Finite Group Databasebeta

← C2×#11740909 #14225185

Subgroups — C2×#11740909 #14225185

Order 1792.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic, complemented
2C2×#90217C211yesmaximal, characteristic, complemented
3#11740909C2116yesmaximal, direct product factor
4C2×#89861C211yesmaximal, characteristic, complemented
5C2×#89865C211yesmaximal, characteristic, complemented
6C2×#89832C211yesmaximal, characteristic, complemented
7C2×#89831C211yesmaximal, characteristic, complemented
8C2×#89822C211yesmaximal, characteristic, complemented
9C2×#89819C211yesmaximal, characteristic, complemented
10C2×#89812C211yesmaximal, characteristic, complemented
11C2×#89809C211yesmaximal, characteristic
12C2×#89803C211yesmaximal, characteristic, complemented
13C2×#89800C211yesmaximal, characteristic, complemented
14C2×#89791C211yesmaximal, characteristic, complemented
15C2×#89788C211yesmaximal, characteristic, complemented
16C2×#89772C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C7×#542—24no—
20C7×#542C2218yescomplemented
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×#126—21no—
23C2×C7×#124—21no—
24C2×C7×#124C2211yescharacteristic
25C2×C7×#123—21no—
26C2×C7×C22⋊Q8—21no—
27C2×C7×C22⋊Q8C2211yescharacteristic
28C2×C7×#121C2211yescharacteristic
29C2×C4×C7×Q8C2211yescharacteristic
30C2×C4×C7×D4C2211yescharacteristic
31C2×C7×#117C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C22×#1144C2211yescharacteristic
34C22×#1144C2211yescharacteristic
35C22×#1143C2211yescharacteristic
36C22×#1142C2211yescharacteristic
37C22×#1142C2211yescharacteristic
38C22×#1142C2211yescharacteristic
39C22×#1141C2211yescharacteristic
40#90217—24no—
41#90217C2218yescomplemented
42C2×#6460—21no—
43C2×#6460—21no—
44C2×#6449—21no—
45C2×#6449—21no—
46C2×#6438C2211yescharacteristic
47C2×#6438C2211yescharacteristic
48C2×#6432C2211yescharacteristic
49C2×#6432C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52#89865C2218yescomplemented
53#89861C2218yescomplemented
54#89832C2218yescomplemented
55#89831C2218yescomplemented
56#89822C2218yescomplemented
57#89819C2218yescomplemented
58#89812C2218yescomplemented
59#89809C2218yes—
60#89803C2218yescomplemented
61#89800C2218yescomplemented
62#89791C2218yescomplemented
63#89788C2218yescomplemented
64#89772C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6384C2211yescharacteristic
70C2×#6384C2211yescharacteristic
71C2×#6383C2211yescharacteristic
72C2×#6383C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3225—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—21no—
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C2×#1157—22no—
87C2×#1157—42no—
88C2×#1157—42no—
89C2×#1157C2314yes—
90C22×D28C2311yescharacteristic
91C22×C4×D7—21no—
92C22×Dic14—21no—
93C22×Dic14—22no—
94C22×Dic14—42no—
95C22×Dic14—42no—
96C22×Dic14C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C22×Dic14C2314yes—
100C7×C4⋊Q8—22no—
101C7×C4⋊Q8C2314yes—
102C7×#126—28no—
103C7×#124—28no—
104C7×#124—22no—
105C7×#124C2314yes—
106C7×#123—28no—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—28no—
109C7×C22⋊Q8C2314yes—
110C7×#121—22no—
111C7×#121C2314yes—
112C4×C7×Q8—22no—
113C4×C7×Q8C2314yes—
114C4×C7×D4—22no—
115C4×C7×D4C2314yes—
116C7×#117D414yes—
117C7×#117C2314yes—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4—21no—
