Finite Group Databasebeta

← C2×#11737210 #14234817

Subgroups — C2×#11737210 #14234817

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90259C211yesmaximal, characteristic, complemented
2C2×#90233C211yesmaximal, characteristic, complemented
3C2×C7×#440C211yesmaximal, characteristic, complemented
4C2×#89939C211yesmaximal, characteristic, complemented
5C2×#89940C211yesmaximal, characteristic
6C2×#89803C211yesmaximal, characteristic, complemented
7C2×#89788C211yesmaximal, characteristic
8#11737210C2116yesmaximal, direct product factor
9C2×#89661C211yesmaximal, characteristic, complemented
10C2×#89645C211yesmaximal, characteristic, complemented
11C2×#89570C211yesmaximal, characteristic, complemented
12C2×#89565C211yesmaximal, characteristic, complemented
13C2×#89539C211yesmaximal, characteristic, complemented
14C2×#89559C211yesmaximal, characteristic
15C2×#89487C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6510C2211yescharacteristic
21C2×#6507C2211yescharacteristic
22C22×#1144C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C2×#6499C2211yescharacteristic
25C2×#6499C2211yescharacteristic
26C22×#1142C2211yescharacteristic
27C22×#1141C2211yescharacteristic
28C2×#6489—21no—
29C2×#6487—21no—
30C22×Dic28C2211yescharacteristic
31C22×Dic28C2211yescharacteristic
32C22×#1132C2211yescharacteristic
33C22×#1132C2211yescharacteristic
34#90259—24no—
35#90259C2218yescomplemented
36#90233—24no—
37#90233C2218yescomplemented
38C2×#6461—21no—
39C2×#6459—21no—
40C2×#6456C2211yescharacteristic
41C2×#6450C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6450C2211yescharacteristic
44C2×#6442—21no—
45C2×#6442—21no—
46C2×#6439—21no—
47C2×#6438C2211yescharacteristic
48C2×#6435—21no—
49C2×#6432C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C7×#440C2218yescomplemented
52C2×C7×#107C2211yescharacteristic
53C2×C7×#103C2211yescharacteristic
54C2×C7×#102C2211yescharacteristic
55C2×C7×#97C2211yescharacteristic
56#89940C2218yes—
57#89939C2218yescomplemented
58C2×#6389C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×C8×Dic7C2211yescharacteristic
62#89803C2218yescomplemented
63#89788C2218yes—
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×C4⋊(C7⋊C8)C2211yescharacteristic
69#89661C2218yescomplemented
70#89645C2218yescomplemented
71#89570C2218yescomplemented
72#89565C2218yescomplemented
73#89559C2218yes—
74#89539C2218yescomplemented
75#89487C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3402—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×D28C2311yescharacteristic
82C22×C4×D7—21no—
83C22×Dic14D411yescharacteristic
84C22×Dic14C2311yescharacteristic
85C22×Dic14C2311yescharacteristic
86C22×Dic14C2311yescharacteristic
87C2×C7×SD16—24no—
88C2×C7×SD16C2314yes—
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C4×C7×Q8—22no—
92C4×C7×Q8C2314yes—
93C4×C7×D4—22no—
94C4×C7×D4C2314yes—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C22⋊C4—21no—
99C2×C42×C7—21no—
100C2×C42×C7C2311yescharacteristic
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105#6510—22no—
106#6510C2314yes—
107#6507—22no—
108#6507C2314yes—
109C2×#1144—42no—
110C2×#1144—42no—
111C2×#1144C2314yes—
112C2×#1144C2314yes—
113#6499—22no—
114#6499—22no—
115#6499C2314yes—
116#6499C2314yes—
117C2×#1142—42no—
118C2×#1142C2314yes—
119C2×#1141—42no—
120C2×#1141C2314yes—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126#6489—28no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7D411yescharacteristic
130#6487—28no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4D411yescharacteristic
