Finite Group Databasebeta

← C2×#11741036 #14232243

Subgroups — C2×#11741036 #14232243

Order 1792.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#552C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic
3#11741036C2116yesmaximal, direct product factor
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89836C211yesmaximal, characteristic, complemented
6C2×#89820C211yesmaximal, characteristic, complemented
7C2×#89820C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10C2×#89794C211yesmaximal, characteristic, complemented
11C2×C4×#1143C211yesmaximal, characteristic, complemented
12C2×D4×C7⋊C8C211yesmaximal, characteristic, complemented
13C2×#89775C211yesmaximal, characteristic, complemented
14C2×#89770C211yesmaximal, characteristic, complemented
15C2×#89739C211yesmaximal, characteristic, complemented
16C22×#6382C211yesmaximal, characteristic, complemented
17C7×#552—24no—
18C7×#552C2218yescomplemented
19C2×C7×#126—21no—
20C2×C7×#125—21no—
21C2×C7×#125C2211yescharacteristic
22C2×C7×#123—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117—21no—
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C2×#6502—21no—
32C2×#6493C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×#6489C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C23×C7⋊C8C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90256—24no—
39#90256C2218yes—
40C2×#6461—21no—
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6433C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89838C2218yescomplemented
51#89836C2218yescomplemented
52#89820C2218yescomplemented
53#89820C2218yescomplemented
54#89817C2218yescomplemented
55#89816C2218yescomplemented
56C4×#1143C2218yescomplemented
57#89794C2218yescomplemented
58D4×C7⋊C8C2218yescomplemented
59#89775C2218yescomplemented
60#89770C2218yescomplemented
61#89739C2218yescomplemented
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2218yescomplemented
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3337—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4D411yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C7×#126—28no—
89C7×#125—28no—
90C7×#125—22no—
91C7×#125C2314yes—
92C7×#123—28no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8C2314yes—
96C7×C22⋊Q8C2314yes—
97C4×C7×Q8—22no—
98C4×C7×Q8C2314yes—
99C4×C7×D4D414yes—
100C4×C7×D4C2314yes—
101C7×#117—22no—
102C7×#117—28no—
103C7×#117C2314yes—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—22no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2314yes—
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×C7—21no—
123C2×C42×C7C2311yescharacteristic
124C2×C22⋊Dic7—21no—
125C2×#1143—24no—
126C2×#1143C2314yes—
127#6502—28no—
128#6493—22no—
129#6493—22no—
130#6493C2314yes—
131#6493C2314yes—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135#6489—22no—
136#6489C2314yes—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7—22no—
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yes—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C22×C7⋊C8—24no—
147C22×C7⋊C8—24no—
148C22×C7⋊C8C2311yescharacteristic
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2314yes—
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6461—28no—
155#6446—28no—
156(C22⋊D7)⋊C4—28no—
157C4×D28—22no—
158C4×D28C2314yes—
159#6433—22no—
160#6433C2314yes—
161#6409C2314yes—
162#6409C2314yes—
163#6409C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6383C2314yes—
167#6383C2314yes—
168#6383C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6382C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#553—71no—
181C2×#552D711yescharacteristic, complemented
182#3337—716no—
183C2×#499—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#465—71no—
191C2×#465—71no—
192C2×C4×SD16—71no—
193C2×C8×D4—71no—
194C2×#427—71no—
195C22×#106—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C2×C7×D4—24no—
204C2×C7×D4C2×D414yes—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—44no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2411yescharacteristic
224C2×C22⋊D7—24no—
225C2×C22⋊D7—24no—
226C2×C22⋊D7—44no—
227C2×C22⋊D7—82no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—24no—
232C22×Dic7—82no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—21no—
236C2×D28C2412yes—
237C2×C4×D7—24no—
238C2×C4×D7—82no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4C2×D414yes—