121C2×C7×C4⋊C4D411yescharacteristic
122C2×C7×C4⋊C4D411yescharacteristic
123C2×C7×C4⋊C4C2311yescharacteristic
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C22⋊C4—21no—
126C2×C7×C22⋊C4—21no—
127C2×C7×C22⋊C4—21no—
128C2×C7×C22⋊C4—21no—
129C2×C7×C22⋊C4—21no—
130C2×C7×C22⋊C4D411yescharacteristic
131C2×C7×C22⋊C4D411yescharacteristic
132C2×C42×C7—21no—
133C2×C42×C7C2311yescharacteristic
134C2×C42×C7C2311yescharacteristic
135C2×#1144—42no—
136C2×#1144—42no—
137C2×#1144—42no—
138C2×#1144C2314yes—
139C2×#1144C2314yes—
140C2×#1144C2314yes—
141C2×#1143—42no—
142C2×#1143C2314yes—
143C2×#1142—42no—
144C2×#1142—42no—
145C2×#1142—42no—
146C2×#1142C2314yes—
147C2×#1142C2314yes—
148C2×#1142C2314yes—
149C2×#1141—42no—
150C2×#1141C2314yes—
151C2×(C2×D7)⋊C4—21no—
152C2×(C2×D7)⋊C4—21no—
153C2×(C2×D7)⋊C4—21no—
154C2×(C2×D7)⋊C4—21no—
155C2×C4⋊Dic7—21no—
156C2×C4⋊Dic7—21no—
157C2×C4⋊Dic7—21no—
158C2×C4⋊Dic7—21no—
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2311yescharacteristic
162C22×C7⋊C8C2311yescharacteristic
163#6460—28no—
164#6460—28no—
165#6449—28no—
166#6449—28no—
167#6438—22no—
168#6438—22no—
169#6438C2314yes—
170#6438C2314yes—
171#6432—22no—
172#6432—22no—
173#6432C2314yes—
174#6432C2314yes—
175C22⋊(C7⋊C8)C2314yes—
176C22⋊(C7⋊C8)C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6384C2314yes—
181#6384C2314yes—
182#6384C2314yes—
183#6383C2314yes—
184#6383C2314yes—
185C4⋊(C7⋊C8)C2314yes—
186C4⋊(C7⋊C8)C2314yes—
187#6377C2314yes—
188C4×C7⋊C8C2314yes—
189C2×#542D711yescharacteristic, complemented
190C2×#536—71no—
191#3225—716no—
192C2×#497—71no—
193C2×#495—71no—
194C2×#489—71no—
195C2×#487—71no—
196C2×#464—71no—
197C2×#462—71no—
198C2×#463—71no—
199C2×#461—71no—
200C2×#452—71no—
201C2×#449—71no—
202C2×#451—71no—
203C2×#448—71no—
204C2×#433—71no—
205C24×C7—21no—
206C24×C7C2×D411yescharacteristic
207C23×D7—21no—
208C2×C7×Q8—21no—
209C2×C7×Q8—24no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—82no—
213C2×C7×Q8C2412yes—
214C2×C7×D4—24no—
215C2×C7×D4—21no—
216C2×C7×D4—22no—
217C2×C7×D4—22no—
218C2×C7×D4—82no—
219C2×C7×D4C2412yes—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—24no—
226C22×C4×C7—82no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C2×C22⋊D7—24no—
236C2×C22⋊D7—44no—
237C22×Dic7—24no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—44no—
242#1157—44no—
243#1157—44no—
244#1157—48no—
245C2×D28—22no—
246C2×D28—22no—
247C2×D28—21no—
248C2×D28C2412yes—
249C2×C4×D7—24no—
250C2×C4×D7—44no—
251C2×Dic14—22no—
252C2×Dic14—22no—
253C2×Dic14—22no—
254C2×Dic14—22no—
255C2×Dic14—22no—
256C2×Dic14—22no—
257C2×Dic14—21no—
258C2×Dic14—21no—
259C2×Dic14—21no—
260C2×Dic14—24no—
261C2×Dic14—44no—
262C2×Dic14—44no—
263C2×Dic14—44no—
264C2×Dic14—48no—
265C2×Dic14C2412yes—
266C2×Dic14C2412yes—
267C2×Dic14C2412yes—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—24no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—21no—
273C7×C4⋊C4C2×D414yes—
274C7×C4⋊C4C2×D414yes—
275C7×C4⋊C4C2412yes—
276C7×C4⋊C4C2412yes—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—24no—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—24no—
281C7×C22⋊C4—24no—
282C7×C22⋊C4C2×D414yes—
283C7×C22⋊C4C2×D414yes—
284C42×C7—24no—
285C42×C7C2×D412yes—
286C42×C7C2×D412yes—
287C42×C7C2412yes—
