Finite Group Databasebeta

← C2×C7×#3388 #13238578

Subgroups — C2×C7×#3388 #13238578

Order 1792.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2C2×C7×#554C211yesmaximal, characteristic
3C7×#3388C2116yesmaximal, direct product factor
4C2×C7×#501C211yesmaximal, characteristic, complemented
5C2×C7×#501C211yesmaximal, characteristic, complemented
6C2×C7×#499C211yesmaximal, characteristic, complemented
7C2×C7×#479C211yesmaximal, characteristic, complemented
8C2×C7×#479C211yesmaximal, characteristic, complemented
9C2×C7×#475C211yesmaximal, characteristic, complemented
10C2×C7×#478C211yesmaximal, characteristic
11C2×C7×#478C211yesmaximal, characteristic
12C2×C7×#476C211yesmaximal, characteristic
13C2×C7×#446C211yesmaximal, characteristic, complemented
14C2×C7×#440C211yesmaximal, characteristic
15C2×C7×#440C211yesmaximal, characteristic
16C2×C4×C7×SD16C211yesmaximal, characteristic
17C22×C7×SD16C2211yescharacteristic
18C7×#557—24no—
19C7×#557C2218yescomplemented
20C7×#554—24no—
21C7×#554C2218yes—
22C2×C7×C4⋊Q8—21no—
23C2×C7×C4⋊Q8C2211yescharacteristic
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×#125—21no—
26C2×C7×#125—21no—
27C2×C7×#125C2211yescharacteristic
28C2×C7×#125C2211yescharacteristic
29C2×C7×#125C2211yescharacteristic
30C2×C7×#125C2211yescharacteristic
31C2×C7×C22⋊Q8—21no—
32C2×C7×C22⋊Q8—21no—
33C2×C7×C22⋊Q8—21no—
34C2×C4×C7×Q8—21no—
35C2×C4×C7×Q8C2211yescharacteristic
36C2×C4×C7×Q8C2211yescharacteristic
37C2×C4×C7×Q8C2211yescharacteristic
38C2×C4×C7×Q8C2211yescharacteristic
39C2×C4×C7×D4C2211yescharacteristic
40C2×C4×C7×D4C2211yescharacteristic
41C2×C4×C7×D4C2211yescharacteristic
42C22×C7×C4⋊C4—21no—
43C7×#501C2218yescomplemented
44C7×#501C2218yescomplemented
45C7×#499C2218yescomplemented
46C7×#479C2218yescomplemented
47C7×#479C2218yescomplemented
48C7×#478C2218yes—
49C7×#478C2218yes—
50C7×#476C2218yes—
51C7×#475C2218yescomplemented
52C7×#446C2218yescomplemented
53C7×#440C2218yes—
54C7×#440C2218yes—
55C4×C7×SD16C2218yes—
56C2×C7×#107C2211yescharacteristic
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×C4⋊C8C2211yescharacteristic
66C2×C7×C4⋊C8C2211yescharacteristic
67C2×C7×C4⋊C8C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#103C2211yescharacteristic
70C2×C7×#103C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×#102C2211yescharacteristic
74C2×C7×#97C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3388C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×Q8D411yescharacteristic
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C23×C4×C7—21no—
84C23×C4×C7—21no—
85C23×C4×C7—21no—
86C2×C7×SD16Q818yescomplemented
87C2×C7×SD16C2314yes—
88C22×C7×C8C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C7×C4⋊Q8—28no—
93C7×C4⋊Q8—22no—
94C7×C4⋊Q8—22no—
95C7×C4⋊Q8C2314yes—
96C7×C4⋊Q8C2314yes—
97C7×#125—28no—
98C7×#125—28no—
99C7×#125—22no—
100C7×#125—22no—
101C7×#125—22no—
102C7×#125—22no—
103C7×#125C2314yes—
104C7×#125C2314yes—
105C7×#125C2314yes—
106C7×#125C2314yes—
107C7×C22⋊Q8—28no—
108C7×C22⋊Q8—28no—
109C7×C22⋊Q8—28no—