137C2×Dic7⋊C4D411yescharacteristic
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7C2311yescharacteristic
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×Dic28—24no—
146C2×Dic28—42no—
147C2×Dic28C2314yes—
148C2×Dic28C2314yes—
149C2×#1132—24no—
150C2×#1132—42no—
151C2×#1132C2314yes—
152C2×#1132C2314yes—
153#6461—28no—
154#6459—28no—
155#6456—22no—
156#6456C2314yes—
157#6450—22no—
158#6450—22no—
159#6450—22no—
160#6450C2314yes—
161#6450C2314yes—
162#6450C2314yes—
163#6442—28no—
164#6442—28no—
165#6439—28no—
166#6438—22no—
167#6438C2314yes—
168#6435—28no—
169#6432—22no—
170#6432C2314yes—
171C4×Dic14D414yes—
172C4×Dic14C2314yes—
173C7×#107C2314yes—
174C7×#103C2314yes—
175C7×#102C2314yes—
176C7×#97C2314yes—
177#6389C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180C8×Dic7C2314yes—
181#6384C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6383C2314yes—
185C4⋊(C7⋊C8)C2314yes—
186C2×#556—71no—
187C2×#556—71no—
188#3402—716no—
189C2×#497—71no—
190C2×#497—71no—
191C2×#495—71no—
192C2×#464—71no—
193C2×#464—71no—
194C2×#462—71no—
195C2×#462—71no—
196C2×#463—71no—
197C2×#463—71no—
198C2×#446—71no—
199C2×#440—71no—
200C2×#440D711yescharacteristic, complemented
201C2×C4×Q16—71no—
202C24×C7—21no—
203C23×D7—21no—
204C2×C7×Q8—21no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8C2412yes—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4C2412yes—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—24no—
216C22×C4×C7—44no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2411yescharacteristic
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—21no—
230C2×D28C2412yes—
231C2×C4×D7—24no—
232C2×C4×D7—44no—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14—21no—
241C2×Dic14—21no—
242C2×Dic14—42no—
243C2×Dic14C2×D414yes—
244C2×Dic14C2412yes—
245C2×Dic14C2412yes—
246C2×Dic14C2412yes—
247C7×SD16—28no—
248C2×C7×C8—22no—
249C2×C7×C8#4114yes—
250C2×C7×C8C2412yes—
251C2×C7×C8C2412yes—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C7×C22⋊C4—24no—
258C42×C7—24no—
259C42×C7C2×D412yes—
260C42×C7C2412yes—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265#1144—44no—
266#1144—44no—
267#1142—44no—
268#1141—44no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7C2×D414yes—
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×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7C2×D412yes—
288C4×Dic7C2×D412yes—
289C4×Dic7C2412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295Dic28—28no—
296Dic28—44no—
297#1132—28no—
298#1132—44no—
299C22×Q16—71no—
300C22×Q16—71no—
301C22×Q16—71no—
302C22×Q16—71no—
303C22×SD16—71no—
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16C2×D711yescharacteristic
307C22×D8—71no—
308#556—78no—
309#556—78no—
310#556—144no—
311#556—144no—
312C2×C4⋊Q8—71no—
313C2×C4⋊Q8—71no—
314C2×#126—141no—
315C2×#126—141no—
316C2×#126—141no—
317C2×#126—141no—
318C2×#124—71no—
319C2×#124—71no—
320C2×#124—71no—
321C2×#124—71no—
322C2×C22⋊Q8—141no—
323C2×C22⋊Q8—141no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8—71no—
327C2×C4×Q8—71no—
328C2×C4×Q8C2×D711yescharacteristic
329C2×C4×D4—71no—
330C2×C4×D4C2×D711yescharacteristic
331C2×#117—141no—
332C2×#117—141no—
333#497—78no—
334#497—78no—
335#495—78no—
336#464—78no—
337#464—78no—
338#463—78no—
339#463—78no—
340#462—78no—
341#462—78no—
342#446—78no—
343#440—78no—
344#440C2×D718yescomplemented
345C4×Q16—78no—
346C2×#107C2×D711yescharacteristic
347C2×C4⋊C8—71no—
348C2×C4⋊C8—71no—
349C2×C4⋊C8—71no—
350C2×#103—71no—
351C2×#103—71no—
