Finite Group Databasebeta

← C2×#11738701 #14232382

Subgroups — C2×#11738701 #14232382

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90386C211yesmaximal, characteristic
2C2×#90270C211yesmaximal, characteristic, complemented
3C2×C7×#479C211yesmaximal, characteristic, complemented
4C2×#89837C211yesmaximal, characteristic, complemented
5C2×#89798C211yesmaximal, characteristic, complemented
6#11738701C2116yesmaximal, direct product factor
7C2×#89654C211yesmaximal, characteristic, complemented
8C2×D7×#107C211yesmaximal, characteristic, complemented
9C2×#89635C211yesmaximal, characteristic, complemented
10C2×#89633C211yesmaximal, characteristic, complemented
11C2×#89618C211yesmaximal, characteristic, complemented
12C2×#89608C211yesmaximal, characteristic, complemented
13C2×#89581C211yesmaximal, characteristic, complemented
14C2×#89584C211yesmaximal, characteristic, complemented
15C2×#89579C211yesmaximal, characteristic, complemented
16C2×#89586C211yesmaximal, characteristic, complemented
17C2×C7×#125C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×#6509C2211yescharacteristic
20C2×#6509C2211yescharacteristic
21C22×#1143C2211yescharacteristic
22C22×#1131C2211yescharacteristic
23C22×C8×D7C2211yescharacteristic
24#90386—24no—
25#90386C2218yes—
26#90270—24no—
27#90270C2218yescomplemented
28C2×#6461—21no—
29C2×#6459—21no—
30C2×#6459—21no—
31C2×#6458—21no—
32C2×#6458C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456—21no—
36C2×#6455C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×C4×D28—21no—
41C2×C4×D28C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×#6433—21no—
44C2×#6432C2211yescharacteristic
45C7×#479C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×#6392C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58#89837C2218yescomplemented
59#89798C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6382C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6381C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6377C2211yescharacteristic
67#89654C2218yescomplemented
68D7×#107C2218yescomplemented
69#89635C2218yescomplemented
70#89633C2218yescomplemented
71#89618C2218yescomplemented
72#89608C2218yescomplemented
73#89586C2218yescomplemented
74#89584C2218yescomplemented
75#89581C2218yescomplemented
76#89579C2218yescomplemented
77C2×#3346—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×D28—21no—
80C22×D28—21no—
81C22×D28D411yescharacteristic
82C22×D28C2311yescharacteristic
83C22×C4×D7—21no—
84C22×C4×D7—21no—
85C22×C4×D7—21no—
86C22×C4×D7—21no—
87C22×C4×D7C2311yescharacteristic
88C22×C4×D7C2311yescharacteristic
89C22×Dic14—21no—
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C7×#125—22no—
93C7×#125C2314yes—
94C4×C7×Q8—22no—
95C4×C7×Q8C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C42×C7—21no—
103C2×C42×C7C2311yescharacteristic
104#6509—22no—
105#6509—22no—
106#6509C2314yes—
107#6509C2314yes—
108C2×#1143—24no—
109C2×#1143C2314yes—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4D411yescharacteristic
117C2×(C2×D7)⋊C4D411yescharacteristic
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7D411yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×C4×Dic7—21no—
129C22×C7⋊C8C2311yescharacteristic
130C22×C7⋊C8C2311yescharacteristic
131C2×#1131—24no—
132C2×#1131C2314yes—
133C2×C8×D7—24no—
134C2×C8×D7C2314yes—
135#6461—28no—
136#6459—28no—
137#6459—28no—
138#6458—28no—
139#6458—22no—
140#6458—22no—
