Finite Group Databasebeta

← C2×#11737112 #14223602

Subgroups — C2×#11737112 #14223602

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90274C211yesmaximal, characteristic, complemented
2C2×#90253C211yesmaximal, characteristic
3C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×#89947C211yesmaximal, characteristic, complemented
6C2×#89798C211yesmaximal, characteristic, complemented
7C2×#89790C211yesmaximal, characteristic, complemented
8#11737112C2116yesmaximal, direct product factor
9C2×#89636C211yesmaximal, characteristic, complemented
10C2×#89630C211yesmaximal, characteristic, complemented
11C2×#89584C211yesmaximal, characteristic, complemented
12C2×#89569C211yesmaximal, characteristic, complemented
13C2×#89552C211yesmaximal, characteristic, complemented
14C2×#89536C211yesmaximal, characteristic, complemented
15C2×C4×#1132C211yesmaximal, characteristic, complemented
16C2×#89461C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6509C2211yescharacteristic
21C2×#6507C2211yescharacteristic
22C22×#1143C2211yescharacteristic
23C2×#6503C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C2×#6493—21no—
27C2×#6492—21no—
28C22×#1132C2211yescharacteristic
29C22×#1131C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90274—24no—
32#90274C2218yescomplemented
33#90253—24no—
34#90253C2218yes—
35C2×#6461—21no—
36C2×#6460C2211yescharacteristic
37C2×#6458C2211yescharacteristic
38C2×#6453C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6452—21no—
41C2×#6447—21no—
42C2×#6446—21no—
43C2×#6439—21no—
44C2×C4×D28C2211yescharacteristic
45C2×#6435C2211yescharacteristic
46C2×#6433—21no—
47C2×C4×Dic14C2211yescharacteristic
48C4×C7×SD16C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C4×C7×C8C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55#89947C2218yescomplemented
56#89943C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6389C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62#89798C2218yescomplemented
63#89790C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89636C2218yescomplemented
70#89630C2218yescomplemented
71#89584C2218yescomplemented
72#89569C2218yescomplemented
73#89552C2218yescomplemented
74#89536C2218yescomplemented
75C4×#1132C2218yescomplemented
76#89461C2218yescomplemented
77C2×#3174—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7C2311yescharacteristic
88C22×Dic14C2311yescharacteristic
89C2×C7×SD16—24no—
90C2×C7×SD16C2314yes—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C4×C7×Q8—22no—
94C4×C7×Q8C2314yes—
95C4×C7×D4—22no—
96C4×C7×D4C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C42×C7—21no—
102C2×C42×C7C2311yescharacteristic
103C2×C22⋊Dic7—21no—
104#6509—22no—
105#6509C2314yes—
106#6507—22no—
107#6507C2314yes—
108C2×#1143—24no—
109C2×#1143C2314yes—
110#6503—22no—
111#6503C2314yes—
112#6501—22no—
113#6501C2314yes—
114C2×#1142—24no—
115C2×#1142C2314yes—
116#6493—28no—
117#6492—28no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4D411yescharacteristic
123C2×(C2×D7)⋊C4D411yescharacteristic
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4D411yescharacteristic
136C2×Dic7⋊C4D411yescharacteristic
137C2×C4×Dic7—21no—
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×#1132—24no—
142C2×#1132C2314yes—
143C2×#1131—24no—
144C2×#1131C2314yes—
145C2×C8×D7—24no—
146C2×C8×D7C2314yes—
147#6461—28no—
148#6460—22no—
149#6460C2314yes—
150#6458—22no—
151#6458C2314yes—
