Finite Group Databasebeta

← C2×#11737413 #14218762

Subgroups — C2×#11737413 #14218762

Order 1792.

1706 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90269C211yesmaximal, characteristic
2C2×C7×#446C211yesmaximal, characteristic, complemented
3C2×#89796C211yesmaximal, characteristic, complemented
4#11737413C2116yesmaximal, direct product factor
5C2×#89600C211yesmaximal, characteristic, complemented
6C2×#89600C211yesmaximal, characteristic, complemented
7C2×#89603C211yesmaximal, characteristic, complemented
8C2×#89612C211yesmaximal, characteristic
9C2×#89612C211yesmaximal, characteristic
10C2×#89607C211yesmaximal, characteristic
11C2×#89481C211yesmaximal, characteristic
12C2×#89477C211yesmaximal, characteristic
13C2×#89473C211yesmaximal, characteristic, complemented
14C2×#89473C211yesmaximal, characteristic, complemented
15C2×#89462C211yesmaximal, characteristic
16C2×#89451C211yesmaximal, characteristic, complemented
17C2×C4×C7×Q8C2211yescharacteristic
18C2×#6509C411yescharacteristic
19C2×#6507C411yescharacteristic
20#90269C418yes—
21#90269C2218yes—
22C2×#6460C411yescharacteristic
23C2×#6459C411yescharacteristic
24C2×#6459C411yescharacteristic
25C2×#6452C411yescharacteristic
26C2×#6452C411yescharacteristic
27C2×#6451C411yescharacteristic
28C2×#6435C2211yescharacteristic
29C2×#6435C2211yescharacteristic
30C2×C42×D7C2211yescharacteristic
31C2×C4×Dic14C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C2×C4×Dic14C2211yescharacteristic
34C7×#446C2218yescomplemented
35C2×C7×C4⋊C8C2211yescharacteristic
36C2×C7×C4⋊C8C2211yescharacteristic
37C2×C7×C4⋊C8C2211yescharacteristic
38C2×C7×#97C2211yescharacteristic
39C2×C7×#97C2211yescharacteristic
40C2×C4×C7×C8C2211yescharacteristic
41C2×(C2×D7)⋊C8C2211yescharacteristic
42C2×(C2×D7)⋊C8C2211yescharacteristic
43C2×(C2×D7)⋊C8C2211yescharacteristic
44C2×(C2×D7)⋊C8C2211yescharacteristic
45C2×#6389C2211yescharacteristic
46C2×#6389C2211yescharacteristic
47C2×#6389C2211yescharacteristic
48C2×#6389C2211yescharacteristic
49C2×Dic7⋊C8C2211yescharacteristic
50C2×Dic7⋊C8C2211yescharacteristic
51C2×Dic7⋊C8C2211yescharacteristic
52C2×Dic7⋊C8C2211yescharacteristic
53C2×Dic7⋊C8C2211yescharacteristic
54C2×Dic7⋊C8C2211yescharacteristic
55C2×C8×Dic7C2211yescharacteristic
56C2×C8×Dic7C2211yescharacteristic
57#89796C2218yescomplemented
58C2×C4⋊(C7⋊C8)C2211yescharacteristic
59C2×C4⋊(C7⋊C8)C2211yescharacteristic
60C2×C4⋊(C7⋊C8)C2211yescharacteristic
61C2×#6377C2211yescharacteristic
62C2×#6377C2211yescharacteristic
63C2×C4×C7⋊C8C2211yescharacteristic
64#89612C2218yes—
65#89612C2218yes—
66#89607C2218yes—
67#89603C2218yescomplemented
