Finite Group Databasebeta

← C2×#11741060 #14230428

Subgroups — C2×#11741060 #14230428

Order 1792.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic, complemented
2C2×#90242C211yesmaximal, characteristic, complemented
3#11741060C2116yesmaximal, direct product factor
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89841C211yesmaximal, characteristic, complemented
6C2×#89809C211yesmaximal, characteristic, complemented
7C2×#89809C211yesmaximal, characteristic, complemented
8C2×#89814C211yesmaximal, characteristic, complemented
9C2×#89813C211yesmaximal, characteristic, complemented
10C2×#89791C211yesmaximal, characteristic, complemented
11C2×#89783C211yesmaximal, characteristic, complemented
12C2×#89786C211yesmaximal, characteristic, complemented
13C2×#89768C211yesmaximal, characteristic, complemented
14C2×#89774C211yesmaximal, characteristic, complemented
15C2×#89743C211yesmaximal, characteristic, complemented
16C2×#89738C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C7×#553—24no—
20C7×#553C2218yescomplemented
21C2×C7×#126—21no—
22C2×C7×#125C2211yescharacteristic
23C2×C7×#123—21no—
24C2×C7×#121—21no—
25C2×C7×#121C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×D4—21no—
28C2×C4×C7×D4C2211yescharacteristic
29C2×C4×C7×D4C2211yescharacteristic
30C2×C7×#117C2211yescharacteristic
31C22×C7×C4⋊C4C2211yescharacteristic
32C2×#6501—21no—
33C22×#1142C2211yescharacteristic
34C22×#1142C2211yescharacteristic
35C22×#1141C2211yescharacteristic
36C2×#6487C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90242—24no—
41#90242C2218yescomplemented
42C2×D7×C4⋊C4—21no—
43C2×#6446—21no—
44C2×#6446—21no—
45C2×C4×D28C2211yescharacteristic
46C2×#6432C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89841C2218yescomplemented
51#89838C2218yescomplemented
52#89814C2218yescomplemented
53#89813C2218yescomplemented
54#89809C2218yescomplemented
55#89809C2218yescomplemented
56#89791C2218yescomplemented
57#89786C2218yescomplemented
58#89783C2218yescomplemented
59#89774C2218yescomplemented
60#89768C2218yescomplemented
61#89743C2218yescomplemented
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6384C2211yescharacteristic
68#89738C2218yescomplemented
69C2×#6383C2211yescharacteristic
70C2×#6383C2211yescharacteristic
71C2×#6383C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6382C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3307—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4D411yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7—21no—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C22×C22⋊D7—21no—
87C22×C22⋊D7—21no—
88C2×#1157—22no—
89C2×#1157—22no—
90C2×#1157—24no—
91C2×#1157—24no—
92C2×#1157—42no—
93C2×#1157—42no—
94C2×#1157C2314yes—
95C2×#1157C2314yes—
96C22×D28C2311yescharacteristic
97C22×C4×D7—21no—
98C22×C4×D7—21no—
99C22×C4×D7—21no—
100C22×Dic14C2311yescharacteristic
101C22×Dic14C2311yescharacteristic
102C7×#126—28no—
103C7×#125—22no—
104C7×#125C2314yes—
105C7×#123—28no—
106C7×#121—28no—
107C7×#121—22no—
108C7×#121—22no—
109C7×#121C2314yes—
110C7×#121C2314yes—
111C4×C7×D4—28no—
112C4×C7×D4—22no—
113C4×C7×D4D414yes—
114C4×C7×D4C2314yes—
115C4×C7×D4C2314yes—
116C7×#117—22no—
117C7×#117C2314yes—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—22no—
120C2×C7×C4⋊C4—21no—
121C2×C7×C4⋊C4—21no—
122C2×C7×C4⋊C4D411yescharacteristic
123C2×C7×C4⋊C4C2311yescharacteristic
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C4⋊C4C2314yes—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—21no—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4D411yescharacteristic
132C2×C7×C22⋊C4D411yescharacteristic
133C2×C42×C7—21no—
134C2×C42×C7C2311yescharacteristic
135C2×C22⋊Dic7—21no—
136C2×C22⋊Dic7—21no—
137#6501—28no—
138C2×#1142—42no—
139C2×#1142—42no—
140C2×#1142C2314yes—
141C2×#1142C2314yes—
142C2×#1141—24no—
143C2×#1141C2314yes—
144C2×(C2×D7)⋊C4—21no—
145C2×C4⋊Dic7—21no—