152#6453—22no—
153#6453—22no—
154#6453C2314yes—
155#6453C2314yes—
156#6452—28no—
157#6447—28no—
158#6446—28no—
159#6439—28no—
160C4×D28—22no—
161C4×D28C2314yes—
162#6435D414yes—
163#6435C2314yes—
164#6433—28no—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167C7×#106C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170C4×C7×C8C2314yes—
171#6409C2314yes—
172#6406C2314yes—
173#6395C2314yes—
174#6391C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177C8×Dic7C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182#6377C2314yes—
183C2×#541—71no—
184C2×#540—71no—
185#3174—716no—
186C2×#499—71no—
187C2×#492—71no—
188C2×#491—71no—
189C2×#490—71no—
190C2×#468—71no—
191C2×#468—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#440—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16D711yescharacteristic, complemented
198C2×#405—71no—
199C24×C7—21no—
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8C2412yes—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4C2412yes—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—82no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2411yescharacteristic
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—82no—
222C2×C22⋊D7—82no—
223C2×C22⋊D7—82no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C2×D28—22no—
231C2×D28—22no—
232C2×D28—21no—
233C2×D28—24no—
234C2×D28—82no—
235C2×D28C2412yes—
236C2×C4×D7—22no—
237C2×C4×D7—22no—
238C2×C4×D7—24no—
239C2×C4×D7—82no—
240C2×C4×D7C2×D412yes—
241C2×C4×D7C2412yes—
242C2×Dic14—22no—
243C2×Dic14—22no—
244C2×Dic14—21no—
245C2×Dic14C2412yes—
246C7×SD16—28no—
247C2×C7×C8—22no—
248C2×C7×C8#4114yes—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C42×C7—24no—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260C22⋊Dic7—24no—
261#1143—28no—
262#1142—28no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4C2×D414yes—
268(C2×D7)⋊C4C2×D414yes—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283Dic7⋊C4C2×D414yes—
284C4×Dic7—24no—
285C4×Dic7C2×D412yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8#4114yes—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291#1132—28no—
292#1131—28no—
293C8×D7—28no—
294C22×SD16—71no—
295C22×SD16—71no—
296C22×SD16—71no—
297C22×SD16C2×D711yescharacteristic
298C22×M16—71no—
299C23×C8—71no—
300#541—78no—
301#541—144no—
302#540—78no—
303#540—144no—
304C2×C4⋊Q8—71no—
305C2×#127—71no—
306C2×#126—141no—
307C2×#126—141no—
308C2×#125—71no—
309C2×#125—71no—
310C2×#125—141no—
311C2×#125—141no—
312C2×#123—141no—
313C2×#123—141no—
314C2×C22⋊Q8—71no—
315C2×C22⋊Q8—71no—
316C2×#121—71no—
317C2×#121—71no—
318C2×#121—141no—
319C2×#121—141no—
320C2×C4×Q8—71no—
321C2×C4×Q8C2×D711yescharacteristic
322C2×C4×D4—71no—
323C2×C4×D4C2×D711yescharacteristic
324C2×#117—71no—
325#499—78no—
326#492—78no—
327#491—78no—
328#490—78no—
329#468—78no—
330#468—78no—
331#465—78no—
332#465—78no—
333#440—78no—
334#440—78no—
335C4×SD16—78no—
336C4×SD16C2×D718yescomplemented
337C2×#107—71no—
338C2×#107—71no—
339C2×#106—71no—
340C2×#106C2×D711yescharacteristic
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103C2×D711yescharacteristic
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102C2×D711yescharacteristic
349#405—78no—
350C2×#97—71no—
351C2×#97—71no—
352C2×C4×C8—71no—
353C2×C4×C8C2×D711yescharacteristic