288C42×C7C2412yes—
289#1144—44no—
290#1144—44no—
291#1144—44no—
292#1143—44no—
293#1142—44no—
294#1142—44no—
295#1142—44no—
296#1141—44no—
297(C2×D7)⋊C4—24no—
298(C2×D7)⋊C4—24no—
299(C2×D7)⋊C4—24no—
300(C2×D7)⋊C4—24no—
301C4⋊Dic7—24no—
302C4⋊Dic7—24no—
303C4⋊Dic7—24no—
304C4⋊Dic7—24no—
305C2×C7⋊C8—22no—
306C2×C7⋊C8—22no—
307C2×C7⋊C8—22no—
308C2×C7⋊C8—22no—
309C2×C7⋊C8C2412yes—
310C2×C7⋊C8C2412yes—
311C2×C7⋊C8C2412yes—
312C2×C7⋊C8C2412yes—
313C22×#41—71no—
314C23×Q8—71no—
315C22×Q16—71no—
316C22×Q16—71no—
317C22×Q16—71no—
318C22×SD16—71no—
319C22×SD16—71no—
320C22×SD16—71no—
321C22×SD16—71no—
322C22×D8—71no—
323#542—24no—
324#542C2×D718yescomplemented
325#536—78no—
326#536—144no—
327C2×C4⋊Q8—71no—
328C2×C4⋊Q8—71no—
329C2×C4⋊Q8C2×D711yescharacteristic
330C2×#126—21no—
331C2×#124—21no—
332C2×#124—71no—
333C2×#124—71no—
334C2×#124C2×D711yescharacteristic
335C2×#123—21no—
336C2×#123—141no—
337C2×#123—141no—
338C2×C22⋊Q8—21no—
339C2×C22⋊Q8—141no—
340C2×C22⋊Q8—141no—
341C2×C22⋊Q8C2×D711yescharacteristic
342C2×#121C2×D711yescharacteristic
343C2×C4×Q8C2×D711yescharacteristic
344C2×C4×D4C2×D711yescharacteristic
345C2×#117C2×D711yescharacteristic
346#497—78no—
347#495—78no—
348#489—78no—
349#487—78no—
350#464—78no—
351#463—78no—
352#462—78no—
353#461—78no—
354#452—78no—
355#451—78no—
356#449—78no—
357#448—78no—
358#433—78no—
359C2×C4⋊C8—71no—
360C2×C4⋊C8—71no—
361C2×#103—71no—
362C2×#103—71no—
363C2×#103—71no—
364C2×#103—71no—
365C2×#103—71no—
366C2×#103—71no—
367C2×#102—71no—
368C2×#102—71no—
369C2×C22⋊C8—71no—
370C2×C22⋊C8—71no—
371C2×#97—71no—
372C2×C4×C8—71no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—42no—
378C23×C7—42no—
379C23×C7—42no—
380C23×C7C22×D412yes—
381C23×C7C22×D411yescharacteristic
382C22×D7—22no—
383C22×D7—42no—
384C22×D7—42no—
385C22×D7—42no—
386C7×Q8—22no—
387C7×Q8—22no—
388C7×Q8—42no—
389C7×Q8—84no—
390C7×D4—22no—
391C7×D4—22no—
392C7×D4—42no—
393C7×D4—84no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—24no—
400C2×C4×C7—22no—
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—42no—
408C2×C4×C7—84no—
409C2×C4×C7C22×D412yes—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D412yes—
414C2×C4×C7C22×D411yescharacteristic
415C2×C4×C7H(5,𝔽2)12yes—
416C2×C4×C7H(5,𝔽2)12yes—
417C2×C4×C7C2511yescharacteristic
418C22⋊D7—48no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—48no—
423C2×Dic7—42no—
424C2×Dic7—42no—
425C2×Dic7—42no—
426D28—22no—
427D28—22no—
428D28—42no—
429C4×D7—48no—
430Dic14—22no—
431Dic14—22no—
432Dic14—22no—
433Dic14—22no—
434Dic14—22no—
435Dic14—22no—
436Dic14—48no—
437Dic14—42no—
438Dic14—42no—
439Dic14—42no—
440C7⋊C8—22no—
441C7⋊C8—22no—
442C7⋊C8—22no—
443C7⋊C8—22no—
444C2×#41—74no—
445C2×#41—142no—
446C2×#41—282no—
447C2×#41—282no—
448C22×Q8—21no—
449C22×Q8—71no—
450C22×Q8—71no—
451C22×Q8—71no—
452C22×Q8—74no—
453C22×Q8—141no—
454C22×Q8—142no—
455C22×Q8—282no—
456C22×Q8—282no—
457C22×Q8C22×D711yescharacteristic
458C22×D4—21no—
459C22×D4—71no—
460C22×D4—141no—
461C22×D4C22×D711yescharacteristic
462C23×C4—21no—
463C23×C4—141no—
464C23×C4—141no—
465C23×C4C22×D711yescharacteristic
466C2×Q16—74no—
467C2×Q16—74no—
468C2×Q16—74no—
469C2×Q16—282no—
470C2×Q16—282no—
471C2×Q16—282no—
472C2×SD16—74no—
473C2×SD16—74no—
474C2×SD16—74no—
475C2×SD16—74no—
