Finite Group Databasebeta

← C2×#11741064 #14230492

Subgroups — C2×#11741064 #14230492

Order 1792.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic, complemented
2C2×#90244C211yesmaximal, characteristic, complemented
3#11741064C2116yesmaximal, direct product factor
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89839C211yesmaximal, characteristic, complemented
6C2×#89809C211yesmaximal, characteristic, complemented
7C2×#89809C211yesmaximal, characteristic, complemented
8C2×#89811C211yesmaximal, characteristic, complemented
9C2×#89810C211yesmaximal, characteristic, complemented
10C2×#89787C211yesmaximal, characteristic, complemented
11C2×#89783C211yesmaximal, characteristic, complemented
12C2×#89790C211yesmaximal, characteristic, complemented
13C2×#89775C211yesmaximal, characteristic, complemented
14C2×#89774C211yesmaximal, characteristic, complemented
15C2×#89739C211yesmaximal, 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×#6503—21no—
33C22×#1142C2211yescharacteristic
34C22×#1141C2211yescharacteristic
35C22×#1141C2211yescharacteristic
36C2×#6493C2211yescharacteristic
37C2×#6493C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90244—24no—
41#90244C2218yescomplemented
42C2×#6456—21no—
43C2×#6447—21no—
44C2×#6447—21no—
45C2×#6437C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89839C2218yescomplemented
51#89835C2218yescomplemented
52#89811C2218yescomplemented
53#89810C2218yescomplemented
54#89809C2218yescomplemented
55#89809C2218yescomplemented
56#89790C2218yescomplemented
57#89787C2218yescomplemented
58#89783C2218yescomplemented
59#89775C2218yescomplemented
60#89774C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64#89739C2218yescomplemented
65#89738C2218yescomplemented
66C2×#6383C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6383C2211yescharacteristic
70C2×#6383C2211yescharacteristic
71C2×#6383C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3309—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—
88C22×C22⋊D7—21no—
89C22×C22⋊D7—21no—
90C2×#1157—22no—
91C2×#1157—22no—
92C2×#1157—24no—
93C2×#1157—24no—
94C2×#1157—42no—
95C2×#1157—42no—
96C2×#1157C2314yes—
97C2×#1157C2314yes—
98C22×D28—21no—
99C22×D28—21no—
100C22×D28C2311yescharacteristic
101C22×D28C2311yescharacteristic
102C22×C4×D7—21no—
103C22×C4×D7—21no—
104C22×Dic14C2311yescharacteristic
105C7×#126—28no—
106C7×#125—22no—
107C7×#125C2314yes—
108C7×#123—28no—
109C7×#121—28no—
110C7×#121—22no—
111C7×#121—22no—
112C7×#121C2314yes—
113C7×#121C2314yes—
114C4×C7×D4—28no—
115C4×C7×D4—22no—
116C4×C7×D4D414yes—
117C4×C7×D4C2314yes—
118C4×C7×D4C2314yes—
119C7×#117—22no—
120C7×#117C2314yes—
121C2×C7×C4⋊C4—21no—
122C2×C7×C4⋊C4—22no—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4D411yescharacteristic
126C2×C7×C4⋊C4C2311yescharacteristic
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C4⋊C4C2311yescharacteristic
129C2×C7×C4⋊C4C2314yes—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—21no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C7×C22⋊C4D411yescharacteristic
135C2×C7×C22⋊C4D411yescharacteristic
