Finite Group Databasebeta

← C2×C7×#3345 #13238453

Subgroups — C2×C7×#3345 #13238453

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic, complemented
2C2×C7×#547C211yesmaximal, characteristic, complemented
3C7×#3345C2116yesmaximal, direct product factor
4C2×C7×#501C211yesmaximal, characteristic, complemented
5C2×C7×#481C211yesmaximal, characteristic, complemented
6C2×C7×#481C211yesmaximal, characteristic, complemented
7C2×C7×#482C211yesmaximal, characteristic, complemented
8C2×C7×#480C211yesmaximal, characteristic, complemented
9C2×C7×#478C211yesmaximal, characteristic, complemented
10C2×C7×#476C211yesmaximal, characteristic, complemented
11C2×C7×#469C211yesmaximal, characteristic, complemented
12C2×C7×#466C211yesmaximal, characteristic, complemented
13C2×C7×#442C211yesmaximal, characteristic, complemented
14C2×C7×#435C211yesmaximal, characteristic, complemented
15C2×C7×#428C211yesmaximal, characteristic, complemented
16C22×C7×#106C211yesmaximal, characteristic, complemented
17C22×C7×#41—21no—
18C22×C7×D8C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C7×#553—24no—
22C7×#553C2218yescomplemented
23C7×#547—24no—
24C7×#547C2218yescomplemented
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×#126—21no—
27C2×C7×#125C2211yescharacteristic
28C2×C7×#123—21no—
29C2×C7×#123—21no—
30C2×C7×#123—21no—
31C2×C7×C22⋊Q8—21no—
32C2×C7×#121—21no—
33C2×C7×#121C2211yescharacteristic
34C2×C7×#121C2211yescharacteristic
35C2×C7×#121C2211yescharacteristic
36C2×C7×#121C2211yescharacteristic
37C2×C4×C7×D4—21no—
38C2×C4×C7×D4C2211yescharacteristic
39C2×C4×C7×D4C2211yescharacteristic
40C2×C4×C7×D4C2211yescharacteristic
41C2×C7×#117C2211yescharacteristic
42C22×C7×C4⋊C4C2211yescharacteristic
43C22×C7×C4⋊C4C2211yescharacteristic
44C22×C7×C4⋊C4C2211yescharacteristic
45C7×#501C2218yescomplemented
46C7×#482C2218yescomplemented
47C7×#481C2218yescomplemented
48C7×#481C2218yescomplemented
49C7×#480C2218yescomplemented
50C7×#478C2218yescomplemented
51C7×#476C2218yescomplemented
52C7×#469C2218yescomplemented
53C7×#466C2218yescomplemented
54C7×#442C2218yescomplemented
55C7×#435C2218yescomplemented
56C7×#428C2218yescomplemented
57C2×C7×#107C2211yescharacteristic
58C2×C7×#107C2211yescharacteristic
59C2×C7×#107C2211yescharacteristic
60C2×C7×#106C2211yescharacteristic
61C2×C7×#106C2211yescharacteristic
62C2×C7×#106C2211yescharacteristic
63C2×C7×#106C2211yescharacteristic
64C2×C7×#106C2211yescharacteristic
65C2×C7×#106C2211yescharacteristic
66C2×C7×#106C2218yescomplemented
67C2×C7×C4⋊C8C2211yescharacteristic
68C2×C7×#102C2211yescharacteristic
69C2×C7×#102C2211yescharacteristic
70C2×C7×#102C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×#102C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×C22⋊C8C2211yescharacteristic
76C2×C7×#97C2211yescharacteristic
77C2×#3345C711yesmaximal, characteristic, direct product factor, Sylow
78C2×C7×#41—28no—
79C2×C7×#41—48no—
80C22×C7×Q8—21no—