141#6458C2314yes—
142#6458C2314yes—
143#6457—28no—
144#6456—28no—
145#6455—22no—
146#6455C2314yes—
147D7×C4⋊C4—22no—
148D7×C4⋊C4—22no—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151D7×C4⋊C4C2314yes—
152D7×C4⋊C4C2314yes—
153C4×D28—28no—
154C4×D28—22no—
155C4×D28D414yes—
156C4×D28C2314yes—
157C4×D28C2314yes—
158#6433—28no—
159#6432—22no—
160#6432C2314yes—
161C7×#107C2314yes—
162C7×#106C2314yes—
163C7×C4⋊C8C2314yes—
164C7×#103C2314yes—
165C7×#103C2314yes—
166#6409C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169(C2×D7)⋊C8C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6392C2314yes—
172#6392C2314yes—
173#6383C2314yes—
174#6382C2314yes—
175#6382C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6377C2314yes—
180C2×#554—71no—
181C2×#553—71no—
182#3346—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#481—71no—
186C2×#485—71no—
187C2×#480—71no—
188C2×#479D711yescharacteristic, complemented
189C2×#474—71no—
190C2×#468—71no—
191C2×#465—71no—
192C2×#440—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#107—71no—
196C23×D7—21no—
197C23×D7C2×D411yescharacteristic
198C23×D7C2×D411yescharacteristic
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2411yescharacteristic
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7C2×D411yescharacteristic
214C22×Dic7C2×D411yescharacteristic
215C2×D28—24no—
216C2×D28—22no—
217C2×D28—22no—
218C2×D28—24no—
219C2×D28—21no—
220C2×D28—24no—
221C2×D28—44no—
222C2×D28—82no—
223C2×D28C2×D414yes—
224C2×D28C2412yes—
225C2×C4×D7—22no—
226C2×C4×D7—22no—
227C2×C4×D7—22no—
228C2×C4×D7—22no—
229C2×C4×D7—24no—
230C2×C4×D7—24no—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—82no—
234C2×C4×D7—82no—
235C2×C4×D7—82no—
236C2×C4×D7—82no—
237C2×C4×D7C2×D412yes—
238C2×C4×D7C2×D412yes—
239C2×C4×D7C2412yes—
240C2×C4×D7C2412yes—
241C2×Dic14—24no—
242C2×Dic14—82no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8C2412yes—
246C2×C7×C8C2412yes—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C42×C7—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259#1143—28no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4C2×D414yes—
267(C2×D7)⋊C4C2×D414yes—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7—21no—
272C4⋊Dic7C2×D414yes—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281C4×Dic7—24no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8#4114yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286#1131—28no—
287C8×D7—28no—
288C22×SD16—71no—
289C22×M16—71no—
290C23×C8—71no—
291#554—78no—
292#554—144no—
293#553—78no—
294#553—144no—
295C2×C4⋊Q8—71no—
296C2×#126—141no—
297C2×#125—141no—
298C2×#125C2×D711yescharacteristic
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4—141no—
312C2×#117—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316#501—78no—
317#485—78no—
318#484—78no—
319#481—78no—
320#480—78no—
321#479C2×D718yescomplemented
322#474—78no—
323#468—78no—
324#465—78no—
325#440—78no—
326#435—78no—
327#428—78no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—78no—
334C2×#107C2×D711yescharacteristic
335C2×#106—71no—
336C2×#106—71no—
337C2×#106C2×D711yescharacteristic
338C2×C4⋊C8C2×D711yescharacteristic
339C2×#103—71no—
340C2×#103C2×D711yescharacteristic
341C2×#103C2×D711yescharacteristic
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×C22⋊C8—71no—
346C2×C22⋊C8—71no—
347C2×#97—71no—
348C23×C7C22×D411yescharacteristic
