Finite Group Databasebeta

← C2×#11740913 #14226722

Subgroups — C2×#11740913 #14226722

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2C2×#90209C211yesmaximal, characteristic, complemented
3#11740913C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89866C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic, complemented
7C2×#89826C211yesmaximal, characteristic, complemented
8C2×#89824C211yesmaximal, characteristic, complemented
9C2×#89823C211yesmaximal, characteristic, complemented
10C2×#89814C211yesmaximal, characteristic
11C2×#89813C211yesmaximal, characteristic
12C2×#89803C211yesmaximal, characteristic, complemented
13C2×#89794C211yesmaximal, characteristic, complemented
14C2×#89791C211yesmaximal, characteristic, complemented
15C2×#89781C211yesmaximal, characteristic, complemented
16C2×#89771C211yesmaximal, characteristic, complemented
17C7×#542—24no—
18C7×#542C2218yes—
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#124—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#123—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C22×#1144C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90209—24no—
39#90209C2218yescomplemented
40C2×#6452—21no—
41C2×#6452—21no—
42C2×#6442—21no—
43C2×#6442—21no—
44C2×#6433C2211yescharacteristic
45C2×#6432C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C2×#6409C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89866C2218yescomplemented
53#89863C2218yescomplemented
54#89826C2218yescomplemented
55#89826C2218yescomplemented
56#89824C2218yescomplemented
57#89823C2218yescomplemented
58#89814C2218yes—
59#89813C2218yes—
60#89803C2218yescomplemented
61#89794C2218yescomplemented
62#89791C2218yescomplemented
63#89781C2218yescomplemented
64#89771C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×C4⋊(C7⋊C8)C2211yescharacteristic
77C2×#3258—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—21no—
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C22×Dic14C2311yescharacteristic
85C22×Dic14C2311yescharacteristic
86C7×C4⋊Q8—22no—
87C7×C4⋊Q8C2314yes—
88C7×#126—28no—
89C7×#124—28no—
90C7×#124—22no—
91C7×#124C2314yes—
92C7×#123—28no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—28no—
95C7×C22⋊Q8C2314yes—
96C7×#121—22no—
97C7×#121C2314yes—
98C4×C7×Q8—22no—
99C4×C7×Q8C2314yes—
100C4×C7×D4—22no—
101C4×C7×D4C2314yes—
102C7×#117D414yes—
103C7×#117C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4D411yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4D411yescharacteristic
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C42×C7—21no—
119C2×C42×C7C2311yescharacteristic
120C2×C42×C7C2311yescharacteristic
121C2×C22⋊Dic7—21no—
122C2×C22⋊Dic7—21no—
123C2×#1144—42no—
124C2×#1144—42no—
125C2×#1144C2314yes—
126C2×#1144C2314yes—
127C2×#1142—42no—
128C2×#1142—42no—
129C2×#1142C2314yes—
130C2×#1142C2314yes—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135#6487—22no—
136#6487—22no—
137#6487C2314yes—
138#6487C2314yes—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C2×C4×Dic7—21no—
147C2×#1136—42no—
148C2×#1136C2314yes—
149C22×C7⋊C8—42no—
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C22×C7⋊C8C2311yescharacteristic
154C22×C7⋊C8C2314yes—
155#6452—28no—
156#6452—28no—
157#6442—28no—
158#6442—28no—
159#6433—22no—
160#6433C2314yes—
161#6432—22no—
162#6432C2314yes—
163C4×Dic14—22no—
164C4×Dic14—22no—
165C4×Dic14C2314yes—
166C4×Dic14C2314yes—
167#6409C2314yes—
168#6409C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171#6384C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C4⋊(C7⋊C8)C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#542D711yescharacteristic
184C2×#541—71no—
185#3258—716no—
186C2×#479—71no—
187C2×#477—71no—
188C2×#475—71no—
189C2×#478—71no—
190C2×#470—71no—
191C2×#468—71no—
192C2×#467—71no—
193C2×#465—71no—
194C2×#464—71no—
195C2×#464—71no—
196C2×#462—71no—
197C2×#461—71no—
198C2×#424—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—24no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—82no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—24no—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—82no—
212C2×C7×D4C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—24no—
219C22×C4×C7—82no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2411yescharacteristic