68#89600C2218yescomplemented
69#89600C2218yescomplemented
70#89481C2218yes—
71#89477C2218yes—
72#89473C2218yescomplemented
73#89473C2218yescomplemented
74#89462C2218yes—
75#89451C2218yescomplemented
76C2×#2987—71nomaximal, Sylow
77C22×C7×Q8C2×C411yescharacteristic
78C22×C4×D7C2×C411yescharacteristic
79C22×C4×D7C2×C411yescharacteristic
80C22×C4×D7C2311yescharacteristic
81C22×Dic14C2×C411yescharacteristic
82C22×Dic14C2×C411yescharacteristic
83C22×Dic14C2×C411yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C22×C7×C8C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C4×C7×Q8C2×C414yes—
89C4×C7×Q8C2314yes—
90C2×C7×C4⋊C4C2×C411yescharacteristic
91C2×C7×C4⋊C4C2×C411yescharacteristic
92C2×C7×C4⋊C4C2×C411yescharacteristic
93C2×C42×C7C2311yescharacteristic
94C2×C42×C7C2311yescharacteristic
95C2×C42×C7C2311yescharacteristic
96#6509C2×C418yes—
97#6507C2×C418yes—
98C2×(C2×D7)⋊C4C2×C411yescharacteristic
99C2×(C2×D7)⋊C4C2×C411yescharacteristic
100C2×(C2×D7)⋊C4C2×C411yescharacteristic
101C2×(C2×D7)⋊C4C2×C411yescharacteristic
102C2×C4⋊Dic7C2×C411yescharacteristic
103C2×C4⋊Dic7C2×C411yescharacteristic
104C2×C4⋊Dic7C2×C411yescharacteristic
105C2×Dic7⋊C4C2×C411yescharacteristic
106C2×Dic7⋊C4C2×C411yescharacteristic
107C2×Dic7⋊C4C2×C411yescharacteristic
108C2×Dic7⋊C4C2×C411yescharacteristic
109C2×Dic7⋊C4C2×C411yescharacteristic
110C2×Dic7⋊C4C2×C411yescharacteristic
111C2×Dic7⋊C4C2×C411yescharacteristic
112C2×Dic7⋊C4C2×C411yescharacteristic
113C2×Dic7⋊C4C2×C411yescharacteristic
114C2×Dic7⋊C4C2×C411yescharacteristic
115C2×C4×Dic7C2×C411yescharacteristic
116C2×C4×Dic7C2×C411yescharacteristic
117C2×C4×Dic7C2311yescharacteristic
118C2×C4×Dic7C2311yescharacteristic
119C2×C4×Dic7C2311yescharacteristic
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122C22×C7⋊C8C2311yescharacteristic
123C22×C7⋊C8C2311yescharacteristic
124#6460C2×C418yes—
125#6459C2×C418yes—
126#6459C2×C418yes—
127#6452C2×C418yes—
128#6452C2×C418yes—
129#6451C2×C418yes—
130#6435C2×C414yes—
131#6435C2×C414yes—
132#6435C2314yes—
133#6435C2314yes—
134C42×D7C2×C414yes—
135C42×D7C2314yes—
136C4×Dic14C2×C414yes—
137C4×Dic14C2×C414yes—
138C4×Dic14C2×C414yes—
139C4×Dic14C2314yes—
140C4×Dic14C2314yes—
141C4×Dic14C2314yes—
142C7×C4⋊C8C2314yes—
143C7×C4⋊C8C2314yes—
144C7×C4⋊C8C2314yes—
145C7×#97C2314yes—
146C7×#97C2314yes—
147C4×C7×C8C2314yes—
148(C2×D7)⋊C8C2314yes—
149(C2×D7)⋊C8C2314yes—
150(C2×D7)⋊C8C2314yes—
151(C2×D7)⋊C8C2314yes—
152#6389C2314yes—
153#6389C2314yes—
154#6389C2314yes—
155#6389C2314yes—
156Dic7⋊C8C2314yes—
157Dic7⋊C8C2314yes—
158Dic7⋊C8C2314yes—
159Dic7⋊C8C2314yes—
160Dic7⋊C8C2314yes—
161Dic7⋊C8C2314yes—
162C8×Dic7C2314yes—