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—42no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7#13714yes—
359C22×D7C22×D412yes—
360C22×D7C22×D412yes—
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—42no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C2×#4112yes—
378C2×C4×C72−1+412yes—
379C2×C4×C7C2511yescharacteristic
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7C22×D412yes—
389C2×Dic7C22×D412yes—
390D28—28no—
391D28—22no—
392D28—22no—
393D28—48no—
394D28—42no—
395D28—84no—
396C4×D7—24no—
397C4×D7—24no—
398C4×D7—22no—
399C4×D7—22no—
400C4×D7—22no—
401C4×D7—22no—
402C4×D7—84no—
403C4×D7—84no—
404C4×D7—84no—
405C4×D7—84no—
406Dic14—84no—
407C7×C8—22no—
408C7×C8—22no—
409C7⋊C8—22no—
410C7⋊C8C2×#4114yes—
411C22×Q8—141no—
412C22×Q8C22×D711yescharacteristic
413C22×D4—71no—
414C22×D4—71no—
415C22×D4—141no—
416C22×D4—141no—
417C23×C4—71no—
418C23×C4—71no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4—141no—
422C23×C4—141no—
423C2×SD16—74no—
424C2×SD16—144no—
425C2×M16—74no—
426C2×M16—144no—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8—74no—
430C22×C8—144no—
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D711yescharacteristic
433C4⋊Q8—74no—
434C4⋊Q8—142no—
435#126—148no—
436#125—22no—
437#125—148no—
438#125C22×D714yes—
439#123—148no—
440C22⋊Q8—74no—
441C22⋊Q8—74no—
442C22⋊Q8—148no—
443C22⋊Q8—148no—
444C22⋊Q8—142no—
445C22⋊Q8—142no—
446#121—74no—
447#121—74no—
448#121—142no—
449#121—142no—
450#121—148no—
451C4×Q8—22no—
452C4×Q8C22×D714yes—
453C4×D4—74no—
454C4×D4—74no—
455C4×D4—74no—
456C4×D4—148no—
457C4×D4—148no—
458C4×D4—142no—
459#117—74no—
460#117—142no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—74no—
471C2×C4⋊C4—142no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—71no—
484C2×C22⋊C4—71no—
485C2×C22⋊C4—141no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C42—21no—
492C2×C42—141no—
493C2×C42C22×D711yescharacteristic
494#107—74no—
495#107—74no—
496#107—74no—
497#107—74no—
498#107—74no—
499#107C22×D714yes—
500#106—74no—
501#106—74no—
502#106C22×D714yes—
503C4⋊C8C22×D714yes—
504#103—74no—
505#103C22×D714yes—
506#103C22×D714yes—
507#102—74no—
508#102—74no—
509#102—74no—
510C22⋊C8—74no—
511C22⋊C8—74no—
512#97—74no—
513C22×C7#54712yes—
514C22×C7C2×#13712yes—
515C22×C7#57612yes—
516C22×C7C23×D411yescharacteristic
517C2×D7—28no—
518C2×D7—22no—
519C2×D7—22no—
520C2×D7—22no—
521C2×D7—22no—
522C2×D7—22no—
523C2×D7—44no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—84no—
528C2×D7C2×#13714yes—
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7#54712yes—
536C4×C7C22×#4111yescharacteristic
537C4×C7C2×2−1+411yescharacteristic
538Dic7—22no—
539Dic7—22no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—71no—
544C24—71no—
545C24—141no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—144no—
550C2×Q8—562no—
551C2×Q8C23×D712yes—
552C2×D4—74no—
553C2×D4—72no—
554C2×D4—144no—
555C2×D4—144no—
556C2×D4—144no—
557C2×D4—141no—
558C2×D4—142no—
559C2×D4—142no—
560C2×D4—284no—
561C2×D4—562no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—71no—
567C22×C4—71no—
568C22×C4—72no—
569C22×C4—72no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—144no—
573C22×C4—144no—
574C22×C4—144no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—144no—
583C22×C4—562no—
584C22×C4—562no—
585C22×C4—562no—
586C22×C4—562no—
587C22×C4D4×D711yescharacteristic
588C22×C4D4×D711yescharacteristic
589C22×C4C23×D711yescharacteristic
590SD16—148no—