110C4×C7×Q8—28no—
111C4×C7×Q8—22no—
112C4×C7×Q8—22no—
113C4×C7×Q8—22no—
114C4×C7×Q8D414yes—
115C4×C7×Q8C2314yes—
116C4×C7×Q8C2314yes—
117C4×C7×Q8C2314yes—
118C4×C7×Q8C2314yes—
119C4×C7×D4—22no—
120C4×C7×D4—22no—
121C4×C7×D4—22no—
122C4×C7×D4C2314yes—
123C4×C7×D4C2314yes—
124C4×C7×D4C2314yes—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4—21no—
133C2×C7×C4⋊C4—21no—
134C2×C7×C4⋊C4—21no—
135C2×C7×C4⋊C4—21no—
136C2×C7×C4⋊C4—21no—
137C2×C7×C4⋊C4—21no—
138C2×C7×C4⋊C4—28no—
139C2×C7×C4⋊C4D411yescharacteristic
140C2×C7×C4⋊C4D411yescharacteristic
141C2×C7×C4⋊C4D411yescharacteristic
142C2×C7×C4⋊C4C2311yescharacteristic
143C2×C7×C4⋊C4C2311yescharacteristic
144C2×C7×C4⋊C4C2311yescharacteristic
145C2×C7×C4⋊C4C2311yescharacteristic
146C2×C7×C4⋊C4C2311yescharacteristic
147C2×C7×C4⋊C4C2311yescharacteristic
148C2×C7×C22⋊C4—21no—
149C2×C7×C22⋊C4—21no—
150C2×C7×C22⋊C4—21no—
151C2×C42×C7—21no—
152C2×C42×C7—21no—
153C2×C42×C7—21no—
154C2×C42×C7C2311yescharacteristic
155C2×C42×C7C2311yescharacteristic
156C2×C42×C7C2311yescharacteristic
157C7×#107C2314yes—
158C7×#107C2314yes—
159C7×#107C2314yes—
160C7×#107C2314yes—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×#106C2314yes—
164C7×#106C2314yes—
165C7×#106C2314yes—
166C7×C4⋊C8C2314yes—
167C7×C4⋊C8C2314yes—
168C7×C4⋊C8C2314yes—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#102C2314yes—
173C7×#102C2314yes—
174C7×#102C2314yes—
175C7×#97C2314yes—
176C7×#97C2314yes—
177C4×C7×C8C2314yes—
178C2×#557C2×C711yescharacteristic, complemented
179C2×#554C2×C711yescharacteristic
180#3388C2×C7116yesdirect product factor
181C2×#501C2×C711yescharacteristic, complemented
182C2×#501C2×C711yescharacteristic, complemented
183C2×#499C2×C711yescharacteristic, complemented
184C2×#479C2×C711yescharacteristic, complemented
185C2×#479C2×C711yescharacteristic, complemented
186C2×#475C2×C711yescharacteristic, complemented
187C2×#478C2×C711yescharacteristic
188C2×#478C2×C711yescharacteristic
189C2×#476C2×C711yescharacteristic
190C2×#446C2×C711yescharacteristic, complemented
191C2×#440C2×C711yescharacteristic
192C2×#440C2×C711yescharacteristic
193C2×C4×SD16C2×C711yescharacteristic
194C24×C7—21no—
195C2×C7×Q8—21no—
196C2×C7×Q8—24no—
197C2×C7×Q8—24no—
198C2×C7×Q8—22no—
199C2×C7×Q8—42no—
200C2×C7×Q8—44no—
201C2×C7×Q8—82no—
202C2×C7×Q8C2×D414yes—
203C2×C7×Q8C2×Q814yes—
204C2×C7×Q8C2412yes—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4C2×Q814yes—
208C2×C7×D4C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—24no—
217C22×C4×C7—24no—
218C22×C4×C7—24no—
219C22×C4×C7—44no—
220C22×C4×C7—82no—
221C22×C4×C7—82no—
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2411yescharacteristic
229C7×SD16C2×Q8116yescomplemented
230C2×C7×C8—22no—
231C2×C7×C8—22no—
232C2×C7×C8—22no—
233C2×C7×C8C2×Q814yes—
234C2×C7×C8C2412yes—
235C2×C7×C8C2412yes—
236C2×C7×C8C2412yes—
237C2×C7×C8C2412yes—
238C7×C4⋊C4—24no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
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—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4C2×D414yes—