136C2×C42×C7—21no—
137C2×C42×C7C2311yescharacteristic
138#6503—28no—
139C2×#1142—24no—
140C2×#1142C2314yes—
141C2×#1141—42no—
142C2×#1141—42no—
143C2×#1141C2314yes—
144C2×#1141C2314yes—
145#6493—22no—
146#6493—22no—
147#6493C2314yes—
148#6493C2314yes—
149C2×(C2×D7)⋊C4—21no—
150C2×(C2×D7)⋊C4—21no—
151C2×C4⋊Dic7C2311yescharacteristic
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—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—
162#6456—28no—
163#6447—28no—
164#6447—28no—
165#6437—22no—
166#6437C2314yes—
167C4×Dic14—22no—
168C4×Dic14C2314yes—
169#6406C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171C22⋊(C7⋊C8)C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6383C2314yes—
176#6383C2314yes—
177#6383C2314yes—
178#6383C2314yes—
179#6383C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#553D711yescharacteristic, complemented
187C2×#550—71no—
188#3309—716no—
189C2×#490—71no—
190C2×#482—71no—
191C2×#480—71no—
192C2×#479—71no—
193C2×#469—71no—
194C2×#466—71no—
195C2×#459—71no—
196C2×#449—71no—
197C2×#449—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#417—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C24×C7C2×D411yescharacteristic
205C23×D7—21no—
206C23×D7—21no—
207C2×C7×D4—24no—
208C2×C7×D4—24no—
209C2×C7×D4—21no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—42no—
213C2×C7×D4—44no—
214C2×C7×D4—82no—
215C2×C7×D4C2×D414yes—
216C2×C7×D4C2412yes—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—24no—
225C22×C4×C7—24no—
226C22×C4×C7—82no—
227C22×C4×C7—82no—
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2411yescharacteristic
237C2×C22⋊D7—24no—
238C2×C22⋊D7—24no—
239C2×C22⋊D7—24no—
240C2×C22⋊D7—24no—
241C2×C22⋊D7—44no—
242C2×C22⋊D7—44no—
243C2×C22⋊D7—82no—
244C2×C22⋊D7—82no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247#1157—28no—
248#1157—28no—
249#1157—44no—
250#1157—44no—
251#1157—48no—
252#1157—48no—
253C2×D28—22no—
254C2×D28—22no—
255C2×D28—22no—
256C2×D28—22no—
257C2×D28—21no—
258C2×D28—21no—
259C2×D28—24no—
260C2×D28—24no—
261C2×D28—44no—
262C2×D28—82no—
263C2×D28C2412yes—
264C2×D28C2412yes—
265C2×C4×D7—24no—
266C2×C4×D7—24no—
267C2×C4×D7—44no—
268C2×C4×D7—44no—
269C2×Dic14—21no—
270C2×Dic14—22no—
271C2×Dic14#4114yes—
272C2×Dic14C2412yes—
273C7×C4⋊C4—21no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4—24no—
276C7×C4⋊C4—24no—
277C7×C4⋊C4—24no—
278C7×C4⋊C4—21no—
279C7×C4⋊C4C2×D414yes—
280C7×C4⋊C4C2412yes—
281C7×C4⋊C4C2412yes—
282C7×C4⋊C4C2412yes—
283C7×C22⋊C4—24no—
284C7×C22⋊C4—24no—
285C7×C22⋊C4—24no—
286C7×C22⋊C4—24no—
287C7×C22⋊C4C2×D414yes—
288C7×C22⋊C4C2×D414yes—
289C42×C7—24no—
290C42×C7C2×D412yes—
291C42×C7C2412yes—
292#1142—28no—
293#1141—44no—
294#1141—44no—
295(C2×D7)⋊C4—24no—
296(C2×D7)⋊C4—24no—
297C4⋊Dic7—21no—
298C4⋊Dic7C2412yes—
299Dic7⋊C4—24no—
300C4×Dic7—24no—
301#1136—44no—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8—22no—
305C2×C7⋊C8—22no—
306C2×C7⋊C8—44no—
307C2×C7⋊C8C2412yes—
308C2×C7⋊C8C2412yes—
309C2×C7⋊C8C2412yes—
310C2×C7⋊C8C2412yes—
311C22×#41—71no—
312C22×#41—71no—
313C22×SD16—71no—
314C22×D8—71no—
315C22×D8—71no—