352C2×#103—71no—
353C2×#103C2×D711yescharacteristic
354C2×#102—71no—
355C2×#102C2×D711yescharacteristic
356C2×#97—71no—
357C2×#97C2×D711yescharacteristic
358C2×C4×C8—71no—
359C23×C7—22no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7C22×D411yescharacteristic
364C22×D7—22no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C7×Q8—22no—
369C7×Q8—22no—
370C7×Q8—42no—
371C7×D4—22no—
372C7×D4—22no—
373C7×D4—42no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—48no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4112yes—
387C2×C4×C7H(5,𝔽2)12yes—
388C2×C4×C7C2511yescharacteristic
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403D28—22no—
404D28—22no—
405D28—42no—
406C4×D7—48no—
407Dic14—22no—
408Dic14—22no—
409Dic14—22no—
410Dic14—22no—
411Dic14—22no—
412Dic14—22no—
413Dic14—44no—
414Dic14—42no—
415Dic14—42no—
416Dic14—42no—
417C7×C8—22no—
418C7×C8C2×#4114yes—
419C7⋊C8—22no—
420C7⋊C8—22no—
421C22×Q8—71no—
422C22×Q8—71no—
423C22×Q8—71no—
424C22×Q8—71no—
425C22×Q8C22×D711yescharacteristic
426C22×D4—71no—
427C22×D4C22×D711yescharacteristic
428C23×C4—21no—
429C23×C4—141no—
430C2×Q16—74no—
431C2×Q16—74no—
432C2×Q16—74no—
433C2×Q16—74no—
434C2×Q16—144no—
435C2×Q16—282no—
436C2×Q16—282no—
437C2×Q16—282no—
438C2×SD16—24no—
439C2×SD16—74no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—144no—
443C2×SD16—282no—
444C2×SD16—282no—
445C2×SD16C22×D714yes—
446C2×D8—74no—
447C2×D8—282no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452C4⋊Q8—74no—
453C4⋊Q8—74no—
454C4⋊Q8—142no—
455C4⋊Q8—142no—
456#126—148no—
457#126—148no—
458#126—148no—
459#126—148no—
460#124—74no—
461#124—74no—
462#124—74no—
463#124—74no—
464#124—142no—
465#124—142no—
466#124—142no—
467#124—142no—
468C22⋊Q8—148no—
469C22⋊Q8—148no—
470C4×Q8—22no—
471C4×Q8—74no—
472C4×Q8—74no—
473C4×Q8—74no—
474C4×Q8—74no—
475C4×Q8—74no—
476C4×Q8—142no—
477C4×Q8—142no—
478C4×Q8—142no—
479C4×Q8C22×D714yes—
480C4×D4—22no—
481C4×D4—74no—
482C4×D4—142no—
483C4×D4C22×D714yes—
484#117—148no—
485#117—148no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—71no—
488C2×C4⋊C4—71no—
489C2×C4⋊C4—71no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4C22×D711yescharacteristic
498C2×C4⋊C4C22×D711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C42—21no—
510C2×C42—71no—
511C2×C42—71no—
512C2×C42—141no—
513C2×C42—141no—
514C2×C42—141no—
515C2×C42C22×D711yescharacteristic
516#107C22×D714yes—
517C4⋊C8—74no—
518C4⋊C8—74no—
519C4⋊C8—74no—
520#103—74no—
521#103—74no—
522#103—74no—
523#103C22×D714yes—
524#102—74no—
525#102C22×D714yes—
526#97—74no—
527#97C22×D714yes—
528C4×C8—74no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7—84no—
533C22×C7#55012yes—
534C22×C7#57512yes—
535C22×C7#57812yes—
536C22×C7C23×D411yescharacteristic
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—84no—
541C4×C7—22no—
542C4×C7—22no—
543C4×C7—42no—
544C4×C7—42no—
545C4×C7—42no—
546C4×C7#55012yes—
547C4×C7C22×#4111yescharacteristic
548C4×C7C2×H(5,𝔽2)11yescharacteristic
549Dic7—22no—
550Dic7—22no—
551Dic7—22no—
552Dic7—22no—
553Dic7—42no—
554Dic7—42no—
555Dic7—42no—
556C24—21no—
557C24—141no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—74no—
562C2×Q8—72no—
563C2×Q8—72no—
564C2×Q8—72no—
565C2×Q8—141no—
566C2×Q8—141no—
567C2×Q8—141no—
568C2×Q8—142no—
569C2×Q8—142no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—142no—
574C2×Q8—282no—
575C2×Q8C23×D712yes—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—72no—
580C2×D4—142no—
581C2×D4—141no—
582C2×D4—142no—