146C2×C4⋊Dic7—21no—
147C2×C4⋊Dic7C2311yescharacteristic
148#6487—22no—
149#6487—22no—
150#6487C2314yes—
151#6487C2314yes—
152C2×Dic7⋊C4—21no—
153C2×Dic7⋊C4—21no—
154C2×#1136—42no—
155C2×#1136C2314yes—
156C22×C7⋊C8—42no—
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162D7×C4⋊C4—28no—
163#6446—28no—
164#6446—28no—
165C4×D28—22no—
166C4×D28C2314yes—
167#6432—22no—
168#6432C2314yes—
169#6406C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171C22⋊(C7⋊C8)C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6384C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6383C2314yes—
179#6383C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6382C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#553D711yescharacteristic, complemented
187C2×#547—71no—
188#3307—716no—
189C2×#491—71no—
190C2×#485—71no—
191C2×#483—71no—
192C2×#478—71no—
193C2×#468—71no—
194C2×#465—71no—
195C2×#461—71no—
196C2×#449—71no—
197C2×#449—71no—
198C2×#442—71no—
199C2×#435—71no—
200C2×#417—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C24×C7C2×D411yescharacteristic
205C23×D7—21no—
206C2×C7×D4—24no—
207C2×C7×D4—24no—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—42no—
212C2×C7×D4—44no—
213C2×C7×D4—82no—
214C2×C7×D4C2×D414yes—
215C2×C7×D4C2412yes—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—21no—
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×C7C2×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2411yescharacteristic
236C2×C22⋊D7—24no—
237C2×C22⋊D7—24no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—44no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243#1157—28no—
244#1157—28no—
245#1157—44no—
246#1157—44no—
247#1157—48no—
248#1157—48no—
249C2×D28—21no—
250C2×D28—22no—
251C2×D28#4114yes—
252C2×D28C2412yes—
253C2×C4×D7—24no—
254C2×C4×D7—24no—
255C2×C4×D7—24no—
256C2×C4×D7—44no—
257C2×C4×D7—44no—
258C2×C4×D7—44no—
259C2×Dic14—22no—
260C2×Dic14—22no—
261C2×Dic14—22no—
262C2×Dic14—22no—
263C2×Dic14—21no—
264C2×Dic14—21no—
265C2×Dic14C2412yes—
266C2×Dic14C2412yes—
267C7×C4⋊C4—21no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—24no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—21no—
273C7×C4⋊C4C2×D414yes—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C4⋊C4C2412yes—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—24no—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—24no—
281C7×C22⋊C4C2×D414yes—
282C7×C22⋊C4C2×D414yes—
283C42×C7—24no—
284C42×C7C2×D412yes—
285C42×C7C2412yes—
286C22⋊Dic7—24no—
287C22⋊Dic7—24no—
288#1142—44no—
289#1142—44no—
290#1141—28no—
291(C2×D7)⋊C4—24no—
292C4⋊Dic7—24no—
293C4⋊Dic7—24no—
294C4⋊Dic7—21no—
295C4⋊Dic7C2412yes—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298#1136—44no—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—22no—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—44no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307C2×C7⋊C8C2412yes—
308C22×#41—71no—
309C22×#41—71no—
310C22×SD16—71no—
311C22×SD16—71no—
312C22×D8—71no—
313C22×M16—71no—
314C23×C8—71no—
315#553—24no—
316#553C2×D718yescomplemented
317#547—78no—
318#547—144no—
319C2×C4⋊Q8—71no—
320C2×#126—21no—
321C2×#125C2×D711yescharacteristic
322C2×#123—21no—
323C2×#123—141no—
324C2×#123—141no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×#121—21no—
328C2×#121—141no—
329C2×#121C2×D711yescharacteristic
330C2×#121C2×D711yescharacteristic
331C2×C4×D4—21no—
332C2×C4×D4—71no—
333C2×C4×D4C2×D711yescharacteristic
334C2×C4×D4C2×D711yescharacteristic
335C2×#117C2×D711yescharacteristic
336C22×C4⋊C4—141no—
337C22×C4⋊C4C2×D711yescharacteristic
338#491—78no—
339#485—78no—
340#483—78no—
341#478—78no—
342#468—78no—
343#465—78no—
344#461—78no—
345#449—78no—
346#449—78no—
347#442—78no—
348#435—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#417—78no—
354#416—78no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×C22⋊C8—71no—
366C2×C22⋊C8—71no—
