharacteristic
487C22×C8C22×D711yescharacteristic
488C22×C8C22×D711yescharacteristic
489#126—148no—
490#125—74no—
491#125—142no—
492#124—74no—
493#124—142no—
494#123—148no—
495#123—148no—
496C22⋊Q8—74no—
497C22⋊Q8—142no—
498#121—74no—
499#121—74no—
500#121—74no—
501#121—148no—
502#121—142no—
503#121—142no—
504#121—142no—
505#121—148no—
506#120—148no—
507C4×D4—74no—
508C4×D4—74no—
509C4×D4—148no—
510C4×D4—142no—
511C4×D4—142no—
512C4×D4D2814yes—
513C4×D4C22×D714yes—
514#117—74no—
515#117—142no—
516C2×C4⋊C4—71no—
517C2×C4⋊C4—71no—
518C2×C4⋊C4—74no—
519C2×C4⋊C4—71no—
520C2×C4⋊C4—71no—
521C2×C4⋊C4—141no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—141no—
524C2×C4⋊C4—141no—
525C2×C4⋊C4—141no—
526C2×C4⋊C4D2811yescharacteristic
527C2×C22⋊C4—141no—
528C2×C22⋊C4—141no—
529C2×C22⋊C4—141no—
530C2×C22⋊C4—141no—
531C2×C22⋊C4—141no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4—141no—
536C2×C22⋊C4—148no—
537C2×C22⋊C4D2811yescharacteristic
538C2×C22⋊C4D2811yescharacteristic
539C2×C42—141no—
540C2×C42C22×D711yescharacteristic
541#107—74no—
542#107—74no—
543#106—74no—
544C4⋊C8C22×D714yescomplemented
545#103—74no—
546#103—74no—
547#103—74no—
548#102—74no—
549#102—74no—
550#102—74no—
551#102—74no—
552#102—74no—
553#102—74no—
554#102—74no—
555C22⋊C8C22×D714yes—
556C22⋊C8C22×D714yescomplemented
557C4×C8C22×D714yescomplemented
558C22×C7—22no—
559C22×C7—22no—
560C22×C7—22no—
561C22×C7—22no—
562C22×C7—22no—
563C22×C7—22no—
564C22×C7—44no—
565C22×C7—44no—
566C22×C7#54612yes—
567C22×C7#57512yes—
568C22×C7#57612yes—
569C22×C7C23×D411yescharacteristic
570C2×D7—24no—
571C2×D7—48no—
572C2×D7—42no—
573C2×D7—42no—
574C2×D7—42no—
575C2×D7—42no—
576C2×D7—42no—
577C2×D7—42no—
578C2×D7—42no—
579C2×D7—42no—
580C2×D7—816no—
581C2×D7—84no—
582C2×D7—84no—
583C4×C7—22no—
584C4×C7—22no—
585C4×C7—22no—
586C4×C7—22no—
587C4×C7#54612yes—
588C4×C7C22×#4111yescharacteristic
589C4×C7C2×H(5,𝔽2)11yescharacteristic
590Dic7—42no—
591Dic7—42no—
592Dic7—42no—
593Dic7—42no—
594Dic7—42no—
595C24—141no—
596C24—141no—
597C24—141no—
598C24—144no—
599C24—284no—
600C24—284no—
601C24—562no—
602C24C2×D2811yescharacteristic
603C24C2×D2811yescharacteristic
604#41—148no—
605#41—284no—
606#41—288no—
607C2×Q8—72no—
608C2×Q8—141no—
609C2×Q8—142no—
610C2×Q8—142no—
611C2×D4—42no—
612C2×D4—74no—
613C2×D4—72no—
614C2×D4—72no—
615C2×D4—72no—
616C2×D4—148no—
617C2×D4—144no—
618C2×D4—144no—
619C2×D4—144no—
620C2×D4—144no—
621C2×D4—141no—
622C2×D4—141no—
623C2×D4—144no—
624C2×D4—141no—
625C2×D4—142no—
626C2×D4—142no—
627C2×D4—142no—
628C2×D4—142no—
629C2×D4—142no—
630C2×D4—284no—
631C2×D4—288no—
632C2×D4—284no—
633C2×D4—284no—
634C2×D4—284no—
635C2×D4—562no—
636C2×D4—562no—