163C8×Dic7C2314yes—
164C4⋊(C7⋊C8)C2314yes—
165C4⋊(C7⋊C8)C2314yes—
166C4⋊(C7⋊C8)C2314yes—
167#6377C2314yes—
168#6377C2314yes—
169C4×C7⋊C8C2314yes—
170C2×#533—71no—
171#2987—716no—
172C2×#446—71no—
173C2×#446—71no—
174C2×#446—71no—
175C2×#446—71no—
176C2×#446—71no—
177C2×#446—71no—
178C2×#446—71no—
179C2×#446D711yescharacteristic, complemented
180C2×#433—71no—
181C2×#433—71no—
182C2×#433—71no—
183C2×#433—71no—
184C2×#432—71no—
185C2×#432—71no—
186C23×D7C22×C411yescharacteristic
187C2×C7×Q8—42no—
188C2×C7×Q8C22×C414yes—
189C22×C4×C7C22×C411yescharacteristic
190C22×C4×C7C22×C411yescharacteristic
191C22×C4×C7C22×C411yescharacteristic
192C22×C4×C7C22×C411yescharacteristic
193C22×C4×C7C22×C411yescharacteristic
194C22×C4×C7C22×C411yescharacteristic
195C22×C4×C7C2411yescharacteristic
196C22×Dic7C22×C411yescharacteristic
197C22×Dic7C22×C411yescharacteristic
198C22×Dic7C22×C411yescharacteristic
199C22×Dic7C22×C411yescharacteristic
200C22×Dic7C22×C411yescharacteristic
201C22×Dic7C22×C411yescharacteristic
202C22×Dic7C22×C411yescharacteristic
203C2×C4×D7—22no—
204C2×C4×D7—22no—
205C2×C4×D7—42no—
206C2×C4×D7—42no—
207C2×C4×D7C22×C412yes—
208C2×C4×D7C22×C414yes—
209C2×C4×D7C22×C414yes—
210C2×C4×D7C2412yes—
211C2×Dic14—42no—
212C2×Dic14—42no—
213C2×Dic14—42no—
214C2×Dic14C22×C414yes—
215C2×Dic14C22×C414yes—
216C2×Dic14C22×C414yes—
217C2×C7×C8—22no—
218C2×C7×C8—22no—
219C2×C7×C8—22no—
220C2×C7×C8—22no—
221C2×C7×C8C2412yes—
222C2×C7×C8C2412yes—
223C2×C7×C8C2412yes—
224C2×C7×C8C2412yes—
225C7×C4⋊C4C22×C414yes—
226C7×C4⋊C4C22×C414yes—
227C7×C4⋊C4C22×C414yes—
228C42×C7C22×C412yes—
229C42×C7C22×C412yes—
230C42×C7C22×C412yes—
231C42×C7C2412yes—
232C42×C7C2412yes—
233C42×C7C2412yes—
234(C2×D7)⋊C4C22×C414yes—
235(C2×D7)⋊C4C22×C414yes—
236(C2×D7)⋊C4C22×C414yes—
237(C2×D7)⋊C4C22×C414yes—
238C4⋊Dic7C22×C414yes—
239C4⋊Dic7C22×C414yes—
240C4⋊Dic7C22×C414yes—
241Dic7⋊C4C22×C414yes—
242Dic7⋊C4C22×C414yes—
243Dic7⋊C4C22×C414yes—
244Dic7⋊C4C22×C414yes—
245Dic7⋊C4C22×C414yes—
246Dic7⋊C4C22×C414yes—
247Dic7⋊C4C22×C414yes—
248Dic7⋊C4C22×C414yes—
249Dic7⋊C4C22×C414yes—
250Dic7⋊C4C22×C414yes—
251C4×Dic7C22×C412yes—
252C4×Dic7C22×C412yes—
253C4×Dic7C22×C412yes—
254C4×Dic7C22×C414yes—
255C4×Dic7C22×C414yes—
256C4×Dic7C2412yes—
257C4×Dic7C2412yes—
258C4×Dic7C2412yes—
259C2×C7⋊C8—22no—
260C2×C7⋊C8—22no—
261C2×C7⋊C8—22no—
262C2×C7⋊C8—22no—
263C2×C7⋊C8C2412yes—
264C2×C7⋊C8C2412yes—
265C2×C7⋊C8C2412yes—
266C2×C7⋊C8C2412yes—
267#533—78no—
268#533—78no—
269C2×C4⋊Q8—71no—
270C2×C4⋊Q8—71no—
271C2×#125—71no—
272C2×#125—71no—
273C2×C22⋊Q8—71no—
274C2×C22⋊Q8—71no—
275C2×C22⋊Q8—71no—
276C2×C22⋊Q8—71no—