476C2×SD16—282no—
477C2×SD16—282no—
478C2×SD16—282no—
479C2×SD16—282no—
480C2×D8—74no—
481C2×D8—282no—
482C22×C8—71no—
483C22×C8—71no—
484C22×C8—71no—
485C22×C8—71no—
486C4⋊Q8—22no—
487C4⋊Q8—74no—
488C4⋊Q8—74no—
489C4⋊Q8—142no—
490C4⋊Q8—142no—
491C4⋊Q8C22×D714yes—
492#126—28no—
493#124—28no—
494#124—22no—
495#124—74no—
496#124—74no—
497#124—142no—
498#124—142no—
499#124C22×D714yes—
500#123—28no—
501#123—148no—
502#123—148no—
503C22⋊Q8—22no—
504C22⋊Q8—28no—
505C22⋊Q8—148no—
506C22⋊Q8—148no—
507C22⋊Q8C22×D714yes—
508#121—22no—
509#121C22×D714yes—
510C4×Q8—22no—
511C4×Q8C22×D714yes—
512C4×D4—22no—
513C4×D4C22×D714yes—
514#117C22⋊D714yes—
515#117C22×D714yes—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—141no—
520C2×C4⋊C4—141no—
521C2×C4⋊C4—141no—
522C2×C4⋊C4—141no—
523C2×C4⋊C4C22⋊D711yescharacteristic
524C2×C4⋊C4C22⋊D711yescharacteristic
525C2×C4⋊C4C22×D711yescharacteristic
526C2×C4⋊C4C22×D711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4—141no—
536C2×C22⋊C4C22⋊D711yescharacteristic
537C2×C22⋊C4C22⋊D711yescharacteristic
538C2×C42—21no—
539C2×C42C22×D711yescharacteristic
540C2×C42C22×D711yescharacteristic
541C4⋊C8—74no—
542C4⋊C8—74no—
543#103—74no—
544#103—74no—
545#103—74no—
546#103—74no—
547#103—74no—
548#103—74no—
549#102—74no—
550#102—74no—
551C22⋊C8—74no—
552C22⋊C8—74no—
553#97—74no—
554C4×C8—74no—
555C22×C7—22no—
556C22×C7—22no—
557C22×C7—22no—
558C22×C7—44no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—84no—
563C22×C7#53512yes—
564C22×C7#57712yes—
565C22×C7#57812yes—
566C22×C7C23×D411yescharacteristic
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—84no—
571C4×C7—22no—
572C4×C7—22no—
573C4×C7—22no—
574C4×C7—22no—
575C4×C7—22no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579C4×C7#53512yes—
580C4×C7C2×H(5,𝔽2)11yescharacteristic
581C4×C7C2×H(5,𝔽2)11yescharacteristic
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585C24—21no—
586C24—141no—
587C24C2×C22⋊D711yescharacteristic
588#41—284no—
589#41—284no—
590#41—288no—
591C2×Q8—21no—
592C2×Q8—24no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—72no—
596C2×Q8—72no—
597C2×Q8—72no—
598C2×Q8—82no—
599C2×Q8—144no—
600C2×Q8—141no—
601C2×Q8—141no—
602C2×Q8—141no—
603C2×Q8—142no—
604C2×Q8—142no—
605C2×Q8—142no—
606C2×Q8—142no—
607C2×Q8—142no—
608C2×Q8—142no—
609C2×Q8—284no—
610C2×Q8—284no—
611C2×Q8—284no—
612C2×Q8—288no—
613C2×Q8C23×D712yes—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—72no—
619C2×D4—82no—
620C2×D4—144no—
621C2×D4—142no—
622C2×D4—142no—
623C2×D4—141no—
624C2×D4—284no—
625C2×D4C23×D712yes—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—82no—
633C22×C4—144no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—144no—
638C22×C4—284no—
639C22×C4—284no—
640C22×C4C2×C22⋊D712yes—
641C22×C4C2×C22⋊D711yescharacteristic
642C22×C4C2×C22⋊D711yescharacteristic
643C22×C4C2×C22⋊D711yescharacteristic
644C22×C4C2×C22⋊D711yescharacteristic
645C22×C4C2×C22⋊D711yescharacteristic
646C22×C4C23×D712yes—
647C22×C4C23×D711yescharacteristic
648Q16—284no—
649Q16—284no—
650Q16—284no—
651SD16—284no—
652SD16—284no—
653SD16—284no—
654SD16—284no—
655D8—284no—
656C2×C8—72no—
657C2×C8—72no—
658C2×C8—72no—
659C2×C8—72no—
660C2×C8—142no—
661C2×C8—142no—
662C2×C8—142no—
663C2×C8—142no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—144no—