354C23×C7—22no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7C22×D412yes—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—42no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—42no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—84no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2511yescharacteristic
388C22⋊D7—84no—
389C22⋊D7—84no—
390C22⋊D7—84no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403D28—22no—
404D28—22no—
405D28—42no—
406D28—84no—
407C4×D7—24no—
408C4×D7—22no—
409C4×D7—22no—
410C4×D7—84no—
411Dic14—22no—
412Dic14—22no—
413Dic14—42no—
414C7×C8—22no—
415C7×C8C2×#4114yes—
416C7⋊C8—22no—
417C7⋊C8C2×#4114yes—
418C22×Q8—71no—
419C22×Q8C22×D711yescharacteristic
420C22×D4—71no—
421C22×D4—141no—
422C22×D4—141no—
423C22×D4—141no—
424C22×D4—141no—
425C22×D4C22×D711yescharacteristic
426C23×C4—21no—
427C23×C4—71no—
428C23×C4—141no—
429C2×SD16—24no—
430C2×SD16—74no—
431C2×SD16—74no—
432C2×SD16—74no—
433C2×SD16—144no—
434C2×SD16—144no—
435C2×SD16—144no—
436C2×SD16C22×D714yes—
437C2×M16—74no—
438C2×M16—144no—
439C22×C8—71no—
440C22×C8—71no—
441C22×C8—74no—
442C22×C8—144no—
443C22×C8C22×D711yescharacteristic
444C22×C8C22×D711yescharacteristic
445C4⋊Q8—74no—
446C4⋊Q8—142no—
447#127—74no—
448#127—142no—
449#126—148no—
450#126—148no—
451#125—74no—
452#125—74no—
453#125—148no—
454#125—142no—
455#125—142no—
456#125—148no—
457#123—148no—
458#123—148no—
459C22⋊Q8—74no—
460C22⋊Q8—74no—
461C22⋊Q8—142no—
462C22⋊Q8—142no—
463#121—74no—
464#121—74no—
465#121—148no—
466#121—148no—
467#121—142no—
468#121—142no—
469C4×Q8—22no—
470C4×Q8—74no—
471C4×Q8—142no—
472C4×Q8C22×D714yes—
473C4×D4—22no—
474C4×D4—74no—
475C4×D4—142no—
476C4×D4C22×D714yes—
477#117—74no—
478#117—74no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—71no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C42—21no—
504C2×C42—71no—
505C2×C42—141no—
506C2×C42C22×D711yescharacteristic
507#107—74no—
508#107—74no—
509#106—74no—
510#106C22×D714yes—
511#103—74no—
512#103—74no—
513#103—74no—
514#103C22×D714yes—
515#102—74no—
516#102—74no—
517#102—74no—
518#102C22×D714yes—
519#97—74no—
520#97—74no—
521C4×C8—74no—
522C4×C8C22×D714yes—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—84no—
527C22×C7#53212yes—
528C22×C7#57712yes—
529C22×C7#57712yes—
530C22×C7C23×D411yescharacteristic
531C2×D7—22no—
532C2×D7—22no—
533C2×D7—22no—
534C2×D7—44no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—84no—
539C4×C7—22no—
540C4×C7—22no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7#53212yes—
545C4×C7C22×#4111yescharacteristic
546C4×C7C22×#4111yescharacteristic
547Dic7—22no—
548Dic7—22no—
549Dic7—22no—
550Dic7—42no—
551Dic7—42no—
552Dic7—42no—
553C24—21no—
554C24—71no—
555C24—141no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—72no—
560C2×Q8—141no—
561C2×Q8—142no—
562C2×Q8—142no—
563C2×Q8C23×D712yes—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—72no—
568C2×D4—144no—
569C2×D4—144no—
570C2×D4—144no—
571C2×D4—144no—
572C2×D4—142no—
573C2×D4—141no—
574C2×D4—142no—
575C2×D4—562no—
576C2×D4—562no—
577C2×D4—562no—
578C2×D4—562no—
579C2×D4C23×D712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—71no—
585C22×C4—71no—
586C22×C4—71no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—82no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—144no—
596C22×C4—562no—
597C22×C4D4×D711yescharacteristic
598C22×C4D4×D711yescharacteristic
599C22×C4C23×D711yescharacteristic
600SD16—28no—
601SD16—148no—
602SD16—148no—
603SD16—148no—
604M16—148no—
605C2×C8—22no—
