Finite Group Databasebeta

← C2×#11737294 #14222057

Subgroups — C2×#11737294 #14222057

Order 1792.

2070 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×#90274C211yesmaximal, characteristic, complemented
2C2×#90265C211yesmaximal, characteristic
3C2×C7×#441C211yesmaximal, characteristic, complemented
4C2×#89959C211yesmaximal, characteristic
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×C4×#1144C211yesmaximal, characteristic, complemented
7C2×C4×#1143C211yesmaximal, characteristic, complemented
8#11737294C2116yesmaximal, direct product factor
9C2×#89643C211yesmaximal, characteristic, complemented
10C2×#89634C211yesmaximal, characteristic, complemented
11C2×#89590C211yesmaximal, characteristic, complemented
12C2×#89581C211yesmaximal, characteristic, complemented
13C2×#89582C211yesmaximal, characteristic
14C2×#89568C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89481C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C22×#1144C2211yescharacteristic
25C22×#1143C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27#90274—24no—
28#90274C2218yescomplemented
29#90265—24no—
30#90265C2218yes—
31C2×#6461—21no—
32C2×#6460C2211yescharacteristic
33C2×#6456—21no—
34C2×#6456C2211yescharacteristic
35C2×D7×C4⋊C4—21no—
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6453C2211yescharacteristic
38C2×#6452—21no—
39C2×#6439—21no—
40C2×C4×D28—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6435—21no—
43C2×#6435C2211yescharacteristic
44C2×#6433—21no—
45C2×C4×Dic14C2211yescharacteristic
46C7×#441C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53#89959C2218yes—
54#89954C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C4×#1144C2218yescomplemented
63C4×#1143C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4×C7⋊C8C2211yescharacteristic
69#89643C2218yescomplemented
70#89634C2218yescomplemented
71#89590C2218yescomplemented
72#89582C2218yes—
73#89581C2218yescomplemented
74#89568C2218yescomplemented
75#89482C2218yescomplemented
76#89481C2218yescomplemented
77C2×#3120—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C2×#1161—24no—
81C2×#1161—24no—
82C2×#1161—22no—
83C2×#1161C2314yes—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C2×C7×Q16—24no—
93C2×C7×Q16C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C4×C7×Q8—22no—
97C4×C7×Q8—22no—
98C4×C7×Q8C2314yes—
99C4×C7×Q8C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7—21no—
106C2×C42×C7C2311yescharacteristic
107#6509—22no—
108#6509C2314yes—
109Q8×Dic7—22no—
110Q8×Dic7C2314yes—
111#6507—22no—
112#6507C2314yes—
113C2×#1144—24no—
114C2×#1144C2314yes—
115C2×#1143—24no—
116C2×#1143C2314yes—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4D411yescharacteristic
122C2×(C2×D7)⋊C4D411yescharacteristic
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4D411yescharacteristic
135C2×Dic7⋊C4D411yescharacteristic
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×#1132—24no—
142C2×#1132C2314yes—
143#6461—28no—
144#6460—22no—
145#6460C2314yes—
146#6456—28no—
147#6456—22no—
148#6456C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4—28no—
151D7×C4⋊C4C2314yes—
152#6453—22no—
153#6453C2314yes—
154#6452—28no—
155#6439—28no—
156C4×D28—22no—
157C4×D28—28no—
158C4×D28C2314yes—
159#6435—28no—
160#6435D414yes—
161#6435C2314yes—
162#6433—28no—
163C4×Dic14—22no—
164C4×Dic14C2314yes—
165C7×#106C2314yes—
166C7×#103C2314yes—
167C7×#103C2314yes—
168C7×#97C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6395C2314yes—
172(C2×D7)⋊C8C2314yes—
173(C2×D7)⋊C8C2314yes—
174#6392C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#541—71no—
184C2×#520—71no—
185#3120—716no—
186C2×#484—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#462—71no—
191C2×#461—71no—
192C2×#452—71no—
193C2×#452—71no—
194C2×#441D711yescharacteristic, complemented
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8#4114yes—
207C2×C7×Q8C2412yes—
208C2×C7×Q8C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2411yescharacteristic
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222#1161—216no—
223#1161—28no—
224#1161—28no—
225C2×D28—28no—
226C2×D28—24no—
227C2×D28—21no—
228C2×D28—22no—
229C2×D28#4114yes—
230C2×D28C2412yes—
231C2×C4×D7—28no—
232C2×C4×D7—22no—
233C2×C4×D7—22no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—82no—
239C2×C4×D7—82no—