583C2×D4C23×D712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—71no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—71no—
593C22×C4—144no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—284no—
598C22×C4D4×D711yescharacteristic
599C22×C4D4×D711yescharacteristic
600C22×C4C23×D711yescharacteristic
601Q16—148no—
602Q16—284no—
603Q16—284no—
604Q16—284no—
605SD16—28no—
606SD16—148no—
607SD16—284no—
608SD16—284no—
609D8—284no—
610C2×C8—22no—
611C2×C8—72no—
612C2×C8—72no—
613C2×C8—142no—
614C2×C8—142no—
615C2×C8#115714yes—
616C2×C8C23×D712yes—
617C2×C8C23×D712yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—74no—
622C4⋊C4—74no—
623C4⋊C4—74no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—144no—
631C4⋊C4C23×D712yes—
632C4⋊C4C23×D712yes—
633C22⋊C4—24no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C42—24no—
644C42—72no—
645C42—72no—
646C42—72no—
647C42—72no—
648C42—144no—
649C42—144no—
650C42—144no—
651C42D4×D712yes—
652C42C23×D712yes—
653C2×C7—82no—
654C2×C7#340214yescomplemented
655C2×C7C2×#55011yescharacteristic
656C2×C7C2×#57511yescharacteristic
657C2×C7C2×#57811yescharacteristic
658D7—82no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—142no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—142no—
672Q8—142no—
673Q8—142no—
674Q8—142no—
675Q8—142no—
676Q8—142no—
677Q8—284no—
678Q8—282no—
679Q8—282no—
680Q8—282no—
681D4—22no—
682D4—22no—
683D4—42no—
684D4—142no—
685D4—142no—
686D4—282no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—48no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—72no—
697C2×C4—72no—
698C2×C4—72no—
699C2×C4—72no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—288no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4C2×#115712yes—
712C2×C4C2×D4×D712yes—
713C2×C4C2×D4×D712yes—
714C2×C4C2×D4×D711yescharacteristic
715C2×C4#655312yes—
716C2×C4C24×D711yescharacteristic
717C8—22no—
718C8—142no—
719C8—142no—
720C8C2×#115714yes—
721C7C2×#340211yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—564no—
730C22#9024412yes—
731C22#9046412yes—
732C22#9047012yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—142no—
740C4—142no—
741C4—142no—
742C4—142no—
743C4—282no—
744C4—282no—
745C4—282no—
746C4#9024412yes—
747C4C22×#115711yescharacteristic
748C4C2×#655311yescharacteristic
749C2—82no—
750C2—562no—
751C2#1173721014yesdirect product factor
752C2C2×#9024411yescharacteristic
753C2C2×#9046411yescharacteristic
754C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×#440D7
hypocenterC7C2×#3402
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#90259C2semidirect
2. C2×#90233C2semidirect
3. C2×C7×#440C2semidirect
4. C2×#89939C2semidirect
6. C2×#89803C2semidirect
8. #11737210C2direct (N × H)
9. C2×#89661C2semidirect
10. C2×#89645C2semidirect
11. C2×#89570C2semidirect
12. C2×#89565C2semidirect
13. C2×#89539C2semidirect
15. C2×#89487C2semidirect
16. C2×#89473C2semidirect
35. #90259C22semidirect
37. #90233C22semidirect
51. C7×#440C22semidirect
57. #89939C22semidirect
62. #89803C22semidirect
69. #89661C22semidirect
70. #89645C22semidirect
71. #89570C22semidirect
72. #89565C22semidirect
74. #89539C22semidirect
75. #89487C22semidirect
76. #89473C22semidirect
200. C2×#440D7semidirect
344. #440C2×D7semidirect
654. C2×C7#3402semidirect
721. C7C2×#3402semidirect
751. C2#11737210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902592
C2×#902332
C2×C7×#4402
C2×#899392
C2×#899402
C2×#898032
C2×#897882
#117372102
C2×#896612
C2×#896452
C2×#895702
C2×#895652
C2×#895392
C2×#895592
C2×#894872
C2×#894732
C2×#34027