367C2×#97—71no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—42no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7C22×D412yes—
379C23×C7C22×D412yes—
380C23×C7C22×D411yescharacteristic
381C22×D7—24no—
382C22×D7—22no—
383C22×D7—42no—
384C22×D7—42no—
385C7×D4—22no—
386C7×D4—22no—
387C7×D4—44no—
388C7×D4—48no—
389C7×D4—42no—
390C7×D4—84no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—24no—
396C2×C4×C7—24no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—84no—
408C2×C4×C7—84no—
409C2×C4×C7C22×D412yes—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D411yescharacteristic
414C2×C4×C7C2×#4112yes—
415C2×C4×C7H(5,𝔽2)12yes—
416C2×C4×C7C2511yescharacteristic
417C22⋊D7—48no—
418C22⋊D7—48no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7—42no—
425D28—24no—
426D28—22no—
427D28C2×#4114yes—
428C4×D7—48no—
429C4×D7—48no—
430C4×D7—48no—
431Dic14—22no—
432Dic14—22no—
433Dic14—22no—
434Dic14—22no—
435Dic14—42no—
436Dic14—42no—
437C7⋊C8—22no—
438C7⋊C8—22no—
439C7⋊C8—22no—
440C7⋊C8—22no—
441C2×#41—74no—
442C2×#41—74no—
443C2×#41—144no—
444C2×#41—144no—
445C2×#41—142no—
446C2×#41—142no—
447C2×#41—282no—
448C2×#41—282no—
449C22×Q8—71no—
450C22×Q8—71no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—71no—
454C22×D4—141no—
455C22×D4—141no—
456C22×D4C22⋊D711yescharacteristic
457C22×D4C22×D711yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—141no—
461C23×C4—141no—
462C23×C4—141no—
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465C2×SD16—74no—
466C2×SD16—74no—
467C2×SD16—282no—
468C2×SD16—282no—
469C2×D8—74no—
470C2×D8—144no—
471C2×M16—74no—
472C2×M16—282no—
473C22×C8—71no—
474C22×C8—71no—
475C22×C8—71no—
476C22×C8—71no—
477C22×C8—74no—
478C22×C8—282no—
479C4⋊Q8—74no—
480C4⋊Q8—142no—
481#126—28no—
482#125—22no—
483#125C22×D714yes—
484#123—28no—
485#123—148no—
486#123—148no—
487C22⋊Q8—74no—
488C22⋊Q8—74no—
489C22⋊Q8—142no—
490C22⋊Q8—142no—
491#121—28no—
492#121—22no—
493#121—22no—
494#121—148no—
495#121C22×D714yes—
496#121C22×D714yes—
497C4×D4—28no—
498C4×D4—22no—
499C4×D4—74no—
500C4×D4—142no—
501C4×D4C22⋊D714yes—
502C4×D4C22×D714yes—
503C4×D4C22×D714yes—
504#117—22no—
505#117C22×D714yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—148no—
516C2×C4⋊C4C22⋊D711yescharacteristic
517C2×C4⋊C4C22×D711yescharacteristic
518C2×C4⋊C4C22×D711yescharacteristic
519C2×C4⋊C4C22×D714yes—
520C2×C4⋊C4C22×D711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—141no—
526C2×C22⋊C4—141no—
527C2×C22⋊C4—141no—
528C2×C22⋊C4C22⋊D711yescharacteristic
529C2×C22⋊C4C22⋊D711yescharacteristic
530C2×C42—21no—
531C2×C42C22×D711yescharacteristic
532#107—74no—
533#106—74no—
534#106—74no—
535C4⋊C8—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#103—74no—
542#102—74no—
543#102—74no—
544#102—74no—
545#102—74no—
546C22⋊C8—74no—
547C22⋊C8—74no—
548#97—74no—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—22no—
552C22×C7—22no—
553C22×C7—22no—
554C22×C7—22no—
555C22×C7—44no—
556C22×C7—44no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—84no—
561C22×C7#54612yes—
562C22×C7#57512yes—
563C22×C7#57712yes—
564C22×C7C23×D411yescharacteristic
565C2×D7—24no—
566C2×D7—48no—
567C2×D7—42no—
568C2×D7—42no—
569C4×C7—22no—
570C4×C7—22no—
571C4×C7—22no—
572C4×C7—22no—
573C4×C7—42no—
574C4×C7—42no—
575C4×C7—42no—
576C4×C7#54612yes—
577C4×C7C22×#4111yescharacteristic
578C4×C7C2×H(5,𝔽2)11yescharacteristic
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—21no—
583C24—141no—
584C24C2×C22⋊D711yescharacteristic
585C24C2×C22⋊D711yescharacteristic
586#41—148no—
587#41—148no—
588#41—284no—
589#41—284no—
590#41—288no—
591#41—288no—
592C2×Q8—72no—
593C2×Q8—72no—
594C2×Q8—141no—
595C2×Q8—141no—
596C2×Q8—142no—
597C2×Q8—142no—
598C2×Q8—142no—
599C2×Q8—142no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—44no—
607C2×D4—74no—
608C2×D4—72no—
609C2×D4—82no—
610C2×D4—144no—
611C2×D4—144no—
612C2×D4—142no—
613C2×D4—141no—
614C2×D4—284no—