316C22×M16—71no—
317C23×C8—71no—
318#553—24no—
319#553C2×D718yescomplemented
320#550—78no—
321#550—144no—
322C2×#127—71no—
323C2×#127—141no—
324C2×#126—21no—
325C2×#125C2×D711yescharacteristic
326C2×#123—21no—
327C2×#121—21no—
328C2×#121—71no—
329C2×#121—71no—
330C2×#121—141no—
331C2×#121—141no—
332C2×#121C2×D711yescharacteristic
333C2×#121C2×D711yescharacteristic
334C2×C4×Q8—71no—
335C2×C4×D4—21no—
336C2×C4×D4—141no—
337C2×C4×D4C2×D711yescharacteristic
338C2×C4×D4C2×D711yescharacteristic
339C2×#117C2×D711yescharacteristic
340C22×C4⋊C4C2×D711yescharacteristic
341#490—78no—
342#482—78no—
343#480—78no—
344#479—78no—
345#469—78no—
346#466—78no—
347#459—78no—
348#449—78no—
349#449—78no—
350#440—78no—
351#435—78no—
352C2×#107—71no—
353C2×#107—71no—
354C2×#106—71no—
355C2×C4⋊C8—71no—
356#417—78no—
357#416—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⋊C8—71no—
369C2×C22⋊C8—71no—
370C2×#97—71no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—42no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7C22×D412yes—
382C23×C7C22×D412yes—
383C23×C7C22×D411yescharacteristic
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—42no—
387C22×D7—42no—
388C22×D7—42no—
389C22×D7—42no—
390C22×D7—42no—
391C22×D7—42no—
392C7×D4—22no—
393C7×D4—22no—
394C7×D4—44no—
395C7×D4—48no—
396C7×D4—42no—
397C7×D4—84no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—24no—
403C2×C4×C7—24no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—42no—
412C2×C4×C7—42no—
413C2×C4×C7—42no—
414C2×C4×C7—84no—
415C2×C4×C7—84no—
416C2×C4×C7C22×D412yes—
417C2×C4×C7C22×D412yes—
418C2×C4×C7C22×D412yes—
419C2×C4×C7C22×D412yes—
420C2×C4×C7C22×D411yescharacteristic
421C2×C4×C7C2×#4112yes—
422C2×C4×C7H(5,𝔽2)12yes—
423C2×C4×C7C2511yescharacteristic
424C22⋊D7—48no—
425C22⋊D7—48no—
426C22⋊D7—84no—
427C22⋊D7—84no—
428C2×Dic7—24no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—42no—
432D28—22no—
433D28—22no—
434D28—22no—
435D28—22no—
436D28—48no—
437D28—42no—
438D28—42no—
439D28—84no—
440C4×D7—48no—
441C4×D7—48no—
442Dic14—24no—
443Dic14—22no—
444Dic14C2×#4114yes—
445C7⋊C8—22no—
446C7⋊C8—22no—
447C7⋊C8—22no—
448C7⋊C8—22no—
449C2×#41—74no—
450C2×#41—74no—
451C2×#41—144no—
452C2×#41—144no—
453C2×#41—142no—
454C2×#41—142no—
455C2×#41—282no—
456C2×#41—282no—
457C22×Q8—71no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—71no—
461C22×D4—71no—
462C22×D4—141no—
463C22×D4—141no—
464C22×D4—141no—
465C22×D4—141no—
466C22×D4—141no—
467C22×D4—141no—
468C22×D4C22⋊D711yescharacteristic
469C22×D4C22×D711yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—141no—
473C23×C4—141no—
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C2×SD16—74no—
477C2×SD16—144no—
478C2×D8—74no—
479C2×D8—74no—
480C2×D8—282no—
481C2×D8—282no—
482C2×M16—74no—
483C2×M16—282no—
484C22×C8—71no—
485C22×C8—71no—
486C22×C8—71no—
487C22×C8—71no—
488C22×C8—74no—
489C22×C8—282no—
490#127—74no—
491#127—148no—
492#127—142no—
493#126—28no—
494#125—22no—
495#125C22×D714yes—
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—74no—
501#121—74no—
502#121—142no—
503#121—142no—
504#121—148no—