258C7×C4⋊C4C2×D414yes—
259C7×C4⋊C4C2×D414yes—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C4⋊C4C2412yes—
266C7×C22⋊C4—24no—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C42×C7—24no—
270C42×C7—24no—
271C42×C7—24no—
272C42×C7C2×D412yes—
273C42×C7C2×D412yes—
274C42×C7C2×D412yes—
275C42×C7C2412yes—
276C42×C7C2412yes—
277C42×C7C2412yes—
278C22×SD16C22×C711yescharacteristic
279#557—24no—
280#557C22×C718yescomplemented
281#554—24no—
282#554C22×C718yes—
283C2×C4⋊Q8—21no—
284C2×C4⋊Q8C22×C711yescharacteristic
285C2×C4⋊Q8C22×C711yescharacteristic
286C2×#125—21no—
287C2×#125—21no—
288C2×#125C22×C711yescharacteristic
289C2×#125C22×C711yescharacteristic
290C2×#125C22×C711yescharacteristic
291C2×#125C22×C711yescharacteristic
292C2×C22⋊Q8—21no—
293C2×C22⋊Q8—21no—
294C2×C22⋊Q8—21no—
295C2×C4×Q8—21no—
296C2×C4×Q8C22×C711yescharacteristic
297C2×C4×Q8C22×C711yescharacteristic
298C2×C4×Q8C22×C711yescharacteristic
299C2×C4×Q8C22×C711yescharacteristic
300C2×C4×D4C22×C711yescharacteristic
301C2×C4×D4C22×C711yescharacteristic
302C2×C4×D4C22×C711yescharacteristic
303C22×C4⋊C4—21no—
304#501C22×C718yescomplemented
305#501C22×C718yescomplemented
306#499C22×C718yescomplemented
307#479C22×C718yescomplemented
308#479C22×C718yescomplemented
309#478C22×C718yes—
310#478C22×C718yes—
311#476C22×C718yes—
312#475C22×C718yescomplemented
313#446C22×C718yescomplemented
314#440C22×C718yes—
315#440C22×C718yes—
316C4×SD16C22×C718yes—
317C2×#107C22×C711yescharacteristic
318C2×#107C22×C711yescharacteristic
319C2×#107C22×C711yescharacteristic
320C2×#107C22×C711yescharacteristic
321C2×#106C22×C711yescharacteristic
322C2×#106C22×C711yescharacteristic
323C2×#106C22×C711yescharacteristic
324C2×#106C22×C711yescharacteristic
325C2×#106C22×C711yescharacteristic
326C2×C4⋊C8C22×C711yescharacteristic
327C2×C4⋊C8C22×C711yescharacteristic
328C2×C4⋊C8C22×C711yescharacteristic
329C2×#103C22×C711yescharacteristic
330C2×#103C22×C711yescharacteristic
331C2×#103C22×C711yescharacteristic
332C2×#102C22×C711yescharacteristic
333C2×#102C22×C711yescharacteristic
334C2×#102C22×C711yescharacteristic
335C2×#97C22×C711yescharacteristic
336C2×#97C22×C711yescharacteristic
337C2×C4×C8C22×C711yescharacteristic
338C23×C7—24no—
339C23×C7—22no—
340C23×C7—42no—
341C23×C7—42no—
342C23×C7C22×D411yescharacteristic
343C7×Q8—24no—
344C7×Q8—22no—
345C7×Q8—44no—
346C7×Q8—48no—
347C7×Q8—84no—
348C7×Q8C22×Q814yes—
349C7×D4—24no—
350C7×D4—22no—
351C7×D4C22×Q814yes—
352C2×C4×C7—24no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—48no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—84no—
374C2×C4×C7—84no—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C22×Q812yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C7×C8—22no—
386C7×C8—22no—
387C7×C8—22no—
388C7×C8C22×Q814yes—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8C7×D411yescharacteristic
392C22×Q8C23×C711yescharacteristic
393C22×D4C23×C711yescharacteristic
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—21no—
397C2×SD16C7×Q818yescomplemented
