Finite Group Databasebeta

← C2×#11741054 #14232375

Subgroups — C2×#11741054 #14232375

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×C7×#553C211yesmaximal, characteristic
2C2×#90234C211yesmaximal, characteristic, complemented
3#11741054C2116yesmaximal, direct product factor
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6C2×#89814C211yesmaximal, characteristic, complemented
7C2×#89813C211yesmaximal, characteristic, complemented
8C2×#89806C211yesmaximal, characteristic, complemented
9C2×#89805C211yesmaximal, characteristic, complemented
10C2×#89783C211yesmaximal, characteristic, complemented
11C2×#89779C211yesmaximal, characteristic, complemented
12C2×#89790C211yesmaximal, characteristic, complemented
13C2×#89768C211yesmaximal, characteristic, complemented
14C2×#89767C211yesmaximal, characteristic, complemented
15C2×#89742C211yesmaximal, characteristic, complemented
16C22×#6381C211yesmaximal, characteristic, complemented
17C7×#553—24no—
18C7×#553C2218yes—
19C2×C7×#126—21no—
20C2×C7×#125C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×#121—21no—
23C2×C7×#121C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C2×D4×Dic7—21no—
31C22×#1142C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90234—24no—
39#90234C2218yescomplemented
40C2×#6453—21no—
41C2×#6441—21no—
42C2×#6441—21no—
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89837C2218yescomplemented
51#89835C2218yescomplemented
52#89814C2218yescomplemented
53#89813C2218yescomplemented
54#89806C2218yescomplemented
55#89805C2218yescomplemented
56#89790C2218yescomplemented
57#89783C2218yescomplemented
58#89779C2218yescomplemented
59#89768C2218yescomplemented
60#89767C2218yescomplemented
61#89742C2218yescomplemented
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2218yescomplemented
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3346—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4D411yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7—21no—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×Dic7—21no—
87C23×Dic7—21no—
88C22×Dic14—21no—
89C22×Dic14C2311yescharacteristic
90C7×#126—28no—
91C7×#125—22no—
92C7×#125C2314yes—
93C7×#123—28no—
94C7×#121—28no—
95C7×#121—22no—
96C7×#121—22no—
97C7×#121C2314yes—
98C7×#121C2314yes—
99C4×C7×D4—28no—
100C4×C7×D4—22no—
101C4×C7×D4D414yes—
102C4×C7×D4C2314yes—
103C4×C7×D4C2314yes—
104C7×#117—22no—
105C7×#117C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—22no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4D411yescharacteristic
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C42×C7—21no—
122C2×C42×C7C2311yescharacteristic
123C2×C22⋊Dic7—21no—
124C2×C22⋊Dic7—21no—
125D4×Dic7—28no—
126C2×#1142—24no—
127C2×#1142C2314yes—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—22no—
132C2×C4⋊Dic7—22no—
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2314yes—
137C2×C4⋊Dic7C2314yes—
138#6487—22no—
139#6487—22no—
140#6487C2314yes—
141#6487C2314yes—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C2×#1136—24no—
147C2×#1136C2314yes—
148C22×C7⋊C8—24no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6453—28no—
155#6441—28no—
156#6441—28no—
157#6432—22no—
158#6432C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161#6406C2314yes—
162#6406C2314yes—
163#6406C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6384C2314yes—
167#6384C2314yes—
168#6384C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6381C2314yes—
173#6381C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179#6377C2314yes—
180C2×#554—71no—
181C2×#553D711yescharacteristic
182#3346—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#481—71no—
186C2×#485—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#474—71no—
190C2×#468—71no—
191C2×#465—71no—
192C2×#440—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#107—71no—
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C24×C7C2×D411yescharacteristic
199C2×C7×D4—24no—
200C2×C7×D4—24no—
201C2×C7×D4—24no—
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—44no—
206C2×C7×D4—82no—
207C2×C7×D4C2×D414yes—