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4—21no—
85C22×C7×D4D411yescharacteristic
86C22×C7×D4C2311yescharacteristic
87C22×C7×D4C2311yescharacteristic
88C23×C4×C7—21no—
89C23×C4×C7—21no—
90C23×C4×C7—21no—
91C23×C4×C7—21no—
92C23×C4×C7—21no—
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C2×C7×D8—24no—
96C2×C7×D8C2314yes—
97C2×C7×M16—24no—
98C2×C7×M16C2314yes—
99C22×C7×C8—24no—
100C22×C7×C8C2314yes—
101C22×C7×C8C2311yescharacteristic
102C22×C7×C8C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C7×C4⋊Q8—22no—
106C7×C4⋊Q8C2314yes—
107C7×#126—28no—
108C7×#125—22no—
109C7×#125C2314yes—
110C7×#123—28no—
111C7×#123—28no—
112C7×#123—28no—
113C7×C22⋊Q8—28no—
114C7×#121—28no—
115C7×#121—22no—
116C7×#121—22no—
117C7×#121—22no—
118C7×#121—22no—
119C7×#121C2314yes—
120C7×#121C2314yes—
121C7×#121C2314yes—
122C7×#121C2314yes—
123C4×C7×D4—28no—
124C4×C7×D4—22no—
125C4×C7×D4—22no—
126C4×C7×D4D414yes—
127C4×C7×D4C2314yes—
128C4×C7×D4C2314yes—
129C4×C7×D4C2314yes—
130C7×#117—22no—
131C7×#117C2314yes—
132C2×C7×C4⋊C4—21no—
133C2×C7×C4⋊C4—21no—
134C2×C7×C4⋊C4—21no—
135C2×C7×C4⋊C4—22no—
136C2×C7×C4⋊C4—22no—
137C2×C7×C4⋊C4—22no—
138C2×C7×C4⋊C4—21no—
139C2×C7×C4⋊C4—21no—
140C2×C7×C4⋊C4—21no—
141C2×C7×C4⋊C4D411yescharacteristic
142C2×C7×C4⋊C4C2314yes—
143C2×C7×C4⋊C4C2314yes—
144C2×C7×C4⋊C4C2314yes—
145C2×C7×C4⋊C4C2311yescharacteristic
146C2×C7×C4⋊C4C2311yescharacteristic
147C2×C7×C4⋊C4C2311yescharacteristic
148C2×C7×C4⋊C4C2311yescharacteristic
149C2×C7×C4⋊C4C2311yescharacteristic
150C2×C7×C4⋊C4C2311yescharacteristic
151C2×C7×C22⋊C4—21no—
152C2×C7×C22⋊C4—21no—
153C2×C7×C22⋊C4—21no—
154C2×C7×C22⋊C4—21no—
155C2×C7×C22⋊C4—21no—
156C2×C7×C22⋊C4—21no—
157C2×C7×C22⋊C4—21no—
158C2×C7×C22⋊C4D411yescharacteristic
159C2×C7×C22⋊C4D411yescharacteristic
160C2×C42×C7—21no—
161C2×C42×C7C2311yescharacteristic
162C7×#107C2314yes—
163C7×#107C2314yes—
164C7×#107C2314yes—
165C7×#106C2314yes—
166C7×#106C2314yes—
167C7×#106C2314yes—
168C7×#106C2314yes—
169C7×#106C2314yes—
170C7×#106C2314yes—
171C7×C4⋊C8C2314yes—
172C7×#102C2314yes—
173C7×#102C2314yes—
174C7×#102C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×#102C2314yes—
178C7×C22⋊C8C2314yes—
179C7×C22⋊C8C2314yes—
180C7×#97C2314yes—
181C2×#553C2×C711yescharacteristic, complemented
182C2×#547C2×C711yescharacteristic, complemented
183#3345C2×C7116yesdirect product factor
184C2×#501C2×C711yescharacteristic, complemented
185C2×#481C2×C711yescharacteristic, complemented
186C2×#481C2×C711yescharacteristic, complemented
187C2×#482C2×C711yescharacteristic, complemented
188C2×#480C2×C711yescharacteristic, complemented
189C2×#478C2×C711yescharacteristic, complemented
190C2×#476C2×C711yescharacteristic, complemented
191C2×#469C2×C711yescharacteristic, complemented
192C2×#466C2×C711yescharacteristic, complemented
193C2×#442C2×C711yescharacteristic, complemented
194C2×#435C2×C711yescharacteristic, complemented