277C2×C4×Q8—71no—
278C2×C4×Q8—71no—
279C2×C4×Q8—71no—
280C2×C4×Q8C2×D711yescharacteristic
281C2×#117—71no—
282C2×#117—71no—
283C22×C42—71no—
284#446—78no—
285#446—78no—
286#446—78no—
287#446—78no—
288#446—78no—
289#446—78no—
290#446—78no—
291#446C2×D718yescomplemented
292#433—78no—
293#433—78no—
294#433—78no—
295#433—78no—
296#432—78no—
297#432—78no—
298C2×C4⋊C8—71no—
299C2×C4⋊C8—71no—
300C2×C4⋊C8—71no—
301C2×C4⋊C8—71no—
302C2×C4⋊C8—71no—
303C2×C4⋊C8—71no—
304C2×C4⋊C8—71no—
305C2×C4⋊C8—71no—
306C2×C4⋊C8—71no—
307C2×C4⋊C8C2×D711yescharacteristic
308C2×C4⋊C8C2×D711yescharacteristic
309C2×C4⋊C8C2×D711yescharacteristic
310C2×C22⋊C8—71no—
311C2×C22⋊C8—71no—
312C2×C22⋊C8—71no—
313C2×C22⋊C8—71no—
314C2×#97—71no—
315C2×#97—71no—
316C2×#97—71no—
317C2×#97—71no—
318C2×#97—71no—
319C2×#97—71no—
320C2×#97C2×D711yescharacteristic
321C2×#97C2×D711yescharacteristic
322C2×C4×C8—71no—
323C2×C4×C8—71no—
324C2×C4×C8—71no—
325C2×C4×C8C2×D711yescharacteristic
326C23×C7C23×C411yescharacteristic
327C22×D7—22no—
328C22×D7—22no—
329C22×D7—22no—
330C22×D7C23×C412yes—
331C7×Q8—44no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7C23×C412yes—
339C2×C4×C7C23×C412yes—
340C2×C4×C7C23×C412yes—
341C2×C4×C7C23×C412yes—
342C2×C4×C7C23×C412yes—
343C2×C4×C7C23×C412yes—
344C2×C4×C7C23×C411yescharacteristic
345C2×C4×C72−1+412yes—
346C2×C4×C72−1+412yes—
347C2×C4×C7C2511yescharacteristic
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7C23×C412yes—
356C2×Dic7C23×C412yes—
357C2×Dic7C23×C412yes—
358C2×Dic7C23×C412yes—
359C2×Dic7C23×C412yes—
360C2×Dic7C23×C412yes—
361C2×Dic7C23×C412yes—
362C4×D7—24no—
363C4×D7—22no—
364C4×D7—22no—
365C4×D7—44no—
366C4×D7—44no—
367Dic14—44no—
368Dic14—44no—
369Dic14—44no—
370C7×C8—22no—
371C7×C8—22no—
372C7×C8—22no—
373C7×C8—22no—
374C7⋊C8—22no—
375C7⋊C8—22no—
376C7⋊C8—22no—
377C7⋊C8—22no—
378C22×Q8—71no—
379C22×Q8—71no—
380C22×Q8—71no—
381C22×Q8C4×D711yescharacteristic
382C23×C4—71no—
383C23×C4—71no—
384C23×C4—71no—
385C22×C8—71no—
386C22×C8—71no—
387C22×C8—71no—
388C22×C8—71no—
389C22×C8C22×D711yescharacteristic
390C22×C8C22×D711yescharacteristic
391C22×C8C22×D711yescharacteristic
392C22×C8C22×D711yescharacteristic
393C4⋊Q8—78no—
394C4⋊Q8—78no—
395#125—78no—
396#125—78no—
397C22⋊Q8—78no—
398C22⋊Q8—78no—
399C22⋊Q8—78no—
400C22⋊Q8—78no—
401C4×Q8—74no—
402C4×Q8—74no—
403C4×Q8—74no—
404C4×Q8—74no—
405C4×Q8—74no—
406C4×Q8—74no—
407C4×Q8C4×D714yes—
408C4×Q8C22×D714yes—
409#117—74no—
410#117—74no—
411#117—74no—
412#117—74no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—71no—
420C2×C4⋊C4—71no—
421C2×C4⋊C4—71no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—71no—