505#121—148no—
506#121C22×D714yes—
507#121C22×D714yes—
508C4×Q8—74no—
509C4×Q8—142no—
510C4×D4—28no—
511C4×D4—22no—
512C4×D4—148no—
513C4×D4C22⋊D714yes—
514C4×D4C22×D714yes—
515C4×D4C22×D714yes—
516#117—22no—
517#117C22×D714yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—71no—
523C2×C4⋊C4—141no—
524C2×C4⋊C4C22⋊D711yescharacteristic
525C2×C4⋊C4C22×D711yescharacteristic
526C2×C4⋊C4C22×D711yescharacteristic
527C2×C4⋊C4C22×D714yes—
528C2×C4⋊C4C22×D711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4C22⋊D711yescharacteristic
536C2×C22⋊C4C22⋊D711yescharacteristic
537C2×C42—21no—
538C2×C42—141no—
539C2×C42C22×D711yescharacteristic
540#107—74no—
541#107—74no—
542#106—74no—
543C4⋊C8—74no—
544#103—74no—
545#103—74no—
546#103—74no—
547#102—74no—
548#102—74no—
549#102—74no—
550#102—74no—
551#102—74no—
552#102—74no—
553#102—74no—
554C22⋊C8—74no—
555C22⋊C8—74no—
556#97—74no—
557C22×C7—22no—
558C22×C7—22no—
559C22×C7—22no—
560C22×C7—22no—
561C22×C7—22no—
562C22×C7—22no—
563C22×C7—44no—
564C22×C7—44no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—84no—
569C22×C7#54612yes—
570C22×C7#57512yes—
571C22×C7#57612yes—
572C22×C7C23×D411yescharacteristic
573C2×D7—42no—
574C2×D7—42no—
575C2×D7—42no—
576C2×D7—42no—
577C2×D7—42no—
578C2×D7—42no—
579C2×D7—84no—
580C2×D7—84no—
581C4×C7—22no—
582C4×C7—22no—
583C4×C7—22no—
584C4×C7—22no—
585C4×C7—42no—
586C4×C7—42no—
587C4×C7—42no—
588C4×C7#54612yes—
589C4×C7C22×#4111yescharacteristic
590C4×C7C2×H(5,𝔽2)11yescharacteristic
591Dic7—24no—
592Dic7—42no—
593C24—21no—
594C24—141no—
595C24—141no—
596C24C2×C22⋊D711yescharacteristic
597C24C2×C22⋊D711yescharacteristic
598#41—148no—
599#41—148no—
600#41—284no—
601#41—284no—
602#41—288no—
603#41—288no—
604C2×Q8—74no—
605C2×Q8—72no—
606C2×Q8—142no—
607C2×Q8—141no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—72no—
616C2×D4—72no—
617C2×D4—82no—
618C2×D4—144no—
619C2×D4—144no—
620C2×D4—144no—
621C2×D4—144no—
622C2×D4—142no—
623C2×D4—142no—
624C2×D4—142no—
625C2×D4—142no—
626C2×D4—144no—
627C2×D4—141no—
628C2×D4—141no—
629C2×D4—144no—
630C2×D4—284no—
631C2×D4—284no—
632C2×D4—284no—
633C2×D4—562no—
634C2×D4—562no—
635C2×D4—562no—
636C2×D4C2×C22⋊D714yes—
637C2×D4C23×D712yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—82no—
648C22×C4—82no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—144no—
652C22×C4—144no—
653C22×C4—284no—
654C22×C4—284no—
655C22×C4C2×C22⋊D712yes—
656C22×C4C2×C22⋊D712yes—
657C22×C4C2×C22⋊D711yescharacteristic
658C22×C4C2×C22⋊D711yescharacteristic
659C22×C4C2×C22⋊D711yescharacteristic
660C22×C4C2×C22⋊D711yescharacteristic
661C22×C4C23×D712yes—
662C22×C4C23×D712yes—
663C22×C4C23×D711yescharacteristic
664SD16—148no—
665D8—284no—
666D8—284no—
667M16—284no—
668C2×C8—72no—
669C2×C8—72no—
670C2×C8—72no—
671C2×C8—72no—
672C2×C8—142no—
673C2×C8—142no—
674C2×C8—142no—
675C2×C8—142no—
676C2×C8—284no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—72no—
684C4⋊C4—144no—
685C4⋊C4—141no—
686C4⋊C4C2×C22⋊D714yes—
687C4⋊C4C23×D712yes—
688C4⋊C4C23×D712yes—
689C4⋊C4C23×D712yes—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—144no—