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C2×Dic14—22no—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—22no—
236C2×Dic14—21no—
237C2×Dic14—21no—
238C2×Dic14C2412yes—
239C2×Dic14C2412yes—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4C2×D414yes—
246C7×C4⋊C4C2×D414yes—
247C7×C4⋊C4C2412yes—
248C7×C4⋊C4C2412yes—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4—24no—
253C7×C22⋊C4—24no—
254C7×C22⋊C4C2×D414yes—
255C7×C22⋊C4C2×D414yes—
256C42×C7—24no—
257C42×C7C2×D412yes—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260C42×C7C2412yes—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
263#1144—44no—
264#1144—44no—
265#1142—44no—
266#1142—44no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279C4×Dic7—24no—
280C4×Dic7—24no—
281#1136—44no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—44no—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291C22×Q16—71no—
292C22×Q16—71no—
293C22×SD16—71no—
294C22×SD16—71no—
295C22×M16—71no—
296C23×C8—71no—
297#542—24no—
298#542C2×D718yes—
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8C2×D711yescharacteristic
303C2×#126—21no—
304C2×#126—141no—
305C2×#126—141no—
306C2×#125—71no—
307C2×#125—141no—
308C2×#125—141no—
309C2×#124—21no—
310C2×#124C2×D711yescharacteristic
311C2×#123—21no—
312C2×C22⋊Q8—21no—
313C2×C22⋊Q8—71no—
314C2×C22⋊Q8—71no—
315C2×C22⋊Q8C2×D711yescharacteristic
316C2×#121C2×D711yescharacteristic
317C2×C4×Q8—71no—
318C2×C4×Q8—71no—
319C2×C4×Q8C2×D711yescharacteristic
320C2×C4×D4C2×D711yescharacteristic
321C2×#117C2×D711yescharacteristic
322#479—78no—
323#478—78no—
324#477—78no—
325#475—78no—
326#470—78no—
327#468—78no—
328#467—78no—
329#465—78no—
330#464—78no—
331#464—78no—
332#462—78no—
333#461—78no—
334C2×#107—71no—
335C2×#107—71no—
336C2×#106—71no—
337C2×#106—71no—
338#424—78no—
339C2×C4⋊C8—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7C22×D412yes—
359C23×C7C22×D411yescharacteristic
360C7×Q8—22no—
361C7×Q8—22no—
362C7×Q8—42no—
363C7×Q8—84no—
364C7×D4—22no—
365C7×D4—22no—
366C7×D4—42no—
367C7×D4—84no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—24no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—84no—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D411yescharacteristic
389C2×C4×C7H(5,𝔽2)12yes—
390C2×C4×C72−1+412yes—
391C2×C4×C7C2511yescharacteristic
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400Dic14—22no—
401Dic14—22no—
402Dic14—22no—
403Dic14—22no—
404Dic14—42no—
405Dic14—42no—
406C7⋊C8—22no—
407C7⋊C8—22no—
408C7⋊C8—22no—
409C7⋊C8—22no—
410C22×Q8—21no—
411C22×Q8—71no—
412C22×Q8—71no—
413C22×Q8C22×D711yescharacteristic
414C22×D4—21no—
415C22×D4C22×D711yescharacteristic
416C23×C4—21no—
417C23×C4C22×D711yescharacteristic
418C2×Q16—74no—
419C2×Q16—74no—
420C2×Q16—282no—
421C2×Q16—282no—
422C2×SD16—74no—
423C2×SD16—74no—
424C2×SD16—282no—
425C2×SD16—282no—
426C2×M16—74no—
427C2×M16—282no—
428C22×C8—71no—
429C22×C8—71no—
430C22×C8—71no—
431C22×C8—71no—
432C22×C8—74no—
433C22×C8—282no—
434C4⋊Q8—22no—
435C4⋊Q8—74no—
436C4⋊Q8—142no—
437C4⋊Q8C22×D714yes—
438#126—28no—
439#126—148no—
440#126—148no—
441#125—74no—
442#125—148no—
443#125—148no—
444#125—142no—
445#124—28no—
446#124—22no—
447#124C22×D714yes—
448#123—28no—
449C22⋊Q8—22no—
450C22⋊Q8—28no—
451C22⋊Q8—74no—
452C22⋊Q8—74no—
453C22⋊Q8—142no—
454C22⋊Q8—142no—
455C22⋊Q8C22×D714yes—
456#121—22no—
457#121C22×D714yes—
458C4×Q8—22no—
459C4×Q8—74no—
460C4×Q8—74no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8C22×D714yes—
464C4×D4—22no—
465C4×D4C22×D714yes—
466#117C22⋊D714yes—
467#117C22×D714yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—141no—
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⋊C4—141no—
481C2×C4⋊C4C22⋊D711yescharacteristic
482C2×C4⋊C4C22⋊D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4C22⋊D711yescharacteristic
493C2×C22⋊C4C22⋊D711yescharacteristic
494C2×C42—21no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42C22×D711yescharacteristic
498C2×C42C22×D711yescharacteristic
499#107—74no—
500#107—74no—
501#106—74no—
502#106—74no—
503C4⋊C8—74no—
504C4⋊C8—74no—
505C4⋊C8—74no—
506C4⋊C8—74no—
507#103—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#102—74no—
514#102—74no—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—44no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—84no—
523C22×C7#53712yes—
524C22×C7#57712yes—