398C2×SD16C23×C714yes—
399C22×C8C23×C711yescharacteristic
400C22×C8C23×C711yescharacteristic
401C22×C8C23×C711yescharacteristic
402C22×C8C23×C711yescharacteristic
403C4⋊Q8—28no—
404C4⋊Q8—22no—
405C4⋊Q8—22no—
406C4⋊Q8C23×C714yes—
407C4⋊Q8C23×C714yes—
408#125—28no—
409#125—28no—
410#125—22no—
411#125—22no—
412#125—22no—
413#125—22no—
414#125C23×C714yes—
415#125C23×C714yes—
416#125C23×C714yes—
417#125C23×C714yes—
418C22⋊Q8—28no—
419C22⋊Q8—28no—
420C22⋊Q8—28no—
421C4×Q8—28no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8C7×D414yes—
426C4×Q8C23×C714yes—
427C4×Q8C23×C714yes—
428C4×Q8C23×C714yes—
429C4×Q8C23×C714yes—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4C23×C714yes—
434C4×D4C23×C714yes—
435C4×D4C23×C714yes—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—28no—
450C2×C4⋊C4C7×D411yescharacteristic
451C2×C4⋊C4C7×D411yescharacteristic
452C2×C4⋊C4C7×D411yescharacteristic
453C2×C4⋊C4C23×C711yescharacteristic
454C2×C4⋊C4C23×C711yescharacteristic
455C2×C4⋊C4C23×C711yescharacteristic
456C2×C4⋊C4C23×C711yescharacteristic
457C2×C4⋊C4C23×C711yescharacteristic
458C2×C4⋊C4C23×C711yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C711yescharacteristic
466C2×C42C23×C711yescharacteristic
467C2×C42C23×C711yescharacteristic
468#107C23×C714yes—
469#107C23×C714yes—
470#107C23×C714yes—
471#107C23×C714yes—
472#106C23×C714yes—
473#106C23×C714yes—
474#106C23×C714yes—
475#106C23×C714yes—
476#106C23×C714yes—
477C4⋊C8C23×C714yes—
478C4⋊C8C23×C714yes—
479C4⋊C8C23×C714yes—
480#103C23×C714yes—
481#103C23×C714yes—
482#103C23×C714yes—
483#102C23×C714yes—
484#102C23×C714yes—
485#102C23×C714yes—
486#97C23×C714yes—
487#97C23×C714yes—
488C4×C8C23×C714yes—
489C22×C7—24no—
490C22×C7—48no—
491C22×C7—42no—
492C22×C7—42no—
493C22×C7D4×Q812yes—
494C22×C7#57512yes—
495C22×C7#57712yes—
496C22×C7C23×D411yescharacteristic
497C4×C7—24no—
498C4×C7—22no—
499C4×C7—22no—
500C4×C7—22no—
501C4×C7—22no—
502C4×C7—22no—
503C4×C7—22no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7D4×Q812yes—
511C4×C7C23×Q811yescharacteristic
512C4×C7C2×2−1+411yescharacteristic
513C24—21no—
514C2×Q8—21no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8—22no—
518C2×Q8—42no—
519C2×Q8—44no—
520C2×Q8—82no—
521C2×Q8C2×C7×D414yes—
522C2×Q8C2×C7×Q814yes—
523C2×Q8C24×C712yes—
524C2×D4—21no—
525C2×D4—22no—
526C2×D4C2×C7×Q814yes—
527C2×D4C24×C712yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—44no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4C2×C7×D411yescharacteristic
542C22×C4C2×C7×D411yescharacteristic
543C22×C4C2×C7×D411yescharacteristic
544C22×C4C2×C7×D411yescharacteristic
545C22×C4C2×C7×D411yescharacteristic
546C22×C4C2×C7×D411yescharacteristic
547C22×C4C24×C711yescharacteristic
548SD16C2×C7×Q8116yescomplemented
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8C2×C7×Q814yes—
553C2×C8C24×C712yes—
554C2×C8C24×C712yes—
555C2×C8C24×C712yes—
556C2×C8C24×C712yes—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4C2×C7×D414yes—
577C4⋊C4C2×C7×D414yes—
578C4⋊C4C2×C7×D414yes—
579C4⋊C4C24×C712yes—