249C7×C4⋊C4C2412yes—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C7×C22⋊C4—24no—
253C7×C22⋊C4—24no—
254C7×C22⋊C4—24no—
255C7×C22⋊C4C2×D414yes—
256C7×C22⋊C4C2×D414yes—
257C42×C7—24no—
258C42×C7—24no—
259C42×C7C2×D412yes—
260C42×C7C2412yes—
261C22⋊Dic7—24no—
262#1143—28no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275C4×Dic7—24no—
276C2×C7⋊C8—22no—
277C2×C7⋊C8—22no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—28no—
280C2×C7⋊C8—28no—
281C2×C7⋊C8#4114yes—
282C2×C7⋊C8C2412yes—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C22×SD16—71no—
287C23×C8—71no—
288C23×C8—71no—
289#553—78no—
290#553—144no—
291#552—24no—
292#552C2×D718yescomplemented
293C2×#126—21no—
294C2×#126—141no—
295C2×#125—21no—
296C2×#125—71no—
297C2×#125C2×D711yescharacteristic
298C2×#123—21no—
299C2×#123—141no—
300C2×C22⋊Q8C2×D711yescharacteristic
301C2×C22⋊Q8C2×D711yescharacteristic
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—141no—
305C2×C4×Q8C2×D711yescharacteristic
306C2×C4×D4—71no—
307C2×C4×D4—141no—
308C2×C4×D4C2×D711yescharacteristic
309C2×#117—21no—
310C2×#117—71no—
311C2×#117C2×D711yescharacteristic
312C22×C4⋊C4—71no—
313C22×C4⋊C4C2×D711yescharacteristic
314#499—78no—
315#485—78no—
316#484—78no—
317#482—78no—
318#480—78no—
319#479—78no—
320#478—78no—
321#465—78no—
322#465—78no—
323C4×SD16—78no—
324C8×D4—78no—
325#427—78no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106—71no—
334C2×#106—71no—
335C2×#106—71no—
336C2×C4⋊C8—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×C22⋊C8—71no—
344C2×C22⋊C8—71no—
345C2×C4×C8—71no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7#13514yes—
352C23×C7C22×D412yes—
353C23×C7C22×D412yes—
354C23×C7C22×D411yescharacteristic
355C22×D7—22no—
356C22×D7—42no—
357C22×D7—42no—
358C22×D7—42no—
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—42no—
362C7×D4—28no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—24no—
368C2×C4×C7—24no—
369C2×C4×C7—22no—
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—22no—
377C2×C4×C7—42no—
378C2×C4×C7—48no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D411yescharacteristic
387C2×C4×C7C2×#4112yes—
388C2×C4×C72−1+412yes—
389C2×C4×C7C2511yescharacteristic
390C22⋊D7—48no—
391C22⋊D7—84no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7—84no—
399D28—22no—
400D28—22no—
401D28—42no—
402C4×D7—84no—
403C7⋊C8—22no—
404C7⋊C8—22no—
405C7⋊C8—22no—
406C7⋊C8C2×#4114yes—
407C22×Q8C22×D711yescharacteristic
408C22×D4—71no—
409C22×D4—141no—
410C22×D4—141no—
411C22×D4C22⋊D711yescharacteristic
412C23×C4—21no—
413C23×C4—141no—
414C23×C4—141no—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D711yescharacteristic
417C2×SD16—74no—
418C2×SD16—144no—
419C22×C8—71no—
420C22×C8—71no—
421C22×C8—71no—
422C22×C8—74no—
423C22×C8—74no—
424C22×C8—71no—
425C22×C8—144no—
426C22×C8—144no—
427#126—28no—
428#126—148no—
429#125—28no—
430#125—22no—
431#125—74no—
432#125—142no—
433#125C22×D714yes—
434#123—28no—
435#123—148no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8C22×D714yes—
439C22⋊Q8C22×D714yes—
440#121—74no—
441#121—74no—
442#121—148no—
443#121—142no—
444#121—142no—
445C4×Q8—22no—
446C4×Q8C22×D714yes—
447C4×D4—74no—
448C4×D4—148no—
449C4×D4—142no—
450C4×D4C22⋊D714yes—
451C4×D4C22×D714yes—
452#117—22no—
453#117—28no—
454#117—74no—
455#117—142no—
456#117C22×D714yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—142no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4C22⋊D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C4⋊C4C22×D714yes—
476C2×C4⋊C4C22×D711yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4C22⋊D711yescharacteristic
485C2×C22⋊C4C22⋊D711yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—141no—
489C2×C42C22×D711yescharacteristic
490#107—74no—
491#107—74no—
492#107—74no—
493#107—74no—
494#106—74no—
495#106—74no—
496#106—74no—
497#106—74no—
498#106—74no—
499C4⋊C8—74no—
500#103—74no—
501#103—74no—
502#103—74no—
503#102—74no—
504#102—74no—
505#102—74no—
506C22⋊C8—74no—
507C22⋊C8—74no—
508C4×C8—74no—
509C22×C7—28no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—44no—
516C22×C7#54712yes—
517C22×C7C2×#13514yes—
518C22×C7C2×#13512yes—
519C22×C7#57712yes—
520C22×C7C23×D411yescharacteristic
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—84no—
525C4×C7—22no—
526C4×C7—22no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7#54712yes—
534C4×C7C22×#4111yescharacteristic