240C2×C4×D7—82no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2412yes—
243C2×Dic14—22no—
244C2×Dic14—22no—
245C2×Dic14—21no—
246C2×Dic14C2412yes—
247C7×Q16—28no—
248C2×C7×C8—22no—
249C2×C7×C8—22no—
250C2×C7×C8C2412yes—
251C2×C7×C8C2412yes—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4C2412yes—
257C7×C4⋊C4C2412yes—
258C42×C7—24no—
259C42×C7—24no—
260C42×C7C2×D412yes—
261C42×C7C2412yes—
262#1144—28no—
263#1143—28no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4C2×D414yes—
269(C2×D7)⋊C4C2×D414yes—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7—24no—
273C4⋊Dic7—24no—
274C4⋊Dic7—24no—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4C2×D414yes—
284Dic7⋊C4C2×D414yes—
285C4×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7C2×D412yes—
288C4×Dic7C2412yes—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8C2412yes—
292C2×C7⋊C8C2412yes—
293#1132—28no—
294C22×#41—71no—
295C22×Q16—71no—
296C22×Q16C2×D711yescharacteristic
297C22×SD16—71no—
298C22×SD16—71no—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#126—141no—
304C2×#125—71no—
305C2×#125—141no—
306C2×#125—141no—
307C2×C22⋊Q8—71no—
308C2×C22⋊Q8—71no—
309#520—78no—
310#520—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8C2×D711yescharacteristic
314C2×C4×Q8C2×D711yescharacteristic
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—141no—
318C2×C4×D4—141no—
319C2×#117—71no—
320C2×#117—141no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—141no—
323#484—78no—
324#483—78no—
325#479—78no—
326#478—78no—
327#462—78no—
328#461—78no—
329#452—78no—
330#452—78no—
331#441C2×D718yescomplemented
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#106—71no—
339C2×#106C2×D711yescharacteristic
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103C2×D711yescharacteristic
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8—71no—
352C2×#97C2×D711yescharacteristic
353C2×C4×C8—71no—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—24no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7C22×D412yes—
363C7×Q8—24no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—22no—
367C7×Q8—42no—
368C7×Q8C2×#4114yes—
369C2×C4×C7—24no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C7C2×#4112yes—
384C2×C4×C7C2511yescharacteristic
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397D28—216no—
398D28—24no—
399D28—22no—
400D28C2×#4114yes—
401C4×D7—216no—
402C4×D7—24no—
403C4×D7—22no—
404C4×D7—22no—
405C4×D7—84no—
406C4×D7—84no—
407C4×D7—84no—
408Dic14—22no—
409Dic14—22no—
410Dic14—42no—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C2×#41—74no—
416C2×#41—142no—
417C2×#41—144no—
418C2×#41—144no—
419C22×Q8—71no—
420C22×Q8C22×D711yescharacteristic
421C22×Q8C22×D711yescharacteristic
422C22×D4—71no—
423C22×D4—141no—
424C23×C4—71no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4—141no—
428C23×C4—141no—
429C2×Q16—24no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16C22×D714yes—
433C2×SD16—74no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16—144no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8C22×D711yescharacteristic
440C22×C8C22×D711yescharacteristic
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#125—74no—
446#125—148no—
447#125—142no—
448#125—148no—
449C22⋊Q8—74no—
450C22⋊Q8—74no—
451C22⋊Q8—142no—
452C22⋊Q8—142no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×Q8—142no—
459C4×Q8C22×D714yes—
460C4×Q8C22×D714yes—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—148no—
464C4×D4—142no—
465C4×D4—148no—
466C4×D4—142no—
467#117—74no—
468#117—74no—
469#117—148no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—148no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C22⋊C4—71no—
491C2×C22⋊C4—71no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—71no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42C22×D711yescharacteristic
502#107—74no—
503#107—74no—
504#106—74no—
505#106C22×D714yes—
506C4⋊C8—74no—
507C4⋊C8—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103C22×D714yes—
513#103C22×D714yes—
514#102—74no—
515#102—74no—
516C22⋊C8—74no—
517C22⋊C8—74no—
518#97C22×D714yes—
519C4×C8—74no—
520C22×C7#52512yes—
521C22×C7#57712yes—
522C22×C7#57812yes—
523C22×C7C23×D411yescharacteristic
524C2×D7—22no—
525C2×D7—24no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—44no—
529C2×D7—48no—