426C2×C4⋊C4C4×D711yescharacteristic
427C2×C4⋊C4C4×D711yescharacteristic
428C2×C4⋊C4C4×D711yescharacteristic
429C2×C22⋊C4—71no—
430C2×C22⋊C4—71no—
431C2×C22⋊C4—71no—
432C2×C22⋊C4—71no—
433C2×C42—71no—
434C2×C42—71no—
435C2×C42—71no—
436C2×C42—71no—
437C2×C42—71no—
438C2×C42—74no—
439C2×C42—74no—
440C2×C42C22×D711yescharacteristic
441C2×C42C22×D711yescharacteristic
442C2×C42C22×D711yescharacteristic
443C4⋊C8—74no—
444C4⋊C8—74no—
445C4⋊C8—74no—
446C4⋊C8—74no—
447C4⋊C8—74no—
448C4⋊C8—74no—
449C4⋊C8—74no—
450C4⋊C8—74no—
451C4⋊C8—74no—
452C4⋊C8C22×D714yes—
453C4⋊C8C22×D714yes—
454C4⋊C8C22×D714yes—
455C22⋊C8—74no—
456C22⋊C8—74no—
457C22⋊C8—74no—
458C22⋊C8—74no—
459#97—74no—
460#97—74no—
461#97—74no—
462#97—74no—
463#97—74no—
464#97—74no—
465#97C22×D714yes—
466#97C22×D714yes—
467C4×C8—74no—
468C4×C8—74no—
469C4×C8—74no—
470C4×C8C22×D714yes—
471C22×C7#51912yes—
472C22×C7#56812yes—
473C22×C7#56812yes—
474C22×C7C24×C411yescharacteristic
475C2×D7—22no—
476C2×D7—22no—
477C2×D7—22no—
478C2×D7—44no—
479C4×C7—22no—
480C4×C7—22no—
481C4×C7—22no—
482C4×C7—22no—
483C4×C7—22no—
484C4×C7—22no—
485C4×C7#51912yes—
486C4×C7C2×2−1+411yescharacteristic
487C4×C7C2×2−1+411yescharacteristic
488Dic7—22no—
489Dic7—22no—
490Dic7—22no—
491Dic7—22no—
492Dic7—22no—
493Dic7—22no—
494Dic7—22no—
495C24—71no—
496C2×Q8—42no—
497C2×Q8—74no—
498C2×Q8—74no—
499C2×Q8—74no—
500C2×Q8—282no—
501C2×Q8—282no—
502C2×Q8—282no—
503C2×Q8C2×C4×D714yes—
504C22×C4—71no—
505C22×C4—71no—
506C22×C4—71no—
507C22×C4—71no—
508C22×C4—71no—
509C22×C4—71no—
510C22×C4—71no—
511C22×C4—72no—
512C22×C4—72no—
513C22×C4—74no—
514C22×C4—74no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—282no—
518C22×C4—282no—
519C22×C4C2×C4×D711yescharacteristic
520C22×C4C2×C4×D711yescharacteristic
521C22×C4C2×C4×D711yescharacteristic
522C22×C4C2×C4×D711yescharacteristic
523C22×C4C2×C4×D711yescharacteristic
524C22×C4C2×C4×D711yescharacteristic
525C22×C4C23×D711yescharacteristic
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—72no—
531C2×C8—72no—
532C2×C8—72no—
533C2×C8—72no—
534C2×C8—142no—
535C2×C8—142no—
536C2×C8—142no—
537C2×C8—142no—
538C2×C8C23×D712yes—
539C2×C8C23×D712yes—
540C2×C8C23×D712yes—
541C2×C8C23×D712yes—
542C4⋊C4—74no—
543C4⋊C4—74no—
544C4⋊C4—74no—
545C4⋊C4—74no—
546C4⋊C4—74no—
547C4⋊C4—74no—
548C4⋊C4—74no—
549C4⋊C4—74no—
550C4⋊C4—74no—
551C4⋊C4—74no—
552C4⋊C4—74no—
553C4⋊C4—74no—
554C4⋊C4—74no—
555C4⋊C4C2×C4×D714yes—
556C4⋊C4C2×C4×D714yes—
557C4⋊C4C2×C4×D714yes—
558C22⋊C4—74no—
559C22⋊C4—74no—
560C22⋊C4—74no—
561C22⋊C4—74no—
562C42—72no—
563C42—74no—
564C42—74no—
565C42—72no—
566C42—72no—
567C42—72no—
568C42—72no—
569C42—72no—