195C2×#428C2×C711yescharacteristic, complemented
196C22×#106C2×C711yescharacteristic, complemented
197C24×C7—21no—
198C24×C7—21no—
199C24×C7C2×D411yescharacteristic
200C24×C7C2×D411yescharacteristic
201C7×#41—432no—
202C2×C7×Q8—24no—
203C2×C7×Q8—44no—
204C2×C7×D4—24no—
205C2×C7×D4—24no—
206C2×C7×D4—24no—
207C2×C7×D4—24no—
208C2×C7×D4—24no—
209C2×C7×D4—21no—
210C2×C7×D4—21no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—22no—
214C2×C7×D4—22no—
215C2×C7×D4—44no—
216C2×C7×D4—44no—
217C2×C7×D4—44no—
218C2×C7×D4—82no—
219C2×C7×D4C2×D414yes—
220C2×C7×D4C2412yes—
221C2×C7×D4C2412yes—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—24no—
227C22×C4×C7—24no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—24no—
235C22×C4×C7—24no—
236C22×C4×C7—24no—
237C22×C4×C7—44no—
238C22×C4×C7—44no—
239C22×C4×C7—44no—
240C22×C4×C7—82no—
241C22×C4×C7—82no—
242C22×C4×C7C2×D412yes—
243C22×C4×C7C2×D412yes—
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2412yes—
249C22×C4×C7C2412yes—
250C22×C4×C7C2411yescharacteristic
251C7×D8—28no—
252C7×M16—28no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8—28no—
257C2×C7×C8#4114yescomplemented
258C2×C7×C8C2412yes—
259C2×C7×C8C2412yes—
260C2×C7×C8C2412yes—
261C2×C7×C8C2412yes—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—24no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—24no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4C2×D414yes—
275C7×C4⋊C4C2412yes—
276C7×C4⋊C4C2412yes—
277C7×C4⋊C4C2412yes—
278C7×C4⋊C4C2412yes—
279C7×C4⋊C4C2412yes—
280C7×C4⋊C4C2412yes—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—24no—
284C7×C22⋊C4—24no—
285C7×C22⋊C4—24no—
286C7×C22⋊C4—24no—
287C7×C22⋊C4—24no—
288C7×C22⋊C4C2×D414yes—
289C7×C22⋊C4C2×D414yes—
290C42×C7—24no—
291C42×C7C2×D412yes—
292C42×C7C2412yes—
293C22×#41—21no—
294C22×D8C22×C711yescharacteristic
295C22×M16C22×C711yescharacteristic
296C23×C8C22×C711yescharacteristic
297#553—24no—
298#553C22×C718yescomplemented
299#547—24no—
300#547C22×C718yescomplemented
301C2×C4⋊Q8C22×C711yescharacteristic
302C2×#126—21no—
303C2×#125C22×C711yescharacteristic
304C2×#123—21no—
305C2×#123—21no—
306C2×#123—21no—
307C2×C22⋊Q8—21no—
308C2×#121—21no—
309C2×#121C22×C711yescharacteristic
310C2×#121C22×C711yescharacteristic
311C2×#121C22×C711yescharacteristic
312C2×#121C22×C711yescharacteristic
313C2×C4×D4—21no—
314C2×C4×D4C22×C711yescharacteristic
315C2×C4×D4C22×C711yescharacteristic
316C2×C4×D4C22×C711yescharacteristic
317C2×#117C22×C711yescharacteristic
318C22×C4⋊C4C22×C711yescharacteristic
319C22×C4⋊C4C22×C711yescharacteristic
320C22×C4⋊C4C22×C711yescharacteristic
321#501C22×C718yescomplemented
322#482C22×C718yescomplemented
323#481C22×C718yescomplemented
324#481C22×C718yescomplemented
325#480C22×C718yescomplemented
326#478C22×C718yescomplemented
327#476C22×C718yescomplemented
328#469C22×C718yescomplemented
329#466C22×C718yescomplemented
330#442C22×C718yescomplemented
331#435C22×C718yescomplemented