530C2×D7—42no—
531C2×D7—42no—
532C4×C7—24no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7#52512yes—
539C4×C7C22×#4111yescharacteristic
540C4×C7C22×#4111yescharacteristic
541Dic7—22no—
542Dic7—22no—
543Dic7—22no—
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547C24—71no—
548C24—141no—
549#41—148no—
550#41—1416no—
551#41—148no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—72no—
558C2×Q8—141no—
559C2×Q8—142no—
560C2×Q8—142no—
561C2×Q8#115714yes—
562C2×Q8C23×D712yes—
563C2×Q8C23×D712yes—
564C2×D4—74no—
565C2×D4—72no—
566C2×D4—144no—
567C2×D4—148no—
568C2×D4—142no—
569C2×D4—141no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—71no—
575C22×C4—71no—
576C22×C4—71no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—144no—
580C22×C4—144no—
581C22×C4—148no—
582C22×C4—144no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—144no—
589C22×C4—562no—
590C22×C4—562no—
591C22×C4—562no—
592C22×C4D4×D711yescharacteristic
593C22×C4D4×D711yescharacteristic
594C22×C4C23×D711yescharacteristic
595Q16—28no—
596Q16—148no—
597SD16—148no—
598SD16—148no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—142no—
604C2×C8—142no—
605C2×C8C23×D712yes—
606C2×C8C23×D712yes—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—74no—
612C4⋊C4—74no—
613C4⋊C4—72no—
614C4⋊C4—72no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—141no—
625C4⋊C4—141no—
626C4⋊C4C23×D712yes—
627C4⋊C4C23×D712yes—
628C22⋊C4—74no—
629C22⋊C4—74no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—24no—
635C42—24no—
636C42—72no—
637C42—72no—
638C42—144no—
639C42—144no—
640C42D4×D712yes—
641C42C23×D712yes—
642C2×C7#312014yescomplemented
643C2×C7C2×#52511yescharacteristic
644C2×C7C2×#57711yescharacteristic
645C2×C7C2×#57811yescharacteristic
646D7—42no—
647D7—44no—
648C23—72no—
649C23—142no—
650C23—142no—
651C23—144no—
652C23—142no—
653C23—142no—
654C23—282no—
655C23—282no—
656C23C2×D4×D711yescharacteristic
657Q8—24no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—142no—
663Q8—142no—
664Q8—282no—
665Q8C2×#115714yes—
666D4—74no—
667D4—1416no—
668D4—144no—
669D4—142no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—72no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—1416no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—144no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—564no—
697C2×C4—564no—
698C2×C4—564no—
699C2×C4C2×#115712yes—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D712yes—
702C2×C4C2×D4×D711yescharacteristic
703C2×C4D7×#4112yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#312011yescharacteristic, complemented, Sylow
710C22—142no—
711C22—142no—
712C22—144no—
713C22—142no—
714C22—282no—
715C22—282no—
716C22—284no—
717C22—288no—
718C22#9023812yes—
719C22#9046912yes—
720C22#9047012yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—142no—
729C4—142no—
730C4—142no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4#9023812yes—
735C4C22×#115711yescharacteristic
736C4C2×D7×#4111yescharacteristic
737C2—282no—
738C2—284no—
739C2#1173729414yesdirect product factor
740C2C2×#9023811yescharacteristic
741C2C2×#9046911yescharacteristic
742C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#441C2
socleC23×C7C22×D4
prime radicalC22×#1161C22
hypercenterC2×#441D7
hypocenterC7C2×#3120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#90274C2semidirect
3. C2×C7×#441C2semidirect
5. C2×#89954C2semidirect
6. C2×C4×#1144C2semidirect
7. C2×C4×#1143C2semidirect
8. #11737294C2direct (N × H)
9. C2×#89643C2semidirect
10. C2×#89634C2semidirect
11. C2×#89590C2semidirect
12. C2×#89581C2semidirect
14. C2×#89568C2semidirect
15. C2×#89482C2semidirect
16. C2×#89481C2semidirect
28. #90274C22semidirect
46. C7×#441C22semidirect
54. #89954C22semidirect
62. C4×#1144C22semidirect
63. C4×#1143C22semidirect
69. #89643C22semidirect
70. #89634C22semidirect
71. #89590C22semidirect
73. #89581C22semidirect
74. #89568C22semidirect
75. #89482C22semidirect
76. #89481C22semidirect
194. C2×#441D7semidirect
331. #441C2×D7semidirect
642. C2×C7#3120semidirect
709. C7C2×#3120semidirect
739. C2#11737294direct (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×#902652
C2×C7×#4412
C2×#899592
C2×#899542
C2×C4×#11442
C2×C4×#11432
#117372942
C2×#896432
C2×#896342
C2×#895902
C2×#895812
C2×#895822
C2×#895682
C2×#894822
C2×#894812
C2×#31207