591M16—148no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—74no—
595C2×C8—72no—
596C2×C8—72no—
597C2×C8—148no—
598C2×C8—142no—
599C2×C8C23×D712yes—
600C2×C8C23×D712yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—74no—
608C4⋊C4—72no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—141no—
617C4⋊C4—141no—
618C4⋊C4—141no—
619C4⋊C4—144no—
620C4⋊C4C23×D712yes—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C22⋊C4—74no—
624C22⋊C4—74no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—24no—
632C42—144no—
633C42D4×D712yes—
634C42C23×D712yes—
635C2×C7#334614yescomplemented
636C2×C7C2×#54711yescharacteristic
637C2×C7C22×#13711yescharacteristic
638C2×C7C2×#57611yescharacteristic
639D7—24no—
640D7—42no—
641D7—82no—
642C23—74no—
643C23—72no—
644C23—72no—
645C23—142no—
646C23—142no—
647C23—142no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—282no—
652C23—282no—
653C23—282no—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—564no—
659D4—148no—
660D4—142no—
661D4—142no—
662D4—288no—
663D4—282no—
664D4—564no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—72no—
676C2×C4—72no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—144no—
680C2×C4—144no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—564no—
692C2×C4—564no—
693C2×C4—564no—
694C2×C4—564no—
695C2×C4C2×D4×D712yes—
696C2×C4C2×D4×D712yes—
697C2×C4C2×D4×D711yescharacteristic
698C2×C4#655112yes—
699C2×C4D7×#4112yes—
700C2×C4C24×D711yescharacteristic
701C8—22no—
702C8—22no—
703C8—74no—
704C8—142no—
705C7C2×#334611yescharacteristic, complemented, Sylow
706C22—74no—
707C22—142no—
708C22—148no—
709C22—142no—
710C22—142no—
711C22—142no—
712C22—142no—
713C22—284no—
714C22—282no—
715C22—282no—
716C22—282no—
717C22—564no—
718C22#9032212yes—
719C22#9046012yes—
720C22D7×#13712yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—142no—
729C4—142no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4#9032212yes—
734C4C2×#655111yescharacteristic
735C4C2×D7×#4111yescharacteristic
736C2—144no—
737C2—282no—
738C2—562no—
739C2#1173870114yesdirect product factor
740C2C2×#9032211yescharacteristic
741C2C2×#9046011yescharacteristic
742C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#479C2
socleC23×C7C22×D4
prime radicalC2×#90386C2
hypercenterC2×#479D7
hypocenterC7C2×#3346
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×#90270C2semidirect
3. C2×C7×#479C2semidirect
4. C2×#89837C2semidirect
5. C2×#89798C2semidirect
6. #11738701C2direct (N × H)
7. C2×#89654C2semidirect
8. C2×D7×#107C2semidirect
9. C2×#89635C2semidirect
10. C2×#89633C2semidirect
11. C2×#89618C2semidirect
12. C2×#89608C2semidirect
13. C2×#89581C2semidirect
14. C2×#89584C2semidirect
15. C2×#89579C2semidirect
16. C2×#89586C2semidirect
27. #90270C22semidirect
45. C7×#479C22semidirect
58. #89837C22semidirect
59. #89798C22semidirect
67. #89654C22semidirect
68. D7×#107C22semidirect
69. #89635C22semidirect
70. #89633C22semidirect
71. #89618C22semidirect
72. #89608C22semidirect
73. #89586C22semidirect
74. #89584C22semidirect
75. #89581C22semidirect
76. #89579C22semidirect
188. C2×#479D7semidirect
321. #479C2×D7semidirect
635. C2×C7#3346semidirect
705. C7C2×#3346semidirect
739. C2#11738701direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903862
C2×#902702
C2×C7×#4792
C2×#898372
C2×#897982
#117387012
C2×#896542
C2×D7×#1072
C2×#896352
C2×#896332
C2×#896182
C2×#896082
C2×#895812
C2×#895842
C2×#895792
C2×#895862
C2×#33467