332#428C22×C718yescomplemented
333C2×#107C22×C711yescharacteristic
334C2×#107C22×C711yescharacteristic
335C2×#107C22×C711yescharacteristic
336C2×#106C22×C711yescharacteristic
337C2×#106C22×C711yescharacteristic
338C2×#106C22×C711yescharacteristic
339C2×#106C22×C711yescharacteristic
340C2×#106C22×C711yescharacteristic
341C2×#106C22×C711yescharacteristic
342C2×#106C22×C718yescomplemented
343C2×C4⋊C8C22×C711yescharacteristic
344C2×#102C22×C711yescharacteristic
345C2×#102C22×C711yescharacteristic
346C2×#102C22×C711yescharacteristic
347C2×#102C22×C711yescharacteristic
348C2×#102C22×C711yescharacteristic
349C2×#102C22×C711yescharacteristic
350C2×C22⋊C8C22×C711yescharacteristic
351C2×C22⋊C8C22×C711yescharacteristic
352C2×#97C22×C711yescharacteristic
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7AGL(1,ℤ/8)14yes—
367C23×C7C22×D412yes—
368C23×C7C22×D412yes—
369C23×C7C22×D411yescharacteristic
370C7×Q8—48no—
371C7×D4—28no—
372C7×D4—22no—
373C7×D4—22no—
374C7×D4—22no—
375C7×D4—22no—
376C7×D4—48no—
377C7×D4—48no—
378C7×D4—48no—
379C7×D4—42no—
380C7×D4—42no—
381C7×D4—84no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—24no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—48no—
399C2×C4×C7—48no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—42no—
403C2×C4×C7—48no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—84no—
408C2×C4×C7—84no—
409C2×C4×C7C22×D412yes—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D411yescharacteristic
414C2×C4×C7C2×#4112yes—
415C2×C4×C72−1+412yes—
416C2×C4×C7C2511yescharacteristic
417C7×C8—22no—
418C7×C8—22no—
419C7×C8—22no—
420C7×C8C2×#4114yescomplemented
421C2×#41—28no—
422C2×#41—48no—
423C22×Q8—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C7×D411yescharacteristic
429C22×D4C23×C711yescharacteristic
430C22×D4C23×C711yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C711yescharacteristic
437C23×C4C23×C711yescharacteristic
438C2×D8—24no—
439C2×D8C23×C714yes—
440C2×M16—24no—
441C2×M16C23×C714yes—
442C22×C8—24no—
443C22×C8C23×C711yescharacteristic
444C22×C8C23×C714yes—
445C22×C8C23×C711yescharacteristic
446C22×C8C23×C711yescharacteristic
447C22×C8C23×C711yescharacteristic
448C4⋊Q8—22no—
449C4⋊Q8C23×C714yes—
450#126—28no—
451#125—22no—
452#125C23×C714yes—
453#123—28no—
454#123—28no—
455#123—28no—
456C22⋊Q8—28no—
457#121—28no—
458#121—22no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121C23×C714yes—
463#121C23×C714yes—
464#121C23×C714yes—
465#121C23×C714yes—
466C4×D4—28no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4C7×D414yes—
470C4×D4C23×C714yes—
471C4×D4C23×C714yes—
472C4×D4C23×C714yes—
473#117—22no—
474#117C23×C714yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4C7×D411yescharacteristic
485C2×C4⋊C4C23×C711yescharacteristic
486C2×C4⋊C4C23×C711yescharacteristic
487C2×C4⋊C4C23×C711yescharacteristic
488C2×C4⋊C4C23×C711yescharacteristic
489C2×C4⋊C4C23×C711yescharacteristic