208C2×C7×D4C2412yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—24no—
217C22×C4×C7—24no—
218C22×C4×C7—82no—
219C22×C4×C7—82no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2411yescharacteristic
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—24no—
234C22×Dic7—24no—
235C22×Dic7—82no—
236C22×Dic7—82no—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—82no—
242C2×Dic14C2412yes—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4C2×D414yes—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C7×C4⋊C4C2412yes—
253C7×C22⋊C4—24no—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C7×C22⋊C4C2×D414yes—
258C7×C22⋊C4C2×D414yes—
259C42×C7—24no—
260C42×C7C2×D412yes—
261C42×C7C2412yes—
262C22⋊Dic7—24no—
263C22⋊Dic7—24no—
264#1142—28no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277C4×Dic7—24no—
278#1136—28no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—28no—
283C2×C7⋊C8#4114yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288C22×SD16—71no—
289C22×M16—71no—
290C23×C8—71no—
291#554—78no—
292#554—144no—
293#553—24no—
294#553C2×D718yes—
295C2×C4⋊Q8—71no—
296C2×#126—21no—
297C2×#125—141no—
298C2×#125C2×D711yescharacteristic
299C2×#123—21no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×#121—21no—
305C2×#121C2×D711yescharacteristic
306C2×#121C2×D711yescharacteristic
307C2×C4×Q8—71no—
308C2×C4×D4—21no—
309C2×C4×D4—141no—
310C2×C4×D4C2×D711yescharacteristic
311C2×C4×D4C2×D711yescharacteristic
312C2×#117C2×D711yescharacteristic
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4C2×D711yescharacteristic
316#501—78no—
317#485—78no—
318#484—78no—
319#481—78no—
320#480—78no—
321#479—78no—
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—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×C4⋊C8—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×C22⋊C8—71no—
346C2×C22⋊C8—71no—
347C2×#97—71no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7#13714yes—
358C23×C7C22×D412yes—
359C23×C7C22×D412yes—
360C23×C7C22×D411yescharacteristic
361C7×D4—28no—
362C7×D4—22no—
363C7×D4—22no—
364C7×D4—48no—
365C7×D4—42no—
366C7×D4—84no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—24no—
372C2×C4×C7—24no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—84no—
384C2×C4×C7—84no—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D411yescharacteristic
390C2×C4×C7C2×#4112yes—
391C2×C4×C72−1+412yes—
392C2×C4×C7C2511yescharacteristic
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—84no—
402C2×Dic7—84no—
403Dic14—22no—
404Dic14—22no—
405Dic14—42no—
406Dic14—84no—
407C7⋊C8—22no—
408C7⋊C8—22no—
409C7⋊C8—22no—
410C7⋊C8C2×#4114yes—
411C22×Q8—71no—
412C22×Q8—141no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C22⋊D711yescharacteristic
416C22×D4C22×D711yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4C22×D711yescharacteristic
422C23×C4C22×D711yescharacteristic
423C2×SD16—74no—
424C2×SD16—144no—
425C2×M16—74no—
426C2×M16—144no—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8—74no—
430C22×C8—71no—
431C22×C8—71no—
432C22×C8—144no—
433C4⋊Q8—74no—
434C4⋊Q8—142no—
435#126—28no—
436#125—22no—
437#125—148no—
438#125C22×D714yes—
439#123—28no—
440C22⋊Q8—74no—
441C22⋊Q8—74no—
442C22⋊Q8—142no—
443C22⋊Q8—142no—
444C22⋊Q8—148no—
445C22⋊Q8—148no—
446#121—28no—
447#121—22no—
448#121—22no—
449#121C22×D714yes—
450#121C22×D714yes—
451C4×Q8—74no—
452C4×Q8—142no—
453C4×D4—28no—
454C4×D4—22no—
455C4×D4—148no—
456C4×D4C22⋊D714yes—
457C4×D4C22×D714yes—
458C4×D4C22×D714yes—
459#117—22no—
460#117C22×D714yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
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⋊C4C22⋊D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D714yes—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4C22⋊D711yescharacteristic
490C2×C22⋊C4C22⋊D711yescharacteristic
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#107—74no—
500#106—74no—
501#106—74no—
502#106—74no—
503C4⋊C8—74no—
504#103—74no—
505#103—74no—
506#103—74no—
507#102—74no—
508#102—74no—
509#102—74no—
510C22⋊C8—74no—
511C22⋊C8—74no—
512#97—74no—
513C22×C7—28no—