615C2×D4—284no—
616C2×D4C2×C22⋊D714yes—
617C2×D4C23×D712yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—144no—
633C22×C4—144no—
634C22×C4—144no—
635C22×C4—284no—
636C22×C4—284no—
637C22×C4—284no—
638C22×C4C2×C22⋊D712yes—
639C22×C4C2×C22⋊D712yes—
640C22×C4C2×C22⋊D711yescharacteristic
641C22×C4C2×C22⋊D711yescharacteristic
642C22×C4C2×C22⋊D711yescharacteristic
643C22×C4C2×C22⋊D711yescharacteristic
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647SD16—284no—
648SD16—284no—
649D8—148no—
650M16—284no—
651C2×C8—72no—
652C2×C8—72no—
653C2×C8—72no—
654C2×C8—72no—
655C2×C8—142no—
656C2×C8—142no—
657C2×C8—142no—
658C2×C8—142no—
659C2×C8—284no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—21no—
666C4⋊C4—72no—
667C4⋊C4—144no—
668C4⋊C4—144no—
669C4⋊C4—141no—
670C4⋊C4—144no—
671C4⋊C4—144no—
672C4⋊C4C2×C22⋊D714yes—
673C4⋊C4C23×D712yes—
674C4⋊C4C23×D712yes—
675C4⋊C4C23×D712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C22⋊C4—144no—
683C22⋊C4C2×C22⋊D714yes—
684C22⋊C4C2×C22⋊D714yes—
685C42—24no—
686C42C2×C22⋊D712yes—
687C42C23×D712yes—
688C2×C7—42no—
689C2×C7—42no—
690C2×C7—82no—
691C2×C7#330714yescomplemented
692C2×C7C2×#54611yescharacteristic
693C2×C7C2×#57511yescharacteristic
694C2×C7C2×#57711yescharacteristic
695D7—44no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—144no—
707C23—142no—
708C23—282no—
709C23—282no—
710C23C22×C22⋊D712yes—
711C23C22×C22⋊D712yes—
712C23C22×C22⋊D711yescharacteristic
713Q8—142no—
714Q8—142no—
715Q8—142no—
716Q8—142no—
717Q8—282no—
718Q8—282no—
719D4—22no—
720D4—22no—
721D4—44no—
722D4—48no—
723D4—42no—
724D4—74no—
725D4—84no—
726D4—144no—
727D4—142no—
728D4—288no—
729D4—288no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—288no—
752C2×C4—288no—
753C2×C4—288no—
754C2×C4—282no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4D7×#4112yes—
758C2×C4#655312yes—
759C2×C4C22×C22⋊D712yes—
760C2×C4C22×C22⋊D712yes—
761C2×C4C22×C22⋊D712yes—
762C2×C4C22×C22⋊D712yes—
763C2×C4C22×C22⋊D711yescharacteristic
764C2×C4C24×D711yescharacteristic
765C8—142no—
766C8—142no—
767C8—142no—
768C8—142no—
769C7C2×#330711yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—144no—
783C22—282no—
784C22—282no—
785C22—288no—
786C22#9051312yes—
787C22#9052012yes—
788C22#9052712yes—
789C22C23×C22⋊D711yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—282no—
798C4—282no—
799C4—282no—
800C4#9052012yes—
801C4C2×D7×#4111yescharacteristic
802C4C2×#655311yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—284no—
807C2#1174106014yesdirect product factor
808C2C2×#9051311yescharacteristic
809C2C2×#9052011yescharacteristic
810C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#553C2
socleC23×C7C22×D4
hypercenterC2×#553D7
hypocenterC7C2×#3307
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×C7×#553C2semidirect
2. C2×#90242C2semidirect
3. #11741060C2direct (N × H)
4. C2×#89838C2semidirect
5. C2×#89841C2semidirect
6. C2×#89809C2semidirect
7. C2×#89809C2semidirect
8. C2×#89814C2semidirect
9. C2×#89813C2semidirect
10. C2×#89791C2semidirect
11. C2×#89783C2semidirect
12. C2×#89786C2semidirect
13. C2×#89768C2semidirect
14. C2×#89774C2semidirect
15. C2×#89743C2semidirect
16. C2×#89738C2semidirect
20. C7×#553C22semidirect
41. #90242C22semidirect
50. #89841C22semidirect
51. #89838C22semidirect
52. #89814C22semidirect
53. #89813C22semidirect
54. #89809C22semidirect
55. #89809C22semidirect
56. #89791C22semidirect
57. #89786C22semidirect
58. #89783C22semidirect
59. #89774C22semidirect
60. #89768C22semidirect
61. #89743C22semidirect
68. #89738C22semidirect
186. C2×#553D7semidirect
316. #553C2×D7semidirect
691. C2×C7#3307semidirect
769. C7C2×#3307semidirect
807. C2#11741060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5532
C2×#902422
#117410602
C2×#898382
C2×#898412
C2×#898092
C2×#898142
C2×#898132
C2×#897912
C2×#897832
C2×#897862
C2×#897682
C2×#897742
C2×#897432
C2×#897382
C2×#33077