535C4×C7C2×2−1+411yescharacteristic
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539C24—141no—
540C24C2×C22⋊D711yescharacteristic
541C24C2×C22⋊D711yescharacteristic
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8C23×D712yes—
546C2×D4—24no—
547C2×D4—72no—
548C2×D4—144no—
549C2×D4—144no—
550C2×D4—142no—
551C2×D4—142no—
552C2×D4—141no—
553C2×D4—284no—
554C2×D4—562no—
555C2×D4C2×C22⋊D714yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—44no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—144no—
570C22×C4—144no—
571C22×C4—562no—
572C22×C4—562no—
573C22×C4C2×C22⋊D712yes—
574C22×C4C2×C22⋊D712yes—
575C22×C4C2×C22⋊D711yescharacteristic
576C22×C4C2×C22⋊D711yescharacteristic
577C22×C4C2×C22⋊D711yescharacteristic
578C22×C4C2×C22⋊D711yescharacteristic
579C22×C4C23×D712yes—
580C22×C4C23×D712yes—
581C22×C4C23×D711yescharacteristic
582SD16—148no—
583C2×C8—74no—
584C2×C8—72no—
585C2×C8—72no—
586C2×C8—72no—
587C2×C8—72no—
588C2×C8—148no—
589C2×C8—148no—
590C2×C8—142no—
591C2×C8—142no—
592C2×C8—142no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—72no—
603C4⋊C4—72no—
604C4⋊C4—72no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—141no—
608C4⋊C4—141no—
609C4⋊C4—144no—
610C4⋊C4—141no—
611C4⋊C4C2×C22⋊D714yes—
612C4⋊C4C23×D712yes—
613C4⋊C4C23×D712yes—
614C4⋊C4C23×D712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—144no—
619C22⋊C4—144no—
620C22⋊C4—144no—
621C22⋊C4—144no—
622C22⋊C4C2×C22⋊D714yes—
623C22⋊C4C2×C22⋊D714yes—
624C42—24no—
625C42—24no—
626C42—144no—
627C42C2×C22⋊D712yes—
628C42C23×D712yes—
629C2×C7—24no—
630C2×C7—42no—
631C2×C7#333714yescomplemented
632C2×C7C2×#54711yescharacteristic
633C2×C7C22×#13511yescharacteristic
634C2×C7C2×#57711yescharacteristic
635D7—82no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—142no—
642C23—282no—
643C23—282no—
644C23—282no—
645C23#651314yes—
646C23C22×C22⋊D712yes—
647C23C22×C22⋊D712yes—
648C23C22×C22⋊D711yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652D4—28no—
653D4—142no—
654D4—142no—
655D4—288no—
656D4—282no—
657D4—564no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—48no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—282no—
681C2×C4—282no—
682C2×C4—282no—
683C2×C4—564no—
684C2×C4—564no—
685C2×C4D7×#4112yes—
686C2×C4#655412yes—
687C2×C4C22×C22⋊D712yes—
688C2×C4C22×C22⋊D712yes—
689C2×C4C22×C22⋊D712yes—
690C2×C4C22×C22⋊D712yes—
691C2×C4C22×C22⋊D711yescharacteristic
692C2×C4C24×D711yescharacteristic
693C8—74no—
694C8—142no—
695C8—142no—
696C8—142no—
697C7C2×#333711yescharacteristic, complemented, Sylow
698C22—22no—
699C22—22no—
700C22—28no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—282no—
706C22—282no—
707C22—282no—
708C22—564no—
709C22C2×#651314yes—
710C22C2×#651312yes—
711C22#9051512yes—
712C22#9052812yes—
713C22C23×C22⋊D711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—282no—
723C4—282no—
724C4—282no—
725C4#9051512yes—
726C4C2×D7×#4111yescharacteristic
727C4C2×#655411yescharacteristic
728C2—24no—
729C2—42no—
730C2—562no—
731C2#1174103614yesdirect product factor
732C2C22×#651311yescharacteristic
733C2C2×#9051511yescharacteristic
734C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#552C2
socleC23×C7C22×D4
prime radicalC2×#90256C2
hypercenterC2×#552D7
hypocenterC7C2×#3337
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C7×#552C2semidirect
3. #11741036C2direct (N × H)
4. C2×#89838C2semidirect
5. C2×#89836C2semidirect
6. C2×#89820C2semidirect
7. C2×#89820C2semidirect
8. C2×#89816C2semidirect
9. C2×#89817C2semidirect
10. C2×#89794C2semidirect
11. C2×C4×#1143C2semidirect
12. C2×D4×C7⋊C8C2semidirect
13. C2×#89775C2semidirect
14. C2×#89770C2semidirect
15. C2×#89739C2semidirect
16. C22×#6382C2semidirect
18. C7×#552C22semidirect
50. #89838C22semidirect
51. #89836C22semidirect
52. #89820C22semidirect
53. #89820C22semidirect
54. #89817C22semidirect
55. #89816C22semidirect
56. C4×#1143C22semidirect
57. #89794C22semidirect
58. D4×C7⋊C8C22semidirect
59. #89775C22semidirect
60. #89770C22semidirect
61. #89739C22semidirect
70. C2×#6382C22semidirect
181. C2×#552D7semidirect
292. #552C2×D7semidirect
631. C2×C7#3337semidirect
697. C7C2×#3337semidirect
731. C2#11741036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5522
C2×#902562
#117410362
C2×#898382
C2×#898362
C2×#898202
C2×#898162
C2×#898172
C2×#897942
C2×C4×#11432
C2×D4×C7⋊C82
C2×#897752
C2×#897702
C2×#897392
C22×#63822
C2×#33377