514C22×C7—22no—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—44no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—84no—
524C22×C7#54712yes—
525C22×C7C2×#13714yes—
526C22×C7C2×#13712yes—
527C22×C7#57612yes—
528C22×C7C23×D411yescharacteristic
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#54712yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—21no—
544C24C2×C22⋊D711yescharacteristic
545C24C2×C22⋊D711yescharacteristic
546C2×Q8—72no—
547C2×Q8—141no—
548C2×Q8—144no—
549C2×Q8—142no—
550C2×Q8—142no—
551C2×Q8—562no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—44no—
559C2×D4—82no—
560C2×D4C2×C22⋊D714yes—
561C2×D4C23×D712yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—562no—
580C22×C4—562no—
581C22×C4C2×C22⋊D712yes—
582C22×C4C2×C22⋊D712yes—
583C22×C4C2×C22⋊D711yescharacteristic
584C22×C4C2×C22⋊D711yescharacteristic
585C22×C4C2×C22⋊D711yescharacteristic
586C22×C4C2×C22⋊D711yescharacteristic
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D711yescharacteristic
590SD16—148no—
591M16—148no—
592C2×C8—74no—
593C2×C8—72no—
594C2×C8—72no—
595C2×C8—72no—
596C2×C8—72no—
597C2×C8—148no—
598C2×C8—142no—
599C2×C8—142no—
600C2×C8—142no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—72no—
608C4⋊C4—72no—
609C4⋊C4—72no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—141no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—141no—
617C4⋊C4—141no—
618C4⋊C4—144no—
619C4⋊C4C2×C22⋊D714yes—
620C4⋊C4C23×D712yes—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4C2×C22⋊D714yes—
630C22⋊C4C2×C22⋊D714yes—
631C42—24no—
632C42—144no—
633C42C2×C22⋊D712yes—
634C42C23×D712yes—
635C2×C7—24no—
636C2×C7—42no—
637C2×C7—82no—
638C2×C7#334614yescomplemented
639C2×C7C2×#54711yescharacteristic
640C2×C7C22×#13711yescharacteristic
641C2×C7C2×#57611yescharacteristic
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#651414yes—
652C23C22×C22⋊D712yes—
653C23C22×C22⋊D712yes—
654C23C22×C22⋊D711yescharacteristic
655Q8—142no—
656Q8—142no—
657Q8—282no—
658Q8—564no—
659D4—28no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—84no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—84no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—564no—
692C2×C4—564no—
693C2×C4D7×#4112yes—
694C2×C4#655412yes—
695C2×C4C22×C22⋊D712yes—
696C2×C4C22×C22⋊D712yes—
697C2×C4C22×C22⋊D712yes—
698C2×C4C22×C22⋊D712yes—
699C2×C4C22×C22⋊D711yescharacteristic
700C2×C4C24×D711yescharacteristic
701C8—74no—
702C8—142no—
703C8—142no—
704C8—142no—
705C7C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22C2×#651414yes—
718C22C2×#651412yes—
719C22#9051512yes—
720C22#9052612yes—
721C22C23×C22⋊D711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4#9051512yes—
734C4C2×D7×#4111yescharacteristic
735C4C2×#655411yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#1174105414yesdirect product factor
740C2C22×#651411yescharacteristic
741C2C2×#9051511yescharacteristic
742C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#553C2
socleC23×C7C22×D4
hypercenterC2×#553D7
hypocenterC7C2×#3346
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
2. C2×#90234C2semidirect
3. #11741054C2direct (N × H)
4. C2×#89835C2semidirect
5. C2×#89837C2semidirect
6. C2×#89814C2semidirect
7. C2×#89813C2semidirect
8. C2×#89806C2semidirect
9. C2×#89805C2semidirect
10. C2×#89783C2semidirect
11. C2×#89779C2semidirect
12. C2×#89790C2semidirect
13. C2×#89768C2semidirect
14. C2×#89767C2semidirect
15. C2×#89742C2semidirect
16. C22×#6381C2semidirect
39. #90234C22semidirect
50. #89837C22semidirect
51. #89835C22semidirect
52. #89814C22semidirect
53. #89813C22semidirect
54. #89806C22semidirect
55. #89805C22semidirect
56. #89790C22semidirect
57. #89783C22semidirect
58. #89779C22semidirect
59. #89768C22semidirect
60. #89767C22semidirect
61. #89742C22semidirect
74. C2×#6381C22semidirect
638. C2×C7#3346semidirect
705. C7C2×#3346semidirect
739. C2#11741054direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5532
C2×#902342
#117410542
C2×#898352
C2×#898372
C2×#898142
C2×#898132
C2×#898062
C2×#898052
C2×#897832
C2×#897792
C2×#897902
C2×#897682
C2×#897672
C2×#897422
C22×#63812
C2×#33467