580C4⋊C4C24×C712yes—
581C4⋊C4C24×C712yes—
582C4⋊C4C24×C712yes—
583C4⋊C4C24×C712yes—
584C4⋊C4C24×C712yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C42—24no—
589C42—24no—
590C42—24no—
591C42C2×C7×D412yes—
592C42C2×C7×D412yes—
593C42C2×C7×D412yes—
594C42C24×C712yes—
595C42C24×C712yes—
596C42C24×C712yes—
597C2×C7—44no—
598C2×C7#338814yesdirect product factor
599C2×C7C2×D4×Q811yescharacteristic
600C2×C7C2×#57511yescharacteristic
601C2×C7C2×#57711yescharacteristic
602C23—22no—
603C23—24no—
604C23—42no—
605C23—42no—
606C23C22×C7×D411yescharacteristic
607Q8—22no—
608Q8—24no—
609Q8—44no—
610Q8—48no—
611Q8—84no—
612Q8C22×C7×Q814yes—
613D4—22no—
614D4—24no—
615D4C22×C7×Q814yes—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—48no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4C22×C7×D412yes—
640C2×C4C22×C7×D412yes—
641C2×C4C22×C7×D412yes—
642C2×C4C22×C7×D412yes—
643C2×C4C22×C7×D412yes—
644C2×C4C22×C7×D412yes—
645C2×C4C22×C7×D411yescharacteristic
646C2×C4C22×C7×Q812yes—
647C2×C4C7×2−1+412yes—
648C2×C4C25×C711yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8C22×C7×Q814yes—
653C7C2×#338811yescharacteristic, direct product factor, Sylow
654C22—24no—
655C22—42no—
656C22—42no—
657C22—48no—
658C22C7×D4×Q812yes—
659C22C7×#57512yes—
660C22C7×#57712yes—
661C22C23×C7×D411yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—24no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4C7×D4×Q812yes—
676C4C23×C7×Q811yescharacteristic
677C4C2×C7×2−1+411yescharacteristic
678C2—44no—
679C2C7×#338814yesdirect product factor
680C2C2×C7×D4×Q811yescharacteristic
681C2C2×C7×#57511yescharacteristic
682C2C2×C7×#57711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC22×C7×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. C7×#3388C2direct (N × H)
4. C2×C7×#501C2semidirect
5. C2×C7×#501C2semidirect
6. C2×C7×#499C2semidirect
7. C2×C7×#479C2semidirect
8. C2×C7×#479C2semidirect
9. C2×C7×#475C2semidirect
13. C2×C7×#446C2semidirect
19. C7×#557C22semidirect
43. C7×#501C22semidirect
44. C7×#501C22semidirect
45. C7×#499C22semidirect
46. C7×#479C22semidirect
47. C7×#479C22semidirect
51. C7×#475C22semidirect
52. C7×#446C22semidirect
77. C2×#3388C7direct (N × H)
86. C2×C7×SD16Q8semidirect
178. C2×#557C2×C7semidirect
180. #3388C2×C7direct (N × H)
181. C2×#501C2×C7semidirect
182. C2×#501C2×C7semidirect
183. C2×#499C2×C7semidirect
184. C2×#479C2×C7semidirect
185. C2×#479C2×C7semidirect
186. C2×#475C2×C7semidirect
190. C2×#446C2×C7semidirect
229. C7×SD16C2×Q8semidirect
280. #557C22×C7semidirect
304. #501C22×C7semidirect
305. #501C22×C7semidirect
306. #499C22×C7semidirect
307. #479C22×C7semidirect
308. #479C22×C7semidirect
312. #475C22×C7semidirect
313. #446C22×C7semidirect
397. C2×SD16C7×Q8semidirect
548. SD16C2×C7×Q8semidirect
598. C2×C7#3388direct (N × H)
653. C7C2×#3388direct (N × H)
679. C2C7×#3388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×C7×#5542
C7×#33882
C2×C7×#5012
C2×C7×#4992
C2×C7×#4792
C2×C7×#4752
C2×C7×#4782
C2×C7×#4762
C2×C7×#4462
C2×C7×#4402
C2×C4×C7×SD162
C2×#33887