490C2×C4⋊C4C23×C714yes—
491C2×C4⋊C4C23×C714yes—
492C2×C4⋊C4C23×C714yes—
493C2×C4⋊C4C23×C711yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4C7×D411yescharacteristic
502C2×C22⋊C4C7×D411yescharacteristic
503C2×C42—21no—
504C2×C42C23×C711yescharacteristic
505#107C23×C714yes—
506#107C23×C714yes—
507#107C23×C714yes—
508#106C23×C714yes—
509#106C23×C714yes—
510#106C23×C714yes—
511#106C23×C714yes—
512#106C23×C714yes—
513#106C23×C714yes—
514C4⋊C8C23×C714yes—
515#102C23×C714yes—
516#102C23×C714yes—
517#102C23×C714yes—
518#102C23×C714yes—
519#102C23×C714yes—
520#102C23×C714yes—
521C22⋊C8C23×C714yes—
522C22⋊C8C23×C714yes—
523#97C23×C714yes—
524C22×C7—28no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—22no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—44no—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—84no—
538C22×C7—84no—
539C22×C7#54712yes—
540C22×C7C2×AGL(1,ℤ/8)14yes—
541C22×C7C2×AGL(1,ℤ/8)12yes—
542C22×C7#57712yes—
543C22×C7C23×D411yescharacteristic
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—22no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7#54712yes—
555C4×C7C22×#4111yescharacteristic
556C4×C7C2×2−1+411yescharacteristic
557C24—21no—
558C24—21no—
559C24C2×C7×D411yescharacteristic
560C24C2×C7×D411yescharacteristic
561#41—432no—
562C2×Q8—24no—
563C2×Q8—44no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—82no—
579C2×D4C2×C7×D414yes—
580C2×D4C24×C712yes—
581C2×D4C24×C712yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4C2×C7×D411yescharacteristic
603C22×C4C2×C7×D411yescharacteristic
604C22×C4C2×C7×D411yescharacteristic
605C22×C4C2×C7×D411yescharacteristic
606C22×C4C2×C7×D412yes—
607C22×C4C2×C7×D412yes—
608C22×C4C24×C712yes—
609C22×C4C24×C712yes—
610C22×C4C24×C711yescharacteristic
611D8—28no—
612M16—28no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—28no—
617C2×C8C7×#4114yescomplemented
618C2×C8C24×C712yes—
619C2×C8C24×C712yes—
620C2×C8C24×C712yes—
621C2×C8C24×C712yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4C2×C7×D414yes—
635C4⋊C4C24×C712yes—
636C4⋊C4C24×C712yes—
637C4⋊C4C24×C712yes—
638C4⋊C4C24×C712yes—
639C4⋊C4C24×C712yes—
640C4⋊C4C24×C712yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4C2×C7×D414yes—
649C22⋊C4C2×C7×D414yes—
650C42—24no—
651C42C2×C7×D412yes—
652C42C24×C712yes—
653C2×C7—24no—
654C2×C7—42no—
655C2×C7—82no—
656C2×C7—82no—
657C2×C7#334514yesdirect product factor
658C2×C7C2×#54711yescharacteristic
659C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
660C2×C7C2×#57711yescharacteristic
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C7×AGL(1,ℤ/8)14yes—
675C23C22×C7×D412yes—
676C23C22×C7×D412yes—
677C23C22×C7×D411yescharacteristic
678Q8—48no—
679D4—28no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—48no—
686D4—48no—
687D4—42no—
688D4—42no—
689D4—84no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4C22×C7×D412yes—
718C2×C4C22×C7×D412yes—
719C2×C4C22×C7×D412yes—