637C2×D4C2×D2814yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—144no—
648C22×C4—144no—
649C22×C4—144no—
650C22×C4—144no—
651C22×C4—284no—
652C22×C4—562no—
653C22×C4—562no—
654C22×C4—562no—
655C22×C4C2×D2812yes—
656C22×C4C2×D2812yes—
657C22×C4C2×D2811yescharacteristic
658C22×C4C2×D2811yescharacteristic
659C22×C4C2×D2811yescharacteristic
660C22×C4C2×D2811yescharacteristic
661C22×C4C23×D712yes—
662C22×C4C23×D712yes—
663C22×C4C23×D711yescharacteristic
664SD16—284no—
665D8—148no—
666D8—284no—
667M16—44no—
668M16—44no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8C23×D712yes—
674C2×C8C23×D712yes—
675C2×C8C23×D712yes—
676C2×C8C23×D712yes—
677C4⋊C4—72no—
678C4⋊C4—72no—
679C4⋊C4—72no—
680C4⋊C4—72no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—144no—
684C4⋊C4—141no—
685C4⋊C4—141no—
686C4⋊C4—144no—
687C4⋊C4—141no—
688C4⋊C4—141no—
689C4⋊C4C2×D2814yes—
690C22⋊C4—144no—
691C22⋊C4—144no—
692C22⋊C4—144no—
693C22⋊C4—144no—
694C22⋊C4—144no—
695C22⋊C4—144no—
696C22⋊C4—144no—
697C22⋊C4—144no—
698C22⋊C4—144no—
699C22⋊C4C2×D2814yes—
700C22⋊C4C2×D2814yes—
701C42—144no—
702C42C2×D2812yes—
703C42C23×D712yes—
704C2×C7—42no—
705C2×C7—42no—
706C2×C7#332214yescomplemented
707C2×C7C2×#54611yescharacteristic
708C2×C7C2×#57511yescharacteristic
709C2×C7C2×#57611yescharacteristic
710D7—44no—
711D7—82no—
712D7—82no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—144no—
720C23—142no—
721C23—142no—
722C23—142no—
723C23—288no—
724C23—288no—
725C23—282no—
726C23—282no—
727C23—282no—
728C23—282no—
729C23—282no—
730C23—282no—
731C23—282no—
732C23—282no—
733C23—564no—
734C23—5616no—
735C23C22×D2812yes—
736C23C22×D2812yes—
737C23C22×D2811yescharacteristic
738Q8—142no—
739Q8—142no—
740Q8—282no—
741D4—44no—
742D4—74no—
743D4—144no—
744D4—142no—
745D4—142no—
746D4—142no—
747D4—142no—
748D4—142no—
749D4—288no—
750D4—288no—
751D4—288no—
752D4—282no—
753D4—282no—
754D4—564no—
755D4—564no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—288no—
772C2×C4—282no—
773C2×C4—282no—
774C2×C4—282no—
775C2×C4—282no—
776C2×C4—282no—
777C2×C4—564no—
778C2×C4—564no—
779C2×C4—564no—
780C2×C4C22×D2812yes—
781C2×C4C22×D2812yes—
782C2×C4C22×D2812yes—
783C2×C4C22×D2812yes—
784C2×C4C22×D2811yescharacteristic
785C2×C4#654812yes—
786C2×C4D7×#4112yes—
787C2×C4C24×D711yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—22no—
792C7C2×#332211yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—144no—
802C22—288no—
803C22—282no—
804C22—282no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—282no—
809C22—282no—
810C22—282no—
811C22—5616no—
812C22—564no—
813C22—564no—
814C22#9024512yes—
815C22#9043912yes—
816C22#9044312yes—
817C22C23×D2811yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—282no—