570C42C2×C4×D712yes—
571C42C2×C4×D712yes—
572C42C2×C4×D712yes—
573C42C23×D712yes—
574C42C23×D712yes—
575C42C23×D712yes—
576C2×C7#298714yescomplemented
577C2×C7C2×#51911yescharacteristic
578C2×C7C2×#56811yescharacteristic
579C2×C7C2×#56811yescharacteristic
580D7—42no—
581C23—72no—
582C23—142no—
583C23—142no—
584C23—142no—
585C23C22×C4×D711yescharacteristic
586Q8—44no—
587Q8—284no—
588Q8—284no—
589Q8—284no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—72no—
597C2×C4—72no—
598C2×C4—72no—
599C2×C4—72no—
600C2×C4—72no—
601C2×C4—72no—
602C2×C4—72no—
603C2×C4—142no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—142no—
608C2×C4—142no—
609C2×C4—142no—
610C2×C4—144no—
611C2×C4—142no—
612C2×C4—142no—
613C2×C4—284no—
614C2×C4—284no—
615C2×C4C22×C4×D712yes—
616C2×C4C22×C4×D712yes—
617C2×C4C22×C4×D712yes—
618C2×C4C22×C4×D712yes—
619C2×C4C22×C4×D712yes—
620C2×C4C22×C4×D712yes—
621C2×C4C22×C4×D711yescharacteristic
622C2×C4#655112yes—
623C2×C4#655412yes—
624C2×C4C24×D711yescharacteristic
625C8—22no—
626C8—22no—
627C8—22no—
628C8—22no—
629C8—142no—
630C8—142no—
631C8—142no—
632C8—142no—
633C7C2×#298711yescharacteristic, complemented, Sylow
634C22—142no—
635C22—142no—
636C22—142no—
637C22—284no—
638C22#9026312yes—
639C22#9043612yes—
640C22#9044112yes—
641C22C23×C4×D711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—142no—
649C4—142no—
650C4—142no—
651C4—142no—
652C4—142no—
653C4—142no—
654C4—142no—
655C4#9026312yes—
656C4C2×#655111yescharacteristic
657C4C2×#655411yescharacteristic
658C2—282no—
659C2#1173741314yesdirect product factor
660C2C2×#9026311yescharacteristic
661C2C2×#9043611yescharacteristic
662C2C2×#9044111yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#446C2
socleC23×C7C23×C4
prime radicalC23×D7C22×C4
cosocleC2×C4×C7C25
hypercenterC2×#446D7
hypocenterC7C2×#2987
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×C7×#446C2semidirect
3. C2×#89796C2semidirect
4. #11737413C2direct (N × H)
5. C2×#89600C2semidirect
6. C2×#89600C2semidirect
7. C2×#89603C2semidirect
13. C2×#89473C2semidirect
14. C2×#89473C2semidirect
16. C2×#89451C2semidirect
34. C7×#446C22semidirect
57. #89796C22semidirect
67. #89603C22semidirect
68. #89600C22semidirect
69. #89600C22semidirect
72. #89473C22semidirect
73. #89473C22semidirect
75. #89451C22semidirect
179. C2×#446D7semidirect
291. #446C2×D7semidirect
576. C2×C7#2987semidirect
633. C7C2×#2987semidirect
659. C2#11737413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902692
C2×C7×#4462
C2×#897962
#117374132
C2×#896002
C2×#896032
C2×#896122
C2×#896072
C2×#894812
C2×#894772
C2×#894732
C2×#894622
C2×#894512
C2×#29877