720C2×C4C22×C7×D412yes—
721C2×C4C22×C7×D411yescharacteristic
722C2×C4C2×C7×#4112yes—
723C2×C4C7×2−1+412yes—
724C2×C4C25×C711yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8C2×C7×#4114yescomplemented
729C7C2×#334511yescharacteristic, direct product factor, Sylow
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—84no—
745C22C7×#54712yes—
746C22C2×C7×AGL(1,ℤ/8)14yes—
747C22C2×C7×AGL(1,ℤ/8)12yes—
748C22C7×#57712yes—
749C22C23×C7×D411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4C7×#54712yes—
761C4C22×C7×#4111yescharacteristic
762C4C2×C7×2−1+411yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—82no—
767C2C7×#334514yesdirect product factor
768C2C2×C7×#54711yescharacteristic
769C2C22×C7×AGL(1,ℤ/8)11yescharacteristic
770C2C2×C7×#57711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#553C2semidirect
2. C2×C7×#547C2semidirect
3. C7×#3345C2direct (N × H)
4. C2×C7×#501C2semidirect
5. C2×C7×#481C2semidirect
6. C2×C7×#481C2semidirect
7. C2×C7×#482C2semidirect
8. C2×C7×#480C2semidirect
9. C2×C7×#478C2semidirect
10. C2×C7×#476C2semidirect
11. C2×C7×#469C2semidirect
12. C2×C7×#466C2semidirect
13. C2×C7×#442C2semidirect
14. C2×C7×#435C2semidirect
15. C2×C7×#428C2semidirect
16. C22×C7×#106C2semidirect
22. C7×#553C22semidirect
24. C7×#547C22semidirect
45. C7×#501C22semidirect
46. C7×#482C22semidirect
47. C7×#481C22semidirect
48. C7×#481C22semidirect
49. C7×#480C22semidirect
50. C7×#478C22semidirect
51. C7×#476C22semidirect
52. C7×#469C22semidirect
53. C7×#466C22semidirect
54. C7×#442C22semidirect
55. C7×#435C22semidirect
56. C7×#428C22semidirect
66. C2×C7×#106C22semidirect
77. C2×#3345C7direct (N × H)
181. C2×#553C2×C7semidirect
182. C2×#547C2×C7semidirect
183. #3345C2×C7direct (N × H)
184. C2×#501C2×C7semidirect
185. C2×#481C2×C7semidirect
186. C2×#481C2×C7semidirect
187. C2×#482C2×C7semidirect
188. C2×#480C2×C7semidirect
189. C2×#478C2×C7semidirect
190. C2×#476C2×C7semidirect
191. C2×#469C2×C7semidirect
192. C2×#466C2×C7semidirect
193. C2×#442C2×C7semidirect
194. C2×#435C2×C7semidirect
195. C2×#428C2×C7semidirect
196. C22×#106C2×C7semidirect
257. C2×C7×C8#41semidirect
298. #553C22×C7semidirect
300. #547C22×C7semidirect
321. #501C22×C7semidirect
322. #482C22×C7semidirect
323. #481C22×C7semidirect
324. #481C22×C7semidirect
325. #480C22×C7semidirect
326. #478C22×C7semidirect
327. #476C22×C7semidirect
328. #469C22×C7semidirect
329. #466C22×C7semidirect
330. #442C22×C7semidirect
331. #435C22×C7semidirect
332. #428C22×C7semidirect
342. C2×#106C22×C7semidirect
420. C7×C8C2×#41semidirect
617. C2×C8C7×#41semidirect
657. C2×C7#3345direct (N × H)
728. C8C2×C7×#41semidirect
729. C7C2×#3345direct (N × H)
767. C2C7×#3345direct (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×C7×#5472
C7×#33452
C2×C7×#5012
C2×C7×#4812
C2×C7×#4822
C2×C7×#4802
C2×C7×#4782
C2×C7×#4762
C2×C7×#4692
C2×C7×#4662
C2×C7×#4422
C2×C7×#4352
C2×C7×#4282
C22×C7×#1062
C2×#33457