695C22⋊C4—144no—
696C22⋊C4C2×C22⋊D714yes—
697C22⋊C4C2×C22⋊D714yes—
698C42—24no—
699C42—144no—
700C42C2×C22⋊D712yes—
701C42C23×D712yes—
702C2×C7—42no—
703C2×C7—42no—
704C2×C7—82no—
705C2×C7#330914yescomplemented
706C2×C7C2×#54611yescharacteristic
707C2×C7C2×#57511yescharacteristic
708C2×C7C2×#57611yescharacteristic
709D7—82no—
710D7—82no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—142no—
722C23—142no—
723C23—282no—
724C23—282no—
725C23—282no—
726C23—282no—
727C23—282no—
728C23—282no—
729C23C22×C22⋊D712yes—
730C23C22×C22⋊D712yes—
731C23C22×C22⋊D711yescharacteristic
732Q8—74no—
733Q8—144no—
734Q8—142no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—42no—
740D4—84no—
741D4—142no—
742D4—142no—
743D4—142no—
744D4—142no—
745D4—288no—
746D4—288no—
747D4—288no—
748D4—282no—
749D4—282no—
750D4—564no—
751D4—564no—
752D4—564no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4—144no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—288no—
775C2×C4—288no—
776C2×C4—282no—
777C2×C4D7×#4112yes—
778C2×C4#655312yes—
779C2×C4C22×C22⋊D712yes—
780C2×C4C22×C22⋊D712yes—
781C2×C4C22×C22⋊D712yes—
782C2×C4C22×C22⋊D712yes—
783C2×C4C22×C22⋊D711yescharacteristic
784C2×C4C24×D711yescharacteristic
785C8—142no—
786C8—142no—
787C8—142no—
788C8—142no—
789C7C2×#330911yescharacteristic, complemented, Sylow
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—564no—
809C22—564no—
810C22#9051312yes—
811C22#9052012yes—
812C22#9052612yes—
813C22C23×C22⋊D711yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—144no—
822C4—282no—
823C4#9052012yes—
824C4C2×D7×#4111yescharacteristic
825C4C2×#655311yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—562no—
830C2—562no—
831C2#1174106414yesdirect product factor
832C2C2×#9051311yescharacteristic
833C2C2×#9052011yescharacteristic
834C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#553C2
socleC23×C7C22×D4
hypercenterC2×#553D7
hypocenterC7C2×#3309
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×#90244C2semidirect
3. #11741064C2direct (N × H)
4. C2×#89835C2semidirect
5. C2×#89839C2semidirect
6. C2×#89809C2semidirect
7. C2×#89809C2semidirect
8. C2×#89811C2semidirect
9. C2×#89810C2semidirect
10. C2×#89787C2semidirect
11. C2×#89783C2semidirect
12. C2×#89790C2semidirect
13. C2×#89775C2semidirect
14. C2×#89774C2semidirect
15. C2×#89739C2semidirect
16. C2×#89738C2semidirect
20. C7×#553C22semidirect
41. #90244C22semidirect
50. #89839C22semidirect
51. #89835C22semidirect
52. #89811C22semidirect
53. #89810C22semidirect
54. #89809C22semidirect
55. #89809C22semidirect
56. #89790C22semidirect
57. #89787C22semidirect
58. #89783C22semidirect
59. #89775C22semidirect
60. #89774C22semidirect
64. #89739C22semidirect
65. #89738C22semidirect
186. C2×#553D7semidirect
319. #553C2×D7semidirect
705. C2×C7#3309semidirect
789. C7C2×#3309semidirect
831. C2#11741064direct (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×#902442
#117410642
C2×#898352
C2×#898392
C2×#898092
C2×#898112
C2×#898102
C2×#897872
C2×#897832
C2×#897902
C2×#897752
C2×#897742
C2×#897392
C2×#897382
C2×#33097