670C4⋊C4—144no—
671C4⋊C4—144no—
672C4⋊C4—144no—
673C4⋊C4C2×C22⋊D714yes—
674C4⋊C4C2×C22⋊D714yes—
675C4⋊C4C23×D712yes—
676C4⋊C4C23×D712yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—144no—
683C22⋊C4—144no—
684C22⋊C4—144no—
685C22⋊C4—144no—
686C22⋊C4C2×C22⋊D714yes—
687C22⋊C4C2×C22⋊D714yes—
688C42—24no—
689C42C2×C22⋊D712yes—
690C42C2×C22⋊D712yes—
691C42C23×D712yes—
692C42C23×D712yes—
693C2×C7—42no—
694C2×C7—82no—
695C2×C7#322514yescomplemented
696C2×C7C2×#53511yescharacteristic
697C2×C7C2×#57711yescharacteristic
698C2×C7C2×#57811yescharacteristic
699D7—82no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—142no—
708C23—282no—
709C23—282no—
710C23—282no—
711C23C22×C22⋊D712yes—
712C23C22×C22⋊D711yescharacteristic
713Q8—22no—
714Q8—22no—
715Q8—42no—
716Q8—84no—
717Q8—142no—
718Q8—142no—
719Q8—142no—
720Q8—142no—
721Q8—142no—
722Q8—142no—
723Q8—288no—
724Q8—282no—
725Q8—282no—
726Q8—282no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—142no—
732D4—142no—
733D4—288no—
734D4—282no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—84no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—288no—
754C2×C4—288no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4—282no—
758C2×C4#655312yes—
759C2×C4#655312yes—
760C2×C4C22×C22⋊D712yes—
761C2×C4C22×C22⋊D712yes—
762C2×C4C22×C22⋊D712yes—
763C2×C4C22×C22⋊D712yes—
764C2×C4C22×C22⋊D712yes—
765C2×C4C22×C22⋊D711yescharacteristic
766C2×C4C24×D711yescharacteristic
767C8—142no—
768C8—142no—
769C8—142no—
770C8—142no—
771C7C2×#322511yescharacteristic, complemented, Sylow
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—564no—
784C22#9052112yes—
785C22#9052712yes—
786C22#9052912yes—
787C22C23×C22⋊D711yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—282no—
797C4—282no—
798C4—282no—
799C4#9052112yes—
800C4C2×#655311yescharacteristic
801C4C2×#655311yescharacteristic
802C2—42no—
803C2—82no—
804C2—562no—
805C2#1174090914yesdirect product factor
806C2C2×#9052111yescharacteristic
807C2C2×#9052711yescharacteristic
808C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
prime radicalC2×#89809C2
hypercenterC2×#542D7
hypocenterC7C2×#3225
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C7×#542C2semidirect
2. C2×#90217C2semidirect
3. #11740909C2direct (N × H)
4. C2×#89861C2semidirect
5. C2×#89865C2semidirect
6. C2×#89832C2semidirect
7. C2×#89831C2semidirect
8. C2×#89822C2semidirect
9. C2×#89819C2semidirect
10. C2×#89812C2semidirect
12. C2×#89803C2semidirect
13. C2×#89800C2semidirect
14. C2×#89791C2semidirect
15. C2×#89788C2semidirect
16. C2×#89772C2semidirect
20. C7×#542C22semidirect
41. #90217C22semidirect
52. #89865C22semidirect
53. #89861C22semidirect
54. #89832C22semidirect
55. #89831C22semidirect
56. #89822C22semidirect
57. #89819C22semidirect
58. #89812C22semidirect
60. #89803C22semidirect
61. #89800C22semidirect
62. #89791C22semidirect
63. #89788C22semidirect
64. #89772C22semidirect
189. C2×#542D7semidirect
324. #542C2×D7semidirect
695. C2×C7#3225semidirect
771. C7C2×#3225semidirect
805. C2#11740909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×#902172
#117409092
C2×#898612
C2×#898652
C2×#898322
C2×#898312
C2×#898222
C2×#898192
C2×#898122
C2×#898092
C2×#898032
C2×#898002
C2×#897912
C2×#897882
C2×#897722
C2×#32257