823C4—282no—
824C4—282no—
825C4—282no—
826C4—282no—
827C4#9024512yes—
828C4C2×#654811yescharacteristic
829C4C2×D7×#4111yescharacteristic
830C2—42no—
831C2—42no—
832C2—284no—
833C2—562no—
834C2—562no—
835C2#1173699814yesdirect product factor
836C2C2×#9024511yescharacteristic
837C2C2×#9043911yescharacteristic
838C2C2×#9044311yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#436C2
socleC23×C7C22×D4
hypercenterC2×#436D7
hypocenterC7C2×#3322
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#90241C2semidirect
2. C2×#90256C2semidirect
3. C2×C7×#436C2semidirect
4. C2×#89907C2semidirect
5. C2×#89906C2semidirect
6. C2×#89905C2semidirect
7. C2×#89903C2semidirect
8. #11736998C2direct (N × H)
9. C2×#89619C2semidirect
10. C2×#89616C2semidirect
11. C2×#89506C2semidirect
12. C2×#89504C2semidirect
13. C2×#89495C2semidirect
14. C2×#89508C2semidirect
15. C2×#89469C2semidirect
16. C2×C4×D56C2semidirect
20. C22×C7×M16C22semidirect
26. C2×#6493C22semidirect
28. C22×C4⋊Dic7C22semidirect
32. C22×#1132C22semidirect
34. #90256C22semidirect
36. #90241C22semidirect
45. C2×C4×D28C22semidirect
46. C2×#6433C22semidirect
47. C7×#436C22semidirect
48. C2×C7×C4⋊C8C22semidirect
50. C2×C7×C22⋊C8C22semidirect
51. C2×C4×C7×C8C22semidirect
52. #89907C22semidirect
53. #89906C22semidirect
54. #89905C22semidirect
55. #89903C22semidirect
62. C2×#6395C22semidirect
63. C2×#6392C22semidirect
64. C2×#6392C22semidirect
65. C2×#6391C22semidirect
66. C2×#6390C22semidirect
67. C2×#6390C22semidirect
68. C2×#6390C22semidirect
69. #89619C22semidirect
70. #89616C22semidirect
71. #89508C22semidirect
72. #89506C22semidirect
73. #89504C22semidirect
74. #89495C22semidirect
75. #89469C22semidirect
76. C4×D56C22semidirect
106. C2×C7×M16C23semidirect
126. #6493C23semidirect
142. C2×C4⋊Dic7C23semidirect
154. C2×#1132C23semidirect
166. C4×D28C23semidirect
168. #6433C23semidirect
169. C7×C4⋊C8C23semidirect
171. C7×C22⋊C8C23semidirect
172. C4×C7×C8C23semidirect
179. #6395C23semidirect
180. #6392C23semidirect
181. #6392C23semidirect
182. #6391C23semidirect
183. #6390C23semidirect
184. #6390C23semidirect
185. #6390C23semidirect
199. C2×#436D7semidirect
317. C22×M16C2×D7semidirect
351. #436C2×D7semidirect
355. C2×C4⋊C8C2×D7semidirect
369. C2×C22⋊C8C2×D7semidirect
370. C2×C4×C8C2×D7semidirect
484. C2×M16C22×D7semidirect
544. C4⋊C8C22×D7semidirect
556. C22⋊C8C22×D7semidirect
557. C4×C8C22×D7semidirect
706. C2×C7#3322semidirect
792. C7C2×#3322semidirect
835. C2#11736998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902412
C2×#902562
C2×C7×#4362
C2×#899072
C2×#899062
C2×#899052
C2×#899032
#117369982
C2×#896192
C2×#896162
C2×#895062
C2×#895042
C2×#894952
C2×#895082
C2×#894692
C2×C4×D562
C2×#33227