525C22×C7#57812yes—
526C22×C7C23×D411yescharacteristic
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—22no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7#53712yes—
536C4×C7C2×H(5,𝔽2)11yescharacteristic
537C4×C7C2×2−1+411yescharacteristic
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542C24—21no—
543C24C2×C22⋊D711yescharacteristic
544C2×Q8—21no—
545C2×Q8—24no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—72no—
549C2×Q8—72no—
550C2×Q8—82no—
551C2×Q8—141no—
552C2×Q8—141no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8—142no—
556C2×Q8—142no—
557C2×Q8C23×D712yes—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—82no—
563C2×D4C23×D712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—82no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4C2×C22⋊D712yes—
576C22×C4C2×C22⋊D711yescharacteristic
577C22×C4C2×C22⋊D711yescharacteristic
578C22×C4C2×C22⋊D711yescharacteristic
579C22×C4C2×C22⋊D711yescharacteristic
580C22×C4C2×C22⋊D711yescharacteristic
581C22×C4C23×D712yes—
582C22×C4C23×D711yescharacteristic
583Q16—284no—
584Q16—284no—
585SD16—284no—
586SD16—284no—
587M16—284no—
588C2×C8—72no—
589C2×C8—72no—
590C2×C8—72no—
591C2×C8—72no—
592C2×C8—142no—
593C2×C8—142no—
594C2×C8—142no—
595C2×C8—142no—
596C2×C8—284no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—72no—
603C4⋊C4—72no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—144no—
609C4⋊C4—144no—
610C4⋊C4—141no—
611C4⋊C4—141no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4C2×C22⋊D714yes—
615C4⋊C4C2×C22⋊D714yes—
616C4⋊C4C23×D712yes—
617C4⋊C4C23×D712yes—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—144no—
624C22⋊C4—144no—
625C22⋊C4C2×C22⋊D714yes—
626C22⋊C4C2×C22⋊D714yes—
627C42—24no—
628C42—144no—
629C42—144no—
630C42C2×C22⋊D712yes—
631C42C2×C22⋊D712yes—
632C42C23×D712yes—
633C42C23×D712yes—
634C2×C7—42no—
635C2×C7—82no—
636C2×C7#325814yescomplemented
637C2×C7C2×#53711yescharacteristic
638C2×C7C2×#57711yescharacteristic
639C2×C7C2×#57811yescharacteristic
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D712yes—
648C23C22×C22⋊D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652Q8—84no—
653Q8—142no—
654Q8—142no—
655Q8—142no—
656Q8—142no—
657Q8—282no—
658Q8—282no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—84no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—84no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—282no—
683C2×C4—282no—
684C2×C4—282no—
685C2×C4—282no—
686C2×C4#655312yes—
687C2×C4#655412yes—
688C2×C4C22×C22⋊D712yes—
689C2×C4C22×C22⋊D712yes—
690C2×C4C22×C22⋊D712yes—
691C2×C4C22×C22⋊D712yes—
692C2×C4C22×C22⋊D712yes—
693C2×C4C22×C22⋊D711yescharacteristic
694C2×C4C24×D711yescharacteristic
695C8—142no—
696C8—142no—
697C8—142no—
698C8—142no—
699C7C2×#325811yescharacteristic, complemented, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#9052412yes—
709C22#9052712yes—
710C22#9052912yes—
711C22C23×C22⋊D711yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—282no—
721C4—282no—
722C4—282no—
723C4—282no—
724C4#9052412yes—
725C4C2×#655311yescharacteristic
726C4C2×#655411yescharacteristic
727C2—42no—
728C2—82no—
729C2#1174091314yesdirect product factor
730C2C2×#9052411yescharacteristic
731C2C2×#9052711yescharacteristic
732C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
hypercenterC2×#542D7
hypocenterC7C2×#3258
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
2. C2×#90209C2semidirect
3. #11740913C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89866C2semidirect
6. C2×#89826C2semidirect
7. C2×#89826C2semidirect
8. C2×#89824C2semidirect
9. C2×#89823C2semidirect
12. C2×#89803C2semidirect
13. C2×#89794C2semidirect
14. C2×#89791C2semidirect
15. C2×#89781C2semidirect
16. C2×#89771C2semidirect
39. #90209C22semidirect
52. #89866C22semidirect
53. #89863C22semidirect
54. #89826C22semidirect
55. #89826C22semidirect
56. #89824C22semidirect
57. #89823C22semidirect
60. #89803C22semidirect
61. #89794C22semidirect
62. #89791C22semidirect
63. #89781C22semidirect
64. #89771C22semidirect
636. C2×C7#3258semidirect
699. C7C2×#3258semidirect
729. C2#11740913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×#902092
#117409132
C2×#898632
C2×#898662
C2×#898262
C2×#898242
C2×#898232
C2×#898142
C2×#898132
C2×#898032
C2×#897942
C2×#897912
C2×#897812
C2×#897712
C2×#32587