606C2×C8—74no—
607C2×C8—72no—
608C2×C8—72no—
609C2×C8—142no—
610C2×C8—148no—
611C2×C8#115714yes—
612C2×C8C23×D712yes—
613C2×C8C23×D712yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—74no—
618C4⋊C4—74no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—141no—
631C4⋊C4—141no—
632C4⋊C4C23×D712yes—
633C4⋊C4C23×D712yes—
634C22⋊C4—24no—
635C22⋊C4—74no—
636C22⋊C4—74no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C42—24no—
643C42—72no—
644C42—72no—
645C42—144no—
646C42D4×D712yes—
647C42C23×D712yes—
648C2×C7—82no—
649C2×C7#317414yescomplemented
650C2×C7C2×#53211yescharacteristic
651C2×C7C2×#57711yescharacteristic
652C2×C7C2×#57711yescharacteristic
653D7—42no—
654D7—82no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—72no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—142no—
672Q8—142no—
673Q8—282no—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—142no—
678D4—142no—
679D4—282no—
680D4—564no—
681D4—564no—
682D4—564no—
683D4—564no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—72no—
693C2×C4—72no—
694C2×C4—72no—
695C2×C4—84no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—144no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—282no—
708C2×C4—564no—
709C2×C4C2×#115712yes—
710C2×C4C2×D4×D712yes—
711C2×C4C2×D4×D712yes—
712C2×C4C2×D4×D711yescharacteristic
713C2×C4D7×#4112yes—
714C2×C4C24×D711yescharacteristic
715C8—22no—
716C8—74no—
717C8—142no—
718C8C2×#115714yes—
719C7C2×#317411yescharacteristic, complemented, Sylow
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—142no—
725C22—142no—
726C22—142no—
727C22—284no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—564no—
732C22#9023912yes—
733C22#9045312yes—
734C22#9046112yes—
735C22C22×D4×D711yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—142no—
742C4—142no—
743C4—142no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4#9023912yes—
748C4C22×#115711yescharacteristic
749C4C2×D7×#4111yescharacteristic
750C2—82no—
751C2—282no—
752C2—562no—
753C2#1173711214yesdirect product factor
754C2C2×#9023911yescharacteristic
755C2C2×#9045311yescharacteristic
756C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×SD16C2
socleC23×C7C22×D4
prime radicalC2×#90253C2
hypercenterC2×C4×SD16D7
hypocenterC7C2×#3174
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#90274C2semidirect
3. C2×C4×C7×SD16C2semidirect
4. C2×#89943C2semidirect
5. C2×#89947C2semidirect
6. C2×#89798C2semidirect
7. C2×#89790C2semidirect
8. #11737112C2direct (N × H)
9. C2×#89636C2semidirect
10. C2×#89630C2semidirect
11. C2×#89584C2semidirect
12. C2×#89569C2semidirect
13. C2×#89552C2semidirect
14. C2×#89536C2semidirect
15. C2×C4×#1132C2semidirect
16. C2×#89461C2semidirect
32. #90274C22semidirect
48. C4×C7×SD16C22semidirect
55. #89947C22semidirect
56. #89943C22semidirect
62. #89798C22semidirect
63. #89790C22semidirect
69. #89636C22semidirect
70. #89630C22semidirect
71. #89584C22semidirect
72. #89569C22semidirect
73. #89552C22semidirect
74. #89536C22semidirect
75. C4×#1132C22semidirect
76. #89461C22semidirect
197. C2×C4×SD16D7semidirect
336. C4×SD16C2×D7semidirect
649. C2×C7#3174semidirect
719. C7C2×#3174semidirect
753. C2#11737112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902742
C2×#902532
C2×C4×C7×SD162
C2×#899432
C2×#899472
C2×#897982
C2×#897902
#117371122
C2×#896362
C2×#896302
C2×#895842
C2×#895692
C2×#895522
C2×#895362
C2×C4×#11322
C2×#894612
C2×#31747